Optomechatronic Actuators, Manipulation, and Systems Control

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Volume 6374

Optomechatronic Actuators, Manipulation, and Systems Control Yukitoshi Otani, Farrokh Janabi-Sharifi, Editors , October 2006 Conference Location: Boston, MA, USA Conference Date: 1 October 2006 Publisher: SPIE-International Society for Optical Engine ISBN-10: 0819464724 ISBN-13: 978-0819464729

TABLE OF CONTENTS

OPTICAL ACTUATOR Laser motor Hideki Okamura Proc. SPIE Vol. 6374, 637401 (Oct. 19, 2006)

Light-driven polymer actuators for propulsion and light control LaQuieta Huey, Sergey S. Sarkisov, Michael J. Curley, Grigory Adamovsky, and Jai-Ching Wang Proc. SPIE Vol. 6374, 637402 (Oct. 19, 2006)

Positioning control of Nafion-Au ionic polymer metal composite: the effect of counter ion on the deformation patterns of IPMC Akitoshi Itoh, Tetsuichi Amari, and Toshihiro Tanaka Proc. SPIE Vol. 6374, 637403 (Oct. 19, 2006)

Optical driving of actuator using poly-vinylidine difluoride cantilever Y. Mizutani, S. Nishimura, Y. Otani, and N. Umeda Proc. SPIE Vol. 6374, 637404 (Oct. 19, 2006)

Two-dimensional magnetic force actuator using temperature sensitive ferrite driven by light beam Y. Mizutani, Y. Otani, and N. Umeda

Proc. SPIE Vol. 6374, 637405 (Oct. 19, 2006)

OPTOMECHATRONIC MEASUREMENT Analysis of mechanical characteristics by birefringence microscope Mizue Ebisawa, Yukitoshi Otani, and Norihiro Umeda Proc. SPIE Vol. 6374, 637407 (Oct. 19, 2006)

Simultaneous measurement of nanometric longitudinal displacement and micrometric lateral displacement by using one line CCD camera Masaaki Adachi and Yasuto Nishide Proc. SPIE Vol. 6374, 637408 (Oct. 19, 2006)

MEMS acoustic sensor using PMN-PT single-crystal diaphragm Sung Q. Lee, Hae Jin Kim, Kang Ho Park, Yong K. Hong, and Kee S. Moon Proc. SPIE Vol. 6374, 637409 (Oct. 19, 2006)

OPTOMECHATRONIC ACTUATION DEVICES PMN-PT piezoelectric near field optical probe for data storage Yong K. Hong, Sung Q. Lee, Eun Kyoung Kim, Kang Ho Park, and Kee S. Moon Proc. SPIE Vol. 6374, 63740A (Oct. 19, 2006)

Real-time high-displacement amplified bimorph scanning mirror Paul E. Patterson and Jason M. Zara Proc. SPIE Vol. 6374, 63740B (Oct. 19, 2006)

Optimization of electrostatic side-drive micromotor torque using a new rotor-poleshaping technique Mohamed A. Basha and S. Safavi-Naeini Proc. SPIE Vol. 6374, 63740C (Oct. 19, 2006)

Liquid crystal optics for laser beam modulation M. Kurihara and N. Hashimoto Proc. SPIE Vol. 6374, 63740D (Oct. 19, 2006)

Reconfigurable microfluidic chip based on a light-sensitive hydrogel Khaled Al-Aribe, George K. Knopf, and Amarjeet S. Bassi Proc. SPIE Vol. 6374, 63740E (Oct. 19, 2006)

Low-cost deformable mirror for laser focussing

W. Greger, T. Hösel, T. Fellner, A. Schoth, C. Mueller, J. Wilde, and H. Reinecke Proc. SPIE Vol. 6374, 63740F (Oct. 19, 2006)

The simple and practical variable optical attenuator using a piezoelectric sheet containing an optical fiber Seungtaek Kim, Heuiseok Kang, Sungbok Kang, Won Kim, Hoon Jeong, and Youngjune Cho Proc. SPIE Vol. 6374, 63740G (Oct. 19, 2006)

A novel capacitive type miniature microphone with a flexure hinge diaphragm Hye Jin Kim, Sung Q. Lee, and Kang Ho Park Proc. SPIE Vol. 6374, 63740H (Oct. 19, 2006)

Liquid pressure varifocus lens using a fibrous actuator Ryoichi Kuwano, Yasuhiro Mizutani, Tsuyoshi Tokunaga, and Yukitoshi Otani Proc. SPIE Vol. 6374, 63740I (Oct. 19, 2006)

Sol-Gel-based 1x2 power splitter for a plastic optical fiber H. Jeong, Y. J. Cho, and S. T. Kim Proc. SPIE Vol. 6374, 63740J (Oct. 19, 2006)

OPTICAL ACTUATOR AND MICRO/NANO MANIPULATION Liquid crystal laser manipulation system for controlling microscopic particles Marenori Kawamura, Mao Ye, and Susumu Sato Proc. SPIE Vol. 6374, 63740K (Oct. 19, 2006)

Imaging technology of three-dimensional distribution for sugar chain on single living cell membrane Kazuya Yamamoto, Ichirou Ishimaru, Yoshiki Fujii, Toshiki Yasokawa, Katsumi Ishizaki, Makoto Yoshida, Kaoru Takegawa, Naotaka Tanaka, Shigeki Kuriyama, Tsutomu Masaki, and Seiji Nakai Proc. SPIE Vol. 6374, 63740L (Oct. 19, 2006)

Laser irradiation induced vibrations in solids Bodo Richert and Hideki Okamura Proc. SPIE Vol. 6374, 63740M (Oct. 19, 2006)

Light-driven micromanipulator and its application for 3D fabrications Yukitoshi Otani, Yuji Hirai, Yasuhiro Mizutani, Norihiro Umeda, and Toru Yoshizawa Proc. SPIE Vol. 6374, 63740N (Oct. 19, 2006)

Optimal actuation of microcantilevers by a laser beam Sagnik Pal and Anjan K. Ghosh Proc. SPIE Vol. 6374, 63740O (Oct. 19, 2006)

Development of PC controlled laser manipulation system with image processing functions Yoshio Tanaka, Akitsugu Murakami, Ken Hirano, Hideya Nagata, and Mitsuru Ishikawa Proc. SPIE Vol. 6374, 63740P (Oct. 19, 2006)

VISION-BASED TRACKING AND CONTROL A robust vision-based technique for human arm kinematics identification Omid Talakoub and Farrokh Janabi Sharifi Proc. SPIE Vol. 6374, 63740Q (Oct. 12, 2006)

A fuzzy adaptive PD-controller-based micro-assembly system Junping Wang, Xiaodong Tao, Deokhwa Hong, and Hyungsuck Cho Proc. SPIE Vol. 6374, 63740R (Oct. 12, 2006)

An algorithm of calculating the scanning start angle and the scanning angle of linear array CCD panoramic aerial camera Gang Zhou and Lin-Pei Zhai Proc. SPIE Vol. 6374, 63740S (Oct. 12, 2006)

Mark position measurement by visual feedback with laser S. Nara and S. Takahashi Proc. SPIE Vol. 6374, 63740T (Oct. 12, 2006)

SYSTEM IDENTIFICATION AND MODELING I Catheter kinematics and control to enhance cardiac ablation Yusof Ganji and Farrokh Janabi-Sharifi Proc. SPIE Vol. 6374, 63740U (Oct. 12, 2006)

An investigation of phenomenal parasitics and robust control of parallel-plate electrostatic micro-actuators Guchuan Zhu, Jean-François Chianetta, Mehran Hosseini, and Yves-Alain Peter Proc. SPIE Vol. 6374, 63740V (Oct. 12, 2006)

Hybrid neural networks and genetic algorithms for identification of complex Bragg gratings Ali Rostami, Arash Yazdanpanah-Goharrizi, Amin Yazdanpanah-Goharrizi, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740W (Oct. 12, 2006)

Identification of complex Bragg gratings based on optical transfer function estimation using genetic algorithm A. Rostami, A. Yazdanpanah-Goharrizi, A. Yazdanpanah-Goharrizi, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740X (Oct. 12, 2006)

Physical parameters identification of nonuniform fiber Bragg gratings using interpolation method A. Rostami, A. Yazdanpanah, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740Y (Oct. 12, 2006)

SYSTEM IDENTIFICATION AND MODELING II Circuit modeling of multiple quantum well lasers optimized by carrier tunneling A. Rostami, H. Rasooli, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 63740Z (Oct. 12, 2006)

A micro-optical electromechanical system (MOEMS) for high-precision displacement sensor design using ring resonator array A. Rostami, A. Ghanbari, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 637410 (Oct. 12, 2006)

Tunable dispersion management using thermo-optical effect in ring resonator G. Rostami, A. Rostami, and F. Janabi-Sharifi Proc. SPIE Vol. 6374, 637411 (Oct. 12, 2006)

Invited Paper

Laser motor Hideki Okamura* Dept. of Physics, International Christian University, 3-10-2 Osawa, Mitaka, Tokyo, JAPAN 181-8585; ABSTRACT Light driven actuators that have already been proposed are intended for applications on a rather small scale, however, commercially available laser oscillators have sufficient energy to drive much larger objects. Is it possible to realize light-driven actuators that can replace electrical motors? In this paper, a discussion regarding this goal is presented on basis of the conversion efficiencies from light energy into mechanical energy. Several methods of actuation, including the one that is based on radiation pressure, were compared from this perspective. The energy conversion efficiencies for converting the motion of the actuator element into a useful form of motion are separately considered. It was concluded that light-absorption type actuators with a continuous operation scheme are the most promising for achieving a high efficiency. Based on these findings, a new scheme, called the laser motor, is proposed. In the proposed scheme, a pulsed laser shines on an elastic material and induces a specific form of vibrations in it. By using two lasers, a traveling wave is formed. Another object is pressed against the vibrating surface and a relative movement between the two objects is then created. Keywords: Optomechanical actuator, laser, energy conversion, radiation pressure, elastic wave, traveling wave, stationary wave, space elevator, micro robot

1. INTRODUCTION There have been many reports and proposals about manipulating objects by light. It is well known that light has not only energy, but also momentum and these actuators can use either of these two properties. The optical tweezer was the earliest example to utilize the momentum of light. One can manipulate small dielectric materials using a focused laser beam 1, 2. Manipulation of atoms is also realized which can be used for laser cooling 3. A similar manipulation is also possible for molecules 4. Other types of actuators utilize the energy of light. The most common type is based on the photothermal effect 5, 6. The light energy is converted into heat, and then through thermal expansion, the material bends by itself and asserts a force on the neighboring object. The temperature dependent phase transition, photostrictive effect 7, and photochemical reaction 8 can also induce changes in the dimensions of a material. In this type of actuator element, the material bends, shrinks, or stretches, which can be reclaimed as a mechanical motion. Also, applications using the photovoltaic effect or solar cell could also be included in the discussion since it also performs the conversion of light energy into different kinds of energy which can eventually be converted into mechanical energy 9. Light-driven actuators share the property that energy is delivered in a non-contact mode and an object can be remotely driven, and that these devices can be controlled by light so other methods for control are unnecessary. There is no need to carry batteries or other energy sources, therefore they can be very small and light. Another advantage is their high tolerance toward electro-magnetic noise. Based on these properties, they will be able to be used in various environments in which conventional actuators cannot be used. These properties make them applicable to new applications such as micro-robots and light-driven climber. The light-driven actuators reported so far can produce only small forces. Optical tweezers can produce a force in the range of pN or nN. A polymer film can produce a force of 10-5 N when bending upon irradiation 6. Due to these small forces, it cannot actuate large objects, thus applications are limited to small objects. Optical tweezers, for instance, can handle a size only up to 100 µm. *[email protected]; http://subsite.icu.ac.jp/people/okamura/

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637401, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689380

Proc. of SPIE Vol. 6374 637401-1

However, the energy of light is actually high enough to manipulate much larger objects. Commercial laser oscillators of more than 10W of output power are easily obtainable. This is a power capable of accelerating a 1kg object to 5m/s in one second, or moving a 1kg object upward at a constant speed of 1m/s. As will be explained later, the currently proposed light-driven actuators have conversion efficiencies much less than unity, and application of these techniques for larger objects seems impossible. If in some way the efficient conversion of light energy into mechanical energy is realized, all these things will be able to be performed using light. It will be possible to replace applications which could only be performed by a motor or some other means. Various new applications will then become feasible. In this paper, various types of light-driven actuators are reviewed from the viewpoint of energy conversion. This discussion will give us some insights into how one can achieve an efficient conversion of light energy into mechanical energy. Conversion efficiency is not a concern for small objects, because even if most of the energy is wasted, these techniques are still useful. For a larger object, the situation is different. One definitely needs a high efficiency in order to obtain a large magnitude of force. Finally, I will propose a scheme that can potentially offer a high efficiency and continuous linear or rotational motion.

2. ENERGY CONVERSION EFFICIENCIES Energy conversion efficiency is defined as the ratio between the work that is done by the actuator and the light energy that fell upon the actuator. Light driven actuators have various shapes and mechanisms, however, they all share the same property that they convert light energy into mechanical energy. Therefore, in the following discussions, the efficiencies are compared for several types of actuator elements. This will give us some insight into realizing an energy efficient energy conversion. We divide the light-driven actuators into two groups, that is, one that uses radiation pressure and one that uses light energy, and each type will be considered below. Note that these are the efficiencies for the actuator elements. The efficiency as a system includes the mechanism to convert the motion of the actuator element into a useful form of motion. This will be separately discussed. 2.1 Radiation pressure type actuators Light can assert a force on objects through radiation pressure, or the momentum of light. Optical tweezers, laser cooling, and the solar sail all fall in this category. It is also possible to oscillate a microscopic oscillator with light 10, 11. The force induced by this effect is usually very small. One example to show this is that a very large sail is required for solar sailing. For optical tweezers the force is on the order of pN. This is too small a force to manipulate macroscopic objects, and therefore, optical tweezers are useful only for microscopic objects. Why is this force so small? This is a natural consequence from the property of light. The energy, E of light and its momentum, p are given by E = hν and p = h/λ = E/c, respectively, where ν is frequency, λ is wavelength, c is the speed of light, and h is Planck’s constant. Also, the force F is given by F = dp dt . Since c is a very large number, p becomes much smaller than E. Thus there is a limitation on the force for this type of actuator. Let us estimate the efficiency of the optical tweezers. The typical laser power for an optical tweezer is 10mW and the force produced at this laser power is on the order of pN. If we displace the object by 1 mm in 1 sec, therefore, the work done is 1 pN × 1 mm = 1 × 10-15 J, and the light energy during this period is 10 mW × 1 s = 10 mJ. The conversion efficiency is then roughly 1 × 10-15 J/ 10 mJ = 10-12 = 10-10 %. For the actuation of an object by radiation pressure, most of the light energy is not used. Light retains most of its energy after an interaction with matter. Only a small red-shift in the wavelength of the scattered or refracted light due to the Doppler effect accounts for the mechanical energy that is produced. 2.2 Light absorption type actuators In this type of actuator, light is absorbed and its energy is used to change the state of the material. Some of the effects used for actuators are summarized in Table 1. All these types of effects convert light into different forms of energy. The first 4 types of actuators in Table 1 are accompanied by a volume change. Ablation utilizes the reaction force from the particle leaving the object upon irradiation of an intense laser pulse. The ferroelectric transition can also be used for actuators. The last one may seem different from the rest of the listings, but it is also the conversion of light energy into another form of energy (in this case, electricity) so it can be included here.


Table 1. Various types of light-absorption type light-driven actuators Type of effect

Principle

Materials

Photothermal effect

Heat expansion, etc

Optical fiber, PVDF Polymer film, etc

Photochemical effect

Isomerization

Liquid-crystal network with azobenzene chromophore

Photostrictive effect

Piezoelectric

PLZT ceramics

Vaporization,

Vaporization of water,

Structural change, etc

Shape Memory alloy, etc

Ablation

Reaction of particles

Metal, etc

Ferroic transition

Temperature increase

Temperature sensitive magnet, etc

Solar cell, photovoltaic effect

Electronic excitation

Phase transition (Volume change)

Si semiconductor, etc

Next, we will compare these processes in terms of efficiency. Firstly, let us take up the actuator using the PVDF polymer film 6. This actuator is mainly based on the photothermal effect. It bends upon irradiation and assert force. The force was measured to be 6.6 × 10-5 N and the efficiency was obtained to be 8.3 × 10-5 %. There are not many reports about the evaluation of efficiency other than this report, so we will make estimations for the rest. Temperature sensitive transition type actuators are expected to have a rather high efficiency because the energy of the laser beam can be easily converted into heat with only a small loss. In our lab, we are testing an actuator based on a temperature sensitive alloy. A rough estimate of the conversion efficiency was on the order of 1%. Photochemical type and ferroic tansion type actuators are supposed to give similar efficiency since the cause of the energy loss is similar. Ablation is unlikely to score better than these types of actuators because some energy is wasted in unwanted heating of the body. Also, there is a loss due to the velocity distribution of the leaving particles. Only the perpendicular component of them to the surface is effective for propulsion, and the rest of the energy is averaged out and does not contribute. The efficiency of the solar cell can reach 50% if one chooses the right wavelength. The one for a motor is 80% under favorable conditions. The overall efficiency is the product of these two, so for a carefully designed system, the overall efficiency from light energy into mechanical energy will be close to 40%. NASA demonstrated the practicality of this combination by a model airplane that is propelled by a laser beam. The light energy is converted to electrical energy by a solar panel that is attached to the bottom of the airplane. It does not need to carry any fuel and can fly for an unlimited time as long as the laser beam is tracking the airplane 9. 2.3 What is the method of choice? The results of these discussions are summarized in Table 2. The phase-transition type actuator seems to be the most promising among these, except for the solar cell. The photothermal effect is not a very efficient process, but still provides a higher efficiency than the optical tweezer. The efficiency of the optical tweezer is by far the lowest. Considering that there is a theoretical limitation for the force due to radiation pressure, it can be naturally concluded that an efficient conversion will have to resort to absorption type actuators. Table 2. Energy conversion efficiencies for various types of light-driven actuator elements.

Category Radiation Pressure Absorption (photo-thermal) Absorption (Phase transition, heat induced) Absorption (photo-current)

Type

Typical Force

Efficiency

Optical tweezer

~ 1 pN

~10-10 %

6.6 × 10-5 N

8.3 × 10-5 %

Polymer film (PVDF) Temperature sensitive alloy Solar cell + motor


~3 N

~1 % (estimate) ~40% (Theoretical)

2.4 Conversion to a linear/rotary motion In the previous section, we focused on the actuator elements and discussed the principle of actuation. In this section, we examine the manner in which actuators produce force. The strokes of light driven actuators are typically on the order of micrometers. An oscillating object at such a small amplitude is of little use, therefore, for this type of motions a conversion into a linear/rotary motion is usually desirable. Some examples are shown in Fig. 1. For a volume-change type actuator, the typical motion is bending. Actuators that use ablation or vaporization make use of the reaction force from the substance that leaves an object. Another example shown here is an actuator based on the temperature sensitive magnet. By making use of the property that magnets lose their magnetic properties above the Curie temperature, the force between the magnets can be turned on and off by irradiation. Upon irradiation, the magnet loses its magnetic property, and the two magnets will move apart from each other by a spring. Bending Light

Reaction of ablation/vaporization Light

Temperature sensitive magnet

Light

Fig. 1. Some examples of actuator motions.

The conversion to a linear or rotary motion usually requires that a cycle be formed. For instance, a bending motion is repeated for a microactuator to walk 12. Another example of a cycle is depicted in Fig. 2. In this case, two actuator elements are combined so that they form a 90° angle. Each one moves at a time, forming a 4-stroke cycle, and by repeating this cycle, they could rotate a disk 6. This is a demonstration of conversion from a bending motion to a rotary motion.

sssssssa

U

a

—%4su-#44'

sssa sssssa Fig. 2. An example of a conversion from a bending motion to a translational motion.


One will notice that the translational motion is produced during only one of the four steps. The force in the return path does not do any work. Even so it requires a similar amount of energy to bend. Therefore, roughly speaking, only one fourth of the energy produced by the actuator is converted into a translational motion. Force is used for propulsion only in a fraction of the steps in the whole cycle, so some waste of energy cannot be avoided if a cycle is to be formed. There is another kind of problem for this kind of walking motion. For one thing, there is no retaining force for the object while the actuator is not in contact with the object. This will lead to a backlash and will further degrade the efficiency. Another problem is the translation of an object based on bending or expansion that becomes a walking type motion. It tends to be slow and inefficient, i.e., the speed will suffer. As can be seen from the above discussion, through the process of conversion from a oscillating motion into a linear or rotary motion, only a fraction of the energy can be converted into a translational energy. The overall efficiency is reduced by this process.

3. NEW PROPOSAL – LASER MOTOR In this report, we would like to propose a new scheme involving a potentially efficient light-driven actuator, which can convert light energy into mechanical energy in a more direct way. As is evident from the above discussions, if one wants to manipulate macroscopic objects by light, it has to use the energy of light, not its momentum. This suggests that the actuator cannot generate a momentum by itself and the relative motion has to be generated between two objects. Naturally it will consist of two parts, and to avoid exploiting a walking cycle, which will ruin the efficiency and speed, the two objects will be in physical contact with each other and directly induces a relative motion. Based on the above argument, one can draw the sketch that is shown in Fig. 3. This is one possible scheme for realizing the efficient conversion from light energy into mechanical energy. We called this a laser motor due to its resemblance to a conventional motor.

Fig. 3. Schematic drawing for rotary and linear laser motors.

How will it be possible to induce a relative motion between the two objects? This will be realized by generating traveling elastic waves in the object with light pulses. Fig. 4 shows the case where a Rayliegh wave is employed (the bulk wave will also work). The Rayligh wave is a surface wave, and has the characteristic that each portion along the surface takes a circular motion. The direction of rotation is the opposite to the direction that the wave is propagating. Therefore, if one presses another object against the surface, this object is driven in the opposite direction of the wave propagation. As will be explained later, the direction of wave propagation can be reversed by changing the laser irradiation timing.


j—L

V

Direction of wave propagation Fig. 4. Schematic of actuation. The surface Rayliegh wave pushes the object into the efficient as

The principle of laser motor is summarized in Fig. 4. It is known that a laser can induce elastic waves in solids 14. It is one of the advantages of using lasers. Lasers can produce intense light pulses whose energy is concentrated in a fraction of time. Also, the timing and position of the irradiation can be precisely controlled. The irradiation timing of the laser pulses are tailored and induce the desired wavelength of the elastic wave. Positions of the irradiation are controlled by a mask or filter on the surface of the object. Light is selectively absorbed in either or both of the two objects. Various kinds of schemes, including heat deposition, ablation, phase transition, and photostrictive effects, can be used for exciting a vibration. For the best performance, the most efficient method will have to be found. By changing the schedule of light irradiations, one can control the speed and direction of the motion. The diagram for the laser motor is summarized in Fig. 5.

Laser irradiation Vibration

Heat deposition (photothermal effect) Radiation pressure Light-induced phase transition Ablation Photon-phonon coupling Photovoltaic effect Photostrictive effect

Linear/rotary motion Fig. 5. Diagram for the laser motor. A pulsed laser shines on some elastic material and induces vibration on the surface. By using two lasers of different wavelengths, a traveling wave is formed. A linear or rotary motion is induced between the vibrating object and the other object that is in contact with the vibrating object.

3.1 How to induce a traveling wave laser pulse irradiation can induce a vibration in an object. In this case, a clearly defined wave of a fixed wavelength needs to be excited. This could be realized by irradiating an object at its resonant frequency. By tuning the interval of the irradiation, one can induce a stationary wave with a single frequency, A1 (z, t) = sin(ω t)cos(kz) . A second laser oscillator induces another stationary wave on the object with a different phase, A2 (z,t) = sin(ω t + π / 2)cos(kz + π / 2) . When the two stationary waves are superposed, one obtains, A1 (z,t) + A2 (z,t) = sin(ω t)cos(kz) + sin(ω t + π / 2)cos(kz + π / 2) = sin(ω t − kz)

(1)

This is the traveling wave that we are looking for. If one wishes to reverse the direction of the motor, one simply changes the irradiation timing. There is no need to change the location of the excitation. Now, the second wave A2(z, t) becomes, A2′ (z,t) = sin(ω t − π / 2)cos(kz + π / 2) . Therefore,


A1 (z,t) + A2′ (z,t) = sin(ω t)cos(kz) + sin(ω t − π / 2)cos(kz + π / 2) = sin(ω t + kz)

(2)

Eq. (2) represents a traveling wave going in the opposite direction to eq. (1) The scheme for the irradiation timing is depicted in Fig. 6. Time Å® éû ä‘ B1 B2

Time Å® éû ä‘

B1 B2

Fig. 6. Irradiation timing. B1 and B2 refer to the timing scheme of laser irradiation. The top and the bottom irradiation schemes induce a traveling wave propagating in the opposite directions.

3.2 Experimental

—

——

r

r

r :-= -

t I

.—

J

c-'

T—

____ L2______

—1

To demonstrate that clearly defined elastic waves of single frequency can be induced by laser, we conducted an experiment using a Q-sw Nd:YAG laser (wavelength 1064 nm) and a copper ring as a target. In Fig. 7, the experimental result is shown. The repetition rate was tuned to the resonant frequency of the ring. The bottom trace indicates laser irradiations. The upper trace is the voltage from the transducer attached to the surface of the target. A vibration that is in phase with the exciting laser is induced. The amplitude of the vibration can be estimated from the voltage of the transducer that is on the order of 10 nm 13. In this experiment the vibration was induced by the photothermal effect. By using more efficient mechanism, and by using a material with higher Q-factor, the amplitude can become much larger.

Fig. 7. Experimental result for the induction of a stationary wave in a copper ring.


3.3 Advantages of Laser Motor This method has the advantage that the light doubles as a method to convey energy and as a method to control the operation. In the case of NASA’s light plane, light is used to transmit just the energy, so the control of a motor has to be done by a separate transmission channel such as a radio wave. In the case of the laser motor, one can even reverse the direction by simply changing the irradiation timing. To summarize the advantages of the laser motor, No wire, no battery Fully controllable by light Light weight, small size. Much faster than walk-type motion Not affected by electric or magnetic disturbances High holding force, zero backlash - (very useful when used for elevators) Long range operation. (Laser can reach a great distance) 3.4 Possible Applications In this section, some possible applications are illustrated. For the application as a space elevator (Fig. 8b), the laser motor has to cling to a ribbon. For this special purpose, a variant of the laser motor that can move along a ribbon is shown in Fig. 10. The rippon is sandwiched between 2 motors which hold it. Due to the high holding force of the laser motor, this will be a particularly suitable example of such an application.

(a)

Iazer2

(b)

—Ribbon 20 Laser —motor 23

— 34 Laser — 31 Motor 1

35 Laser Motor 2

Fig. 8. Possible applications. (a) Micro car that can be controlled and driven by laser pulses of three different wavelengths. (b) A space elevator. The laser station fixed on the ground irradiates the elevator to supply energy.


(a)

111111

11111111111I 11111111111I I

Laser motor

Laser

I

I

11111111111111I 11111111111 I

I

Laser

(b)

Fig. 9. Possible applications. (a) Remote control slider/adjuster for hard to reach locations. Each knob on the board is equipped with a laser motor and can be remotely operated. (b) Remote adjustment of the angle of mirror/screen/tile on the building from the outside. The adjuster screw can be operated by the laser motor.

Laser V un bbon

Laser Fig. 10. A variant of the laser motor. The laser motor itself will slide on the rail/ribbon.

4. CONCLUSION We investigated the possibility of realizing a light-driven actuator that can manipulate macroscopic objects. The energy conversion efficiency is the key factor, therefore, we compared energy conversion efficiencies of various types of actuators, both on the element itself and on the process to convert the motion into a usable form of motion. We showed that an efficient actuator has to be an energy absorbing type, and therefore, it will require at least two objects to induce a relative motion between them. Also, it was found that a continuous operation is desirable. Based on these finings, we proposed a new scheme, called the laser motor, which continuously operates and is potentially fast. It uses pulsed lasers to induce a traveling elastic wave, and then the induced elastic wave is converted into a linear or rotary motion. A mathematical treatment showed that two independent waves should be excited, which is easily attainable using two lasers and appropriate filters. A traveling wave can be formed by a superposition of the two independent waves. Reversing the direction can easily be done by changing the irradiation timing. Some results from preliminary experiments of inducing vibrations in solids were also shown.


REFERENCES 1. A. Ashkin, Phys. Rev. Lett. 24, 156-159 (1970). 2. A. Ashkin, "History of Optical Trapping and Manipulation of Small-Neutral Particle, Atoms, and Molecules." IEEE Journal of Selected Topics in Quantum Electronics 6(6), 841-856 (2000). 3. H. Okamura, P. Corkum, and D. Villeneuve, “Trapping H2 molecules with intense laser pulse,” The 49th Spring Meeting of Japan Society of Applied Physics and Related Societies, Kawasaki, 2002, 30aD5/III, p.902. 4. H. Okamura, "Molecular Optics - control of molecular motion by strong laser field," Bunko-kenkyu, Journal of the spectroscopical Society of Japan, 50, 101-109 (2001) (in Japanese). 5. S. Inaba, H. Kumazaki, and K. Hane, "Photothermal vibration of fiber core for vibration-type sensor", Jpn. J. Appl. Phys., 34, 2018-2021 (1995). 6. S. S. Sarkisov, M. J. Curley, L. Huey, A. Fields, S. S. Sarkisov II, G. Adamovsky, “Light-driven actuators based on polymer films,” Opt. Eng., 45, 034302 (2006). 7. P. Poosanaas, K. Tonooka, K. Uchino, “Photostrictive actuators,” Machanics 10, 467-487 (2000). 8. Y. Yu, M. Nakano, T. Ikeda, “Directed bending of a polymer film by light,” Nature, 425, 145 (2003). 9. NASA: NASA research team successfully flies first laser-powered aircraft, http://www.nasa.gov/lb/vision/earth/improvingflight/laser_plane.html 10. O. Hahtela and I. Tittonen, “Optical actuation of a macroscopic mechanical oscillator”, Appl. Phys. B, 81, 589-596 (2005). 11. T. Carmon, H. Rokhsara, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal Behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett., 94, 223902 (2005). 12. Y. Otani, “Light driven running machine,” Hikari-aliance, 10, 40−42 (1999)． 13. B. V. Richert, R. Hamamura, R. Ono, and H. Okamura, ”Observation of resonant standing waves in a copper ring induced by laser irradiation”, The 53rd Spring Meeting of Japan Society of Applied Physics and Related Societies, Tokyo, 2006, 25a-ZD-9/III, p.1062. 14. Z. Shen, S. Zhang, and J. Cheng, “Theoretical study on surface acoustic wave generated by a laser pulse in solids,” Anal. Sci., 17 , S204-s207 (2001).

Proc. of SPIE Vol. 6374 637401-10

Light-driven polymer actuators for propulsion and light control LaQuieta Huey,*a Sergey S. Sarkisov,b Michael J. Curley,a Grigory Adamovskyc Jai-Ching Wanga a

Alabama Agricultural and Mechanical University, Department of Physics, Normal, Alabama 35762, USA b SSS Optical Technologies, LLC, Huntsville, Alabama 35816, USA c NASA Glenn Research Center, Cleveland, Ohio 44135, USA ABSTRACT

New light-driven actuators based on films of polymer polyvinylidene fluoride are described. The actuators employ the photomechanical bending of the polymer film caused by low power (10 mW and less) laser radiation. The photomechanical effect combines various physical mechanisms, such as anisotropic thermal expansion, converse piezoelectric mechanism along with photovoltaic and pyroelectric ones, while the mechanism of thermal expansion is dominant for slow motion. Mechanical vibrations of the strips of the photomechanical polymer were observed with periodic pulsed laser excitation. The resonance frequency is inversely proportional to the square of the length of the strip, in full agreement with the theory. Resonance frequency measurements were used to determine the modulus of elasticity of the films, which was close to 3.0x109 Pa. Two possible applications were discussed: optical fiber switch and adaptive mirror propelled by the proposed actuators. The actuators have a potential of being used as the components of future light-driven micro/nano systems. Keywords: photomechanical effect, optical actuator, photomechanical polymer

1. INTRODUCTION Modern optical smart structures,1 which adapt themselves to external and internal changes measured by various optical sensors, lack simple and compact actuators that can be driven by the same low power light radiation used to operate sensors. Current solutions utilize electrically driven actuators, which require electric current to be delivered by wires from an electric power source. Rapidly growing industry of optical switching experiences similar problem. Currently available optical switches typically use electrically driven piezoelectric actuator elements requiring an external high voltage for actuation.2 Consequently, there is a great need for a simple, efficient and compact photomechanical actuator, which can be driven by low power light radiation in visible or mid-infrared range delivered through conventional optic fibers. The photomechanical (or optomechanical) effect could be defined as a bulk dimensional change in a photosensitive body induced by the influence of an applied optical field.3 Several physical mechanisms have been reported in the literature to generate a significant photomechanical effect: photothermal mechanism,3-6 photostriction,7 and molecular re-orientation caused by polarized light.8, 9 The focus of this study was on the applications of the light-driven actuators using photomechanical effect in thin films of polymer polyvinylidene fluoride known as PVDF.

2. EXPERIMENT It has been shown in the past that the illumination of a strip of PVDF film with continuous laser radiation produces a static bending of the strip.10 The direction of bending is always the same, no matter which side of the strip is illuminated. The bending strip exerts a static force to an external object. The force is proportional to the power of the incident laser beam. It can be as high as 10-4 N per 10 mW of the laser beam power. The force, as well as the deflection, does not depend on the shape of the beam and its position in the strip as long as the beam *

E-mail: [email protected] Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 637402, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684337


stays away from the edges. In this study our focus was on the vibrations of PVDF strip produced by pulsed laser radiation, which is important for propulsion-related applications. Thin film samples of PVDF (β-phase, solid solution of polycrystalline phase in amorphous phase) with a thickness of 28, 52, and 110 µm were studied. The films were uniaxially stretched and polarized with a positive corona during the extrusion process and then rolled up and stored in rolls. Fig. 1 shows microscopic images of a typical film. Optical image reveals some phase inhomogeneities in the volume probably due to the crystalline phase of PVDF dissolved in polymer phase. AFM image reveals surface imperfections such as scratches and pits created by the corona discharge during the electrostatic poling process. The density of the defects is such that they do not affect the performance of the films as photomechanical actuators. Rectangular strips of various length and width were cut from the films with long dimension along or across the direction of stretching. In order to increase the absorption of an incident laser beam, the strips were coated with 80-nm chromium layers on one side using DC magnetron sputtering. The experimental setup is presented in Fig. 2. The illumination of a strip of a PVDF film with a pulsed beam from an infrared laser generates periodic vibration of the strip. In order to visualize the vibration, a weak continuous probe laser beam from a semiconductor laser was pointed on the free end of the strip, close to the edge. The reflected beam made a spot on a distant screen. Vibration of the strip produced displacement of the probe ∆y, as is shown in Fig. 2. Pulses of laser light were produced by a mechanical chopper placed after the laser. The frequency of the light pulses was varied by varying the frequency of the chopper wheel. The frequency reading was taken form the digital display of the chopper. The amplitude of vibrations (in arbitrary units) was evaluated as ∆y/2.

3. EXPERIMENTAL RESULTS AND DISCUSSION It was possible to observe the mechanical resonance of the vibrations of the strips periodically illuminated with laser pulses. Typical resonance curve of a vibrating strip is presented in Fig. 3. In this particular case (5-mm wide strip) two resonances at 12 and 33 Hz were observed. The vibration at the higher resonance frequency had greater amplitude. The theoretical model of a vibrating beam with one fixed end was applied to this case.11 The resonance frequency of the 1-st vibrating mode of the beam can be expressed as

f =

3.516 t 4πl 2

E , 3ρ

(1)

where f is the frequency, E is the Young’s modulus of elasticity, t is the thickness of the film, l is the length, ρ is the mass density of the film (1.917 X103 kg/m3). Eq. (1) was used to determine the Young’s modulus of PVDF strips of different sizes, thicknesses, and cuts. Experimental data is presented in Figs. 4 through 6. The resonance frequency was plotted versus the inverse square of the length of a strip. According to Eq. (1) the linear fit of the data must give a slope factor that can be used to find the modulus of elasticity, with all the other parameters known. The modulus of elasticity was determined as close to 3.0x109 Pa for the films of 52 and 110 µm, and twice as high for the 28-µm film, regardless of the cut. The difference in moduli needs to be further investigated. The elasticity of 28-µm or thinner film of PVDF could be higher due to some unaccounted fabrication peculiarities. On the other side, it could be an indication that the simple model of an elastic vibrating beam fails to describe thinner films. Experimental investigation of the effects of thermo-mechanical fatigue was conducted with the films used for the actuators. In the first experiment, a strip of chromium-coated 52-µm polymer film clamped between two glass plates with dimensions 2 by 22 mm was periodically activated by a 15-mW laser beam from a He-Ne laser at a resonance frequency of 43.5 Hz. The amplitude of the vibrations of its free end and its position was monitored with a weak probe beam from a semiconductor laser (laser pointer, 635-nm wavelength). The total time of the continuous operation of the actuator was 77 hours (equivalent to 1.2x107 cycles of switching of an optical switch based on the actuator) until the probe laser broke down. During this time no noticeable decrease of the amplitude of the vibration or shift of the position of the free end due to some inelastic bending was observed. The actuator turned out to be more reliable then the laser source. In the second experiment, a strip of the same film was illuminated with a beam from an Nd:YAG laser (1064-nm wavelength) at significantly higher power. The beam


with a power of 150 mW produced almost immediately inelastic deformation of the film, in other words melted it down, and no light-driven actuation was observed afterwards. However, periodic illumination of a 3 by 25-mm strip with a 63-mW beam at a resonance frequency of 24 Hz performed over 10 hours did not show any degradation of the amplitude of the vibrations or inelastic bending of the film. The amplitude and the shift were also monitored with a weak probe beam from a probe semiconductor laser. That was equivalent to approximately 9.0x105 cycles of vibration. These experimental results point to sufficiently good performance of the polymer actuator in terms of its lifetime.

4. APPLICATIONS 4.1. Photonic switch A prototype photonic switch was built using thin films of PVDF.12 All the components of the switch are mounted on platform 1 (Fig. 7). The core element of the switch is a flexible reflector (2, 3) made of metal-coated PVDF film. The reflector is fixed on holder 4. In its inactive state the reflector takes position 2. In its active, deformed, state the reflector takes position 3. Activation of the reflector into active state is achieved by illumination with light beam 5, which is focused by optical element 6 into beam 7 converging on the back side of the reflector coated with absorbing coating 8. A low-power semiconductor laser 9 sends probe beam 10 to the reflector. When the reflector is in inactive position 2, probe beam 10 is reflected and turns into beam 11 that goes to optical element 12 that focuses it in optical fiber 13. Fiber 13 transmits light to photodetector 14 connected to Channel 1 of a two-channel oscilloscope 15. When the reflector is in active position 3, probe beam 10 is reflected and turns into beam 16. Beam 16 goes through optical element 17 to fiber 18 that transmits light to photodetector 19 connected to Channel 2 of oscilloscope 15. Light beam 5 is chopped by mechanical chopper 20. The chopper synchronizes oscilloscope 15. When light beam 5 is cut off by chopper 20, the reflector is in inactive position 2, and the light from laser 9 goes to photodetector 14 that produces high-level signal in Channel 1 of the oscilloscope. There is no light going to photodetector 19, and the signal in Channel 2 is at zero level. When light beam 5 illuminates the reflector, the signal in Channel 1 is at zero level, and the signal in Channel 2 is at high level. Thus, illumination of the reflector with control light beam 5 produces a switching effect between Channels 1 and 2. The reflector was made as a strip of gold-coated 52-µm-thick PVDF film with dimensions 7x1 mm. It was illuminated with a 15-mW beam from a He-Ne laser. Fig. 8 depicts a typical oscillogram of the signals in the channels of the switch. The minimum switching time observed was 3 ms (for a 1x7-mm strip made of 52-µm film). The speed of switching can be increased by the reduction of the size of the PVDF reflector, in accordance with the findings discussed in Section 3. 4.2. Adaptive mirror The photomechanical polymer films were also tested as a basis for adaptive mirrors.12 Fig. 9 shows the configuration of the experiment with a defocusing convex reflector activated by the primary incident beam (selfdefocusing). Experimental mirror for self-defocusing was made of a 52-µm film coated with chromium. The power of the incident self-defocusing beam was controlled with a set of neutral density filters. The crosssectional view of the beam was obtained with a Spiricon beam profiler (Fig. 10). As one can see, the beam widens up significantly after reflection form the film when its power increases. This is an indication of defocusing caused by the formation of a convex mirror in the illuminated region of the film. A power of 12 mW from a He-Ne laser was sufficient to make a well defined reversible defocusing convex reflector out of initially flat film. In other configurations, the shape of the reflector could be controlled by a secondary control beam dedicated to shape up a relatively weak primary beam (Fig. 11). In this experiment, films of PVDF were coated with high reflectance gold coating on one side and with an absorbing coating on another side. Fig. 12 shows how the control beam defocuses the probe reflected from a convex photomechanical mirror (52-µm-thick in this case). The temporal response of the mirror has two components: fast and slow. The fast response lasts for few hundred milliseconds. The slow response, resulting in final wide spread of the probe, takes up to three seconds. After that the spread of the probe reaches saturation. Fig. 13 shows focusing of the probe by the same control beam using a 110-µm-thick concave mirror. The plot of the focal distance of the mirror versus the power of the control beam is presented in Fig. 14. The focal distance goes down with the power and approaches a saturation level of 4.5 mm. Further decrease of the focal distance (increase of the focusing power) of the mirror can be achieved by the reduction of the size of the control beam.


5. CONCLUSIONS Photomechanical actuators based on PVDF films powered by pulsed mW laser beams can be used to propel optical fiber switches and adaptive reflectors. The theoretical model of a uniform elastic beam with one end clamped turned out to be accurate enough to describe resonance vibrations of the PVDF strips activated by pulsating laser beam, if the thickness of the strips exceeds 28 µm. Using the model and the experimental data on the resonance frequency versus the length of a strip, the modulus of elasticity of PVDF films was determined as close to 3.0x109 Pa. The fatigue effects did not show up for hundreds of hours of continuous operation of the PVDF actuators. Preliminary demonstrations showed the feasibility of a photonic switch and adaptive mirror based on the photo-mechanical actuators.

ACKNOWLEDGMENTS LaQuieta Huey and Michael Curley acknowledge support from the Department of Education HBGI Title III Program at AAMU.

REFERENCES 1.

J. Dakin and B. Culshaw, “Optical Fiber Sensors. Volume 4: Applications, Analysis, and Future Trends”, pp. 409- 435, Artech House, Inc., Boston, MA (1997). 2. P. De Dobbelaere, K. Falta, and S. Gloeckner, “Advances in integrated 2-D MEMS-based solutions for optical network applications,” IEEE Communications Magazine 41, S16-S23 (2003). 3. S. Inaba, H. Kumazaki, and K. Hane, “Photothermal vibration of fiber core for vibration-type sensor,” Jpn. J. Appl. Phys. 34, 2018-2021 (1995). 4. M.G. Kuzyk, D.W. Garvey, S.R. Vigil, and D.J. Welker, “All-optical devices in polymer optical fiber,” Chemical Physics 245, 533-544 (1999). 5. Yu. Otani, Ya. Matsuba, and T. Yoshizawa, “Photothermal actuator composed of optical fibers,” in Optomechatronic Systems II, Hyung Suck Cho, Editor, Proceedings of SPIE Vol. 4564, 216-219 (2001). 6. H. Finkelman, E. Nishikawa, G.G. Pereira, and M. Warner, “A new opto-mechanical effect in solids,” Phys. Rev. Lett. 87, 015501-1- 4 (2001). 7. P. Poosanaas, K. Tonooka, and K. Uchino, “Photostrictive actuators,” Mechatronics 10, 467-487 (2000). 8. P. Krecmer, A.M. Moulin, R.J. Stephenson, T. Rayment, M.E. Welland, and S.R. Elliott, “Reversible nanocontraction and dilation in a solid induced by polarized light,” Science 277, 1799-1802 (1997). 9. Ya. Yu, M. Nakano, and T. Ikeda, “Photomechanics: Directed bending of a polymer film by light,” Nature 425, 145 (2003). 10. Sergey S. Sarkisov, Michael J. Curley, Aisha Fields, Sergey S. Sarkisov II, Grigory Adamovsky, Photomechanical effect in films of polyvinylidene fluoride, Appl. Phys. Lett. 85, No. 14 (2004) 27472749. 11. S. Timoshenko, “Vibration problems in engineering,” Wiley, New York, NY (1974). 12. Sergey S. Sarkisov, Michael J. Curley, Grigory Adamovsky, Sergey S. Sarkisov, Jr., Aisha Fields, U.S. Patent No. 6999221, February 14, 2006, Bimorphic Polymeric Photomechanical Actuator.


(a)

nM nM

300

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20000

10000 NN

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10000

Figure 1. Optical (a) and atomic force (b) microscopic images of the PVDF film (52-µm-thick) used in the experiments. Total magnification of the optical microscope used was x400.


10 9

∆y 8

7 1

5

6

4

3

2

Figure 2. Schematic of the experimental set-up for the study of mechanical vibrations of a PVDF strip initiated by a pulsed laser beam. A strip of metal coated PVDF film 1 is clamped between two glass slides 2. After being illuminated with laser beam 3 (that can be moved laterally in the vertical and horizontal direction with respect to the strip, as shown by arrows 4), the strip bends and takes new position 5. The free end of the strip is illuminated with a low power continuous laser probe beam 6. When the strip is in the initial, inactive position, the probe beam is reflected in direction 7 and makes a light spot 8 on a screen. When the strip driven by beam 3 is deflected, the probe beam is reflected in direction 9 and light spot 10. The light spot made by the probe beam has displacement ∆y. amplitude/2 35 30

amplitude

25 20 15 10 5 0 10

20

30

40

frequency

Figure 3. Amplitude of the vibrations (in arbitrary units) of a rectangular strip of PVDF versus the frequency (in Hz) of the laser pulses illuminating the strip. The data corresponds to a 52-µm thick strip with dimensions 20 by 5 mm. The strip was illuminated with a 70-mW IR laser beam at 1064 nm from a CW Nd:YAG laser. The resonance frequencies observed are 12 and 33 Hz.


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(b) Figure 4. Plot of the resonance frequency (in Hz) versus inversed square of the length (in meters) for the strips made of 28 µm thick PVDF film. Figure (a) is the data plotted for the strips with longer dimensions along the direction of stretching, and figure (b) is for the strips cut across the stretching direction. The Young’s modulus was found to be (6.51 ±0.693) x 109 Pa and (8.15 ±0.97) x 109 Pa for (a) and (b) respectively. The 28 µm strips were suspended in air.


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(b) Figure 5. Plot of the resonance frequency (in Hz) versus inversed square of the length (in meters) for the strips made of 52µm-thick PVDF film. Figure (a) is the data plotted for the strips with longer dimension along the direction of stretching, and figure (b) is for the strips cut across the stretching direction. The Young’s modulus was found to be (2.44 ± 0.48) x 109 Pa and (3.50 ± 0.49) x 109 Pa for (a) and (b) respectively.


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Figure 6. This graph depicts the 110-µm strip (cut along the stretching direction). Young’s modulus here was found to be (3.59 ± 1.29) X 109 Pa. The amplitude of vibrations of the strip cut across the stretching direction was small and hard to measure.

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Figure 7. The configuration of a photonic switch based on the light-driven PVDF actuator.


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Figure 8. Oscillogram of the intensity of light in Channels 1 and 2 (pulses with small dip on the top) of the photonic switch.

Self-focusing

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Figure 9. Self-focusing (a) and self-defocusing (b) of a laser beam illuminating the photomechanical deformable mirror.

Proc. of SPIE Vol. 6374 637402-10

(a)

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(c)

Figure 10. Image of the spot of the beam reflected from a defocusing adaptive mirror made of a 52-µm film when the power of the incident beam increases from (a) 1 (in relative units) to (b) 500, and (c) 800. A power level of 800 rel. units corresponds to 12 mW of radiation from a He-Ne laser. Defocusing of the probe beam with control laser beam


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Figure 11. Defocusing (a) and focusing (b) of a probe laser beam with a control beam coming from the opposite side of the photomechanical mirror.

Proc. of SPIE Vol. 6374 637402-11

(a)

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Figure 12. Image of the spot created by a probe beam (from laser pointer) reflected from a 52-µm-thick photomechanical mirror controlled by a control beam from a 12-mW He-Ne laser when (a) the control beam is OFF and (b) control beam is ON. The control beam causes defocusing of the probe.

(a)

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Figure 13. Image of the spot created by a probe beam (from laser pointer) reflected from a 110-µm-thick photomechanical mirror controlled by a control beam from a 12-mW He-Ne laser when (a) the control beam is OFF and (b) control beam is ON. The control beam causes focusing of the probe.

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Proc. of SPIE Vol. 6374 637402-12

Positioning control of Nafion-Au ionic polymer metal composite (The Effect of Counter Ion on The Deformation Patterns of IPMC) Akitoshi Itoh*a, Tetsuichi Amarib, Toshihiro Tanakab Dept. of Mechanical Engineering, Tokyo Denki Univ. /2-2, Kanda Nishiki-cho, Chiyoda-ku, Tokyo, 101-8457, Japan; b Graduate School Student, Tokyo Denki Univ.

a

ABSTRACT This paper describes the positioning control method of Au-Nafion IPMC. Au-Nafion IPMC can be classified into two types whether the residual strain is generated to the cathode side(SDT) or the anode side(ODT). SDT can be controlled its position by normal integral control. ODT can also be controlled by restricting the maximum changing speed in the integral control. Experimental result showed the close relationship between the direction of the residual strain and the density or the amount of the counter ion. Keywords: Ionic Polymer Metal Composite, Counter ion, Positioning control, Displacement control, Nafion

1. INTRODUCTION Ionic Polymer Metal Composite (IPMC) is a polymer-metal composite that is made by plating metal on the ionic conductive polymer-gel film. IPMC was invented by Oguro, et.al.[1] in 1991. This soft actuator attracts so many researchers' attention by its high speed response, large deformation quantity and softness. So many researches of theoretical, experimental and application have been done up to the present[2]. The positioning control of IPMC, however, has been considered very difficult since the initial large deformation of IPMC decreased rapidly. There was a report that could succeed the positioning control during one second[3]. This was achieved by the tuning of the shape of the application voltage. On the other hand, however, there are some reports that the initial deformation of the Au-plated IPMC was not so attenuated[4]. In this study, the deformation characteristics of the Nafion based Au plated IPMC was investigated. The results showed that the deformation patterns were classified into two types. They were classified by whether the direction of the residual deformation is the same anode side of initial deformation or the reversal cathode side. Both types of IPMC can be controlled its position by the individually fitted control methods. The following frequency limits of both types were clarified. It is considered from many experimental results that the decision of the type classification was closely related to the concentration or the amount of the driving Na+ ion in the Nafion film.

2. MANUFACTURING METHOD OF AU-NAFION IPMC To make IPMC actuator, both sides of the Nafion film surface has to plate metal for the electrodes. Gold (Au) and platinum (Pt) have been used for the material of the plate metal in the most of the previous researches. In the first stage of this research, the authors used Pt for the electrodes. The manufacturing method of Pt-Nafion IPMC, however, was so unstable that it was difficult to acquire the reproducibility of the property. The deformation quantity was also small. In the case of Au-Nafion IPMC, however, it is easier to produce equal quality test peace and the deformation quantity is larger than that of Pt-Nafion IPMC. This is caused by the softness (small Young's modulus) and the high conductivity of Au. Therefore, in this study, Au-Nafion IPMC was mainly used. *[email protected]; phone 81 3 5280 3600; fax 81 3 5280 3569; www.mec.m.dendai.ac.jp



The manufacturing methods of Au-Nafion IPMC in this study were as follows. 1) 30 mm square Nafion film was roughened by a sand paper. 2) The surface of the Nafion film was cleaned by a supersonic cleaner with alkaline detergent. 3) The film was cleaned again by boiled purified water. 4) The film was soaked in the 2.60x10-2 mol/l dichrolo phenanthroline gold complex (AuCl2(Cl2H8N2)Cl) solution and gold ion was adsorbed into Nafion. 5) The film was soaked in the 4.81x10-3 mol/l sodium sulfite (Na2SO4) solution and deoxidization was done in the temperature range between 333K and 353K. 6) Process 3) to 5) was repeated several times to increase the thickness of the gold layer. 7) The film was boiled by the purified water. 8) The film was soaked in the 1.13mol/l sodium hydroxide (NaOH) to introduce Na+ as counter ion. The test peaces made by the above method showed the motion reproducibility constantly and this method was mainly used in this study. The ion conductive polymer-gel film used in this study is above mentioned Nafion made by Dupont. The thickness of the IPMC was the summary of the thickness of Nafion layer and that of the plated metal layers. The thicknesses of the plated metal layers were controlled by the number of reputation of process 3) to 5). The thickness of the Nafion layers does not equal to the original Nafion film by the roughened process. However, it was closely related to the thickness of the original film. In this study, three kinds of Nafion film were used. The thicknesses of each Nafion are, 51µm (NF-112), 127 µm (NF-115) and 183 µm (N-117). Table 1 shows the quantities of the initial deformation of each Au-Nafion IPMC by using same rectangular (2x15mm) shaped IPMC and same application voltage (2V). The thinner the thickness of the Nafion film is, the larger the generated deformation quantity is. Table 1. Differences of the generating displacement of Au-Nafion IPMC by the thickness of the Nafion materials. DEFORMATION QUANTITIES Kind of Nafion N117 NF115 NF112

Thickness of Nafion 183 µm 127 µm 51 µm

Displacement 2.90 mm 8.35 mm 22.68 mm

3. EXPERIMENTAL APPARATUS AND PROCEDURE Fig.1 depicts the schematic diagram of the experimental system. IPMC was cut to the 2x20 mm rectangular shape and an end of the IPMC was fixed between electrodes in the 5mm length in the vertical line. The generated deformation quantities are measured by a laser displacement meter (KEYENCE Co. Ltd, LB-60).

Control PC

IPMC Test Peace

H8 PWM Pulse Driver

Laser Displacement Meter

Fig.1 Schematic diagram of the experimental system

Electric voltage is applied by the form of 100Hz polarity reversal type Pulse Width Modulation (PWM) generated by one-chip computer (Hitachi H8-3048) through amplifier. The duty ratio of the PWM pulse can be controlled with the 14 bit resolution between the duty ratio of 0.1 - 0.9. Personal computer is measured the output voltage of the laser


displacement meter through D/A converter, recorded the data, and decide the application PWM duty ratio by the control equation. The reason why the high frequency PWM pulse was applied instead of the normal DC voltage is as follows. In the first stage of this study, the possibility of PWM pulse to prevent the attenuation of the initial deformation of IPMC was investigated. The results showed that the tendencies of the deformation (especially in the step response) are almost the same between the application of PWM pulse and DC voltage. More precisely, the deformation quantities of the PWM pulse application were larger than the DC voltage in the range of small voltage area (in the case of PWM pulse, average voltage was used). In this system, the resolution of the PWM pulse is higher than the DC voltage and the composition of the experimental system is simpler. Those are the reasons to adopt PWM pulse.

4. DEFORMATION BEHAVIORS OF IPMC ON THE STEP RESPONSE Fig.2 shows an example of the deformation behaviors of Pt-N117 IPMC to 1.5V DC step voltage application. Pt-N117 was the most popular IPMC. In the beginning, initial deformation is generated to the cathode side. Then, the initial deformation was attenuated rapidly. Finally, the residual deformation was appeared to the anode side. It was thought in many researches that this rapid attenuation of the large initial deformation makes the positioning control very difficult. Therefore, the authors started this study from the investigation of the step response of the gold plating three kinds of Nafion IPMC (Au-N117, Au-NF115, Au-NF112). 1.2

Displacement[mm]

1.0 Step Response

0.8 0.6 0.4 0.2 0.0 0.0

1.0

2.0

3.0

4.0 5.0 Time[s]

6.0

7.0

8.0

Fig.2 An example of the step response experiment of Pt-N117 IPMC. Change of the displacement of the tip is shown under the application of DC 1.5V

Fig.3 (Au-N117) and Fig.4 (Au-NF112) are examples of the step response during 60s when a ± 2V polarity reversal type 100Hz PWM pulse was applied in the various duty ratio. The average voltage of each duty ratio is, 1/10=1.6V, 2/10=1.2V, 3/10=0.8V, 4/10=0.4V, 5/10=0V, 6/10=-0.4V, 7/10=-0.8V, 8/10=-1.2V and 9/10=-1.6V.


Displacement[mm]

1.0 Duty Ratio 1/10 (1.6V) 2/10 (1.2V) 3/10 (0.8V) 4/10 (0.4V) 5/10 (0V) 6/10 (-0.4V) 7/10 (-0.8V) 8/10 (-1.2V) 9/10 (-1.6V)

0.5

0.0

-0.5

0

10

20

30 Time[s]

40

50

60

Fig.3 The effect of the duty ratio (applied voltage) on the changing behavior of the IPMC displacement under the application of 100Hz polarity reversal PWM pulse. (Au-N117 IPMC)

Displacement[mm]

4

Duty Ratio 1/10 (1.6V) 2/10 (1.2V) 3/10 (0.8V) 4/10 (0.4V) 5/10 (0V) 6/10 (-0.4V) 7/10 (-0.8V) 8/10 (-1.2V) 9/10 (-1.6V)

2 0

-2 -4 0

10

20

30 Time[s]

40

50

60

Fig.4 The effect of the duty ratio (applied voltage) on the changing behavior of the IPMC displacement under the application of 100Hz polarity reversal PWM pulse. (Au-NF112 IPMC)

The results showed that the deformation behaviors to the step voltage can be classified into two types. One is the "Same Direction Type, (SDT)". In the case of SDT, the direction of both initial deformation and residual deformation are the same anode side. Au-N117 and Au-NF115 belong to SDT. The other is the "Opposite Direction Type, (ODT)". In the case of ODT, the direction of the initial deformation is the cathode side, it was same to SDT. The direction of the residual deformation, however, is the opposite anode side. Pt-N117 and Au-NF112 belong to ODT. The quantity of the residual deformation is increased with the increase of average applied voltage. That is to say, the initial strain of ODT is not simply attenuated but it changes the deformation mode to the residual deformation. Therefore, there is a possibility of positioning control when we use the residual deformation of IPMC in both types.

5. FEEDBACK POSITIONING CONTROL OF IPMC 5.1 Positioning control of SDT-IPMC Above mentioned investigation suggests that there is a possibility of the positioning control of IPMC, especially to the SDT-IPMC. It was confirmed as a preliminary experiment that if the duty ratio of the applied PWM pulse was changed manually, the end of the SDT-IPMC can be moved by changing the duty ratio.


Therefore, a feedback positioning control experiments were done by using the outputs of the laser displacement meter. First, proportional control was applied. SDT-IPMC, however, cannot be controlled its position by proportional control. The problem is that, in the case of proportional control, if the generated deformation quantity was larger than the target value, the controller applied the opposite polarity. This makes the large reversal deformation and causes vibrations. It makes positioning control unstable. Next, an integral control (an integral component of PID control) was applied and positioning control was done successfully. Figs.5 and Fig.6 show examples of feedback experiments of Au-NF115 IPMC. The target values are ± 0.5mm amplitude sine wave. The frequencies of the target sine waves are, 2Hz (Fig.5) and 0.01Hz (Fig.6). Average control deviations of various frequencies are summarized in Fig.7. It shows that the positioning control can be done within 0.5Hz.

Displacement Target Value Deviation

Displacement (mm)

1.0

2Hz

0.5 0.0 -0.5 -1.0 0.0

0.1

0.2

0.3

0.4

Time (s) Fig.5 Examples of the positioning control experiment of Au-NF115 IPMC. Target value is a 2Hz ± 0.5mm sine wave. In the case of 2Hz, there is a large phase delay.

0.6 Displascement Target value Deviation

Displacement (mm)

0.4 0.2 0.0 -0.2 -0.4 -0.6

0

20

40

60

80

100

Time (s) Fig.6 Examples of the positioning control experiment of Au-NF115 IPMC. Target value is a 0.01Hz ± 0.5mm sine wave. In the case of 0.01Hz, deviation is very small and good positioning control was done.


Average control deviation (mm)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 2

0.01

3

4

5

6 7 8 9

2

0.1 Frequency (Hz)

3

4

5

6 7 8 9

1

2

Fig.7 A summary of the average control deviations in each frequency. Target value is ± 0.5mm sine wave. Deviation increases from about 0.5 Hz.

5.2 Positioning control of ODT-IPMC In the case of ODT-IPMC, the deformation behavior is so complex that it makes the positioning control very difficult. Final residual deformation quantity, however, increase / decrease by the average applied voltage. The authors thought that positioning control may be achieved by applying this property. First, the applied duty ratio was changed manually to know the deformation properties as preliminary experiments. If the changing speed of the applied PWM duty ratio is quick, IPMC first react initial deformation, and then the residual deformation generates to the opposite side. If the changing speed is very slow, initial deformation does not appear and the end of the IPMC can move by changing the duty ratio. Therefore, positioning control may be possible if the changing speed is regulated. Fig.8 is an example of the positioning control of ODT by the same control method of SDT (integral control). In this experiment, the target position is the 0mm displacement. You can see the generation of initial deformation at 0-20s and about 650s. 3

Offset Displacement Digital Output

2

14 12

1

10 0

8 6

-1

Digital Output

Offset Displacement [mm]

16x10

4 -2

2 0

200

400

600 800 1000 1200 Measurement Time [s]

1400

1600

0 1800

Fig.8 An example of the positioning control experiment of Au-NF112 ODT-IPMC by normal integral control method. Target value is 0mm constant. Rapid change of the duty ratio causes the initial deformation component.


Next, lamp responses of Au-NF112 IPMC were investigated. The summary of the results showed that if the changing rate of the PWM duty ratio is smaller than 4.9x10-4s-1 (equivalent DC voltage is 2.0x10-4 V/s), the initial deformation component does not generate. Therefore, the maximum changing speed of the output PWM duty ratio was restricted under 4.9x10-4 s-1and a feedback positioning control experiment was examined again by using integral control method. The target value is ± 1mm amplitude sine curve. The direction of the residual deformation is opposite to the SDT, the polarity of the integral coefficient of ODT was reversal to the case of SDT. Fig.9 is an example of the positioning control. Its frequency of the target value is 9.2x10-5Hz. The following frequency limit is about 2.0x10-4Hz and if the frequency is lower than this value, ODT-IPMC can be controlled its position. 9600 Digital Output Target Value IPMC Displacement

0.5

9200 8800 8400

0.0 8000 -0.5

7600 7200

-1.0 0.0

Digital Output

Offset Displacement (mm)

1.0

1.0

2.0

3.0

4.0

5.0 6.0 Time (s)

7.0

8.0

3

6800

10.0x10

Fig.9 An example of the positioning control experiment of Au-NF112 ODT-IPMC. Target value is ± 1mm 9.2x10-5Hz sine wave.

6. THE EFFECT OF THE COUNTER ION ON THE DIRECTION OF RESIDUAL DEFORMATION As mentioned above, positioning control of IPMC was achieved in both types. The following frequency limit of ODTIPMC, however, is too low to find the application. Therefore, to know the factor to divide the deformation type is very important to develop the more practical IPMC for positioning control. Using the standard manufacturing method in this study as mentioned section 2, if we compare in the same gold plating IPMC, The thinnest Au-NF112 is ODT and Au-NF115 and Au-N117 are SDT. Au-NF115, however, was smaller than Au-N117 comparing with the rate of residual deformation quantity / initial deformation quantity. Therefore, Au-NF115 stands the nearest point to the diverging point of the deformation type. The authors found that if Au-NF115 is used for a long time in the purified water, the deformation type of Au-NF115 changes from SDT to ODT. Fig.10 indicates the step responses of Au-NF115 IPMC in the condition of reputation of 60s step response experiments using same test peace (repeat the 1/10(-1.6V) and 9/10(1.6V) duty ratio). You can see the transition of the deformation type.


Displacement (mm)

2.0 1.0 DutyRatio 1/10 (1.6V) 9/10 (-1.6V)

0.0 -1.0 0

10

20

30 40 Time (s)

50

60

Displacement (mm)

(a) Step response in the first experiment

4

DutyRatio 1/10 (1.6V) 9/10 (-1.6V)

2 0 -2 0

10

20

30 40 Time (s)

50

60

(b) Step response after long time usage Fig.10 Changes of the direction of the residual strain by the reputation of use. Au-NF115 IPMC first shows the SDT deformation and it changes to the ODT deformation after long time usage.

The most changeable part in the processing method may be the introduced counter ion (Na+ in this study). Na+ may flow out to the purified water. Therefore, ODT Au-NF115 that had been used for a long time was re-introduced the Na+ ion by the process 8) and measured its step response again. The result shows that re-introduced Au-NF115 shows SDT deformation again. Fig.11 is an example. The re-introduced Au-NF115 shows almost the same reaction to the original one. The deformation quantity, however, is slightly decreased.


Displacement (mm)

0.8 0.6 0.4 New test peace Reuse test peace

0.2 0.0 0

10

20

30

40

50

60

Time (s) Fig.11 Step responses of the Au-NF115 IPMC in the new test peace and the test peace that was re-introduced the Na+ counter ion after long time usage. Au-NF115 can recover the SDT deformation from ODT condition.

Next, many Au-NF115 test peaces by producing various density NaOH solutions in process 8) were prepared and found that Au-NF115 shows ODT deformation in the first step response measurement if the NaOH solutions are thinner than 2.62x10-4 mol/l. In the case of Au-N117, it was confirmed that the Au-N117 also showed the ODT deformation after long time use, and the type changed again to SDT by the re-introduction of Na+ ion. In the case of Au-NF112, the standard IPMC in this study shows ODT. However, if the density of NaOH was 2.27mol/l (twice denser than standard density), Au-NF112 shows the SDT deformation in the first step response measurement. Fig.12 indicates the results. First, the experiment of 1/10 duty ratio (equivalent to DC 1.6V) was done and then the experiment of 9/10 (-1.6V) was done. Therefore, you can see in Fig.13 that this Au-NF112 test peace shows SDT deformation in the first experiment and ODT deformation in the next experiment. 0.8

Displacement (mm)

0.6 0.4 0.2 0.0 -0.2 Duty Ratio 1/10 (1.6V) 9/10 (-1.6V)

-0.4 -0.6 -0.8 0

10

20

30 Time (s)

40

50

60

Fig.12 The step response of Au-NF112 IPMC. This IPMC was given counter ion introduction treatment using twice denser NaOH solution. In the first experiment (duty ratio is 1/10), this IPMC shows SDT deformation. In the next experiment (duty ratio is 9/10), it shows ODT deformation. This indicates the rapid outflow of the counter ion.

All of these results suggest that the decision of the deformation type is related not the thickness of the Nafion film but the density or the quantity of the counter ion.


7. CONCLUSION This study confirmed that the positioning control of IPMC can be done by using integral control method. SDT type deformation was necessary for the high speed positioning control. The decision of the deformation type is closely related to the density or the quantity of the counter ion. The thinner IPMC generates larger deformation quantity. However, it is very difficult to make thin IPMC like Au-NF112 as SDT-IPMC. In the future, the method to keep SDT deformation has to be clarified by investigating the variety and the suitable quantity of the counter ion, chemical composition of the solution of the environment, prevention methods of the outflow of the counter ion.

REFERENCES 1. K. Oguro, et.al., J. Micromachine Soc., 5, pp.27-30, (1992). 2. Y. Bar-Cohen, Robotics2000 and Space2000, pp.188-196 (2000). 3. Sugano, et.al., 74th Annual meetings of the Japan Society of Mechanical Engineers, IV, pp. 329-330, (1996). 4. K. Asaka, "Soft Actuators" NTS Books ISBN4-86043-063-8 C3050, Section2, p83.

Proc. of SPIE Vol. 6374 637403-10

Optical driving of actuator using Poly-Vinylidine DiFluoride cantilever Y. Mizutani, S. Nishimura, Y. Otani, N. Umeda Tokyo University of Agriculture & Technology, 2-24-16 Nakacho Koganei, Tokyo, 184-8588, Japan ABSTRACT Optically driven actuators are a non-contact method for the remote application of light energy. We propose a new method for optically driving actuators which uses three polyvinylidine difluoride (PVDF) cantilevers as the legs and a polymer film as the body. The PVDF cantilevers are coated with silver on one surface. PVDF is a ferroelectric polymer that has both pyroelectric and piezoelectric properties. When one side of the cantilever is irradiated by a laser beam, an electric field is produced along cross-section of the cantilever and mechanical displacement occurs by the piezoelectric effect. We measured the response time and the generated force of the cantilever. Optically driven actuator move via the slip-stick effect. Keywords: optical driven actuator, photo-thermal effect, Poly-Vinilidine DiFluoride, pyroelectricity effect

1.

INTRODUCTION

In recent years, optically driven actuators have attracted considerable attention because they can be operated remotely without the need for wires1). Previous studies of optically driven actuators have indicated their potential usefulness in various situations, such as environments having intense electromagnetic fields2). They can also be used as a non-contact method for the remote application of light energy3,4). They are thus particularly useful in environments such as space and environments have high-intensity radioactive fields. In a previous paper by us, we investigated actuators that are operated using light energy. The displacement mechanism of such actuators is principally the photothermal effect. However, the response time of these actuators is strongly dependent on their size. Finding a method for reducing the response time is a problem that has yet to be solved theoretically. The purpose of the present study is to construct an optically driven actuator using polyvinilidine difluoride (PVDF) cantilevers. Polyvinilidine difluoride is a ferroelectric polymer that has both pyroelectric and piezoelectric properties. Thus, it has fast response times. In previous studies, it has been used in various optical devices5,6,7). However, there have been several attempts to construct optical actuators from PVDF. In this paper, we briefly describe our experimental results for PVDF cantilevers and then describe an actuator based on PVDF cantilevers, along with the experimental results we obtained using such a system.

2.

MOVING PRINCIPLE OF PVDF CANTILEVER AND ITS MECHANISM

The concept of an optically driven actuator using PVDF cantilevers is illustrated in Fig. 1. It is an actuator having multiple legs; the PVDF cantilevers are the legs of the actuator. It can be moved by irradiating it with light from various directions.

Li

t gh

Light

t gh Li

PVDF cantilevers

Fig. 1 Optical driving of actuator using PVDF cantilevers.



Polyvinylidine difluoride is a ferroelectric polymer. It thus has considerable promise as a material that responds rapidly to optical irradiation. It is possible to construct a cantilever from PVDF. Figure 2 shows the principle behind the displacement of a PVDF cantilever. One surface of a PVDF film is coated with Ag. After irradiation by light, it is polarized by the pyroelectric effect in the cross-sectional direction (Fig. 2(1)). Next, conduction electrons are generated and dispersed on the surface of the Ag coating (Fig. 2(2)). As a result, the electric field in the cross-sectional direction of the PVDF film is inhomogeneous and the PVDF cantilever bends in the cross-sectional direction of the PVDF film (Fig. 2(3)). Since the pyroelectric effect is faster than the photothermal effect, the PVDF cantilever is expected to have a fast response time.

light

light

light

PVDF Ag

displacement cross-sectional view of PVDF cantilever

(1) Polarization of pyroelectric effect

(2) dispersion of (3) bending by inverse surface electrical charge piezoelectric effect

Fig. 2 Moving principle of PVDF cantilever.

The PVDF cantilever used in the present study was 28 m thick, 8 mm wide and 10 mm long. Figure 3 shows a photograph of a PVDF cantilever bending in response to laser irradiation. Figure 3(1) shows its cross-sectional profile before laser irradiation and Fig. 3(2) shows its profile after laser irradiation. We used a He-Ne laser as the light source and it had a power of 10 mW. The displacement of the cantilever after laser irradiation was about 250 m.

PVDF

displacement

laser

500µm (1) Before laser irradiation

(2) After laser irradiation

Fig. 3 Photograph of moving of PVDF cantilevers. It is cross sectional view.

To analyze the bending mechanism of a PVDF cantilever, the time dependent response of the PVDF cantilever was measured using a displacement sensor. The Ag-coated surface of the cantilever was irradiated by He-Ne laser pulses that were 0.8 msec in duration and had powers of 5, 7, 9 and 11 mW. Figure 4 shows a plot of the cantilever displacement as a function of time. Large displacements were obtained for irradiation by laser powers of 7, 9 and 11 mW. There is a slight plateau in the curve at 0.1 msec followed by a gradual rise. This fast response is caused by the combination of the pyroelectric and piezoelectric effects. The second response is caused by the photothermal effect in combination with the bimetal effect. However, there is no response due to the pyroelectric effect for the case of


irradiation with a laser power of 5 mW. Therefore, in subsequent experiments we used laser irradiation having a duration of 0.2 msec and a power of 7 mW for operating the PVDF cantilever. irradiation time

400 13mW

displacement [µm]

11mW

300

9mW 7mW

5mW

200

100

0 0.0

0.5

1.0

1.5

2.0

time [s] Fig. 4 Time behaviors of displacement of PVDF cantilever by irradiation light.

displacement [µm]

500 400 15mm

300

10mm

200 100

8mm 5mm

0 0.0

0.5

1.0 time [s]

1.5

2.0

Fig. 5 Time behavior of the displacement of PVDF cantilevers depended on length of Ag coating.

The area of the Ag-coated region is a key parameter for the pyroelectric and piezoelectric effects. Therefore we measured the dependence of the displacement on the area of the Ag-coated region. Figure 5 shows a plot of the displacement as a function of time of PVDF cantilevers which had Ag-coated regions that were 5, 8, 10 and 15 mm in length. Figure 6 shows the relationship between the maximum displacement and the length of the Ag-coated region. Above a coating length of 8 mm, the maximum displacement was the same after irradiation for 0.2 msec. For coating lengths shorter than 8 mm, the maximum displacement decreased. Therefore, it is necessary to coated the PVDF films with Ag for lengths of 8 mm or longer to obtain the greatest displacement.


60 displacement [µm]

50 40 30 20 10 0

0

4 8 12 lentgth of Ag coating [mm]

16

Fig. 6 Dependence of the displacement of PVDF cantilever on length of Ag coating

0

gain [dB]

-10 -20 -30 -40 0.1

1.0 10.0 frequency [Hz]

100.0

Fig. 7 Frequency response of vibration amplitudes for PVDF cantilever.

The frequency response of a PVDF cantilever is higher than that for mechanisms of other optically driven actuators since the mechanism of the PVDF cantilever relies on the pyroelectric and piezoelectric effects. Figure 7 shows the frequency response of the PVDF cantilever. The resonant frequency of the PVDF cantilever is about 20 Hz. One of the most important parameters for constructing optically driven actuators is the generative force of the PVDF cantilever. We measure it by using a glass cantilever the stress parameter of which was known. Figure 8 shows the relationship between the generative force of the cantilever and the laser power. The generative force is proportional to the laser power.


generative force [µN]

1600 1200 800 400 0 0.0

5.0 10.0 laser intensity [mW]

15.0

Fig. 8 Generative force of PVDF cantilever depended on laser intensity.

3.

OPTICALLY DRIVEN ACTUATOR USING PVDF CANTILEVERS

Figure 9 shows the construction of an optically driven actuator based on PVDF cantilevers. It consists of three PVDF cantilevers that form the legs of the actuator joined to a polyethylene film body.

light

moving direction Fig. 9 Unit of optical driving actuator using PVDF cantilever.

Figure 10 is a schematic illustration of the principle of movement of the actuator. These figures show the crosssectional profile of the actuator. Figure 10(1) shows the initial position of the actuator. The position marked 0 is the initial position of the rear leg and 0’ represents the position of the front leg. In Fig. 10(2), the front leg is irradiated by light and it bends due to the pyroelectric and piezoelectric effects. The cantilever slides on the base because of the first response. Then, after laser irradiation (Fig. 10(3)), the front cantilever stops at the point indicated by 1’ which is in front of the initial point 0’ because the frictional force of the front leg exceeds the restorative force of the front cantilever. Furthermore, the back leg slides on the base because the frictional force of the back leg is smaller than the restorative force of the actuator. Finally, in Fig. 10 (4), the actuator can be stabilized.


PVDF cantilevers

light

driving force floor

0

0'

1. before laser irradiation

2. laser irradiation

driving force

displacement

displacement

0

1'O'

4. finishing of movement

3. after stopping laser irradiation

Fig. 10 Moving principle of optical actuator.

light

1mm movement direction

Fig. 11 Photograph of optical driven actuator using PVDF cantilever.

displacement [mm]

3

2Hz 76.7mm/s

2

1 1Hz 33.3mm/s 0

0

5

10

15 20 time [s]

25

30

Fig. 12 Displacement of optical driven actuator with various frequency of irradiation light.

Figure 11 shows a photograph of an actuator on an acrylic surface; it shows the cross-sectional profile. The actuator is 5 mm wide and 10 m high. Light is irradiated from the left of the figure and the direction of movement of the actuator is towards the left. A He-Ne laser was used as the light source and an irradiation power of 10 mW was used. Figure 12 shows the displacement of the actuator irradiated at frequencies of 1 and 2 Hz. Both displacements increase almost linearly with time. The velocities of the actuators are 33.3 mm/sec at 1 Hz and 76.7 mm/sec at 2 Hz.


4.

CONCLUTIONS

We investigated optical driving of an actuator constructed from PVDF cantilevers. The PVDF cantilever uses the pyroelectric and piezoelectric effects and has a response time of less than 0.2 msec. The actuator travels at a velocity of 33.3 mm/sec when irradiated at a frequency of 1 Hz. In the future, we intend to extend the control of the actuator’s displacment to two-dimensions.

5.

ACKNOWLEDGEMENT

We investigated optical driving of an actuator constructed from PVDF cantilevers. The PVDF cantilever uses the pyroelectric and piezoelectric effects and has a response time of less than 0.2 msec. The actuator travels at a velocity of 33.3 mm/sec when irradiated at a frequency of 1 Hz. In the future, we intend to extend the control of the actuator’s displacment to two-dimensions.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

Y. Otani, Y. Matsuba, N. Umeda, T. Yoshizawa, "Micromanipulator by photothermal effect," Proc SPIE 5264, 150153 (2003). K. Fukushima, Y. Otani, T. Yoshizawa "An Optical Driving of a Moving Machine Consisting of Piezoelectric Elements and Temperature Sensitive Ferrite," JSPE 64(10), 1512-1516 (1998). (in Japanese) K. Uchino, "Recent topics of ceramic actuators. How to develop new ceramic devices," Ferroelectrics 91, 281-292 (1989). K. Uchino, "Photostrictive Actuator," Proc IEEE Ultrason Symp 2, 721-723 (1990). S. S. Sarkisov, M. J. Curley, A. Fields, "Photomechanical effect in films of polyvinylidene fluoride," J. Appl. Phys. 85(14), 2747-2749 (2004). Y. Otani, Y. Mizutani, "Next-Generation Actuators Leading Breakthroughs Actuators for Special Environments Light-driven actuators using optical fiber and PVDF," Proc Int Symp Next-Gener Actuators Lead Breakthr Mext Grant-in-Aid Sci Res Prior Area No.438 2006, 165-168 (2006). S. S. Sarkisov, M. J. Curley, L. Huey, A. Fields, G. Adamovsky, "Light-driven actuators based on polymer films," Opt. Eng. 45(3), 034302.1-034302.10 (2006).


Two-dimensional magnetic force actuator using temperature sensitive ferrite driven by light beam Y. Mizutani, Y. Otani, N. Umeda Tokyo University of Agriculture & Technology, 2-24-16 Nakacho Koganei, Tokyo, 184-8588, Japan ABSTRACT A two-dimensional actuator has a feature of a non-contact for applying light energy remotely. It consists of a magnet as a movement, an acrylic plate and the temperature sensitive ferrite mounted on two-dimensional array on the plate. A curie temperature of the ferrite is set about room temperature. For moving the magnet, two ferrites in the opposite direction are irradiated by the laser. The magnetic force decreases by photo-thermal effect. For generating more strong force, a thickness of the plate and ferrite are optimized by analyzing static magnetic field. As a result, the movement is controlled in the two-dimensional area. Moreover, we attempt to control magnetic levitation. Keywords: temperature sensitive ferrite, photo-thermal effect, two-dimensional actuator

1. INTRODUCTION In recent years, optically driven actuators have attracted considerable attention because they can be operated remotely without the need for wires1). Previous studies of optically driven actuators have indicated their potential usefulness in various situations, such as environments having intense electromagnetic fields2). They can also be used as a non-contact method for the remote application of light energy3,4). They are thus particularly useful in environments such as space and environments have high-intensity radioactive fields. In a previous paper by us, we investigated actuators that are operated using light energy. The displacement mechanism of such actuators is principally the photothermal effect. However, the generative force is slightly lower. In this study, a magnetic force is focused on to controlled by optical energy. To control the magnetic force, a temperature sensitive ferrite has attracted much attention because of its magnetic property. Fig.1 shows a variation of its magnetic susceptibility with its temperature. Generally, magnetization changes ferrimagnetism from ferromagnetism at Curie temperature. Curie temperature of this ferrite is low about room temperature. Therefore it is easy to change its magnetism by Photo-thermal effect. And this ferrite is partially useful for optical control.

magnetic susceptibility

Curie temperature

ON

room temperature

OFF

temperature

Fig. 1 Principle of optical switching using temperature sensitive ferrite and permanent magnet.



2. TWO-DIMENSIONAL ACTUATOR 2.1 Principle of two-dimensional controlling Two temperature sensitive ferrites in an opposite direction of moving direction are irradiated by laser. Magnetic susceptibility of ferrites are decrease by photothermal effect.A movement is moved by magnetic force of movement direction. Furthermore, the movement can be controlled by changing of irradiation position.

movement direction

movement

ate — r1 — — = =iii — L LJ LJ (Parmanet magnet)

aciylic ,1

C—__

ferrite

(1) initial position

(2) laser irradiation

(3) finish

Fig. 2 Moving principle of two-dimensional magnetic force actuator using temperature sensitive ferrite

00000 00000 00000 00000 00000 00000 00000 00000

00000 00000 KG 00 0O0 00000 00 00 0 00 00000 coo o 0 00 00 00000 Fig. 3 Moving method of the movement magnet in the two-dimensional area

2.2 Experimental results Figure 4 shows a two-dimensional magnetic force actuator using temperature sensitive ferrite. The actuator consists of a Nd magnet as a movement, an acrylic plate (t0.8mm) and the temperature sensitive ferrite mounted in two-dimensional array on the plate. For shaping form easily, the temperature sensitive ferrite is crushed and mixed with silicon grease. The shaping ferrites are set in a reticular pattern.

..e..i)S$)D .••..

movement (Nd magnet)

. 11)) temperature

4) sensitive ferrite Fig. 4 Two-dimensional magnetic force actuator using temperature sensitive ferrite

Table 1 shows the magnetic field analysis of the actuator in various thickness of temperature sensitive ferrite. A magnetic force between the movement and temperature sensitive ferrite depends on the thickness of the ferrite. Therefore the thickness is optimized by magnetostatic field analysis and experimental results. Fig.5 shows a magnetic force and the thickness of the temperature sensitive ferrite. The magnetic force increased with decreasing the thickness to a maximum value. Consequently, the optimal thickness for magnetic force is determined 0.2mm.


'pa

Table 1 The magnetic field analysis of the actuator in various thickness of temperature sensitive ferrite

1.0mm

thickness

0.5mm

parmanent magnet 永久磁石 line of magnetic force

0.1mm

0.1mm

temperature sensitive 感温フェライト ferrite

magnetic flux density laser レーザ

magnetic force [N]

0.06 0.05

simulation experimental value

0.04 0.03 0.02 0.01 0 0.0

0.5

1.0

1.5

2.0

thickness of temperature sensitive ferrite [mm] Fig. 5 Magnetic force and the thickness of the temperature sensitive ferrite

Figure 6 shows the displacement of the movement magnet in two-dimensional area. The displacement increases almost linearly with time.

displacement [mm]

25

light source: LD laser 450mW

20 15 10 5 0

0

10 20 30 40 50 60 time [s]

Fig. 6 Displacement of the two-dimensional magnetic force actuator using temperature sensitive ferrite


3. THREE-DIMENSIONAL ACTUATOR 3.1 Principle of three-dimensional controlling In the case of the two-dimensional actuation, it can not be controlled stable because of friction between the movement and the floor. Therefore, the movement magnet floated using a characteristic of diamagnetism such as graphite. Furthermore, the floated movement magnet is controlled by photothermal effect using temperature sensitive ferrite. In this study, we pay attention to levitate a magnet by using diamagnetic material. A polar of the diamagnetic material changes toward disturbing to change a relative position of these two objects. To use this characteristic, we levitate a magnet. Specifically, the movement magnet put between two diamagnetic materials. Therefore we make a buffer for keeping balance. Figure 7 shows a schematic illustration of a magnetic levitation using temperature sensitive ferrite. We use graphite as diamagnetic material. And the movement magnet is put between graphite and using assist magnet put on temperature sensitive ferrite. By using this magnet, the movement magnet can be levitated. Furthermore, to control in three-dimensional, a staring magnetic field can be changed by changing magnetic susceptibility of temperature sensitive ferrite. In this study, the movement magnet is Nd magnet (φ3mm, t2mm), a light source is laser diode with 300mW and a diamagnetic material is graphite. assist magnet

leinperature sensitive

P.—

Iernte

movement

(magnet) •

__j

graphite

Fig. 7 Magnetic levitation using temperature sensitive ferrite

Figure 8 shows a moving principle of the levitated magnet in three dimensions. Fig.1 (1) shows an initial position. To move toward vertical position, a temperature sensitive ferrite located immediately above is irradiated. Then a magnetic force toward this direction is weak. So we can control the magnet for vertical position. To move horizontal position, a temperature sensitive ferrite set on opposite side is irradiated. A magnetic force of a request direction is larger than that of opposite direction. Then the movement magnet can be moved toward horizontal direction. To uses these method, the levitated magnet can move in three-dimensions.

F- _.J

U.

:i:i- 1 (I )initial position

(2) vertical

(3) horizontal

Fig.8 Moving principle of the levitated magnet in three-dimensional area

3.2 Experimental results To levitate magnet, the position of the assist magnet is adjusted. Fig.9 shows a photograph of the levitated magnet. In this figure, the magnet can be levitated stability.


graphite

movement (Nd magnet)

2.0 mm

graphite

Fig. 9 Photograph of the magnetic levitation

For confirmation of the principle, we simulated a static magnetic field analysis. Fig. 10 shows typical results of the static magnetic field analysis. In the case of vertical control (Fig.10 (2)), a magnetic field is almost same in vertical direction. Therefore a gravity of the magnet is greater than the magnetic force. Hence the movement magnet can be moved toward vertical position. In the case of horizontal control (Fig. 10 (3)), the magnetic field is homogeneous toward horizontal direction. Therefore the movement magnet can be moved in horizontal direction. Hence it is indicated to be able to control the movement magnet using temperature sensitive ferrite.

(1) initial position

(2) vertical moving

(3) horizontal moving

Fig. 10 Magnet static analysis for three-dimensional actuator using temperature sensitive ferrite

position of movement from lower graphite[mm]

ネオジウム磁石の位置 [ mm]

Figure 11 shows a position of the movement magnet against the position of the assist magnet. The position of the movement magnet drops sharply between about 1mm. However to use micrometer for moving the assist magnet, the movement magnet can be controlled stable. 1.0 0.8 0.6 0.4 0.2 0.0 45.5

46.0 46.5 47.0 [ mm] [mm] positionフェライト磁石の位置 of ferrite magnet from lower graphite

Fig. 11 Position of the movement magnet against the position of the assist magnet


Figure 12 shows a photograph of the movement magnet to control in horizontal direction. Fig.12 (1) shows an initial position and (2) shows the moved magnet after 60sec. An irradiated ferrite is overhead of the movement magnet toward opposite side direction. The movement magnet can be moved in the distance of ∆x toward horizontal direction.

Fig. 12 Photograph of the movement magnet to control in horizontal direction

Figure 13 shows a photograph of the movement magnet to control in vertical direction. Fig.13 (1) shows an initial position and (2) shows the moved magnet after 60sec. An irradiated ferrite is directly overhead of the movement magnet. After 60sec, the movement magnet drops down and keeps its position. The movement magnet can be moved in the distance of ∆x toward vertical direction.

•

jax

(I) initial positon

Fig. 13 Photograph of the movement magnet to control in vertical direction

position of Nd magnet

form lower graphite [mm][ mm] ネオジウム磁石の位置

Figure 14 shows the time dependent of behavior of the movement magnet for controlling toward vertical position. The vertical position of the movement magnet depends on laser power. Therefore we irradiated to control the levitated magnet in vertical position. 0.5

50mW 100mW 150mW 200mW 250mW

0.4 0.3 0.2 0.1 0.0

0

60 120 時間 sec] time [[sec]

180

Fig. 14 Time dependent of behavior of the movement magnet for controlling toward vertical position


4. CONCLUSIONS The magnetic force actuator using temperature sensitive ferrite driven by light beam has been developed. It consists of crashed temperature sensitive ferrite mounted in two-dimensional array and acrylic plate and Nd magnet as movement. The magnetic force is optimized by magnetostatic field analysis. It can be controlled in two-dimensional area. Moreover, we applied for three dimensional controlling of levitation magnet.

REFERENCES 1. 2. 3. 4. 5. 6.

Y. Otani, Y. Matsuba, N. Umeda, T. Yoshizawa, "Micromanipulator by photothermal effect," Proc SPIE 5264, 150153 (2003). K. Fukushima, Y. Otani, T. Yoshizawa "An Optical Driving of a Moving Machine Consisting of Piezoelectric Elements and Temperature Sensitive Ferrite," JSPE 64(10), 1512-1516 (1998). (in Japanese) K. Uchino, "Recent topics of ceramic actuators. How to develop new ceramic devices," Ferroelectrics 91, 281-292 (1989). K. Uchino, "Photostrictive Actuator," Proc IEEE Ultrason Symp 2, 721-723 (1990). S. S. Sarkisov, M. J. Curley, A. Fields, "Photomechanical effect in films of polyvinylidene fluoride," J. Appl. Phys. 85(14), 2747-2749 (2004). Y. Otani, Y. Mizutani, "Next-Generation Actuators Leading Breakthroughs Actuators for Special Environments Light-driven actuators using optical fiber and PVDF," Proc Int Symp Next-Gener Actuators Lead Breakthr Mext Grant-in-Aid Sci Res Prior Area No.438 2006, 165-168 (2006).


Analysis of mechanical characteristics by birefringence microscope Mizue Ebisawa*, Yukitoshi Otani, Norihiro Umeda Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology Koganei, Tokyo, 184-8588, Japan; ABSTRACT The mechanical characteristics of polymer materials are of interest to the chemical industry. There are requirements for observation of changes of internal structure to stress. A number of samples under various stress conditions have provided interesting information upon analysis by microscopic birefringence measurement. In the present paper, we propose a birefringence measurement method for observation of the internal structure of polymer materials and analysis of the relationship between a given stress and the corresponding birefringence distribution. The proposed measurement system consists of a He-Ne laser, polarizers, a half-wave plate and a quarter-wave plate. The birefringence distributions of gelatin, such as the phase difference and azimuthal angle, are shown for the case of applied uniaxial and biaxial stress. Keywords: birefringence, biaxial tensile test, mechanical characteristic

1. INTRODUCTION The mechanical characteristics of polymer materials are of scientific and practical interest. Previous studies have demonstrated that the mechanical characteristics of polymer materials are different from those of metals. The mechanical model of a polymer material’s response to stress requires information on the microscopic deformation behavior of the materials[1]. Although there have been several macroscopic investigations of the behavior of a polymer under stress, such as mechanical experiments using load cells, few microscopic observations of this deformation behavior have been reported. Birefringence measurements are widely adopted for inspecting strain occurring as a result of processing, because the distribution of strain reflects the residual stress and molecular orientation. Therefore, the present study was performed in order to verify the applicability of birefringence measurement to the analysis of the mechanical characteristics of polymer materials.

2.

PRINCIPLE OF BIREFRINGENCE MEASUREMENT

2.1 Experimental setup Figure 1 shows a schematic diagram of the birefringence microscope [2]. An He-Ne laser with a wavelength of 632.8 nm is used as a light source. The laser beam passes through a polarizer (P) with a 0º orientation to horizontal (with respect to the azimuthal angle), a half-wave plate (H) with a θ1 orientation to horizontal, and a quarter-wave plate (Q) with orientation a θ2, in order to establish the initial polarization states. The light transmitted from the sample (S) is detected by a charge-coupled device (CCD) camera after passing through an analyzer (A) with a θ3 orientation. The phase difference and azimuthal angle of birefringence are analyzed based on the known polarization states and the detected light intensity.

*[email protected]; phone +81-42-388-7372; fax +81-42-385-7204



CCD camera θ

Image formation lens

3

A Object lens θ

1

θ

S 2

He-Ne laser Illumination lens Mirror P H Q Polarization generator Fig.1

Birefringence microscope

2.2 Birefringence measurement The detected light intensity is calculated using Mueller matrices and Stokes parameters. The Mueller matrices denote half-wave plate H with set direction θ1, quarter-wave plate Q with set direction θ2, sample X with birefringence (phase difference ∆, azimuthal angle φ), and analyzer A with set direction θ3. With a linearly polarized light beam (0°) as the incident light, the polarization state at the detector (S’) is obtained from the Stokes parameter S as follows: (1)

S' = A θ 3 ⋅ X ⋅ Q θ2 ⋅ H θ1 ⋅ S

The light intensity I detected by the detector is given by

I = I o [1 + cos{4θ1 − 2θ 2 }cos(2θ 3 − 2θ 2 ) − ∆ sin{4θ1 − 2θ 2 }sin( 2θ 3 − 2φ )

(2)

provided that ∆1500pC/N), dielectric constant (kRT~3000) and electromechanical coupling factor (k33~92%) and strain levels are significantly higher than those of the lead zirconate titanate Pb(Zr1-x, Tix)O3, (PZT). Furthermore, their hysteresis is much lower. The single crystal also gives more desirable and predictable resonance characteristics [13-15]. A prototype diaphragm design with two different types of electrode patterns is shown in Fig. 1. A circular electrode configuration consisting of metallic area distributed over the PMN-PT surface can lead to efficient acoustic sensing. Acoustic sensing in the proposed configuration is the result of surface contraction across the diaphragm. It can be noted from the figure 1 that the diaphragm designs include the interdigitated electrode pattern (Fig. 1 upper left). Another piezoelectric diaphragm design uses the d31 mode of a piezoelectric film (Fig. 1 upper right). In case of the interdigitated electrode design (Fig. 1 upper left), an external stress applied to the diaphragm results in output charge or voltage by d33 mode. In many perovskite ferroelectric materials, the d33 coefficient is two or more times larger than d31, and hence our interest is in the d33 mode with interdigitated electrode pattern. In addition, it can be noted that the d33 mode design requires a simpler one-side electrode fabrication process. Ferroelectric materials develop surface charges when subjected to stress, and alternatively exhibit mechanical deformation by applying an electric field. A piezoelectric diaphragm is a sensor that transforms mechanical vibration of membrane into electrical signal using piezoelectric effect. The deformation and stress distribution is important factor in microphone. In order to estimate the deformation, stress distribution, and modal analysis, numerical analysis using ANSYS is conducted. Several parameters for the numerical analysis are depicted in following table1. Based on above parameters, we used a modal analysis to determine the vibration characteristics of the diaphragm design of Fig. 1. The maximum deformation is occurred at its center (Fig.2 upper). The deformation is about 2.419E-3. The natural frequencies and mode shapes are also important parameters in the design of a microphone diaphragm for dynamic loading conditions. The modal analysis to determine the fundamental vibration mode shapes and corresponding frequencies was conducted using ANSYS finite element analysis software. The first and the second modes natural frequency of the diaphragm structure are 84,317 Hz (Fig. 2 middle) and 159,896Hz (Fig. 2 bottom), respectively. The diameter of the circular diaphragm is 500 µm. And the thickness of the diaphragm is 5 µm. The applied pressure is 5 Pa. Still, however, we need to adjust the mechanical properties and model based on the experimental results


d33 IDT design

d31 design

Fig. 1 Design of PMN-PT piezoelectric diaphragms (upper left: d33 mode interdigitated electrode design; upper right: d31 mode circular electrode design; below: three-dimensional view of the diaphragm design)

Table 1. Material parameters for numerical analysis Parameters Thermal conductivity Young’s Modulus Poison ratio

[

value

K : 0.0026 W

]

→ 0.26 E 6 cm ⋅ K E : 20 ~ 25 [GPa ] → 20 ~ 25 E 3 υ : 0.39

Thermal expansion coef.

α : 9.5E − 6 [K −1 ]

Density

ρ : 8.2 ⎡ g

⎤ → 8.2 E − 15 ⎢⎣ cm 3 ⎥⎦


Fig. 2 Vibration characteristics of the diaphragm design of Fig. 1

3. FABRICATION PROCESS OF PMN-PT DIAPHRAGM Figure 3 shows the steps required to fabricate a PMN-PT diaphragm. We have two different type of electrode: Interdigitated electrode pattern and top/bottom electrode. Each fabrication process is shown in figure 3. We use -oriented and poled 500um-thick PMN-PT single crystal plates mounted on a Si substrate. The sample undergoes a mechanical polishing down to 20~30µm-thick film and Cr evaporation processes for the top side to have fine primary Au and Cr electrode layers. The interdigitated electrode pattern is micromachined by typical photolithography processes to have precisely 10µm-gap periodic electrode for the d33 mode design. The back side of the film is then exposed by a back-side wet etching process of Si substrate. Either a chemically assisted ion beam etching (CAIBE) technique or an inductively coupled plasma (ICP) etching process can be used to thinning down the film up to 5µm.


Single crystal PMN-PT (20µm-thick) + Si substrate

Electrode pattern (circular interdigitated electrode)

Wet etching of silicon Thinning PMN-PT film to 5 µm using CAIBE or ICP

(a) The d33 mode design

Single crystal PMN-PT film + Silicon substrate Electrode pattern (plain circular electrode) Wet etching of silicon Thinning PMN-PT film to 5 µm using CAIBE or ICP

(b) The d31 mode design Fig. 3 Fabrication processes of PMN-PT piezoelectric diaphragm

In this paper, we also report the experimental results of dry etching characteristics of PMN-PT single crystal thin film. We used an inductively coupled plasma (ICP) etching process with various gas combinations [16]. A factory-oriented and PMN-PT single crystal 0.5mm-thick plate was used for this research. The material is purchased from IBULE Photonics and has the dimension of 20×20×0.5mm3. In order to obtain a thin film, a bulk sample is polished down to the thickness of 30 µm. The further thinning down of the circular diaphragm area to the thickness of 5 µm can be produced by standard photolithography and the inductively coupled plasma (ICP) etching process. The focus of this study is to study the dry etching properties of the PMN-PT thin film and to obtain the optimum gas combination to maximize the etching rate in the ICP process. The gas mixtures used in this experiment were the combination of Cl2, BCl3, and CH4. The substrate temperature was maintained at 20o and the bias power of the ICP was 200W. The etch rate was measured using a surface profilometer (alpha step). Figure 4 shows the etch rates of the PMN-PT thin film as a function of BCl3/Cl2 gas mixture. When the PMNPT thin films were etched using pure gas of Cl2 was less than 500 Å /min. As BCl3 was added into the gas mixture, the etch rate increased up 1800Å/min. Additional experiments were carried out to investigate the effect of Cl2/ CH4 gas mixture on the etch rate. As shown in Fig. 5, the etch rate using the pure CH4 gas was less than 800Å/min. With the increase of Cl2, the etch rate increased up 1800Å /min at 60% of Cl2 mixture. And further increase of Cl2 decreased the etch rate.


2000 1800

Etch rate (A/min)

1600 1400 1200 1000 800 600 400 200 0

20

40

60

80

100

BCl3 / (BCl3+Cl2 ) (%)

Fig. 4 Etch rate of PMN-PT film using an inductively coupled plasma (ICP) etching process with BCl3/Cl2 gas mixture

2000 1800

Etch rate (A/min)

1600 1400 1200 1000 800 600 400 200 0

20

40

60

80

100

Cl2 / (Cl2+CH 4) (%)

Fig. 5 Etch rate of PMN-PT film using an inductively coupled plasma (ICP) etching process with Cl2/ CH4 gas mixture

4. SENSITIVITY MEASUREMENTS Figure 6 shows fabricated prototype PMN-PT single crystal diaphragms. The sizes of the prototypes are larger than the design of Fig. 1 (2mm diameter). We can get a feasibility of PMN-PT microphone through this scaling factor of 4. The final thinning process was not applied for these prototypes. To fabricate the prototype, we used oriented and poled 500um-thick PMN-PT single crystal plates. The samples were purchased from TRS Ceramics, Inc. For the electrode patterning, a 50nm-thick gold film is sputtered on the surface and patterned using standard photolithography. The interdigitated electrode patterns were micro-machined by photolithography processes to have a100µm-gap periodic electrode for d33 mode design. By using wire cutting followed by electrode patterning, the films were shaped into a square-shaped acoustic sensor as shown in Fig. 1.


Fig. 6 Fabricated PMN-PT single crystal diaphragms

Amplifier

Oscilloscope

Signal generator

Speaker

Fig. 7 Experimental setup for sensitivity measurement

In this study, we carried out experimental measurements to compare the d33 and d31 mode designs shown in Fig. 6. The experimental setup for the sensitivity measurement is given in Fig. 7. Before the poling process, the PMN-PT films had very weak factory poling. The additional poling process establishes a remnant polar domain configuration in the films and a consequent strong piezoelectric response. The proper poling process is critical to maximize the output from the device. Figure 8 shows the voltage output (peak-to-peak), Vpp, from the diaphragms as the function of different poling conditions. It shows that the output voltage increases and saturates around 0.25 mV as the poling voltage increases. The poling process has been conducted under room temperature. The acoustic input for this experiment was given by a small commercial speaker attached to an amplifier and a signal generator. It can be noted from Fig. 8 that the d33 mode design generates no output voltage at 0V poling condition. Then the sensitivity of the design rapidly increases as the poling voltage increases. The phenomenon may be explained from the fact that the d33 mode design requires a different electric field distribution while the d31 mode design needs the electric filed distribution of poling [15,17]. The frequency responses of the prototypes are shown in Fig. 9.


(mV)

£ d31 rre

OF

• d33rrode

I

21i:0o. 0

50

r 150

100

200

250

Poling voltage ('

Fig. 8 Voltage output (peak-to-peak), Vpp, from the diaphragms as the function of poling voltage

(mV)

—1

25

>a

20

ci)

0) 15

C >

= 10 a =

0

5 0 10

—.—a

1000

100

Hz

Fig. 9 Frequency responses of the PMN-PT diaphragm prototypes


I

10000

4. CONCLUSIONS Piezoelectric MEMS acoustic sensors have a wide variety of applications in hearing aids, surveillance, heart monitoring, etc. In this paper, we have presented a piezoelectric MEMS microphone based on PMN-PT single crystal diaphragm. The proposed diaphragm design includes an interdigitated electrode pattern that could be a pioneering effort in the area. The dry etching condition is researched for the future patterning and fabrication of various acoustic sensor structure. From the scaling-factored miniaturized PMN-PT single crystal diaphragms, we can conclude the PMN-PT thin film microphone designs have a potential to show excellent acoustic characteristics, reliability.

ACKNOWLEDGEMENTS The authors thank Dr. S. M. Wang and D. S. Kim for the numerical analysis, and also thank the Ministry of Information and Communication Grant.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

M. Jianmin, L. Rongming, C. Longqing, Z. Quanbo, L. S. Yee, and S. S. Hee, “Design considerations in micromachined silicon microphones,” Microelectronics Journal 33, 21–28 (2002). S. Bouwstra, T. Storgaard-Larsen, P. Scheeper, J. O. Gullov, J. Bay, M. Muellenborg, and P. Rombach, “Silicon microphones—a Danish perspective,” Journal of Micromechanics and Microengineering 8(2), 64–68 (1998). D. Hohm and G. Hess, “A Subminiature Condenser Microphone with Silicon Nitride Membrane and Silicon Back Plate,” J. Acoust. Soc. Am. 85, 476–480 (1989). P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, and P. Bergveld, “A Review of SiliconMicrophones,” Sens. Act. A 44,1–11 (1994). F. W. Fraim and P. V. Murphy, “Miniature Electret Microphones,” J. Audio Eng. Soc. 18,511–517 (1970). J. Sprenkels, R. A. Groothengel, A. J. Verloop, and P. Bergveld, “Development of an Electret Microphone in Silicon,” Sens. Act A 17, 509–512 (1989). R. Schellin and G. Hess, “A Silicon Subminiature Microphone based on Piezoresistive Polysilicon Strain Gauges,” Sens. Act. A 32, 555–559 (1992). R. Shellin, M. Strecker, U. Nothelfer, and G. Schuster, “Low Pressure Acoustic Sensors for Airborne Sound with Piezoresitive Monocrystalline Silicon and Electrochemically Etched Diaphragms,” Sens. Act. A 46–47, 156–160 (1995). D. Arnold, S. Gururaj, S. Bhardwaj, T. Nishida, and M. Sheplak, “A Piezoresisitive Microphone for Aeroacoustic Measurements,” Proc. 2001 ASME Intern. Mech. Eng. Cong. Expos., New York, Nov. (2001). M. Royer. J. O. Holmen, M. A. Wurm, O. S. Aadland, and M. Glenn, “ZnO on Si Integrated Acoustic Sensor,” Sens. Act A 4, 357–362 (1983). R. Reid, E. Kim, D. Hong and R. Muller, “Piezoelectric Microphone with On-Chip CMOS Circuits,” J. MEMS 2, 111–120 (1993). P. Ried Robert, Kim Eun Sok, M. Hong David, and S. Muller Richard, “Piezoelectric Microphone with OnChip CMOS Circuits,” Journal of Mi- croelectromechanical Systems 2(3), 111–120 (1993). H. Fu and R. E. Cohen, “Polarization rotation mechanism for ultrahigh electromechanical response in single- crystal piezoelectrics,” Nature 403, 281-283 (2000). N. W. Hagood, R. Kindel., R. Ghandi, R. Gaudenzi, “Improving transverse actuation of piezoelectrics using interdigitated surface electrodes,” SPIE paper No. 1975-25, Proceedings of the 1993 North American Conference on Smart Structures and Materials, Albuquerque, NM, (1993). R. R. Vanga, M. Levy, K. S. Moon, and Y. K. Hong, “Single-Crystal Relaxor Ferroelectric Piezoactuators with Interdigitated Electrodes,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 51(12), 1593-1599 (2004).


16. J.W. JangU, Y.H. Lee, Y.J. Lee, J. Lee, G.Y. Yeom, “Etching characteristics of lead magnesium niobate lead titanate PMN]PT relaxor ferroelectrics,” Surface and Coatings Technology (131), 252-256 (2000). 17. Y. K. Hong and K.S. Moon, “Interdigitated Single Crystal Piezoelectric Actuator,” Proceedings of the SPIE International Conference on Optomechatronic Actuators and Manipulation, SPIE, ISOT 2005, Sapporo, Japan, Vol. 6048, pp. 6048K-1-7, December (2005).

Proc. of SPIE Vol. 6374 637409-10

Invited Paper

PMN-PT PIEZOELECTRIC NEAR FIELD OPTICAL PROBE FOR DATA STORAGE a

Yong K. Hong, bSung Q Lee, bEun Kyoung Kim, bKang Ho Park, a1Kee S. Moon a

Dept. Of Mechanical Engineering, San Diego Stage University 5500 Campanile Dr. San Diego, CA 92182, U.S.A. b Nano-Sensor Team, ETRI 161 Gajeong-Dong, Yuseong-gu, Daejon, 305-700, S. Korea ABSTRACT

This paper presents the fabrication process of a novel aperture which allows near field optical data storage. We use PMN-PT ((1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3) single crystal material - a new generation oxide material known as relaxor ferroelectrics that exhibits extraordinary piezoelectric properties - to fabricate microlenes using photolithography and dry etching techniques. In this paper, we describe the fabrication processes of a PMN-PT single crystal material microlens prototype with a miniature aperture for near field optical data storage. PMN-PT has the merits of transparency for optical usage and also has a high dielectric coefficient that is suitable for actuator and sensor applications. It provides an advantage of manufacturing both aperture and actuator/sensor with the same material. The thermal reflow technique is used to fabricate photoresist microlenses on a freestanding single crystal PMN-PT film as a mask. The PMN-PT lenses are fabricated by a chemically assisted ion beam etching (CAIBE) technique. Finally the focused ion beam (FIB) machining process is used to place a miniature aperture at the apex of the microlens. We were able to successfully fabricate the 10µm PMN-PT microlenses with less than 100nm apertures. From the experimental measurement, we were able to obtain the optical throughput of 1.83x10-7 from a 50nm aperture. Keywords: PMN-PT, Aperture, Data storage, Near field

1. INTRODUCTION It has been well known that the storage density of the conventional optical data storage using far field optical systems cannot be increased significantly due to the limit of the wavelength of the laser source and the numerical aperture of the objective lens [1,2]. One of the new technologies to overcome the limitation is the near field optical microscopy. Near field scanning optical microscopy (NSOM) has been intensively studied for optical writing. The most crucial part of the NSOM optical writing is a sub-wavelength size aperture at the apex of the probe. Currently, tapered optical fiber probes are most widely used for the NSOM. The conventional tapered optical fiber probes have a few negative aspects. The opening angle of the fiber tip is small. Therefore, most of the light is absorbed at the metal wall, which leads to a low optical transmission efficiency. Moreover, it is very difficult to fabricate the fiber NSOM probe in a mass production because the shape of the tip and the size of the metallic aperture of the fiber tip are not reproducible [3]. Recent attempts using AFM cantilever-style probes have shown improved transmission efficiency as well as AFM-like gap control between the probe and the surface. Figure 1 shows our near field optical storage design using an AFM cantilever-style NSOM probe. So far silicon based AFM cantilever-style probe design has been most popular [4]. Most of the cantilever-style probe designs have a high-throughput aperture patterned on the silicon cantilever directly. In this paper, by the use of an advanced relaxor ferroelectric material ((1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3, PMN-PT) with the thermal reflow and dry etching process, we present a piezoelectric cantilever-style probe having a microlens with an aperture at the apex of it. The material, the single-crystal solid-solutions PMN-PT, has been shown to possess piezoelectric coefficient and electromechanical coupling response significantly larger than conventional piezoelectric 1

[email protected]; phone 1 619 594 8660 Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740A, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.689527

Proc. of SPIE Vol. 6374 63740A-1

ceramics [5-8]. Furthermore, PMN-PT single crystal thin films have the merits of transparency for optical usage [9]. Therefore, PMN-PT single crystal materials are suitable for actuator and sensor applications and provide an advantage of manufacturing both aperture and actuator/sensor with the same material [10]. This paper focuses on the fabrication process of a PMN-PT single crystal optical microlens and a miniature aperture.

Optical fiber Lens

Lens Z motor

PMT(PD) Splitter CCD

Fig. 1. Schematic of the near field optical data storage head system.

2. FABRICATION OF PMN-PT APERTURE In the near field optical data storage device design, the most critical component is the piezoelectric cantilever-style NSOM probe that leads to higher resolution optical writing capability. The integration of an AFM style cantilever with an aperture allows more reliable and better control of the aperture-sample distance than that obtained by traditional NSOM shear-force detection method. The design of the proposed NSOM probe is depicted in Fig. 2. As shown in the figure, an interdigitated electrode is implemented on the PMN-PT cantilever to provide an embedded sensing capability. To construct a near field optical data storage head, a PMN-PT cantilever is also fabricated and a microlens is attached to the end of the cantilever. An aperture is place at the top of the microlens.

Focused UV light

Sensor electrodes

PMN-PT cantilever Sub 100nm aperture

Built-in microlens

Al coating

Fig. 2. Design of piezoelectric cantilever style near field optical probe.


Photoresist coating

————

a

Photolithography and wet etching

300

a

Thermal reflow

10! h

Dry etching (CAIBE) Metal deposition

— .-. 'a, a' .

Focused ion beam machining

Cross sectional view

Fig. 3. Fabrication processes of PMN-PT microlens array with aperture.

This paper focuses on the fabrication of PMN-PT microlenses with an aperture. The prototype is fabricated through the fabrication of freestanding single crystal PMN-PT films and patterning them by photolithography, chemically assisted ion beam etching (CAIBE) and focused ion beam (FIB) machining processes. Figure 2 illustrates the required processes. We prepared a mechanically polished PMN-PT single crystal film with the thickness of 20µm. We used -factory-oriented and poled 0.5mm-thick PMN-PT single crystal plates. The samples were purchased from TRS Ceramics, Inc. Then a photoresist is used to make circular plates on the PMN-PT film by using photolithography process. For the thermal reflow treatment, the sample was heated on a hot plate, with the heating rate of 1oC/min until the working temperature of 170oC was reached. The spherical shape of photoresist is given in Fig. 4. After the thermal reflow process, a chemically-assisted-ion-beam system (CAIBE, Ribetch 160 ECR LL) is used for the formation of PMN-PT microlenses by controlled dry etching of the sample. Figure 4 shows SEM images of a PMN-PT microlens obtained by the CAIBE process. It can be seen from the figure that the shape of the microlenes is pointed. This means that the etching rate of PMN-PT is slightly faster than that of the photoresist. By controlling the CAIBE etching time, we were able to change the microlens to a round shape. The SEM image of the round shaped microlens is shown in Fig. 5. The CAIBE system could produce 10um-thick lenses in about 3-4 hr etch time without any etch gas mixture. After the CAIBE process, a Cr and Au films with the thickness of about 100 nm was entirely deposited onto the surface of the microlenses. Finally, a focused ion beam (FIB, Hitachi FB-2000A) was used for patterning of a small hole on the tip of the lens. The FIB milling enables not only accurate control of the aperture size, but also provides a means of producing specific aperture shapes with nanometer-scale precision. The FIB system uses a beam of focused high-energy (30kV) gallium ions to remove material in a very controlled manner. Note that the actual inner size of the aperture is much smaller than the outer diameter of the aperture observed by scanning electron microscopy (SEM). The SEM images of the fabricated probes and a close up view of the apertures with about 50 nm diameter (inner) are shown in Fig. 5.


~100um

:.

4

(a)

(b)

(c)

(d)

Fig. 4. (a) Photoresist mask after the thermal reflow process (b) PMN-PT microlens microlens fabricated by standard photolithography and chemically assisted ion beam etching (CAIBE)

(c) Zoom image of (b) (d) Aperture (outer diameter: 300nm; inner diameter: 100nm); Gold has been deposited on the surface and an aperture was made by focused ion beam (FIB).

S47005.OkV 132 6O.OkSE(U)

Fig. 5. SEM image of a 10 µm PMN-PT microlens (left). An aperture (outer diameter: 150 nm; inner diameter: 50nm) was made by focused ion beam (FIB) (right).

3. MEASUREMENT OF OPTICAL THROUGHPUT Although minimizing the size of the NSOM probe tip aperture is a primary factor in achieving high image resolution, a sufficient diameter to provide the desired optical signal output level must be maintained. In particular, for the purpose of recording, optical throughput is very important. Optical throughput is the ratio of the near field and corresponding far


field photon intensities. It is well known that the throughput of an aperture NSOM probe is drastically decreased by decreasing the size of the aperture. To evaluate the throughput of the fabricated aperture probe we used a measurement setup as shown in Fig. 6. A photodiode is used to sense the near field laser beam. A laser diode of 405 nm wavelength is focused on the probe. The throughput of the prototype PMN-PT probe was somewhat low. A 50 nm diameter aperture of PMN-PT probe shows an approximately 2x10-7 throughput. The throughput result is similar as that of the conventional optical fiber NSOM probe. Finally, Figure 7 shows the prototype near field optical data storage head. The fabricated NSOM aperture array is attached at the end of a PMN-PT cantilever with interdigitated electrode. The interdigitated electrode provides deflection sensing capability required to control the gap between the probe and the media surface.

Optical chopper

BS

Lens Probe Lens Lens Pin hole

Fig. 6. Optical throughput measurement setup: Laser is delivered to the aperture probe and detected by a photodiode. A lock in amplifier and a chopper are used to enhance sensitivity.

TpII

Fig. 7. PMN-PT cantilever with embedded sensor and aperture.


4. CONCLUSIONS One of the main goals of this research is to fabricate an aperture NSOM probe made of single-crystal piezoelectric materials (PMN-PT and investigate the performance. We used a bulk sample of PMN-33%PT to produce a free standing single crystal film. Then, we were able to successfully fabricate 10µm PMN-PT micro-lenses with less than 100nm apertures using the photolithography, thermal reflow, dry etiching and focused ion beam techniques. We have conducted an optical throughput measurement test. The throughput result is similar as that of the conventional optical fiber NSOM probe. This may be from several reasons. We expect that the throughput of the PMN-PT probe will be improved by higher surface quality of the microlens. We would need to improve the shape of the microlens to minimize the intensity loss inside the lens.

ACKNOWLEDGEMENTS The authors thank the Ministry of Commerce, Industry and Energy (S. Korea) Grant.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Y. Mitsuhashi, “Optical storage: Science and technology: Part 1: Regular Papers & Short Notes & Review Papers,” Japanese Journal of Applied Physics, 37(4B), 2079,1998. T.D. Milster, “Near-field optics: a new tool for data storage,” Proceedings of the IEEE, 88(9), 1480, 2000. P.N. Minh and T. Ono, “Nonuniform silicon oxidation and application for the fabrication of aperture for nearfield scanning optical microscopy,” Applied Physics Letters, 75(26), 27, 1999. K.-B. Song, E.-K. Kim, S.-Q Lee, J. Kim And K.-H. Park, “Fabrication of a High-Throughput Cantilever-Style Aperture Tip by the Use of the Bird’s-Beak Effect,” Jpn. J. Appl. Phys. 42 , 4353, 2003. S. E. Park and T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys., 82, 1804, 1997. H. Fu and R. E. Cohen, “Polarization rotation mechanism for ultrahigh electromechanical response in singlecrystal piezoelectrics,” Nature, 403, 281, 2000. S.-F. Liu, S.-E. Park, T. R. Shrout, and L. E. Cross, “Electric field dependence and piezoelectric properties for rhombohedral 0.955Pb(Zn1/3Nb2/3)O3 – 0.045PbTiO3 single crystals,” J. Appl. Phys., 85, 2810, 1999. E. M. Sabolsky, A. R. James, S. Kwon, S. Trolier-McKinstry, and G. L. Messing, “Piezoelectric properties of textured Pb(Mg1/3Nb2/3)O3–PbTiO3 ceramics,” Appl. Phys. Lett., 78, 2551, 2001. Y. Lu, M. Cronin-Golomb, S.-W. Liu, H. Jiang,F.-L. Wang, J. Zhao, S.-Q. Wang, and A.J. Drehman, “Fabrication and optical characterization of Pb(Mg1/3Nb2/3)O3-PbTiO3 planar thin film optical waveguides,” Applied Physics Letters, 72(23), 2927, 1998.

10. M. Levy, R. Vanga, K.S. Moon, H.K. Park, Y.K. Hong, “Single-crystal relaxor ferroelectric piezoactuators with interdigitated electrodes”, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, , 51, 1593, 2004.


Real-time high-displacement amplified bimorph scanning mirror Paul E. Pattersona, b, Jason M. Zarab a Department of Electrical Engineering and Computer Science, United States Military Academy, West Point NY 10996; b Department of Electrical Engineering and Computer Science, The George Washington University, Washington DC 20052 ABSTRACT This paper provides an overview of recent research in the use of microelectromechanical systems (MEMS) actuators for beam steering applications, including optical coherence tomography (OCT). Prototype scanning devices have been fabricated out of polyimide substrates using conventional integrated circuit technology. The devices utilize piezoelectric bimorphs to mechanically actuate the torsion mirror structure made of polyimide. The material properties of the polyimide allow very large scan angles to be realized in the devices while using low voltages. Prototype devices have demonstrated optical scan angles of over 80 degrees with applied voltages of only 40V. Different device sizes have also been demonstrated with resonant frequencies between 15-60Hz (appropriate for real-time imaging). Analytical models have been developed that predict resonant frequency of the device as well as the angular displacement of the mirror. Further finite element modeling (FEM) has been done using ANSYS. These models closely reflect measured scan angles of the prototype devices. Based upon these models, further refinements can be made to the design to produce specific resonant frequencies for use in a multitude of applications. These models are currently being used to design and fabricate multiple devices on a single wafer with minimal post processing requirements. The ability to fabricate these devices in bulk will reduce their cost and potentially make them disposable to reduce the cost of their use in numerous applications, including patient care when used in biomedical imaging applications. Keywords: Micromirror, Polyimide, Piezoelectric, MEMS 1. INTRODUCTION The field of optical MEMS or MOEMS has seen an explosive growth over the last few years. This growth is expected to continue for the foreseeable future. Emerging Opportunities in Optical MEMS: 2003-2007, a report from the Communications Industry Researchers, Inc. (CIR) states that the growth of MOEMS subsystems will grow from $560 million in 2003 to $1.7 billion in 2007 [1]. Numerous methods have been explored for beam steering applications in the field of MOEMS, and several categories have been developed to classify these micromirrors [2]. A majority of the micromirrors to date have relied on electrostatic actuation. In general, micromirrors that rely on electrostatic actuation require large drive voltages (>50V). Electrostatically actuated micro-mirrors have been fabricated that are capable of achieving rotational angels of 90°with drive voltages of 47V[3]. Other electrostatically actuated micromirrors have demonstrated scans of 21° at 3.6kHz with a driving voltage of 75 V[4]. Recently MEMS flexure lead zirconate titanate (PZT) actuated scanners have been demonstrated which achieve optical angles of up to 40° in static operation and 10° in resonance at 17.4kHz [5]. Micromirrors, which utilize comb-drives for electrostatic actuation, have also been demonstrated. These devices are capable of 8.5° of mechanical deflection at 19.55kHz with an applied voltage of 100V [6]. Similar devices to those described in this paper have also been fabricated out of polyimide and actuated electrostatically. These devices are capable of scanning up to 146° at 50V [7,8]. Most micromirrors utilize silicon hinges that are too stiff to achieve the large scan angles desired in medical imaging systems. The processing required for many of the aforementioned micromirror structures is very specialized and is not a viable means to mass produce such devices for use in medical imaging applications. The micromirrors presented in this paper are prototype scanning devices that have been fabricated out of polyimide substrates using conventional patterning and etch technology and are appropriate for real time imaging.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740B, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686383

Proc. of SPIE Vol. 6374 63740B-1

2. METHODOLOGY The micromirror device is comprised of a table (with attached mirror) suspended by two small torsion hinges. These torsion hinges are fixed at one end to the supporting structure of the device. A gold-coated silicon mirror is then attached to the table of the device. Figure 1a is a schematic of a prototype device without a mirror attached. No dimensions are given, as this is a general schematic that depicts the typical layout of any of the devices. Figure 1b is an exploded view of the hinge structure. Initially 6 different prototype designs were fabricated.

(Torsion Hinges)

Hinge Thickness

Table (without mirror attached) Support cutaway

Hinge Width

Table cutaway

Hinge Length

Support Structure

(a)

(b)

Fig. 1. (a) Schematic of polyimide support structure without mirror. (b) Exploded view of the torsion hinge schematic Table 1 details the dimensions of these prototype devices. Four different gold coated silicon mirrors were fabricated for attachment to the six prototype devices (0.875mm, 1mm, 1.5mm, and 2mm). The mirrors are all 400µm thick. Initial testing of the devices revealed that the device best suited for real-time imaging applications (around 30Hz) a device with a large support structure and 135µm hinges with a 1.5mm mirror attached. The remainder of this paper will focus on devices with those dimensions. Table 1. Table of different prototype devices and their dimensions.

Support Structure Size

Table Size (mm)

Hinge Width (µm)

Hinge Thickness (µm)

Hinge Length (µm)

Large Large Large Small Small Small

2 x 2.25 2 x 2.25 2 x 2.25 1 x 1.125 1 x 1.125 1 x 1.125

90 135 180 60 90 120

3 3 3 3 3 3

250 250 250 250 250 250


Figure 2 is a schematic of the prototype device design selected as the most suitable for use in a real time imaging system. Figure 3 is a picture of an actual prototype device. The entire support structure of the device is made of polyimide. The mirrors are fabricated on a separate wafer of gold-coated single crystal silicon (400µm thick). The mass of the mirror and the dimensions of the hinges can be varied to develop devices with the desired scan deflections and frequency responses for a multitude of real time imaging applications. The mirror pivots about the torsion hinges when the whole structure is subjected to a forced vibration. This forced vibration is generated by a commercially purchased piezoelectric bimorph that is 2mm in width and 25mm in length (piezo.com) and is attached to the base of the device. The support structure of the device has a relatively low resonant frequency (approximately 15-60Hz). This enables us to drive the entire structure at a frequency well below the bimorph resonant frequency of 215Hz. The small tip displacement of the bimorph at low voltages is enough to excite the device when operated at the device’s resonance. The motion it causes in the polyimide structure amplifies the small tip displacement of the bimorph into a large optical scan angle.

(2.25mm) (1.5 mm x1.5 mm)

(Torsion Hinges)

(25 mm)

Gold Coated silicon mirror Polyimide Fig. 2. Schematic of torsion mirror device with a hinge width of 135µm and a mirror that is 1.5mm x 1.5mm Once in motion the mass of the mirror and its moment of inertia cause the hinges to twist. This develops a restoring torque in the hinges. The restoring torque is realized as the bimorph tip displaces in the opposite direction of travel. In a perfect oscillator this motion would continue indefinitely. However, in the case of our device there are numerous factors that cause the oscillating motion of the device to stop rather quickly when no force is applied. Some of the factors that cause the device to stop oscillating are the effect of air damping and the stiffening of the torsion hinges as they twist. Operating the bimorph at the resonant frequency of the support structure allows us to overcome some of these effects. This forced vibration causes the device to behave more like a perfect torsional pendulum or oscillator.


(2.25mm)

Polyimide structure

PZT Bimorph (piezo.com)

Fig. 3. Picture of actual torsion mirror device with the same dimensions as those in 2. The mirror and support structures were modeled using one-dimensional beam theory and fundamental vibration mechanics. The resonant frequency of the structure can be predicted using equation 1 [9].

fr =

1 2π

JG l I 2

(1)

Where J is the polar moment of inertia of the hinge, G is the shear modulus of the hinge, I is the moment of inertia of the mirror, and l is the length of the hinge. The torque applied to the hinges causes a twisting motion. This motion is related to an angle in the hinge. The angle at which a hinge twists is the same angle that the mirror attached to the hinge is displaced. The angle of displacement can be predicted using equation 2.

θ=

TL JG

(2)

Where T is the torque applied, L is the length of the torsion hinge, J is the polar moment of inertia of the torsion hinge and G is the shear modulus. The torque is generated by the tip displacement of the piezoelectric bimorph accelerating the mass of the table and mirror. The structures were also modeled and simulated using finite element analysis program (ANSYS, Inc., Canonsburg, PA). These simulations allow us to alter certain dimensions of the device to achieve the optimal resonant frequencies for use in imaging systems prior to manufacturing the devices. Figure 4a shows the ANSYS modal analysis of the device with 135µm wide hinges. Figure 4b shows the model used for the harmonic analysis. Table 2 shows the material properties used to simulate the device.


b

a

Fig. 4. (a) ANSYS modal animation of the device (b) Device used for ANSYS harmonic analysis of a 135um hinge device with 1.5mm mirror attached. Table 2. Table of key material properties used for ANSYS modeling.

Material

Modulus (GPa)

Density (kg/m3)

Polyimide Silicon PZT

2.5 160 63

1470 2330 7500

Piezoelectric strain coefficient (d31) N/A N/A 1.8e-10 m/V

A harmonic analysis was also done using ANSYS. The results of this analysis can be seen in Figure 5. From the graph it is easy to see that the largest displacements of the mirror occur at approximately 24Hz.

Fig. 5. ANSYS harmonic analysis of a 135um hinge device with 1.5mm mirror attached.


3. RESULTS

The initial prototype mirror assemblies were fabricated at North Carolina State University in the Biomedical Microsensors Laboratory (BMMSL) using a three-layer process on five-inch silicon wafers. A sacrificial silicon oxide layer was deposited on the wafer prior to processing to release the polyimide structures from the wafer. This sacrificial layer was later etched away using hydrofluoric acid (HF). To form the thin hinge layer, a 3 µm layer of polyimide (PI2723, HD Microsystems, Wilmington, DE) was spun onto the wafer and then patterned. Figures 6a and 6b show the cross section of this process and a top-down view. The thicker supports and tables were made of a 30µm thick patterned polyimide layer (Durimide, Arch Chemicals, Norwalk, CT). See figures 6c and 6d. The mirrors are made of gold plated single crystal silicon in a separate process on a separate wafer. Once the devices were released from the wafer using the HF etching solution, the mirrors were mounted. The mirrors were glued to the polyimide table using a fast drying epoxy. The entire device is then mounted to the bimorph using double stick tape. This was a sufficient bonding method as the mass of the device was very small (less than 3mg). Several different device configurations were fabricated Figure 7 shows several of the devices on a wafer prior to being released. Silicon Wafer 3µm Polyimide 30µm Polyimide Silicon Oxide

Si

a b

Si

c d Fig. 6. (a) Cross-section of mirror support structure with first layer of polyimide. (b) Top down view of first layer of polyimide. (c): Cross-section of second layer of polyimide for mirror support structure. (d) Top-down view of second layer of polyimide for mirror support structure.


Fig. 7. Picture of devices before being released from the wafer. The optical displacement of the mirror was determined by using a calibrated target with a grid printed on it. This target was placed a known distance from the mirror. A 3mW HeNe laser was reflected off of the mirror and scanned across the target. Displacements were measured by tracing the path of the beam across the calibrated target as the bimorph was driven at frequencies between 0 – 140 Hz and 10 – 100 volts peak to peak. Figure 8 is an image of a scanned HeNe beam on the target. 1cm

Fig. 8. Scanned HeNe beam on target. Mirror is 25 mm from the target. Large support structure with 135µm hinges. Driving voltage was 40Vpp. Resonant frequency was 33Hz. Approximate scan angle is 85o. A device with a 1.5mm mirror attached and 135µm wide hinges has a predicted resonant frequency of 24.2Hz. The modal analysis by ANSYS predicted a resonant frequency of 22.6Hz. The measured resonant frequency varied between 28Hz-33Hz with multiple devices of the same hinge width and mirror size (1.5mm mirror and 135µm wide hinge). The variations between predicted and actual resonance can be attributed to several unknown device characteristics such as the actual piezoelectric coefficient of the bimorph, the actual modulus of the polyimide being used and the damping coefficient of the device. The variation in resonant frequencies can also be explained by variations in the mass of the mirrors attached to the devices due to non-uniform amounts of epoxy being applied. Prototype scanning mirrors have demonstrated optical scan angles up to 97° at frequencies ranging from 15-60 Hz and drive voltages ranging from 15-40 V. Variations of drive voltage and scanning ranges result from modifying the hinge dimensions and the mirror masses of the structures.


Reliability testing has been conducted on the devices. Multiple devices have been operated for over 1 million cycles with no signs of plastic deformation of the hinges. This would allow for the device to be operated continuously for a 24-hour period without failure of the hinges. This further improves the devices application for real time imaging applications. The structure was also tested in various orientations to ensure that there was minimal if any loss of scan range based upon orientation. Figure 9a and 9b show the device in operation. 1mm

1

(a)

(b)

Fig. 9. (a) Device at rest. (b) Device in motion

4. CONCLUSIONS We have modeled, fabricated, and tested an amplified bimorph scanning mirror for use in numerous imaging applications. The prototype devices have been used in the lateral scanning arm of an optical coherence tomography system. The results from our modeling and testing of the device have shown the devices capable of optical scan angles of up to 97 degrees using applied voltages of 15-40 V at frequencies of 15-60Hz. These figures show that this device is appropriate for real time imaging. We have also modeled the devices using ANSYS. Our ANSYS models accurately allow us to predict changes in the structures behavior based upon changes in the size of the mirror that is used. The results of our various ANSYS models closely predict the measured values we have obtained in the lab. There are several sources of error that explain the discrepancies between our modeled devices and our actual devices. The mass is slightly different in each device due to the unknown quantity of epoxy applied to each device to attach the mirror. There was also some difficulty in modeling the PZT bimorph. The bimorph parameters are unknown since the bimorph was purchased from a third party. These unknown parameters contributed significant error to our dynamic models. A new device fabricated on a single wafer (to include the PZT) will allow us to much more closely model the device since the properties of the PZT being used will be known. Additional sources of error in the models can also be attributed to not knowing the exact damping coefficient. The coefficient used for the ANSYS harmonic analysis was determined using the quality factor of one of the prototype devices. This is a good approximation of the damping factor but most likely contributed to some error in the harmonic analysis. Finally, the bulk properties of the polyimide (specifically, Young’s modulus) were used in the models. In the future, tensile testing will be done to determine the actual modulus of the polyimide being used. We are developing methods to fabricate the entire device on a single silicon wafer using standard processing techniques. This will allow for a more uniform and stable device. These devices can also very easily be tailored to suit specific imaging application needs. Simply changing the size of the mirror or the dimensions of the hinges allows us to choose the resonant frequency of the micro-scanner. Again this has been demonstrated through our ANSYS models and


in experimental data collected from actual devices. Currently new prototype devices are being fabricated on a single wafer using a nine step process. The process includes the deposition of a thin film PZT sol-gel to act as the actuator for the device. The new fabrication process enables an entire device to be made on the same wafer with no post processing requirements. The small size of the device and the large optical scan angles that it can achieve make this device ideally suited for use in various imaging system configurations, including real-time imaging applications.

REFERENCES 1. “New Opportunities for Optical MEMS are emerging outside of Telecom, says new CIR report - Market Intelligence - Communications Industry Researchers Inc”, Fiber Optics Weekly Update, 7 March 2003. 2. Z F Wang et al “Development of scanning micromirror with discrete steering angles” Journal of Physics: Conference Series 34 410-416 (2006). 3. Y S Yoon et al “A low voltage actuated micromirror with an extra vertical electrode for 90° rotation” J. Micromech. Microeng. 13 922-926 (2003). 4. Zhou, LX, Kahn, JM, Pister, KSJ “Scanning micromirrors fabricated by an SOI/SOI wafer-bonding process” J MICROELECTROMECH S 15 (1): 24-32 FEB 2006 5. Johannes G Smits, Koji Fujimoto, and Vladimir Kleptsyn, “Microelectromechanical flexure PZT actated optical scanner: static and resonance behavior”, J. Micromech. Microeng. 15(2005) 1285-1293. 6. Chang-Hyeon Ji et al "An alectrostatic Scanning Micromirror with Diaphragm Mirror Plate and Diamond Shaped Reinforcement Frame," J. Micromech. Microeng. 16 1033-1039 (2006). 7. J. Zara and S. Smith, “Optical Scanner Using a Micromachine Actuator”, Sensors and Actuators: A: Physical, 102 (1-2), pp. 176-184, 2002. 8. Zara, J., S. Yazdanfar, K. Rao, J. Izatt and S. Smith, “Electrostatic MEMS Actuator Scanning Mirror for Optical Coherence Tomography,” Optics Letters, 28(8), pp. 628-630, 2003. 9. K.E. Petersen, Silicon Torsional Scanning Mirror, IBM Journal of Research and Development 24, 631-637 (1980)


OPTIMIZATION OF ELECTROSTATIC SIDE-DRIVE MICROMOTOR TORQUE USING A NEW ROTOR-POLE-SHAPING TECHNIQUE Mohamed A. Basha and S. Safavi-Naeini Electrical and Computer Engineering, University of Waterloo, University Ave. West, Waterloo, Ontario, Canada N2L 3G1 ABSTRACT In this paper we report a new design technique to optimize the driving torque of electrostatic side drive micromotors based on a new technique of rotor-poles-shaping. By reshaping the rotor pole from it regular pie shape, we can modify the distributions and directions of electric field in the gap between rotor and stator poles. Hence, the tangential electrostatic force component exerted on the rotor poles, responsible for driving torque, is maximized. A 2D parametric finite element model using ANSYS APDL programming language is developed for the optimization of the rotor pole shape. The finite element model uses a potential periodic boundary condition to simulate only one micromotor sector. Simulation results show an increase of the driving torque up to 48.75%. Keywords: : Micromotor, rotor-pole shaping, FEM, periodic boundary condition

1. INTRODUCTION The inial design of a functional electrostatic micromotor at Berkeley1 was fabricated using surface micromachining process. The electrostatic excitation of the micromotor is achieved through a sequence of high voltage pulses (100V − 400V ) supplied to different stator poles depending on the stator and rotor poles configurations. Design and fabrication of ultrasonic2, ,3 magnetic4,5 , piezoelectric2 , electrostatic6,7 , and thermally actuated8,9 micromotors have been achieved in the last two decades. The small size of micromotors made micromotors an effective candidate for several emerging applications. Micromotors have been used in precision surgical and medical applications10,11 , optical scanners12,13 , optical switching and routing of wavelengths in optical back bone networks14,15 , high density data storage16 , and constructing a micro-robot.17,18 Electrostatic forces are not significant in the macro scale and not comparable to magnetic forces. Resizing down to microscale, electrostatic forces become significant, more powerful and capable of driving and actuating micromotors. The use of standardized fabrication processes and the small size-scale are advantages of electrostatic micromotors over other types of micromotors. LIGA19 and DRIE of Silicon-On-Insulator (SOI) wafers12 are the two main fabrication methods for micromotors with a high aspect ration rotor. Surface micromachining with two structural layers20 process was used successfully to fabricate planer micromotors with rotor diameters ranging from 100µm − 1200µm6,7,12 for various applications. In this paper, we present a new design technique to maximize the micromotor driving torque for the same driving voltage and dimensions. The new technique is based on reshaping the rotor-poles to optimize the driving torque of the micromotor. The analysis is based on a 2D finite element analysis of the electric field and electrostatic forces on rotor poles. By reshaping rotor poles, we can modify the direction and distribution of induced electric field in the gap between rotor and stator poles and hence the electrostatic force on the rotor poles. As a result, we were able to maximize the driving torque. The organization of the paper is as follows: In section 2, we discuss theoretical design aspects of the micromotors, the new rotor-pole shaping technique, and 2D finite element analysis of the micromotor. In the following section, we present the simulation results from 2D finite element analysis of various micromotors.

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740C, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.687698

Proc. of SPIE Vol. 6374 63740C-1

g

ro

∆r

spp spw

rpw rpp

Figure 1. A schematic drawing of the micromotor design parameters.

2. DESIGN OF ELECTROSTATIC MICROMOTORS 2.1. Classical Micromtors Design Figure 1 depicts the electrostatic micromotor design parameters. Table 1 lists the definitions of the design parameters. The ratio of rotor to stator poles is 2 : 3 for maximum average generated torque and minimum torque ripples.21 The aim of micromotor design is to produce enough driving torque to override the friction between rotor bushings and ground. The micromotor driving torque is a result of the application of a potential difference between rotor and stator poles. The potential difference will generate an electric field in the gap between rotor and stator poles. As a result, an electrostatic force is exerted on the rotor poles causing the rotor to move. The generated torque is usually calculated using the so called stored electrical co-energy concept which is defined as 12 CV 2 , where C and V represent the capacitance and the voltage difference between the driving electrodes of the rotor and stator poles, respectively. The exerted torque is defined as the rate of change of the stored electrical co-energy with respect to a change in the rotor angle θ (i.e. direction of rotation) and is expressed as: T =

V 2 dC 2 dθ

(1)

An other way of calculating the driving torque in an electrostatic micromotor is using Maxwell stress tensor method to calculate the generated electrostatic force on the rotor poles surfaces from a finite element analysis. Integrating the electrostatic force over the surface of the pole to find the driving torque. Analytical21 and finite element formulations22 were previously used to analyze and optimize micromotors for optimum driving torque. All previously designed and fabricated micromotor has the regular pie shape for rotor poles with angular width of ”rpw” as shown in Fig. 1. Electrostatic force is inversely proportional to the gap distance g. Hence, we kept the gap parameter, g, at the minimum allowed by the fabrication process and is 2µm in MUMPs process for maximum driving torque. The optimization process is based on sweeping the micromotor parameters, i.e. r, r, rpw,.....etc, and calculating the resultant driving torque. The rotor pole angular width, rpw, is changed while maintaining the regular shape of the rotor poles in almost all designed and fabricated micromotors.


Table 1. Design parameters of electrostatic micromotors and optimized parameters using analytical formulation.21

P arameter rpp rpw spp spw ro ∇r g Nr Ns

Def inition rotor pole pitch rotor pole width stator pole pitch stator pole width rotor radius rotor tooth height gap between rotor and stator poles number of rotor poles number of stator poles

Optimization 2π/Nr π/Nr 2π/Ns π/Nr specified by the design requirements ro × rpw lower limit of the fabrication 2Ns /3 3πro /20g

2.2. Rotor Pole Shaping Technique We will study the behavior of the electric field in the gap between rotor and stator poles in the micromotor and the generated electrostatic forces on the rotor poles by solving the basic electrostatic equation (∇2 V = 0)using FEM solver with the appropriate boundary conditions. Electric field between two conductors is directed from higher to lower potential conductor. The electric field is normal to the surface of a conductor and can be derived from the potential distribution in the gap region by the simple gradient formula (E = −∇V ), Fig. 2a. The electrostatic forces, calculated by Maxwell stress tensor, acting on the rotor poles have three components: tangential, radial, and axial force components. The upward axial component will reduce the rotor weight and hence has the effect of reducing the friction between the rotor and substrate by levitating the rotor. This force component is ignored in the 2D finite element analysis. The tangential force component acting on the rotor poles is responsible for the driving torque. Because of the micromotor symmetry, a radial force component will be balanced by a similar component in the opposite direction on the other side of the rotor. Radial and tangential force components are shown in Fig. 2b. Generated forces on the rotor pole edges facing the stator pole are usually in the radial direction and have no effect on the driving torque. The tangential force component is usually generated on the side edges of the rotor poles. The shape of the rotor poles, control the distribution and direction of the generated electric field. By changing the shape of the rotor pole, we can modify the electric field direction and distribution to maximize the tangential component of the electrostatic force and hence maximizing the driving torque. The new shape of the rotor poles is a simple trapezoidal shape, Fig. 3. The proposed rotor pole shape is simple and will show the effectiveness of the new design technique. A new design parameter will be introduced

High edge nodes

High edge nodes

High edge nodes

(a)

Low edge nodes

(b)

Figure 2. (a) The electric field in the gap region and (b) the electrostatic force generated on the rotor pole in one micromotor sector.


spp spw

∆θsh

∆r

rpw rpp

Figure 3. A schematic drawing of the micromotor design parameters with the new rotor pole shape.

(θsh ) that specifies the rotor pole shape. Other rotor shapes are possible and will be investigated in future work. By modifying the rotor pole shape from the regular pie shape to the new proposed simple trapezoidal shape, distribution and direction of electric field are changed. As a result, the generated electrostatic force in the tangential direction, with respect to rotor poles, in the rotor pole edges will increase. The driving torque will reach an optimum value that corresponds to an optimum shape of the rotor.

2.3. Finite Element Model Finite element analysis (FEA) is used to calculate the potential and electric field distributions in the gap between rotor and stator poles. The driving electrostatic force and torque on the rotor poles can then be calculated to compare among different rotor pole shapes. The micromotor has an angular symmetry; hence only one sector of the micromotor, Fig. 4, is analyzed. With the rotor to stator poles ratio of 2 : 3 and the number of rotor poles Nr , the micromotor sector angle is θsec = 2rpp = 4π/Nr with a total number of sectors Nsec = Nr /2. In our analysis we exploited the periodicity of the micromotor sectors and considered only one sector for the micromotor in the finite element analysis, thereby significantly minimizing the analysis time especially for large micromotors comprised of many such sectors.The periodic potential boundary conditions are applied between all nodes at one edge of the sector and the corresponding nodes on the other side of the sector and then enforces a potential relationship between both edges of the micromotor sector. The periodic potential boundary conditions (PPBC) between two nodes from low and high edges of the micromotor sector is expressed as V (r, θ)|right edge = V (r, θ + θsec )|lef t edge

(2)

The boundary condition applies between all nodes from the lower and higher edges of the micromotor sector. The uses PPBC accounts for the effect of the potential from other attached sectors at the lower and higher edges of the simulated sector. Rotor and stator poles are modeled as perfect conductors (a very good approximation of polysilicon based on its conductivity). Hence, only air will be meshed with eight-node quadrilateral elements. Figure 5 shows a meshed micromotor sector. The Electric field should be continuous in the air region surrounding the micromotor and can not be terminated by a ground plane. Infinite elements from ANSYS (IN F IN 110) are used to terminate the air region and account for extended free space (Fig. 2). In some cases, by calculating the distance the potential decays away and becomes nonsignificant to the source potential, the zero potential line technique can be used to terminate air region and truncate the electric field. However, infinite element technique is more suitable for parametric models and more accurate representation of the field continuity. To apply the periodic potential boundary conditions in the finite element model between nodes of two edges in a micromotor sector, care should be taken when meshing the air region to generate similar elements on both edges of the micromotor sector to have efficient formulation of the periodic potential boundary conditions. Each


θsec Higher edge

Lower edge

Figure 4. 3D Schematic drawing of the micromotor sector to be used for FEA in ANSYS with the sector angle sec and total number of sectors Nsec = Nr /2.

Infinite Elements

Figure 5. A meshed micromotor sector with eight node element ended with infinite elements to account for the free space extension.

pair of nodes from both edges will have the same radial distance from the center of the micromotor and will be coupled by equation (2)(Fig. 6b). The finite element model of the electrostatic micromotor is written using ANSYS parametric design language (APDL). This model gives a flexible way to automate the meshing as well as changing the micromotor parameters for rotor and pole-shaped optimization to maximize the driving electrostatic force and torque. Maxwell stress tensor method is used to calculate the electrostatic forces on the rotor pole nodes. The driving torque is calculated by integrating the tangential force component along the perimeter of the rotor poles. Figure 7 shows a 2D simulation of the potential distribution in one micromotor sector under a PPBC. A solution for the whole micromotor can be constructed from replicating the solution of the simulated sector. For verification purposes of our 2D finite element model,a micromotor with physical dimensions from [23] are used in our finite element model and the calculated driving torques are compared to those obtained in [23]. The micromotor has a rotor radius of 50µm and gap or 1.5µm and 2.5µm. The calculated driving torques for this micromotor are 11.6pN.m and 7.0pN.m for g = 1.5µm and 2.5µm respectively. The driving torques from our 2D finite element model with the potential periodic boundary condition (PPBC) for the same micromotor


Left edge nodes PBC

Right edge nodes PBC

(a)The red line shows the nodes on both sides of the (b)The green lines between each nodes couple represent micromotor sector that will be used to specify the the constraint equation for the periodic potential periodic potential boundary conditions. boundary conditions. Figure 6. Element nodes distribution in the meshed micromotor sector.

Figure 7. Potential distribution in the air region of the micromotor sector. Note the potential has the same values at both edges of the sector. The potential did not decay to zero at the end of air region because of the infinite element (INFIN110) termination.

dimensions are 11.63pN.m and 7.02pN.m for g = 1.5µm and 2.5µm respectively. The results show a very good agreement.

3. SIMULATION RESULTS Two micromotors with rotor diameters of 400µm and 800µm and air gap of 2µm will be simulated and optimized for driving torques using the rotor pole shaping techniques. The optimization of the driving torque will be based on changing rotor pole shaping parameter θsh from 0 to rpw/3. The corresponding driving torque for each value of θsh is calculated and compared with the case of regular rotor pole shape (i.e. θsh = 0). Figure 8 shows the driving torque of the first micromotor as a function of rotor pole shaping parameter θsh . The curves in the figure correspond to different number of rotor poles. Table 2 lists the optimized dimensions of the micromotor for different number of rotor poles. The simulation results show an increase in the driving torque between 30 − 48.75% from the original driving torque with regular rotor pole shape. The second micromotor example has a rotor diameter of 800µm. Table 3, shows the optimized micromotor dimensions for different number of rotor poles. The rotor pole is again reshaped to optimize the driving torque of the micromotor. Figure 9 shows the driving torque of the micromotor versus the rotor pole shaping parameter


θsh . The new driving torque of the optimized micromotor represents an increase of the driving torque of with regular rotor pie shape. Further optimization of the driving torque of the micromotor can be achieved for different shapes of the micromotor rotor poles. The proposed shape of the rotor, although simple, proves the concept of rotor pole shaping to increase the driving torque of electrostatic micromotors with the same physical dimensions and driving voltage. Hence, lower driving voltage is required to generate the same driving torque to rotor the same micromotor.

300

280 E

260 ci)

=

0 2 240 0)

= >

0

0.1

0.2

0.3 0.4 0.5 Rotor-pole shaping angle 0sh

0.6

0.7

0.8

Figure 8. Driving torque versus the rotor-pole shaping parameter θsh for different number of rotor poles with a gap and rotor diameter of 2µm and 400µm, respectively.

Table 2. The optimized design parameters of electrostatic micromotor for different number of rotor poles (Nr ).

P arameters rpp rpw spp spw Optimum θsh Optimized driving torque Increase of driving torque

Design1 2.4o 1.2o 1.6o 1.2o 0.35o 295 pN.m 47.50%

Design2 3.0o 1.5o 2.0o 1.5o 0.312o 299 pN.m 48.75%


Design3 3.6o 1.8o 2.4o 1.8o 0.45o 289 pN.m 35.0%

Design4 4.0o 2.0o 2.67o 2.0o 0.583o 277 pN.m 30.0%

0 ci)

=

0

01

H 0) = >

0

0.05

0.15 0.2 0.25 Rotor-pole shaping angle 0sh

0.1

0.3

0.35

0.4

Figure 9. Driving torque versus the rotor-pole shaping parameter θsh for different number of rotor poles with a gap and rotor diameter of 2µm and 800µm, respectively. Table 3. The optimized design parameters of electrostatic micromotor for different number of rotor poles (Nr ).

P arameters rpp rpw spp spw Optimum θsh Optimized driving torque Increase of driving torque

Design1 1.4o 0.72o 0.95o 0.72o 0.18o 1200 pN.m 29.17%

Design2 1.5o 0.75o 1.0o 0.75o 0.155o 1180 pN.m 32.84%

Design3 1.8o 0.9o 1.2o 0.9o 0.255o 1140 pN.m 35.55%

Design4 2.0o 1.0o 1.33o 1.0o 0.255o 1100 pN.m 29.56%

Design4 2.25o 1.125o 1.5o 1.125o 0.234o 1030 pN.m 25.01 %

4. CONCLUSIONS We have presented a new technique for increasing the driving the torque of electrostatic side drive micromotors with rotor to stator poles ratio of 2:3 based on rotor pole shaping. In this technique, rotor poles are reshaped to change the electric field in the gap between rotor and stator poles to increase the driving tangential electrostatic forces acting on the rotor. A 2D parametric finite element model was used to simulate only one micromotor sector using periodic potential boundary conditions. The finite element simulations show an increase of the driving torque of up to 48.75% for micromotor with rotors of 400µm and 800µm.

ACKNOWLEDGMENTS The authors would like to acknowledge of the support of the Canadian Microelectronic Corporation (CMC).

REFERENCES 1. L.-S. Fan, Y.-C. Tai, and R. Muller, “Ic-processed electrostatic micromotors,” Sensors and Actuators 20, pp. 41–48, November 1989. 2. S. Dong, S. P. Lim, K. H. Lee, J. Zhang, L. C. Lim, , and K. Uchino, “Piezoelectric ultrasonic micromotor with 1.m mm diameter,” IEEE Trans. Ultrasonic, Ferroelectric, And Frequency Control 50, April 2003.


3. V. J. Snitka and V. Mizariene, “State-of-the-art ultrasonic micromotors and their future applications,” Proceedings of SPIE 4236, pp. 330–338, March 2001. 4. B. Wagner, M. Kreutzer, and W. Benecke, “Permanent magnet micromotors on silicon substrates,” J. Microelectromechanical System 2, March 1993. 5. H. Gucckel, K. J. Skrobis, T. R. Christenson, J. Klein, S. Han, B. Choi, E. G. Lovell, and T. W. Chapman, “Fabrication and testing of the planar magnetic micromotors,” J. Micromech. Microeng. 1, pp. 135–138, 1991. 6. M. Mehregany, P. Nagarkar, S. D. Senturia, and J. H. Lang, “Micromotor fabrication,” IEEE Trans. Electron. Devices 39, pp. 2060–1069, Sept 1992. 7. M. Baltzer, T. Kraus, and E. Obermeier, “Design and fabrication of surface micromachined micromotors with large dimensions.,” J. Micromech. Microeng 7, pp. 196–199, 1997. 8. J. H. Comtois, M. A. Michalicek, , and C. C. Barron, “Electrothermal actuators fabricated in four-level planarized surface micromachined polycrystalline silicon,” Sensors and Actuators A. 70, pp. 23–32, 1998. 9. J.-S. Park, L. L. Chu, A. D. Oliver, and Y. B. Gianchandani, “Bent-beam electrothermal actuators-part ii: Linear and rotarymicroengines,” Journal of Microelectromechanical Systems 10, pp. 255–263, June 2001. 10. W. Xinli, C. Shumei, and C. Shukang, “Advantages of electrostatic micromotor and its application to medical instruments,” Industry Applications Conference 4, pp. 2466–2468, 2002. 11. D. Polla, A. Erdman, D. Peichel, R. Rizq, Y. Gao, and D. Markus, “Precision micromotor for surgery,” 1st Annual International, Conference On Microtechnologies in Medicine and Biology , pp. 180–183, 2000. 12. A. A. Yasseen, J. N. Mitchell, D. A. Smith, and M. Mehregany, “High-aspect-ratio rotary micromotor scanners,” Sensors and Actuators 77, pp. 73–79, 1996. 13. A. A. Yasseen, S. W. Smith, F. L. Merat, and M. Mehregany, “Diffraction grating scanners using polysilicon micromotors,” IEEE J. Selected Topics Quantum Elec. 5, p. Jan./Feb., 1999 1999. 14. M. Simard, Z. Khalid, and A. Kirk, “Digital optical space switch based on micromotor grating scanners,” IEEE Photonic Technology Lerr. 18, pp. 313–315, Jan. 2006. 15. J. Klemic, A. Yasseen, J. Mitchell, and D. Smith., “A rotary electrostatic micromirror 1 8 optical switches,” IEEE J. Selected Topics Quantum Elec. 5, pp. 26–32, Jan./Feb. 1999. 16. L. Fan, “Design and fabrication of micromotors for high density data storage,” IEEE Trans. Magnetics 32, May 1996. 17. P. Dario, M. C. Carrozza, C. Stefanini, and S. D’Attanasio, “A mobile microrobot actuated by a new electromagnetic wobble micromotor,” IEEE/ASME Transction on Mechatronics 3, March 1998. 18. H. Lu, J. Zhu, and Y. Guo, “Development of a slot-less tubular linear interior permanent magnet micromotor for robotic applications,” IEEE Transaction on Magnetics 41, Oct. 2005. 19. V. D. Samper, A. J. Sangster, R. L. Reuben, and U. Wallrable, “Multistator liga-fabricated electrostatic wobble motors with integrated synchronous control,” J. Microelectromechanical System 7, June 1998. 20. D. Koester, A. Cowen, R. Mahadevan, M. Stonefield, and B. Hardy, PolyMUMPs Design Handbook. MEMSCAP, MEMS Business Unit (CORONOS), Research Triangle Park, N.C., USA, revision 9.0 ed., 2001. 21. I. Dufour, E. Sarraute, and A. Abbas, “Optimization of the geometry of electrostatic micromotors using only analytical equations,” J. Micromech. Microeng. 6, pp. 108–111, 1996. 22. T. B. Johansson, M. V. Dessel, R. Belmans, and W. Geysen, “Techniques for finding the optimum geometry of electrostatic micromotors,” IEEE Trans. Industry Applications 30, pp. 912–919, July/August 1994. 23. T. B. Johansson, M. V. Dessel, R. Belmans, and W. Geysen, “Techniques for finding the optimum geometry of electrostatic micromotors,” IEEE Trans. Industry Applications 30, pp. 912–919, July/August 1994.


Liquid crystal optics for laser beam modulation M. Kuriharaa, N. Hashimotob a Citizen Displays Co.,Ltd, Nishi-tokyo-shi, Tokyo, JAPAN b Citizen Watch Co.,Ltd, Tokorozawa-shi,Saitama, JAPAN [email protected] , [email protected] ABSTRACT Liquid crystal devices are one of the suitable devices for wave-front modulation since its extra low operating voltages such as 1~3Vrms. In this paper, we will present about liquid crystal active prisms for laser beam steering and its characteristics to the temperature change which causes an undesired optical power. Further more, we will present a recent result of a variable focus lens using quantized GRIN lens technology. Keywords: Liquid crystal, beam steering, optical power, active prism, GRIN lens

1. INTRODUCTION As recent progress of opt-mechanical engineering, active optics such as active prisms, lenses or phase compensators will play an important role to an optical apparatus. To realize active optics, LCDs are one of the suitable devices since its half-wave voltages are only a few volts and can be driven by COMS ICs. To apply LCDs to optical devices has an old history for example in Kent state or Akita univ1)2). We have demonstrated real-time holography systems using highresolution LCD panels in 19913) and in 2000, we have started math-production of LC active phase compensators for DVD pickups4). Recently, we presented liquid crystal active prisms for laser beam steerings. To steer laser beams, two methods should be considered such as diffraction and refraction. Diffraction can achieve wide angle of steering5), but it is difficult to obtain continuous steering phenomenon. To focus liquid crystal prisms, two methods are exist such as continuous ramp phase modulation6) and stair-case phase modulation7). We have selected the latter case since we can use conventional math-production methods. In this paper, we will present about liquid crystal active prisms for laser beam steering and its characteristics to the temperature change which causes an undesired optical power. Further more, we will present recent results of a variable focus lens using a quantized GRIN lens technology8).

2. LIQUID CRYSTAL WAVE-FRONT MODULATOR9) Figure 1 shows schematic diagram of Liquid crystal devices for laser beam modulations. LC molecules are homogeneous aligned to the ITO coated glass substrates. To assume that ITOs are divided into two areas (upper and lower), while we apply voltages to the lower ITO area, LC molecules will reoriented to Z axis (electric fields). In this case, effective refractive index of lower area should be no and upper area is still ne. So the optical path difference between upper and lower area is (ne-no) d. To control applied voltages precisely, we can control the tilt angle of LC molecules continuously and then effective refractive index neff becomes no 60 o

(15)

In order to improve the scan efficiency, θ s is defined newly as

θ s = 60 o - 2 β min

(16)

But the value of 2 β is not changed. And it is the biggest we can have under the condition that the minimum overlap is no less than 10 percent even though it is not in its maximum theoretically. Fourth, if 2 β min is smaller than θ r /2 , according to the position of the target slope angle θ t , there are five possibilities. (a) If θ t ＞ 60 (b) If

o

- β min , θ s and 2 β are defined as equation (16) and (14) respectively.

β min ＜ θ t ≤ 60 o - β min , θ s

is defined as equation (13),

2β =

2 β is obtained from

2 β min cos(θ s )

(17)

If the end of scan goes beyond the limitation of the window also, i.e. if inequation (15) comes into existence, θ s is not changed,

2 β is defined newly as

2 β = 60 o - (θ t - β min ) (c) If - β min ≤ θ t ≤ β min , (d) If

θs

is defined as equation (13),

2 β is obtained from equation (14).

- 60 o + β min ＜ θ t ＜ - β min , 2 β is calculated according to θ e , which is written as

θ e = θ t + β min Then,

(19)

2 β is calculated by 2 β min cos(θ e )

(20)

θ s = θ e - 2β

(21)

2β =

θs

(18)

is written as

If θ s is less than -60o, θ s is defined newly as -60o. And then combining equation (19),

2 β = 60 o + θ t + β min

Proc. of SPIE Vol. 6374 63740S-6

2 β is defined newly too as (22)

(e) If θ t

< -60 o + β min ， 2 β is set as 2 β min , and θ s is defined as -60o.

3.2 Graphs When η is 0.01, 0.05 and 0.09 respectively, according to TSA, we can get the graphs of TSA, SA, SSA by the above algorithm. Fig. 4 shows the relationship graph of TSA and SA. And the relationship between TSA and SSA is illustrated in figure 5. If η is small enough, i.e. η ≤0.01, SA will reach it’s maximum value 120o with the overlap rate higher than the value appointed. Furthermore, the smaller η is, the higher the minimum overlap rate is. It has to be admitted that when the target is near the edge of FOV, SA might not be the theoretical maximum angle with the minimum overlap higher than the value appointed. However, so long as the target is not near the edge, the algorithm in the paper is excellent which puts the target near the middle of swath covered and makes SA in maximum theoretically achieving overlap rate appointed. of Ut .nd a with dffiutt ii 120

Iii =0.01

100

80

60

40 q3=O.O9

20

6O

-40

-20

0 input value 8t

20

40

60

Fig.4.. The relationship of TSA and SA Graph of et and es with diffrent p 40

20

0

-20

,=O.O5 Iii =0.01

-BC

-60

I

-40

-20

I 0 input value Bt

I

I

20

40

Fig.5.. The relationship of TSA and SSA


60

4. CONCLUSION It is really a hard nut to crack in the controlling system of panoramic aerial Camera to give the reasonable SSA and the appropriate SA. In this paper an algorithm suitable for engineering is put forward, in which the overlap rate is no less than the value appointed. Yet it might not be the most perfect and is to be studied further especially when the target is near the edge of FOV.


Mark Position Measurement by Visual Feedback with Laser S. Nara† and S. Takahashi† †

Department of Intelligent Mechanical Systems Engineering, Kagawa University, 2217-20, Hayashi-Cho, Takamatsu-City, Kagawa 761-0396, JAPAN ABSTRACT

In this paper, we develop an observation device to measure a 3D position for a moving object by using a laser range finder and a CCD camera. Then, we propose a new method for the object recognition and the tracking control, respectively. As for the recognition, we use a special mark which is called the cross mark. For the tracking control, we construct PID control with an extended Kalman filter to realize control system without delay. Through some experiments, we verify performance of observation device and show availability of our proposed method. Keywords: Visual Feedback, Extended Kalman Filter, Cross Mark Recognition

1. INTRODUCTION Recently, many researchers are working on visual feedback which controls robot based on image information from attached camera.3–5 Today, the research is applied to various fields of industrial, thus, it contributes to an automation of various works. However, there are many works that automation is still difficult. In the above work, there is a measurement of a working radius of a crane truck. The working radius means the distance between rotation center and hook of the crane. The measurement is difficult because of the following matters. First, because the measurement is conducted in unknown environment, it is difficult to recognize target objects which include the rotation center and the hook. Next, the crane has many kinds of types, so the working radius changes from few to 100m. Finally, now that the hook is moved by an operation, the movement should be observed. For these problems, camera is the effective sensor, so some research including position measurement based on image processing and stereo camera6 is accomplished. In this paper we develop an observation device to realize the measurement. The observation device is equipped with a CCD camera and a laser range finder (LRF) and AC servo motors. In addition, the camera has a zoom function and each motor has an encoder. Using the camera, we propose a recognition method. Because a shape of the hook is not unique, it is difficult to recognize it. In order to simplify the recognition, we attach a specific mark on the hook and the rotation center. Moreover the position of the mark is measured instead of the hook and the rotation center based on the information of the camera, the LRF and encoders. Furthermore, the observation device has to track the moving mark, in order to take the mark on the camera image. Therefore, we conduct a control system which controls the posture of the observation device. This paper is organized as follows. The section 2 introduces the observation device which we developed. The section 3 explains proposed methods of the mark recognition and position measurement. The section 4 expresses the tracking control based on image information. The section 5 verifies the availability of the observation device by results of some experiments. Finally, the section 6 makes a summary. The corresponding author is S. Takahashi S. Nara: E-mail: [email protected], Phone: +81 87 864 2374 S. Takahashi: E-mail: [email protected], Phone: +81 87 864 2329

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740T, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685749

Proc. of SPIE Vol. 6374 63740T-1

Figure 1. The cross mark

2. OBSERVATION DEVICE This section introduces the observation device which we developed. This device is equipped with power-zoom CCD camera FCB-EX480B (SONY), laser range finder DME-3000 (SICK) and AC servo motors with incremental encoder FHA-8C-100 (HARMONIC DRIVE SYSTEMS). In addition, the camera can 216x zoom, combining 18x optical zoom and 12x digital zoom. In this paper, we use the mark (shown in Fig. 1) which is attached to the crane. The mark has a specific figure in a circle which has diameter of 30cm. In this paper, cross is treated as the specific figure. The details of mark recognition will be described below.

3. METHOD OF MEASUREMENT This section explains about the mark recognition and the position measurement. As for the mark recognition, we explain about the cross mark. Additionally we control zoom lens in order to keep the mark size constant on the image.

3.1. Mark recognition based on image processing We explain about mark recognition based on image processing. In this paper, the mark recognition aims to recognize the cross mark. Mark recognition for the whole image needs huge process time. Therefore, in order to narrow the search area of the mark and decrease process time, we detect circle area. 3.1.1. Detection of the circle area First we make binary image using binary process. However it is difficult to obtain an optimal binary image using general binarization which use constant threshold under the environment where illumination is changed. Also as for the variable threshold method like the moving-average method,2 it needs enormous process time. Then, in order to optimal binary image, we propose the binary method which improved on moving-average method for the mark. Let (i, j) be the coordinate of an any pixel on the image. And the brightness of the pixel is defined as f (i, j). When any pixel is binarized, an average of brightness aij is calculated in a region which has size of M ×M by following equation. aij =

1 M2

f (x, y)

(x,y)∈Rij

(x, y) is position of pixel which constitutes the region Rij , and M is set optional value experimentally. In addition, a variance of brightness Vij in the region Rij is given using the average of brightness aij . Vij =

1 M2

(aij − f (x, y))2

(x,y)∈Rij


Then using the average of brightness aij and the variance of brightness Vij , target pixel is binarized by following conditions. ⎧ 255 if Vij < VT h ∩ f (i, j) ≥ aT h ⎪ ⎪ ⎨ 0 if Vij < VT h ∩ f (i, j) < aT h B(i, j) = 255 if Vij ≥ VT h ∩ f (i, j) ≥ aij ⎪ ⎪ ⎩ 0 if Vij ≥ VT h ∩ f (i, j) < aij where, B(i, j) means binary image (shown in Fig. 2(b)). VT h is threshold of variance which is set experimentally. Further aT h means threshold of brightness, and this value is given by histogram of input image. This paper defines that brightness value 0 is black and brightness value 255 is white.

(a)

(b)

(c)

(d)

Figure 2. (a)Input (b)Binary (c)Labeling (d)Detected circle

Next median filter smoothes the binary image. Then, labels are attached to connecting regions which has white pixel based on a Scan Line Seed Fill Algorithm (shown in Fig. 2(c)). As for the labeling process, an area S and a boundary length L of a connecting region are taken. However the area S does not contain area of cross line which is shown in Fig. 1, Considering these lines area, we use an area Sˆ which is 1.16 times size of area S. Using these parameters of connecting region, a degree of circularity of connecting region e is calculated by e=

4π Sˆ L2

The degree of circularity takes the value of 0 ≤ e ≤ 1, and perfect circle has 1. Then we set a threshold and detect the connection region with a bigger the degree of circularity than the threshold (shown in Fig. 2(d)). In this paper set the threshold 0.6 in order to allow some rotation of the mark. 3.1.2. Recognition of the cross mark Here we detect the cross mark on the search region which is the circle region as mentioned. The search line which is the square region is prepared, and in Fig. 3, the search line is described as a dashed line. Detection of cross mark uses the cross candidate points which are set of a black pixel on the search line. This paper assumes that the cross implements the following conditions. (i)There are four cross candidate points on the search line. (ii)There are two pairs if the angle which cross candidate point and search center make. (iii)There are four cross candidate points that the black pixel continues to the search center. If the cross is detected by above conditions, the mark position on the image is taken as a center of search region (uk , vk ).


sICTJCeIJreL

iT

4—. sIcTJ TIUB

J (a)

(b)

Figure 3. (a)Method of cross detection (b)Detect the cross mark

3.2. Mark position measurement This section explains about the position measurement of the mark. Fig. 4 shows the position relation between observation device and mark and defines coordinates. A device coordinate is showed as OR − XR YR ZR , a camera coordinate is described as OC − XC YC ZC and a laser coordinate is expressed as Ol − Xl Yl Zl . The device coordinate exists in center of the observation device and a world coordinate corresponds with initial condition of the device coordinate, and position measurement is conducted based on this coordinate. Additionally the camera coordinate and the laser coordinate change posture, depending on the rotation of the device coordinate.

Iwe kie K

a

B @' )$

B

Figure 4. Position relation between observation device and mark

That follow describe about the position measurement of the mark. This paper supposes that the mark faces the front to the observation device. Following information is given form the observation device. A rotation angle of each axis of the observation device φenc , θenc is taken by encoders. A distance from the observation device to the mark l is obtained from the laser range finder. Furthermore the CCD camera gives the position of the mark on the image (uk , vk ) which were above mentioned. First a position of camera center which is C in Fig. 4 is calculated, considering the relation between the camera and the laser. Equation (1) and (2) express the distance between OR and C, and posture angle φcam .

l =

a 2 2

+ (l + b)

2

φcam = φenc − arctan

(1)

a

(2)

l


Then, position of the camera center C is given by the following equation using information of distance and angle given by equation (1) and (2). ⎡

⎤ ⎡ ⎤ xc 0 ⎣ yc ⎦ = Rφ Rθ ⎣ 0 ⎦ zc l ⎡

⎤ 0 sin φcam ⎦ 1 0 0 cos φcam

⎡

⎤ 0 − sin θenc ⎦ cos θenc

cos φcam 0 Rφ = ⎣ − sin φcam

1 0 Rθ = ⎣ 0 cos θenc 0 sin θenc

(3)

Then mark position B is given by following equations. xk = xc + s · u · sin φenc yk = yc + s · v zk = zc − s · u · cos φenc

(4)

where s means width of each pixel in actual space. zoom is the zoom value of the zoom lens, and l is the depth information of laser range finder. Then we calculate s as follow. s=

l xCCD · XSIZE f1 · zoom

(5)

where xCCD is width of CCD (mm), f1 means the focal length in case zoom value is 1, and XSIZE is width of image (pixel). And we set these parameters, xCCD = 3.6, f1 = 4.1, XSIZE = 320, respectively. By the way, the mark recognition needs to keep the mark size on the image constant in the situation that distance between camera and mark changes. Therefore an optimal zoom value is given following equation as transformation of equation (5).

zoom =

xCCD l · ximg f1

where ximg means width of image (mm) and given as follow. ximg = XSIZE ·

MSIZE Mpix

where MSIZE means width of the mark (mm) and Mpix is width of mark on image (pixel). And this paper MSIZE = 300 and Mpix .


4. TRACKING CONTROL This section explains a control system. The control system means the posture control in order to let the mark puts on the center of the image. In this paper, the control system uses the image information as a control input. Therefore, using mark position on the image uk and vk , error angle φimg and θimg are given by following equation. s · u k φimg = arctan l s · v k θimg = arctan l We construct the control system in order to revise the error. However, the measurement system which we developed needs calculation time for the whole processing. This processing includes the depth measurement of laser range finder, the image capturing and the image processing. Therefore, because of the calculation time, a time delay occurs to the tracking control. Then, we introduce the extended Kalman filter. Using the extended Kalman filter, we estimate the angle, angular velocity and angular acceleration xˆk = θˆk φˆk θˆ˙k φˆ˙k θˆ¨k φˆ¨k . Then using these estimated values, we improve the tracking performance. We construct PID control system and calculate control values by following equations. dφe φcmd = kP φe + kI φe dt + kD + φm dt (6) dθe + θm θcmd = kP θe + kI θe dt + kD dt φe and θe are error values. And these values are calculated as follow. φe = φimg − φd θe = θimg − θd φd and θd are desired values and this paper set desired values 0, in order to capture the mark on the image center. In addition φm and θm in equation (6) mean estimated variation of the mark based on the extended Kalman filter which is calculated by following equations. 1 ¨ 2 φm = φˆ˙k · ∆T + φˆ k · ∆T 2 1ˆ ˆ θm = θ˙k · ∆T + θ¨k · ∆T 2 2

(7)

where ∆T means the sampling time, and this paper sets it 80ms. This sampling time includes the image capturing and the image processing. In addition, let kP , kI and kD mean feedback gains. These gains are set experimentally, then, we set these parameters, kP = 1.0, kI = 0.01 and kD = 0.5. Fig. 5 shows a block-diagram of control system.

5. EXPERIMENTS This section shows results of experiments and verifies the availability of the observation device. First in order to verify a recognition performance, we conduct an experiment of recognition. Next to verify the tracking performance of the observation device, we conduct a experiment of tracking control. Finally we measure the working radius of the crane, and verify the availability of the observation device.

5.1. Structure of experimental device Fig. 6 shows the observation device which we developed in our research (shown in Fig. 6). In addition, the observation device is controlled by a control computer which has a CPU (Pentium4:3.2 GHz), a memory (1GB). Moreover, its OS is Windows XP.


Figure 5. Block diagram of control system

Figure 6. The observation device

5.2. Experiment of recognition First we verify the recognition performance of the observation device. In this experiment, the distance between the observation device and the mark changes in 10m to 50m. Changing the zoom value, the observation device recognizes the mark. An experimental result is shown in Fig. 8.

(a)

(b)

Figure 7. (a)Capture image of 50m distance (b)Capture image of 10m distance

From the experimental result, the observation device realizes the stable recognition of the mark. Fig. 7 shows the camera images when the mark exists in 50m and 10m. From Fig. 7, we checked that the zoom lens had chosen the right zoom value, since the size on image was keeping constant even if depth distance changed. In addition, Fig. 8 expresses the change of zoom value and the mark size on the image. In this experiment, we control the zoom lens to keep the mark size at 80 pixels. However it is difficult because the zoom value can choose only an integer. From Fig. 8, it keeps the mark size among from 70 pixels to 80 pixels. Though, when the zoom value is 20 times, the mark size on the image becomes small rapidly. The reason is the change of the digital zoom, however, this paper does not consider about this problem.


egomi [Iexiq] looM estono erio

mooS euIv

sic

Figure 8. Change of zoom value and mark size depend on depth distance

5.3. Experiment of tracking control This experiment verifies the tracking performance of the observation device for the moving mark. Fig. 9 shows an arrangement of this experiment. The mark which is attached to an overhead crane is arranged in 5m from the observation device. The mark is moved by operating of the overhead crane. Further, the mark movement is a pendulum movement. This experiment verifies the tracking control using the mark position which is measured by the observation device and posture of the device which given by encoder. The illumination of the environment is 270lx. Fig. 9 expresses the results of tracking the cross mark. As the experimental result, the observation device can track each mark. From the experimental result, the camera position conforms to the mark position. Therefore, the observation device can track the moving mark without time delay. 000r

A1

or

AgJ7oTJ!

r

or

A

or

8r

(V7

o

errñT [a]

(a)

(b)

Figure 9. (a)Arrangement of device in tracking experiment (b)Result of experiment for cross mark

5.4. Experiment of position measurement This experiment verifies the measurement accuracy of the observation device. In this experiment, two marks are arranged in 20m of the front of the observation device as shown in Fig. 10. Then, one mark is a static mark and other mark is a dynamic mark. The observation device measures a distance between these marks. In addition, using a total station DTM-505C (NICON), we measure the distance. The total station is measuring device on the market and this device can measure the distance with accuracy. Then, we compare these measurement results which are taken by each device. In this experiment, we suppose that the mark does not move during measurement. We conduct two kinds of experiments as follow. (a) The moving mark is moved to transverse direction, namely, when the posture of the observation device changes. (b) The moving mark moves in the depth


rPJp4u uJsIrr

3cesqA rnsIJr

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Figure 10. Arrangement of device in static measurement experiment Table 1. Measurement result

Result of (a) Distance [m] Error [mm] 2 -12.79 4 0.67 10 -17.58 20 15.17 30 -17.21 50 -2.41

Result of (b) Distance [m] Error [mm] 15 -6.76 30 -19.13 40 -8.62 50 0.22 60 -8.91 80 -28.73

direction, in other words the posture of the observation device does not change during measurement. Here, the environment of this experiment is conducted in outdoor and illumination is 15000lx. Table 1 shows measurement results of (a) and (b). In the table, a distance is the distance between two marks, and an error is the difference of results of the observation device and the total station. From the error is less than 30mm, measurement of the observation device is high accuracy.

5.5. Measurement of working radius In this experiment, the observation device measures the working radius of the crane. As shown in Fig. 11, the crane, the observation device and total station are arranged in outdoor. Recall that the working radius is the distance between the rotation center of the crane and the crane hook. In this experiment, we want to measure more than 50m working radius, however, the crane which we use has only 20m working radius. Then, we measure the mark which is attached to a cart in stead of the crane hook as shown in Fig. 11. In this paper, we call the cart the crane hook. For the measurement of the working radius, we use the observation device and the total station. Using the observation device, it is difficult to measure the actual position of the rotation center. Then, we attach three marks to the crane, and measure the position of rotation center using position of three marks. As for the total station, the position of the rotation center is measured directly without using three marks. This experiment verifies the measurement accuracy like section 5.2 using total station. In this experiment, working radius are 20m, 30m, 40m, 50m and the result of measurement is shown in Table 2. From the experimental result, since the error is within 2cm, we can say that the observation device enables high accuracy measurement.

6. CONCLUSION The objective of this paper was to measure the working radius of the crane automatically. Then, we developed the observation device with CCD camera and laser range finder. In addition, we proposed the methods of recognition, position measurement of the mark and tracking control system. As for the recognition, we used a


Total station

11 Working radius

Crane hook

Marks

Crane Total station

Cart with mark (Crane hook)

Rotation center

Observation device

Observation device

Figure 11. Arrangement of device in experiment Table 2. Result of measurement

Working radius [m] 20 30 40 50

Error [mm] -19 -14 -16 -16

special marks which are called the cross mark. As for the tracking control, we constructed PID control with the extended Kalman filter to realize control system without time delay. Then, by some experiments, we verified availability of the observation device for the measurement of working radius of the crane. As for the recognition, we realized stable recognition in controlling zoom lens and keeping the mark size on the image constant for the changing depth distance. Then the observation device can track to moving mark without time delay. Moreover, as for the measurement using the crane, the measurement result of working radius using the observation device is very accurate and the error is less than ±2cm. Therefore the observation device which is developed is available for the measurement of working radius of crane.

REFERENCES 1. S. Kaneko, K. Horiuchi and T. Honda, “Estimation of Three Dimensional Motion Based on Multiple Distributed Kalman Filters,” Transactions on the Institute of Electronics, Information and Communication Enginners J79-D-II-5, pp. 840-850, 1996. (in Japanese) 2. S. Murakami, “Image Processing Technology,” Tokyo Denki University Press, 1996. (in Japanese) 3. M. Shibata and T. Honma, “A Control Technique for 3D Object Tracking on Active Stereo Vision Robot,” IEEJ Transactions on Electronics, Information and Systems 125-3, pp. 536-537, 2005. (in Japanese) 4. K. Saruta, H. Fujimoto and Y. Hori, “Visual Servoing System with Feature Prediction using Motion Observer,” IEEJ Transactions on Industry Applications 122-5, pp. 516-521, 2002. (in Japanese) 5. T. Shiozaki and T. Murakami, “3D Position Detection of a Moving Object in Active Stereo Vision System with Multi-DOF Motion,” IEEJ Transactions on Industry Applications 125-6, pp. 561-567, 2005. (in Japanese) 6. K. Sabe, M. Fukuchi, J. S. Gutmannand, T. Ohashi, K. Kawamoto and T. Yoshigahara, “Obstacle Avoidance and Path Planning for Humanoid Robots using Stereo Vision,” Proceedings on International Conference on Robotics and Automation, 2004.


Catheter Kinematics and Control to Enhance Cardiac Ablation Yusof Ganjia , Farrokh Janabi-Sharifib a Department

of Electrical & Computer Engineering, University of Waterloo, 200 University Ave. West, Waterloo, ON, Canada N2L 3G1;

b Department

of Mechanical & Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3 ABSTRACT

Catheter ablation is the preferred minimally invasive treatment for cardiac arrhythmias. Limited maneuverability of currently available catheters undermines the success of this treatment and subjects operations to prolonged repeated attempts to pace suspicious zones and ablate the arrhythmogenic substrates under ionizing radiation of fluoroscopy. To compensate for such inefficiencies, a control system that can replace operators hand during the procedure is desired. This system should be able to direct catheter tip toward the ablation site and maintain its contact with the substrate during ablation, accelerating the process and enhancing its precision. To realize such a system, the first step is to kinematically model the catheter and to devise a control strategy to embed the kinematics of the catheter. This paper proposes a simplified approach to model and control a general singlesegment active catheter as a continuum robot. In this approach, the flexible catheter is modeled as a rigid manipulator having coupled joints. Utilizing the structural coupling of the catheter, joint-variables are reduced to actuatable parameters thus lifting some of the mathematical difficulties in formulation of a control strategy for redundant manipulators. The modeling is validated through experiments with a typical steerable ablation catheter equipped with an electromagnetic tracker in vitro. Keywords: Catheter, cardiac ablation, kinematics, modeling, control

1. INTRODUCTION Arrhythmias are erratic heartbeats caused by irregularities in the heart conduction systems. An estimated 2.3 million people in the United States1 suffer from atrial fibrillation, a common form of arrhythmia. Cardiac catheterization is the minimally invasive approach in treatment of such abnormalities. Radio frequency (RF) ablation is the standard method through which the arrhythmogenic substrate is heated to create a hyperthermic lesion, thus disabling its beating function. As a result, the re-entry circuit is disconnected or the source of irregular beats is made inactive, and the heart regains its normal beating rhythm. Catheters are the tools to perform electrophysiological mapping of the heart to find the type of arrhythmia and its substrate, and to conduct ablation in order to cure or palliate the abnormality. Catheters are either passive, i.e. they are preformed tubes whose shape is not controllable by the operator, or active, i.e. the proximal end can be flexed or extended in at most two directions similar to a hand finger taking the shape of a ’J’ letter. In both cases, the flexibility of the catheter limits the control of the operator over its proximal tip position as the operator can manipulate the catheter using its handle at distal end, outside the body. The handle typically houses a knob though which the proximal end can be deflected. When the catheter is threaded into the heart, it is subject to changes in pressure, volume and flow dynamics in intracardiac cavities. These dynamics hinder the flexible catheter from moving toward the intended position as desired. This means catheter steerability is very restricted. Mechanical deficiencies limit the navigability of the catheters which, in turn, subject catheter-based Further author information: (Send correspondence to Yusof Ganji) Yusof Ganji: E-mail: [email protected], Telephone: 1 519-888-4567, ext. 37266 Farrokh J. Sharifi: E-mail: fsharifi@ryerson.ca, Telephone: 1 416-979-5000, ext. 7097

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740U, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.686434

Proc. of SPIE Vol. 6374 63740U-1

procedures to repeated attempts to reach the target site before it is finally approached and then if contact with the target cannot be maintained long enough for pacing or ablation, closing in on the target is started over. As a result, successful ablation of hard-to-reach substrates is undermined. Cardiac contractions, respiration and patient movements during the operation impede precise targeting of the substrate. In addition, guidance of the catheter by hand has limited agility due to the natural delay in hand-eye coordination and fatigue in prolonged operations. The issues in catheter steering has motivated the design of actuated catheters,2–4 magnetic catheter navigation5 and robotic catheter control system.6 If a system can replace cardiologist’s hand in maneuvering the catheter with more agility, no fatigue and more precision, catheter ablation will be more successful and less costly. The first step to control the catheter position is to model the catheter and to identify a control method for the modeled catheter. In this paper, a typical commercially-available active catheter is modelled as a special robotic manipulator. The paper is organized as follows. Section 2 reviews the existing methods in catheter modeling. In section 3 the proposed model is described. Section 4 explains the experiments performed to verify the model. The paper is concluded by section 5.

2. RELATED WORK Catheter is expected to be modeled as a flexible mechanism that pushing, pulling and twisting actions on its distal end is translated into movements of the proximal end. Most of the literature on catheter modeling is focused on catheter simulation inside vascular structures. This simulation is mostly utilized in catheter navigation training. One approach models the catheter as a multibody system composed of a set of rigid links connected with joints.7 Angular springs fitted on the joints connecting consecutive links approximate length-wise bending of the catheter. Twisting exerted on the distal end also affects all the links. Another multibody approach8 tries to find the most plausible configuration of segments given the mechanical and physical constraints. To obtain a realistic simulation, the multi-body dynamics of the model is needed be known along with model interactions with its surrounding environment. In addition, the flexibility constraint of the catheter requires several small links to be embedded in the model. Another approach constructs a virtual catheter using finite elements based on linear elasticity theory.9 This FEM∗ -based method requires small displacements in catheter movements to remain valid. A hybrid approach have also been recorded.10 In this method, catheter is a multibody of flexible links. Multibody dynamics analysis yields the displacements and FEM characterizes deformations. Non-linear FEM is a requirement for such approaches to account for non-linearities in catheter deformations. Recently, physics-based models for catheter and guidewire simulation have been proposed.11, 12 In this model, catheter is composed of connected flexible beam elements. The model simulates non-linear behaviour of the catheter in real-time and models bending and twisting of the catheter as well. Spline-based deformable models have also been used in similar simulations for one dimensional objects. For instance, surgical threads are modeled as dynamic splines utilizing lagrangian formulations to account for continuous mass distribution along the thread.13 Such a method can be used in catheter modeling if bending and twisting is incorporated in the model. All the preceding methods are used for simulation purposes where the surrounding vascular structure is known priorly enabling the model to adjust to its environment. However, in real world, the constraining intravascular/intracardiac anatomy is not exactly known. This means the catheter model should approximate the catheter configuration with almost no information of the constraints. A few published studies have addressed catheter modeling for the purpose of control. These models, however, are mostly for prototype active catheter with in-situ actuators. For instance, the bending of a multi-segment actuated catheter is modeled as a function of its microrobot segments’ deflections.3 A model of a conventional catheter deployed in catheterization laboratories was not found in the literature. We present an approach to model the catheter as a continuum robotic manipulator based on the method developed by Walker.14, 15 ∗

Finite Element Method


C a tiacter

cg ZI, X4!

2(5

c

0 (a)

(b)

Figure 1. Catheter and its model. (a) Deflectable section of the catheter, (b) Catheter model with assigned D-H coordinate frames.

3. KINEMATIC MODEL OF THE CATHETER We hypothesize that the catheter can be modeled as a robotic manipulator. According to Robinson and Davies16 classification, continuum robots do not contain distinct joints and rigid links. Instead, they bend along their length continuously similar to elephant’s trunk and squid’s tentacles, their biological counterparts. Catheter can be called a continuum robot by this definition. In fact, it is a planar extrinsic continuum robot; it is extrinsic as the actuation mechanism transfers motion to the tip from its distal end, external to the body; and it is planar as the catheter is deflected in a single plane of bending. With this hypothesis, we formulate the kinematic model of the catheter and then verify the formulation through measurement experiments. The proposed catheter modeling is based on the kinematics approach for continuum robots, originally developed by Walker.14, 15 Catheter is modeled as a single-segment continuum robot having constant curvature along its length with no torsion† . The catheter tip can be modelled in 3D space as seen in figure 1. In this figure the assigned Denavit-Hartenberg (D-H) coordinate frames are depicted. When there is no torsion (catheter bends in a single plane) and the curvature is constant (the bent catheter is like an arc), movement along the planar catheter curve can be described in three steps: rotation by an angle θ, translation by a displacement of ||d||, and rotation by the angle θ again.14 These steps inspire us to replace rotations with two revolute joints and the translation by one prismatic joint. Hence, the flexible catheter can be modelled by rigid components. This simplified model is applied to the spatial case adding two more revolute joints as shown in figure 1(b). In this figure, the preceding angle θ is denoted by θ3 . The catheter, is composed of a bending tip and a long body as seen in figure 1(a). Since the catheter body is constrained by the lumen of the vasculature on its way to the heart, it can be modelled as a rigid prismatic joint. This assumption is valid since pushing/pulling on the distal shaft is linearly translated to the tip. As long as the motion rate of the body (d1 ) and not actual position of the model base is of concern, kinematic calculations are valid. Now, using Denavit-Hartenberg (D-H) convention, the kinematics of the catheter can be constructed (see figure 1(b)). D-H parameters are presented in table 1. Curvature constancy and the coupling †

Curvature and torsion are defined in classical differential geometry.


link 1 2 3 4 5 6

a 0 0 0 0 0 0

α 0 π/2 π/2 π/2 π/2 π/2

d d∗1 0 0 d∗4 0 0

θ 0 π − θ2∗ π/2 + θ3∗ 0 θ5∗ θ6∗

Table 1. D-H table. Joint variables are denoted with asterisks.

in the parameters yields θ5 = 3π/2 − θ3 and θ6 = θ2 . Finally based on table 1 the transformation matrix of the catheter tip position and orientation from its distal end pose is computed. Matrix (1) is the simplified forward kinematics transformation matrix computed with D-H parameters in table 1. In this matrix, c stands for cos and s denotes sin function. ⎡

2

(cθ2 ) c2θ3 − (sθ2 )

2

⎢ ⎢ − (1 + c2θ ) sθ cθ 3 2 2 ⎢ ⎢ ⎢ −cθ2 s2θ3 ⎣ 0

−cθ2 s2θ3

(1 + c2θ3 ) sθ2 cθ2

sθ2 s2θ3

− (sθ2 ) c2θ3 + (cθ2 )

−c2θ3

−sθ2 s2θ3

0

0

2

−cθ2 cθ3 d4

2

⎤

⎥ ⎥ ⎥ ⎥ d4 sθ3 + d1 ⎥ ⎦ sθ2 cθ3 d4

(1)

1

3.1. A Note on Control In order to control and plan catheter tip path, the relationship between joint-space parameters and actuation mechanism is required to be known. In the forward kinematics, four parameters of d1 , θ2 , θ3 , and d4 are present. d1 and θ2 are directly actuatable. θ3 is also actuated by the knob on the catheter handle and the angle θ3 as a function of knob rotation can be found experimentally or analytically. However, d4 is not directly actuated and is coupled with θ3 . As shown by Hannan et. al.14 the relationship between d4 and θ3 can be easily formulated. Assuming the length of bending segment of the catheter to be constant L, we have d4 =

L sin(θ3 ). θ3

(2)

Equation 2 holds as long the catheter is curved and not straight which means θ3 = 0. Thus, having three actuators there are three parameters to control. A note on the forward kinematic formulations is necessary. The bending section of the catheter is not directly connected to the ablative tip. Instead a short section, housing several electrodes comprises the final end of the catheter along with the ablative tip (see figure 1(a)). This final section is not as flexible as the bending part and cannot be deflected. In formulations presented here this section is assumed to be of length zero. In catheter navigation, the main concern is position of the catheter tip. Having the formulated kinematics, inverse kinematic position control can be achieved. Position of the catheter can be tracked using an electromagnetic tracker mounted on the catheter as used in available navigation systems.17 Having the position feedback of the catheter tip and position Jacobian derived from forward kinematics the control loop can be devised.

4. EXPERIMENTAL VALIDATION 4.1. Setup To validate kinematic formulations that calculate position of catheter tip, a fixture was built on which the catheter is mounted. The catheter handle is housed in the fixture so that push/pull/twist on the handle could be measured. The rotation of the knob is also measured using a jig with built-in protractor connected to the knob. The catheter is a standard-curve SteeroCath-T (BostonScientific, Natik, MA) ablation catheter. The catheter


Parameter Position accuracy Orientation accuracy Sensor dimensions (diameter × length) Maximum number of sensors Maximum update rate Measurement volume

Value 0.9 mm 0.8◦ 1.8 × 9 mm 4 (6DOF) or 8 (5DOF) 45 Hz (up to 6 sensors) or 20 Hz (up to 8 sensors) 500 × 500 × 500 mm3

Table 2. Electromagnetic tracking system specifications.

H (a)

(b)

Figure 2. Experiment setup. (a) measurement fixture (b) catheter tip with an Aurora sensor in front of EM field generator.

body is threaded in a PVC flexible tubing to mimic the vasculature. The tubing was fixed on a V-shaped support which keeps the tubing straight. The deflectable section of the catheter was left unsupported out of the tubing. To track the position of the desired points on the deflectable section of the catheter, Aurora system (NDI, Waterloo, Canada) was used. Aurora is an electromagnetic tracking system that enables touchless position and orientation measurement of an object placed in the volume covered by its (electromagnetic) field generator. Sensor coils are mounted on the object of interest for tracking. The specifications of the system are summarized in table 2. The measurement fixture and the catheter tip equipped with an Aurora tracker are shown in figure 2. In the experiments, one sensor was mounted at the tip of the deflecting section of the catheter, and provided the position of the tip. The other sensor was fixed at the other end of the deflecting section where joints 2 and 3 intersect in the model (figure 1(b)). With this sensor configuration, parameters θ2 and θ3 was measured and their relationship with twisting of the catheter handle and rotation of the knob was investigated respectively.

4.2. Experiments and Results Assuming that the effects of push/pull on the catheter handle, twisting the handle and rotating the knob to bend the distal end section are decoupled motions, meaning their contribution to the pose of the catheter tip is independent of each other, the experiments were conducted. This assumption is evident in the catheter modeling formulations as well (see forward kinematics transformation matrix (1)). According to (1) position vector of the catheter tip is P =

−cθ2 cθ3 d4

sθ2 cθ3 d4

d4 sθ3 + d1


.

(3)

To validate this vector formula, the catheter was translated or rotated for each degree of freedom and the compliance of the position readings with the calculated position vector was studied. In order to unveil the possible hysteresis in catheter motion, steering in any direction was followed by steering in the reverse direction. Figure 3 illustrates the measured readings when catheter is pushed/pulled or deflected. From (3), it is expected that translation of catheter tip linearly translates catheter tip in Z direction, (d1 ). Figure 3(a) verifies this relationship. X and Y elements of the measured position vector exhibit small changes that can be attributed to Aurora system’s resolution and precision of position readings as well as the effects of catheter and sensor weight. Z element of the position vector changes linearly as expected during the course of backward and forward translation. To verify the validity of vector (3) in terms of θ3 , i.e. when catheter tip is bent, catheter was placed so that its planar deflection lies in X − Z plane while weight vector of the catheter is along Y axis. Figure 3(b) and (c) show the measured and expected position vector elements. The effect of hysteresis in backward and forward motion is apparent in the measured data. The X and Z profiles follow the expected curve but the dynamic effect of weight is not negligible in Y measurements and induces a large error compared to X and Z measurements. Table 3 presents the error values associated with kinematic calculations. 0.5

50

0

0.4

45

0.3

40

0.2

35

0.1

30

−0.5

−1.5

Y (mm)

X (mm)

−1

−2 −2.5 −3 −3.5 −4

Z (mm)

0.5

0

20

−0.2

15

−0.3

10

−0.4 0

10

20 30 Handle Displacement (mm)

40

−0.5

50

25

−0.1

5 0

10


40

0

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0

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40

50

(a) 55

5

50 40

50 0

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40 35 30

Measured Z (mm)

Measured Y (mm)

Measured X (mm)

45

−5

−10

25

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−15 20 15 −60

20

−30

−40

−20

0 20 Deflection Angle (deg)

40

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−20


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(b) 55

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Calculated Z (mm)

20 Calculated Y (mm)

Calculated X (mm)

45

−5

−10

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−15 20 15 −60

−30

−40

−20


40

60

80

−20 −60

−40

−20


40

60

80

−40 −60

(c) Figure 3. Calculated and measured position profiles, (a) measured position during translation along d1 (push/pull), (b) measured position while deflecting the catheter tip, (c) expected position profile (as a result of knob rotation).


Parameter d1 θ3

X -1.44±0.98 mm 0.29±4.38 mm

Y -0.15±0.19 mm 4.84±4.52 mm

Z 0.59±0.51 mm -1.78 mm±4.9 mm

Table 3. Error values in position calculations (mean±standard deviation)

Tip Twist Angle (deg)

150

100

50

0

−50

0

50

100

150 200 250 Handle Twist Angle (deg)

300

350

Figure 4. Catheter tip rotation angle (θ2 )

To study the effect of catheter twist, the rotation angle was measured directly. Figure 4 illustrates the measured rotation of catheter tip in response to handle rotation. Change of rotation direction induces hysteresis again as can be seen in the figure. In addition, figure 4 reveals that twisting of the handle does not create the same rotation at the tip. It is noted that though the rotations are not equal, their relationship is linear with a correlation coefficient of 0.9861 at confidence level of 95%. The results presented above indicate that the rigid model of the flexible catheter approximates the catheter with a bounded error especially in the absence of external forces and dynamics. The aim of this study is to achieve a model to be utilized in catheter position controller design, and the proposed simplified model is the first step to this end. Evidently, the controller should compensate for any unmodeled non-linearities.

5. CONCLUSION Dexterity of the current state-of-the-art catheters is very limited. In order to enhance the steering of the catheter in procedures like ablation, a control system that can direct the catheter and react to disturbances faster than human operator is desired. In an attempt to achieve such a system, a rigid model for a deflectable catheter is proposed and the kinematic relations of the model are derived. The validity of the predicted catheter tip position is tested through experiments. Based on this model, position control will become feasible. Realizing such a control system is the future work of the authors.

ACKNOWLEDGMENTS The authors wish to thank Devin Ostrom, Ryerson University, for his efforts in the design and preparation of the measurement fixture.


REFERENCES 1. A. Go, E. Hylek, K. Phillips, Y. Chang, L. Henault, J. Selby, and D. Singer, “Prevalence of Diagnosed Atrial Fibrillation in Adults. National Implications for Rhythm Management and Stroke Prevention: the Anticoagulation and Risk Factors In Atrial Fibrillation (ATRIA) Study,” May 2001. 2. K. Ikuta, H. Ichikawa, K. Suzuki, and D. Yajima, “Multi-degree of freedom hydraulic pressure driven safety active catheter,” in Robotics and Automation (ICRA 2006). Proceedings of the 2006 IEEE International Conference on, pp. 4161–4166, May 2006. 3. Y. Bailly and Y. Amirat, “Modeling and control of a hybrid continuum active catheter for aortic aneurysm treatment,” in Robotics and Automation (ICRA 2005). Proceedings of the 2005 IEEE International Conference on, pp. 924–929, April 2005. 4. Y. Haga, Y. Muyari, T. Mineta, T. Matsunaga, H. Akahori, and M. Esashi, “Small diameter hydraulic active bending catheter using laser processed super elastic alloy and silicone rubber tube,” in Microtechnology in Medicine and Biology, 2005. 3rd IEEE/EMBS Special Topic Conference on, pp. 245–248, 2005. 5. C. Pappone, G. Vicedomini, F. Manguso, F. Gugliotta, P. Mazzone, S. Gulletta, N. Sora, S. Sala, A. Marzi, G. A. amd Laura Livolsi, A. Santagostino, and V. Santinelli, “Robotic Magnetic Navigation for Atrial Fibrillation Ablation,” Journal of the American College of Cardiology 47, pp. 1390–1400, April 2006. 6. W. Saliba, J. Cummings, S. Oh, Y. Zhang, T. Mazgalev, R. Schweikert, J. Burkhardt, and A. Natale, “Novel Robotic Catheter Remote Control System: Feasibility and Safety of Transseptal Puncture and Endocardial Catheter Navigation,” J Cardiovasc Electrophysiol 17, pp. 1–4, 2006. 7. S. Cotin, S. Dawson, D. Meglan, D. Shaffer, M. Ferrell, R. Bardsley, F. Morgan, T. Nagano, J. Nikom, P. Sherman, et al., “ICTS, an interventional cardiology training system.,” Stud Health Technol Inform 70, pp. 59–65, 2000. 8. M. Kukuk and B. Geiger, “A real-time deformable model for flexible instruments inserted into tubular structures,” in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002: 5th International Conference Proceedings, pp. 331 – 338, (Tokyo, Japan), September 2002. 9. W. L. Nowinski and C.-K. Chui, “Simulation of interventional neuroradiology procedures,” MIAR , p. 87, 2001. 10. Y. Wang, C. Chui, H. Lim, Y. Cai, and K. Mak, “Real-time interactive simulator for percutaneous coronary revascularization procedures,” Computer Aided Surgery 3(5), pp. 211–227, 1998. 11. S. Cotin, C. Duriez, J. Lenoir, P. F. Neumann, and S. Dawson, “New approaches to catheter navigation for interventional radiology simulation.,” in MICCAI (2), J. S. Duncan and G. Gerig, eds., Lecture Notes in Computer Science 3750, pp. 534–542, Springer, 2005. 12. J. Lenoir, S. Cotin, C. Duriez, and P. Neumann, “Interactive physically-based simulation of catheter and guidewire.,” Computers & Graphics 30(3), pp. 416–422, 2006. 13. J. Lenoir, P. Meseure, L. Grisoni, and C. Chaillou, “Surgical thread simulation,” in Modelling and Simulation for Computer-aided Medecine and Surgery (MS4CMS), pp. 102–107, November 2002. 14. M. W. Hannan and I. D. Walker, “Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots,” Journal of Robotic Systems 20, pp. 45–63, February 2003. 15. B. A. Jones and I. D. Walker, “Kinematics for multisection continuum robots,” IEEE Transactions on Robotics 22, pp. 43–55, February 2006. 16. G. Robinson and J. Davies, “Continuum robots-a state of the art,” Robotics and Automation, 1999. Proceedings. 1999 IEEE International Conference on 4, pp. 2849–2854, 1999. 17. S. A. Ben-Haim, “Catheter navigation in modern electrophysiology,” Journal of Cardiovascular Electrophysiology 11, pp. 1193–1195, November 2000.


An Investigation of Phenomenal Parasitics and Robust Control of Parallel-Plate Electrostatic Micro Actuators Guchuan Zhua , Jean-François Chianettab , Mehran Hosseinib , and Yves-Alain Peterb a Department of Electrical Engineering, Ecole ´ Polytechnique de Montréal, C.P. 6079, Succursale centre-ville, Montreal, QC, Canada H3C 3A7 b Engineering Physics Department, Ecole ´ Polytechnique de Montréal, C.P. 6079, Succursale centre-ville, Montreal, QC, Canada H3C 3A7 ABSTRACT This paper extends the modeling of the effect of fringing field, proposed in our recent work,1 to more generic devices: electrostatic parallel-plate actuators with deformations. Though these devices can be model as two parallel capacitors with a variable factor depending on the displacement,2 it is difficult to determine the analytical expression of such a function. It is shown that, like the effect of fringing field, the modeling error of the effective actuator due to deformations can be compensated by introducing a variable serial capacitor. When a suitable robust control is used, the full knowledge of the introduced serial capacitor is not required, but merely its boundaries of variation. Based on this model, a robust control scheme is constructed using the theory of input-to-state stability (ISS) and backstepping state feedback design. This method allows loosening the stringent requirements on modeling accuracy without compromising the performance. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation. Keywords: Phenomenal parasitics; modeling of electrostatic MEMS; FEM based simulation; input-to-state stability; robust nonlinear control.

1. INTRODUCTION In the most popular model of electrostatic parallel-plate actuators, the moveable plate is supposed to be a rigid body without deformation and only the main electrical field (perpendicular to both electrodes) is considered. The capacitance of such structures is computed by A , (1) C= G(t) where A is the area of electrodes, G the air gap, and the permittivity in the gap. This model is subject to modeling errors due to, e.g., deformations, fringing field effect, and parasitics related to the layout. Fabrication deviations and environmental fluctuations may also introduce parameter variations, affecting the reliability of the model. The performance of the controller obtained from the simplified model might be compromised for applications where the precise positioning is required, e.g. adaptive optics.3 To assure a high performance, one might want to use more accurate model. However, this might result in more complicated mathematical model and, consequently, make the control system difficult to implement and unreliable. For examples, modeling the fringing field and deformations leads in general to distributed parameter systems described by partial differential equations. The control of such systems requires distributed sensing and actuation, which is very hard to implement for microsystems. We have proposed, in our recent work,1 to model the effect of fringing field by a serial capacitor. Combined with an appropriate robust control, the full knowledge of the introduced serial capacitor is not required, but only its boundaries of variation, which can be obtained by simulations using off-the-shelf commercial software tools, e.g. ANSYSTM , COMSOLTM , and CoventorWareTM , or by experimental measurements. This ideal considerably simplified the complexity of the model without compromising the performance of the control system. In this work, we will extend this method to Further author information: (Send correspondence to G. Zhu or Y.-A. Peter) G. Zhu: E-mail: [email protected] Y.-A. Peter: E-mail: [email protected] Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740V, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.692301

Proc. of SPIE Vol. 6374 63740V-1

deformed structure and will shown that in the presence of deformation, the modeling error can also be compensated by introducing a suitable serial capacitor. The robust control scheme used in this work is based on the theory of input-to-state stabilization (ISS) and backstepping state feedback design. The nominal model used in control law design is the simplified parallel-plate actuator, but the controller is made robust against parasitics and parametric uncertainties. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation. The rest of the paper is organized as follows. Section 2 models the capacitance of 1DOF parallel-plate electrostatic actuator in the presence of deformation. Section 3 is devoted to the construction of control law. The simulation results are reported in Section 4 and Section 5 contains some concluding remarks.

2. MODELING OF PARALLEL-PLATE ELECTROSTATIC MICRO ACTUATORS IN THE PRESENCE OF PHENOMENAL PARASITICS 2.1. Modeling of Ideal Devices Denote by m the weight of the moveable plate, by k the elastic constant of the suspension beams, and by b the damping coefficient of the structure. The equation of motion of the actuator is then given by ¨ + bG(t) ˙ mG(t) + k(G(t) − G0 ) = F (t),

(2)

where G0 is the zero voltage gap and F (t) the force due to electrical field. Let Q(t) be the charge on the device and Va (t) the actuation voltage. One can deduced from the capacitance (1) the electrostatic force of ideal parallel-plate actuator which reads F (t) =

AV 2 Q2 (t) Va2 ∂C =− 2a =− . 2 ∂G 2G (t) 2A

(3)

Note that the electrostatic force is always attractive regardless of the polarization of the control signal. Assuming the system started operating from an initially uncharged state at t = 0, then the charge on the electrodes at the time t is: t

Q(t) = 0

Is (τ )dτ,

(4)

or equivalently ˙ Q(t) = Is (t),

(5)

where Is (t) is the source current through the loop resistor R. By a simple application of Kirchhoff’s Voltage Law we obtain:4 1 Q(t)G(t) ˙ Q(t) = Vs (t) − , (6) R A where Vs (t) is the source voltage, which is the actual control variable.

2.2. Capacitance Model of Deformed Devices When deformation happens, the displacement is no longer uninform: the center portion is largest whereas the portions near the step-up supports hardly move at all. The deformed device can be modeled as the sum of two onedimensional (1-D) capacitances: a variable capacitor, representing the effective actuator, in parallel with another one whose equivalent surface is parameterized by the air gap, as shown in Fig. 1. The total capacitance of such devices can be expressed as:2 C = Ca + Cp ∝

γ 1−γ + , G G0

(7)

where Ca is the capacitance of the actuator, Cp is the the capacitance of the parallel capacitor, and γ is a proper function that increases as the gap closes. To illustrate the effect of deformation, we have simulated a micro structure using finite element methods (FEM) based MEMS CAD software package CoventorwareTM . The electrodes are square of 206×206 µm2 and the moveable plate is


+0 KI

,

=

Figure 1. Schematic representation of the deformed structure and its equivalent circuit.

—— O.M

,I.?3, •j t.•á

111.1

Figure 2. FEM based simulation of a deformed micro-structure.

sustained by four beams clamped at the corners. The thickness of the moveable plate is 1.5088µm and the initial gap is 5µm. The deformation and the distribution of charge density at a position of deflection is shown in Fig. 2. The capacitance of the device obtained from CoventorWareTM simulation and the one calculated from the rigid body approximation (1) are given in Table 1. It can be seen that for small deflections, the deformation is not significant and the capacitance of the simulated device is higher than the one calculated from the rigid body approximation (about 17% higher at the zero voltage position). This is due to the unmodeled phenomena, e.g., the effect of fringing field. For large deflections, the deformation becomes important. In this case, the capacitance calculated from (1) is overestimated. For a deflection of 4.8431 µm, the modeling error can be as high as 47%. Note that the effect of fringing field decreases as the gap closes. Therefore, the modeling error for large deflections is mainly due to the deformation. Obviously, it is very difficult to determining the function γ in (7), because it changes with the structure, the geometry, and the material of the actuator. To overcome this difficulty, we adopted the method developed in our recent work1 by modeling the device as an ideal rigid body, called also the nominal structure, combined with an appropriate variable serial capacitor. The capacitance of the nominal structure, Ca , follows the ideal model (1), but uses an effective area Aef f to compensate the modeling errors at the zero voltage position. Since the deformation has effect of decreasing the capacitance and the effect of fringing field is maximum at the initial gap, the nominal structure gives overestimated capacitance for any non zero deflection. The introduced serial capacitor has the effect of reducing the total capacitance and, hence, it will eliminate the modeling error. The value of the introduced serial capacitor is a function of the gap and can be expressed as 1 1 1 = − . Csp Creal Ca

(8)

Obviously, since Creal is unknown, one can not determine Csp . However, as mentioned earlier, for an appropriate robust control scheme, the full knowledge of the relationship between serial capacitance and deflection is not required, but only its variation boundaries.


Table 1. Capacitances for different deflections.

Deflection (µm) 0 0.6459 1.1798 1.9488 2.4944 3.1086 3.5897 4.1133 4.5522 4.7492 4.8431

Capacitance (pF) FEM Simulation Rigid Body Approximation 0.0909 0.0751 0.1004 0.0863 0.1103 0.0983 0.1292 0.1231 0.1485 0.1499 0.1811 0.1986 0.2220 0.2663 0.3049 0.4236 0.4973 0.8386 1.0253 1.4972 1.6286 2.3934

4 FEM based simulation 3.5

rigid structure approximation nominal rigid structure

Capacitance (pF)

3

equivelant serial capacitor

2.5 2 1.5 1 0.5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized Deflection

Figure 3. Capacitance of the simulated device, the rigid structure approximation, the nominal structure, and the introduced serial capacitor.

Figure 3 shows the capacitance of the simulated device, the rigid body approximation, and the nominal structure. The introduced serial capacitor is computed from (8) using the capacitances of the simulated device and the nominal structure. The value of the nominal capacitor at the initial gap is equal to 0.0909 pF (the same as the real capacitor at this position). Except for the initial separation gap, there is a difference between the value of nominal capacitor and the real one. The role of the serial capacitor is to compensate this difference. As shown in Fig. 3, this serial capacitance is infinite at the initial gap and has a minimum that is about 0.7126 pF for this structure. Since the smaller the introduced serial capacitance, the bigger the influence of modeling errors, we can use this value to determine the boundary of the introduced serial capacitor in the model. As the introduced serial capacitor and the parallel capacitor due to the deformation are essentially unknown, following the terminology of Ref. 2, we can call them phenomenal parasitics. Obviously, the effect of fringing field can also be considered as serial parasitics.1 A generic capacitance model of the deformed parallel-plate is given in Fig. 1, in which Cpp is composed of different unmodeled parallel capacitors due to, e.g., the deformation and the layout.


2.3. Dynamics of the Actuator in the Presence of Parasitics When taking into account for parasitics, the dynamic equation of the electrical subsystem is given by1 G˙ G0 1 G ˙ Vs − Qa (t) = + ρs + Rρp Qa , G A A G0 R 1 + ρp ρs + ρp G0 where ρp =

(9)

Cpp C0 , ρs = , C0 Csp

with C0 = Aef f /G0 , the capacitance of the nominal structure at the initial gap G0 . In our modeling, ρp and ρs represent the influence of parasitics. When their value is set to zero, the dynamics of the electrical subsystem will be reduced to the one for ideal devices given in (6). It can be seen from (9) that the parallel parasitic capacitance will not change the static behavior of the device. However, the dynamics of the electrical subsystem will be affected: the bigger the parallel parasitic capacitance, the slower the dynamics of the driving circuit. Consequently, the performance of the system will be degraded if the parallel parasitic capacitance is not taken into account in the design of the control system. The serial parasitic capacitance will affect both the static and the dynamic behavior of the system. It is straightforward to show that the serial parasitic capacitance will change the position of pull-in. Note that since the nominal plan is an ideal rigid body, the mechanical subsystem still follows (2) with electrostatic force given in (3). Therefore the parasitics affect only the dynamics of the electrical subsystem. To make the system analysis and control design easier, we transform (2) and (9) into normalized coordinates by changing the time scale, τ = ω0 t, and performing a normalization as follows:5 x=1−

G Qa Vs Is , q= , u= , i= , r = ω0 C0 R, G0 Qpi Vpi Vpi ω0 C0

where Vpi = 8kG20 /27C0 is the nominal pull-in voltage, Qpi = 32 C0 Vpi the nominal pull-in charge, ω0 = k/m the undamped natural frequency, and ζ = b/2mω0 the damping ratio. We then have dq 1 2 dx = u − (1 − x)q − ρs q + rρp q . (10) dτ r (1 + ρp (1 − x) + ρp ρs ) 3 dτ Let x1 = x, x2 = v, and x3 = q 2 . System (2)-(10) can then be written in the normalized coordinates as dx1 =x2 dτ dx2 1 = − 2ζx2 − x1 + x3 dτ 3 √ 4 x3 dx3 =β u − 2(1 − x1 )x3 − 2ρs x3 + 2rρp x2 x3 dτ 3

(11a) (11b) (11c)

where

1 r (1 + ρp (1 − x) + ρp ρs ) is a function of deflection. System (11) is defined on the state space X = (x1 , x2 , x3 ) ⊂ R3 | x1 ≤ 1, x3 ≥ 0 . β=

(12)

Note that the considered actuator exhibits switching behavior. First of all, when the moveable plate hits the fixed one (x1 = 1), the dynamics of the mechanical subsystem collapse.6 In addition, q = 0 (x3 = 0) is a singular point at which System (11) is not linearly controllable (see, e.g., Ref. 6). However, it is easy to see that the system is symmetric except for the sign of the charge. For simplicity, we ignore the contact dynamics and consider only the branch defined by (11c). Consequently, the stability property obtained through the proposed control will hold locally. Since in what follows we deal only with normalized quantities, we can use t to denote the time and omit the qualifier “normalized.”


3. ROBUST CONTROL DESIGN 3.1. Preliminaries of input-to-state stability The concept of input-to-state stability is introduced by Sontag7 and ISS-based design is a popular tool in the field of system control. We present here only the notations required in the development of the control law. The interested reader is referred to, for example, Ref. 8, 9 for a formal presentation. The following comparison functions are required for presenting the method of input-to-state stabilization. A function α : [0, a) → [0, ∞) is said to belong to class-K if it is continuous, strictly increasing, and α(0) = 0. If a = ∞ and α is unbounded, the function is said to belong to K∞ . A function β : [0, a) × [0, ∞) → [0, ∞) is said to belong to KL if it is nondecreasing in its first argument, nonincreasing in its second argument, and lims→0+ β(s, t) = limt→∞ β(s, t) = 0. The system x˙ = f (x, u)

(13)

is said to be input-to-state stable if for any x(0) and for any input u(·) continues and bounded on [0, ∞) the solution exists for all t ≥ 0 and satisfies |x(t)| ≤ β(x(0), t) + γ

sup u(|τ |) , ∀t ≥ 0,

0≤τ ≤t

(14)

where β(s, t) ∈ KL and γ(s) ∈ K. System (13) is ISS if and only if there exists a smooth positive define radially unbounded function V and class K∞ functions α1 and α2 such that the time derivative of V along the solutions of (13) verifies ∂V V˙ = f (x, u) ≤ −α1 (|x|) + α2 (|u|). ∂x

(15)

The function V satisfying the above inequality is called ISS-Lyapunov function. Note that the method of ISS provides a convenient framework for robust system control, which amounts to finding a control with which the closed-loop system is stable with respect to the disturbances, considered now as the inputs to the system.

3.2. Control synthesis In this work, we consider both the parasitics and parametric uncertainties, such as the variations of damping coefficient and loop resistance. We make then the following assumptions on the uncertainties in System (11). A SSUMPTION 1. The parasitic capacitances are bounded by known constants: 0 ≤ ρp ≤ ρ¯p , 0 ≤ ρs ≤ ρ¯s .

(16)

A SSUMPTION 2. The damping ratio is positive and bounded and can be written as: ζ = ζ0 + ∆ζ,

(17)

where ζ0 is positive-valued representing the nominal damping ratio and ∆ζ the modeling error. A SSUMPTION 3. The upper and lower bounds of the resistance in the loop, r, are known: 0 < r ≤ r ≤ r.

(18)

Since x1 ≤ 1, β in (12) may be bounded as follows: 0 < β ≤ β ≤ β,

(19)

where β = 1/r. Note that since the electrostatic force is always attractive, the control allowing the moveable plate to move as far as possible beyond the initial gap is the one that can remove the charge from the device in an arbitrary small


time interval. However there is no equilibrium beyond the zero voltage gap and the mechanical subsystem (11-a)-(11-b) globally exponentially converges to the origin with zero input (x3 = 0).10 This implies that x1 should not be smaller than −1. Therefore, in a normal operational condition, β should be lower bounded by 1

. r 1 + ρp (2 + ρs )

(20)

|β − β0 | ≤ β − β ∆β.

(21)

β= Furthermore, the variation of β is denoted by

where β0 is the nominal value of β. In this work, we will consider the tracking problem with y = x1 as the output. Following a classical approach, we choose a sufficiently smooth reference trajectory yr for x1 as a function of time and then make this trajectory attractive. A recursive procedure, called also backstepping design (see, e.g., Ref. 9 for a detailed presentation of this technique), is used in the design of the control law, which consists of, for System (11), the following three steps. Step 1. Consider the control of the subsystem (11a) with x2 as a virtual input. Let z1 = x1 − yr be the position tracking error and select a Lyapunov-like function 1 V1 = z12 . 2 The time derivative of V1 along the solutions of (11.a) is V˙ 1 = z1 (x2 − y˙ r ). The desired input (also called stabilizing function) can be chosen as: x2d = y˙ r − k1 z1 , k1 > 0.

(22)

Step 2. Consider now the subsystem (11a)-(11b) with x3 as a virtual input. Define z2 = x2 − x2d and augment V1 to yield: 1 V2 = V1 + z22 . 2 Letting z3 = x3 − x3d , the time derivative of V2 along the solutions of the corresponding subsystem is given by V˙ 2 = − k1 z12 + z2 (z1 + x˙ 2 − x˙ 2d ) 1 = − k1 z12 + z2 z1 − 2(ζ0 + ∆ζ)x2 − x1 + (z3 + x3d ) − x˙ 2d . 3 In order to counteract the uncertainty ∆ζ, a nonlinear damping term should be added to the stabilizing function. The desired input in this case is of the following form:

(23) x3d = 3 2ζ0 x2 + x1 + x˙ 2d − z1 − κ2 ζ0 x22 z2 − k2 z2 , where k2 > 0 and κ2 is the gain of the nonlinear damping term, the lower bound of which will be given latter on. Step 3. Finally the Lyapunov function candidate for System (11) is chosen to be 1 1 1 1 V3 = V2 + z32 = z12 + z22 + z32 2 2 2 2 whose time derivative along the solutions of System (11) is given by z 2 − 3(ab1 + b2 ) + 6∆ζb1 x2 V˙ 3 = − k1 z12 − k2 z22 − 2∆ζx2 z2 − κ2 ζ0 x22 z22 + z3 3 √ 4 x3 u − 2x3 (1 − x1 ) + 2rρp x2 x3 − 2ρs x3 +β 3


(24)

where 1 a = − 2ζ0 x2 − x1 + x3 , 3

b1 =2ζ0 − k1 − k2 − κ2 ζ0 2x2 z2 + x22 ,

b2 =yr(3) + k1 y¨r + y˙ r + κ2 ζ0 x22 + k2 x˙ 2d . Let U =

4√ 3 x3 u.

The proposed backstepping controller is given by:

3 z2 1 1 z 2 2 1 ab1 + b2 − − k3 z3 − κ31 ab1 + b2 − z3 − κ32 ζ0 b21 x22 z3 β 9 β β 9 β 1 1 − κ33 x22 x23 z3 − κ34 x23 z3 β β

U =2x3 (1 − x1 ) +

(25)

with k3 > 0, where κ31 , κ32 , κ33 , and κ34 are the gains of the nonlinear damping terms. T HEOREM 3.1. For System (11) with the uncertainties satisfying Assumptions 1-3 and yr being sufficiently smooth, the backstepping controller (25) with κ2 >

1 1 1 , κ31 > 1, κ32 > , κ33 > 1, κ34 > 2 , 2ζ0 ζ0 r

(26)

renders the closed-loop error dynamics locally ISS with respect to the uniformly bounded inputs ∆β, ρp , ρs , and ∆ζ. Furthermore, the ultimate bound for the tracking error z1 can be rendered arbitrarily small by picking the feedback gains k1 , k2 , and k3 large enough. The proof the the above theorem is given in Appendix A. Note that the actual control u is singular when x3 = 0. This is due to the uncontrollability of System (11) at the zero voltage position. However this situation happens only at this point. It is easy to see that System (11) is stabilizing at this position with an input u = 0. By defining an open ball Bε = {X| X < ε} ⊂ X of radius ε centered at the origin, where X = (x1 , x2 , x3 )T and · the usual Euclidean norm, a more practical control law can be expressed as ⎧ ⎨ √3 U, for X ∈ / Bε u = 4 x3 (27) ⎩ 0, for X ∈ Bε where U is given by (25).

3.3. Reference Trajectory Design In general, reference trajectories can be chosen to be any sufficiently smooth function t → y(t), connecting the initial point at time ti to a desired point at time tf , such that the initial and final conditions are verified. The reference trajectory used in our control schemes is a polynomial of the following form: yr (t) = y(ti ) + (y(tf ) − y(ti ))τ 5 (t)

4

ai τ i (t),

(28)

i=0

where τ (t) = (t − ti )/(tf − ti ). For a set-point control, the coefficients in (28) can be determined by imposing the initial and final conditions ˙ f ) = y¨(ti ) = y¨(tf ) = y (3) (ti ) = y (3) (tf ) = 0, y(t ˙ i ) = y(t which yield a0 = 126, a1 = −420, a2 = 540, a3 = −315, and a4 = 70. The polynomial in (28) is one of the most used reference trajectories in flatness based control. A more general formulation can be found in Ref. 11.


(b)

0.5



(a)

0.4 0.3 ρ = 0.1276 s

0.2

ρs = 1.0

0.1 0 0

ρs = 2.0 5

10

0.5 0.4 0.3 ρp = 1.0

0.2

ρp = 3.0

0.1

ρ = 5.0 p

0 0

15

5

10

15

Normalized Time

Normalized Time

Figure 4. Influence of parasitics: (a) variation of serial parasitics ρs ; (b) variation of parallel parasitics ρp . (b)

0.5



(a)

0.4 0.3 0.2 ζ = 0.2 ζ = 5.0

0.1 0 0

5

10

15

0.5 0.4 0.3 0.2 r = 0.5 r = 2.0

0.1 0 0

5

10

15

Normalized Time

Normalized Time

Figure 5. Robustness against parametric uncertainties: (a) variation of damping coefficient ζ; (b) variation of resistance in the loop r.

4. SIMULATION STUDY In our simulation study, the parameters of the nominal plant are ζ0 = 1, r0 = 1, ρp = 0, and ρs = 0. The actuator is supposed to be driven by a bipolar voltage source. The boundaries of parasitics and parametric uncertainties are fixed to be ρs = 2, ρp = 5, r = 2, and r = 0.5. We have then β = 0.0238. Note that a small bias voltage is applied to the device in order to avoid the singularity at the origin. Firstly we consider only the influence of the parasitics. Based on the simulation in Section 2.2 we have for the device considered ρsmax = 0.1276. Therefore ρs >> ρsmax and the tested system should support more important modeling errors. It can be seen from Fig. 4 that in the simulated range of variation of the parasitics, the system performs nearly identically.


The second test is concerned with the uncertainties in the damping coefficient ζ and the resistance in the loop r. It is shown (see Fig. 5) that the system still performs very well even for very important parameter variations.

1 0.8 0.6 0.4 0.2 0 0

5

10 Normalized Time

Figure 6. Simulation results of set-point control.


15

In the last test, we simulated the system for set-point control. The parameters for the simulated system are chosen as ρs = 0.1276, ρp = 1.0, ζ = 0.5, and r = 1.5. It can be seen from Fig. 6 that the performance of the system is quite uniform for different deflections. Note that the performance of the controller presented in this work is quite similar to the one obtained by cascade ISS synthesis proposed in our previous work.1

5. CONCLUSIONS This paper considered the effect of deformation of the moveable plate of parallel-plate electrostatic micro-actuators and extended the idea of introducing a variable serial capacitor to compensate modeling errors due to deformation. Combined with an appropriate robust control scheme, the exact analytical expression of the serial capacitance is not required, but merely its boundary represented by the ratio of its minimal value and the equivalent nominal capacitance at the initial position. CoventorWareTM has been used to estimate the variation range of the introduced serial capacitor for a microstructure. A state feedback robust control scheme using the technique of ISS and backstepping design is constructed and the closed-loop stability of the system is demonstrated. Numerical simulations show that the proposed control system has satisfactory performance and robustness vis-à-vis parasitics and parametric uncertainties. It has been shown that presenting different type of modeling errors by parasitics, using numerical simulation or experimental measurements to determine the variation boundaries of parasitics, and then employing robust control techniques will considerably simplify the modeling of micro-devices. Obviously, this idea can be applied to micro-devices with more complex structure for which building accurate model is a very challenging task.

APPENDIX A. PROOF OF THEOREM 3.1 Substituting the input in (24) by the backstepping controller (25) and taking into account the bounds (16), (18), and (19) yields β z2 β 2 2 2 2 ˙ ab1 + b2 − V3 = − k1 z1 − k2 z2 − 2∆ζx2 z2 − 2κ2 ζ0 x2 z2 + z3 − k3 z3 + 3 −1 β β 9 z 2 2 β β β z3 + 6∆ζx2 b1 − κ32 ζ0 b21 x22 z3 + 2βρp rx2 x3 − κ33 x22 x23 z3 − κ31 ab1 + b2 − β 9 β β β −2βρs x3 − κ34 x23 z3 β β−β β z2 β z2 2 2 ab1 + b2 − = − k1 z12 − k2 z22 − k3 z32 − 2∆ζx2 z2 − 2κ2 ζ0 x22 z22 + 3 z3 − κ31 ab1 + b2 − z3 β β 9 β 9 β β β + 6∆ζx2 b1 z3 − κ32 ζ0 b21 x22 z32 + 2βρp rx2 x3 z3 − κ33 x22 x23 z32 − 2βρs x3 z3 − κ34 x23 z32 . (29) β β β Applying Young’s inequality and noting that β ≥ β and βr ≤

1 , 1 + ρp (2 + ρs )

the last expression can be bounded as follows β β z 2 2 2 V˙ 3 ≤ − k1 z12 − k2 z22 − k3 z32 − (2κ2 ζ0 − 1) x22 z22 − κ31 − 1 ab1 + b2 − z3 − κ32 ζ0 − 1 b21 x22 z32 β 9 β 2 2 ρp + ρs β β 1 9 − κ33 − 1 x22 x23 z32 − κ34 − 2 x23 z32 + 10∆ζ 2 + + ∆β 2 . (30) 2 β β r (1 + ρp (2 + ρs )) 4 If (26) is satisfied, then V˙ 3 ≤ −α(z) + 10∆ζ 2 +

ρ2p + ρ2s 9 + ∆β 2 (1 + ρp (2 + ρs ))2 4


(31)

where

α(z) = −k1 z12 − k2 z22 − k3 z32

is obviously a class K∞ function. Noting that (ρ2p + ρ2s )/(1 + ρp (2 + ρs ))2 is uniformly bounded, the closed-loop error dynamics are thus ISS with ∆ζ, ρp , ρs , and ∆β as the inputs.

REFERENCES 1. M. Hosseini, G. Zhu, and Y.-A. Peter, “A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators,” in 2006 DTIP of MEMS & MOEMS, pp. 211–216, (Stresa, Italy), 26-28 April 2006. 2. E. Chan and R. Dutton, “Electrostatic micromechanical actuator with extended range of travel,” 9, pp. 321–328, Spet. 2000. 3. N. Doble and D. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Select. Topics Quantum Electron. 10, pp. 629–635, May/June 2004. 4. S. Senturia, Microsystem Design, Kluwer Academic Publishers, Norwell, MA, 2002. 5. J. Pont-Nin, A. Rodr´ıguez, and L. Castañer, “Voltage and pull-in time in current drive of electrostatic actuators,” 11(3), pp. 196–205, 2002. 6. D. H. S. Maithripala, J. M. Berg, and W. P. Dayawansa, “Control of an electrostatic MEMS using static and dynamic output feedback,” ASME Journal of Dynamic Systems, Measurement and Control 127, pp. 443–450, 2005. 7. E. Sontag, “Smooth stabilization implies coprime factorization,” 34, pp. 435–443, 1989. 8. E. Sontag, “The ISS philosophy as a unifying framework for stability-like behavior,” in Nonlinear Control in the Year 2000 (Volume 2), A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, eds., Lecture Notes in Control and Information Sciences, pp. 443–468, Springer-Verlag, Berlin, 2000. 9. M. Krstić, I. Kanellakopoulos, and P. Kokotović, Nonlinear and Adaptative Control Design, John Wiley & Sons Ltd, New York, 1995. 10. D. Maithripala, J. Berg, and W. Dayawansa, “Nonlinear dynamic output feedback stabilization of electostatically actuated MEMS,” in Proc. of the 42nd IEEE Conference on Decision and Control, pp. 61–66, (Maui, Hawaii), December 2003. 11. J. Lévine, Analyse et Commande des Systmes Non Linaires, [Online] Available: http://cas.ensmp.fr/%7Elevine/Enseignement /CoursENPC.pdf, 2004.


Hybrid Neural Networks and Genetic Algorithms for identification of complex Bragg Gratings Ali Rostamia, Arash Yazdanpanah-Goharrizia, Amin Yazdanpanah-Goharrizib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT In this paper a novel method for investigation of inverse scattering in optical complex mediums is proposed. The proposed method is based on Radial Basis Function Neural Networks (RBFNN) and Genetic Algorithms (GAs). Medium discrimination is performed by RBFNN and corresponding medium parameters identification is done using GAs. In the proposed method for simplicity the apodized, chirped and simultaneously apodized and chirped types of mediums are considered as RBFNN library. The proposed method tries to open a new insight to inverse scattering in optical devices and systems identification. The simulated results closely follow full numerical simulations to illustrate the ability of the proposed algorithm. Key words- Hybridization, RBFNN, Complex Bragg Gratings, Inverse Scattering, Identification.

1. INTRODUCTION The problem of synthesizing or reconstructing of non-uniform Fiber Bragg Gratings (FBG) from the corresponding reflection coefficient is important in device design for high-speed optical fiber communication (e.g., selection of wavelength multiplexed channels), compensation of the link dispersion and optical computing. For these devices and systems, design strategy needs some standard design rules and values. For obtaining these values and rules, the design ideas should be examined in practice. On the other hand, one needs to check the theoretical idea with practical measurements. In optical domain, for example, device design with optical complex Bragg Gratings need to measure manufactured structure. For this purpose, a model for medium should be assumed and optimized with numerical methods. For example, in reconstruction of optical mediums based on the measured reflection coefficient intelligence methods are used to obtain optimum medium parameters. These structures have some interesting applications such as information gathering, measurement of strain or temperature, etc. [1-5]. Several experimental techniques have been demonstrated to fabricate non-uniform gratings, permitting an accurate control of both the local grating pitch and the apodization profile along the structure [6, 7]. These techniques give substantial flexibility to the grating design process. For all of these applications, inverse scattering techniques [8] are needed, offering a great variety of possibilities for the design of gratings. For weak gratings, the synthesis problem of fiber gratings reduces to an inverse Fourier transform of the reflection coefficient. This is known as the first-order Born approximation, and applies only to gratings for which the reflectivity is small. Several modifications on the method have been applied and have improved its performance at high reflectivity [9, 10]. Fourier transform technique has been extended by Winick and Roman

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740W, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684880

Proc. of SPIE Vol. 6374 63740W-1

[4], yielding a better approximation, enabling the design of practical fiber grating filters. However, this synthesis procedure is approximate in nature and consequently, not reliable for the design of very complex filters. An exact solution of this inverse scattering problem was found by Song and Shin [8] who solved the coupled Gel’fand–Levitan–Marchenko (GLM) integral equations that appear in quantum mechanics. Their method is exact, but is restricted to reflection coefficients that can be expressed as a rational function. However, the need to approximate the desired spectral response by rational functions is difficult and also can result in inaccuracies. To overcome this limitation, an iterative solution of the GLM system was proposed by Peral to synthesize arbitrary spectral responses [2, 11]. Some fiber grating designs calculated with this method have already been fabricated, proving the usefulness of the method [12]. The iterative solution of the GLM equations [13] has some weaknesses. However, the solution is approximate due to the finite number of iterations computed, which translates into considering only a limited number of reflections within the medium. This is particularly noticeable for strong gratings with discontinuities in the coupling function. Also, when specifying ideal filter responses, it is desirable to have a weighting mechanism, which makes it easier to weight the different requirements. The iterative GLM method does not support such a mechanism in a satisfactory way. Another group of exact inverse scattering algorithms, as known as differential or direct methods [14–17], developed by geophysicists like Robinson and Goupillaud [14, 15], exploit fully the physical properties and structure of the layered media in which the waves propagates. The methods are based again on causality arguments and identify the medium recursively layer by layer. For this reason, they are sometimes called layerpeeling or dynamic de-convolution algorithms. Recently, several heuristic approaches have been developed for the solution of the inverse problem with the goal of designing gratings as filters for telecommunication applications. Skaar, Risvik and Cormier et al developed genetic algorithms (GAs) to obtain physical parameters of the Bragg gratings from the measured reflected intensity spectrum [18,19]. Skaar and Risvik encoded the grating coupling coefficient using a real number formulation and used a Runge–Kutta algorithm to calculate the spectral response of the grating [18]. Cormier et al reduced the spectral response calculation time using the transfer-matrix (T-matrix) formulation [19]. This formulation is based on approximating the grating coupling coefficients as a piecewise constant function along the grating. Cormier et al characterized the Bragg grating in terms of three parameters: the length, period and amplitude of the index of refraction modulation [19]. While this method is excellent for the design of Bragg gratings as filters, the parameterization of Cormier et al does not allow for a period variation along the grating (e.g., due to a non-constant applied strain). In these presented works, the type of medium was well known and only extraction of medium parameters was a problem. But, there is a basic question that if there is a problem without information about medium type, how one can proceed. Here, we try to present a novel method to incorporate this problem. For this purpose combination of RBFNN and GAs is examined. In our method there are a large classes of medium types predefined to RBFNN. The RBFNN has access to these mediums through the learning process. Now, if there is an unknown (belongs to one of predefined medium types) reflection coefficient, which is applied to this RBFNN, the trained RBFNN would recognize medium type. Now, the input vector is passed to special GA block corresponding to determined medium type. Then, the corresponding GA starts to determine the parameters of the recognized medium. After this process the real and extracted medium are compared with each other where our results show excellent agreement. The presented method provides excellent method for practical cases with a large library. The organization of the paper is as follows. In section 2, mathematical formulation of the problem is presented. In this section coupled mode and the Riccati equations are presented. RBF neural network and genetic algorithms are reviewed in section 3. In section 4 identification algorithm are presented. Simulation results and discussion are discussed in section 5. Finally the paper ends with a conclusion.


2. MATHEMATICAL FORMULATION In this section the coupled mode theory (CMT) leading to the Riccati equation and the transfer matrix method (TMM) for calculation of the reflection coefficient of the complex Bragg Gratings are reviewed. For these structures, the index of refraction is given as follows [20]. ⎛ 2π ⎞ n( z ) = n0 + ∆ndc + A( z ) ∆nac cos ⎜ z + Φ (z )⎟ , Λ ⎝ ⎠

(1)

where n0 , ∆n dc , ∆n ac , A(z ) , Λ , Φ (z ) and z are the refractive index of core, average refractive index of core, ac index of refraction, Apodization function, fixed period of Grating, arbitrary spatially varying phase, and the light propagation axis along the medium ( 0 ≤ z ≤ L , where L is the grating length) respectively. For these structures after some mathematical manipulation of the Maxwell’s equations the coupled wave equations can be obtained [21-23]. Using these coupled wave equations, the Riccati equation for managing of the reflection coefficient can be obtained as follows.

(

) (

)

dρ ( z , ω ) = ik ( z ) 1 + ρ 2 ( z, ω ) + i 2ω − Φ ' ( z ) ρ ( z, ω ) , dz

(2)

where ρ ( z, ω ), k ( z ) and ω are the reflection coefficient at given position ( z ) and frequency ( ω ), the coupling coefficient and the detuning frequency respectively. Now, the following relations can be used for the mentioned above constants. ⎛ π ⎞ ∆nac ⎟⎟ A( z ) = k 0 A( z ) , k ( z ) = ⎜⎜ ⎝ λD ⎠

(3)

where λ D = 2neff Λ is the Bragg wavelength. In this relation neff is effective index of refraction.

ω=

2π

λ

neff −

π Λ

.

(4)

The Range-Kutta numerical method can be applied on Eq. (2) and using the following boundary condition the reflection coefficient for the proposed structures can be obtained.

ρ ( L, ω ) = 0 .

(5)

For obtaining the reflection coefficient of a fiber Bragg grating, we use the transfer matrix method as follows. The transfer matrix method can be used to solve non-uniform gratings. This method is effective in the analysis of the almost-periodic grating. A non-uniform fiber Bragg grating can be divided into many uniform sections th

along the fiber. The incident light wave propagated through each uniform section ( i layer) can be described by a transfer matrix Fi . For the structure of the fiber Bragg grating, the matrix Fi can be written as follows [22]. ) σ ⎡ γ cosh( z ) i sinh(γ B ∆n( z ) ∆ − B ⎢ γB ⎢ Fi = ⎢ k ⎢i γ sinh(γ B ∆z ) ⎣ B


⎤ sinh(γ B ∆z )⎥ γB ⎥ , (6) ) σ ⎥ cosh(γ B ∆z ) + i sinh(γ B ∆n( z ) ⎥ γB ⎦ −i

k

where γ B is denoted as )

γ B = k2 −σ 2 .

(7)

The whole grating can be represented in matrix form as

⎡ R ( L)⎤ ⎢ S ( L) ⎥ = FM .FM −1 . ⎣ ⎦

.

.. Fi .

.

.

⎡ R ( 0) ⎤ ⎥, ⎣ S ( 0) ⎦

.. F1 .⎢

.

(8)

where L is the length of the medium. The amplitude of the reflection coefficient can be written as

ρ=

S ( 0) . R ( 0)

(9)

3. RBF NEURAL NETWORKS AND GENETIC ALGORITHM In this section a short overview to RBFNN is presented. The RBFNN for pattern classification and functional approximation have been used. The proposed network has single hidden layer, which main classification algorithm is done here [24]. Neurons in hidden layer have radial transfer function. Also, neurons in output layer have linear, usually, transfer function. Fig. 1 shows typical RBFNN.

Input Layer

hidden Layer

Output Layer ZI

Output

/3 Fig. 1. Schematics of RBFNN.

The following definitions for description of Fig. 1 chould be made.

[ x1 ,..., xl1 ]T : Input vector l1 : Dimension of the input vector


l2 : Number of neurons in hidden layer

vm : Prototype vector corresponding to the m th hidden cell ( [v1m ,..., vl1m ]T ). V: matrix of prototype vectors ( [v1 ,..., vl 2 ] ) ym : Output of m th hidden cell l3 : Dimension of the output vector u j : Weight vector of the j th output cell ( [u1 j ,..., ul 2 j ]T )

U : Weight matrix of output layer ( [u1 ,..., ul 3 ] ) z j : Actual output of the j th output cell Since in this paper we need to identify medium profiles then we consider pattern recognition aspect of RBFNN. In this treatment the input space should be classified to subclasses and a prototype vector to each class is assigned. For these classified space the membership function ( f m (x ) ) of input vector for each subclass is determined by a function of its distance from the prototype vector ( f m ( x ) = f ( x − vm ) ). The suitable choice for the function f m (x ) is the Gaussian function. For each subclass, one can consider some neurons to incorporate feasibility in learning process. After obtaining the membership values of input vector in the subclasses the results should be combined to obtain the membership degrees in every class. The two-layered feedforward neural network of RBF type is illustrated in Fig. 1. The neurons in the hidden layer of network have a Gaussian activation function and their input–output relationship is given as follows.

y m = f m ( x ) = exp(−

x − vm 2 2σ m

2

),

(6)

where σ m is the Gauss width parameter. th

The operation field region of the m neuron is part of input space, where f m (x ) is high. The neurons in the output layer could be sigmoid, linear, or pseudo-linear, i.e. linear with some squashing property, such that the output could be calculated using one of the following equations:

⎧ 1 , Sigmoid, ⎪ −s ⎪1 + e j ⎪⎪ s j 1 z j = ⎨ , Linear, with squashing function, l2 ⎪ l2 ⎪ sj 1 ⎪ , Pseudo − linear, with squashing function, ⎪⎩ ∑ y m ∑ ym

where s j =

l2

∑ ym umj

m =1

(7)

j = 1,..., l3 .

In the most of literature, the neurons with linear, pseudo-linear or sigmoidal activation functions have been considered for the output layer.


Now, training algorithm for this network is presented as follows. Training algorithms- Here, we present the back propagation (BP) based algorithm for training of the RBFNN. Before starting the training, a cost function should be defined and then minimized through the training process by gradient calculations and weight-updating corresponding to the appropriate parameters. Total sum-squared error (TSSE) is the most popular cost function. For implementing this method, the error gradients versus the ∂E ∂E ∂E parameters ( , , ) should be calculated layer by layer, starting from the output layer and 2 ∂umj ∂vim ∂σ m

proceeding backwards. In the following updated weight parameters are calculated for the next step. umj (n + 1) = umj ( n ) − α1

∂E , ∂umj

(8)

vim ( n + 1) = vim ( n ) − α 2

∂E , ∂vim

(9)

σ 2 m ( n + 1) = σ 2 m ( n ) − α 3

∂E ∂σ 2 m

,

(10)

where, α1 ,α 2 ,α 3 are learning rate factors in the range [0, 1]. The algorithm for all training inputs should be repeated in epochs. In our case, two-dimensional input vectors for all three considered mediums including bandwidth and central wavelength (wavelength at maximum reflection) for training are used. For example, in our experiments, the RBF neural network has been trained with the respected input data and a TSSE of 0.000804086 after 312 epochs has been obtained. After this the algorithm works such that an 3 × 1 output vector is made to illustrate the result of classification. Genetic Algorithm- A GA is designed to efficiently search in a large and poorly understood search space, where expert knowledge is limited. The basic principles of GAs are well described in [25, 26]. GAs form search algorithms based on the process of biological evolution [27]. In GAs the mechanics of natural selection and genetics are emulated artificially. The search for a global optimum in an optimization problem is conducted by moving from an old population of individuals to a new population using genetics-like operators. Each individual (chromosome) represents a candidate to the optimization solution where a population is an array of individuals. An individual is modeled as a fixed length string of symbols. An evaluation function, called fitness function, assigns a fitness value to each individual within the population. This fitness value is a measure for the quality of an individual. The fitness function presents an objective function in optimization. The basic optimization procedure involves nothing more than processing highly fit individuals in order to produce better individuals as the search progresses. Three basic operators used in a conventional GA, to create the next generation from the current population, are Selection, Crossover and Mutation. Here, the GAs operators are described as follows. Selection- Selection operator selects the individuals, called parents that contribute to the population at the next generation. It is clear that the more fit individual from the old population have more chance to be selected to the next generation. On the other hand, selection options specify how the genetic algorithms choose parents for the next generation. We choose this function stochastically uniform. Crossover- Crossover operator combines two parents to form children for the next generation or this option specifies how the genetic algorithm combines two individuals, or parents, to form a crossover child for the next generation. Crossover function specifies the function that performs the crossover. We used the single point function for crossover. Mutation- Mutation operator applies random changes to individual parents to form children. This option specifies how the genetic algorithm makes small random changes in the individuals in the population to create


mutation children. Mutation provides genetic diversity and enables the genetic algorithm to search a broader space. We choose the Gaussian function as the mutation operator.

4. PROPOSED IDENTIFICATION ALGORITHM In this section whole algorithm for classification of medium type and identification of medium parameters are presented. The algorithm is illustrated in Fig. 2. The measured reflection coefficient is input of the algorithm. After entering the measured reflection coefficient, the type of medium is determined by RBFNN. After determining the types of medium with RBFNN then the algorithm chooses a suitable GA block that corresponds to the specified medium type. In this step the GA starts to iterate for obtaining the specified medium type parameters.

Fig. 2. Identification Algorithm based on RBFNN and Gas.

For the GAs the initial population for individuals and fitness function are considered as follows. The initial population for each block of GAs depends on the necessary unknown parameters of the medium according to physical model for the complex Bragg gratings. Therefore we consider a N p × M matrix as follows.

U = [u1

u2

.

.

.

um ] N p × M ,

(11)

where N p and M denote the number of population for each variable and the number of variables respectively. The choice of the fitness function is fundamental in order that a correct and efficient search of the solution is carried out by the algorithm. In our problem, the fitness is a function that measures the distance between the theoretical and the experimental reflection coefficient, bandwidth, and the maximum reflection. In this paper the fitness function is proposed as follows: ns

E = ∑ ρ exp (λ j ) − ρ Cal. (λ j ) + BWexp (λ ) − BWcal . (λ ) + ρ exp (λ ) − ρ cal . (λ ) ,

(12)

j

where ρ exp . , ρ Cal. , BWexp . , BWCal. λ j and n s are the experimental reflection coefficient, calculated reflection coefficient, the experimental bandwidth, calculated bandwidth, sampled wavelengths of the reflection coefficient and the number of samples respectively.


5. SIMULATION RESULTS AND DISCUSSION For illustration of the method three types of medium including Gaussian Apodization, Linear Chirping and simultaneous Apodization-Chirping are considered. For these three cases medium classification by RBFNN and parameters identification by GAs are carried out. For uniform FBG the following values are considered. 1. The length of grating ( L ) = 10 mm, 2. The period of grating ( Λ ) = 0.5356 µm , 3. The effective refractive index ( n eff ) = 1.447. For all of histogram figures (best current individual versus number of variables), the parameters are normalized. 1. Gaussian Apodization- In this case the Gaussian profile for apodization is considered and the coupling coefficient ( k (z ) ) is defined as follows.

k ( z) =

⎡ π ⎛ z − 0.5L ⎞⎤ ∆n ( z ) exp ⎢− 20⎜ ⎟⎥ . λ B ac ⎝ α ⎠⎦ ⎣

(13)

For this Apodization, the amplitude of the index modulation ( ∆nac ( z ) ) and the Gaussian parameter ( α ) are important and affect the FBG characteristics strongly. The simulated results for this case are presented in Figs. (3-5). Fig. 3 shows the fitness value and best individuals ( α and ∆nac ( z ) ) for this case. Approximately, after 100 iterations optimum condition is reached. The reflection coefficients for real (full numerical simulation) and reconstructed ones are illustrated in Fig. 4. The presented method extracts medium reflection coefficient completely compatible with real case. Finally the coupling coefficient for this case is illustrated in Fig. 5 demonstrating excellent compatibility.

Best: 0.0028087 Mean: 0.0095998

Fitness value

15 Best fitness Mean fitness 10

5

Current best individual

0

10

20

30

40

50

60

70

80

90

100

Generation Current Best Individual 10

5

0

1

2

Number of variables (2) Fig. 3. The evaluated fitness function and the normalized calculated parameters.


1 Real profile Reconstracted profile

0.9

Reflection coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.549

1.5495

1.55

1.5505

1.551

1.5515

Weavelenght(micrometre) Fig. 4. The Reflection Coefficient for real parameters (solid line) and reconstructed ones (dotted line). −3

4

x 10

Real profile Reconstracted profile

Coupling coefficient k(z)

3.5 3 2.5 2 1.5 1 0.5 0

0

2000

4000

6000

8000

10000

Position(micrometre) Fig. 5. The coupling coefficient for real parameters (solid line) and reconstructed ones (dotted line).

For this case the initial population for individuals considered as

U = [ ∆nac ( z ) α ]20× 2

(14)

The measured reflection coefficient for Gaussian apodization corresponds to the full numerical simulation with α = 0.8 × L , ∆nac ( z ) = 9 × 10 −4 , and the reconstructed medium parameters using our proposed approach with α = 0.798987 × L and ∆nac ( z ) = 9.00234 × 10 −4 . As it is shown the reconstructed values closely follow input measured values. 2. Linear Chirping- In this case linear chirped is considered. According to linear chirp function the following relation is defined.


z 1 dΦ =F 2, 2 dz L

(15)

where F is the chirp parameter, defined as follows: L2 dλ D L2 F = 2 Φ ( z ) = −4πneff 2 λ D dz z

(16)

dλ D is the rate of the chirp in the complex Bragg grating. For this case the amplitude of the index dz dλ modulation ( ∆nac (z ) ) and the rate of the chirp ( D ) are important and affect the FBG characteristics dz strongly. The simulated results for this case are presented in Figs. 6-8. Fig. 6 shows the fitness value and best dλ D individuals ( ∆nac (z ) and ) for this case. Approximately after 50 iterations optimum condition is reached. dz The reflection coefficient for real (full numerical simulation) and reconstructed ones is illustrated in Fig. 7. Presented method extracts medium reflection coefficient closely matching the real case. Finally the chirp function for this case is illustrated in Fig. 8, demonstrating close agreement.

where

Best: 0.034431 Mean: 0.26121

Fitness value

40 Best fitness Mean fitness

30 20 10


0

5

10

15

20

25

30

35

40

45

50

Generation Current Best Individual 6 4 2 0

1

2

Number of variables (2) Fig. 6. The evaluated fitness function and the normalized calculated parameters


1 Real profile Reconstracted profile

0.9


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.548 1.549

1.55

1.551 1.552 1.553 1.554 1.555 1.556 1.557

Weavelenght(micrometre) Fig. 7. The reflection coefficient for real parameters (solid line) and reconstructed ones (dotted line) 5

0

x 10

Real profile Reconstracted profile

−2

Chirp function

−4 −6 −8 −10 −12 −14 −16

0

2000

4000

6000

8000

10000

Position(micrometre)

Fig. 8. The chirp function for real parameters (solid line) and reconstructed ones (dotted line)

For this case, the initial population for individuals considered as U = [ ∆n ( z )

dλ D ]20× 2 . dz

(17)

The measured reflection coefficient for linear chirped function corresponds to the full numerical simulation dλ D with = 2 × 10 − 7 , ∆n( z ) = 5 × 10 − 4 , and the reconstructed medium parameters using our proposed dz


dλ D = 2.00001 × 10 − 7 and ∆n( z ) = 5.00581 × 10 −4 . As it is shown, the reconstructed dz values closely follow input measured values.

approach with

3. Simultaneous Apodization-Chirping- In this case, we consider simultaneously the Gaussian apodization and linear chirp functions. For this case, the amplitude of the index modulation ( ∆nac (z ) ), the Gaussian dλ D ) are important and affect the FBG characteristics strongly. The dz simulated results for this case are presented in Figs. 9-11. Fig. 9 shows the fitness value and best individuals dλ D ( ∆nac (z ) , α and ) for this case. Approximately after 100 iterations optimum condition is reached. The dz reflection coefficients for real (full numerical simulation) and reconstructed ones are illustrated in Fig. 10. Presented method extracts medium reflection coefficient with values completely compatible with real case. Finally the coupling coefficient and chirp functions for this case are illustrated in Fig. 11, demonstrating excellent match.

parameter ( α ), and the rate of the chirp (

Best: 0.038761 Mean: 0.10928

Fitness value

15 Best fitness Mean fitness 10 5


0

10

20

30

40

50

60

70

80

90

100

Generation Current Best Individual 6 4 2 0

1

2

3

Number of variables (3) Fig. 9. The evaluated fitness function and the normalized calculated parameters.


0.9 Real profile Reconstracted profile

0.8


0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.551 1.5515 1.552 1.5525 1.553 1.5535 1.554 1.5545 1.555 1.5555

Weavelenght(micrometre)

Coupling coefficient k(z)

Fig. 10. The reflection coefficient for real parameters (solid line) and reconstructed ones (dotted line).

−3

3

x 10

Real profile Reconstracted profile 2

1

0

0

2000

4000

6000

8000

10000

8000

10000

Position(micrometre)

Chirp function

0

−100

−200

−300

0

2000

4000

6000

Position(micrometre) Fig. 11. The coupling coefficient and chirp function for real parameters (solid line) and reconstructed ones (dotted line).


For this case the initial population for individuals considered as U = [ ∆n ( z )

dλ D α ]20×3 dz

(18)

The measured reflection coefficients for simultaneous Gaussian apodization and linear chirped function correspond to the full numerical simulation for simulated parameters with dλ D = 3 × 10 − 7 , ∆n( z ) = 6 × 10 − 4 ,α = 0.5 × L , and the reconstructed medium parameters using the dz dλ D proposed approach are = 3.00158 × 10 − 7 , α = 0.501529 × L and ∆n ( z ) = 5.97715 × 10 −4 , dz respectively. As it is shown the reconstructed values follow closely input measured values. The proposed method was examined with several other examples and the results illustrated graphically. Presented results illustrated that the developed method could be of high interest for inverse problem solving.

6. CONCLUSION In this paper a novel method including combination of RBF neural network and Genetic Algorithm for classification and identification of complex Bragg Gratings has been developed. In this work large classes of predefined medium types can be defined and applied to RBF neural network that would enable widely-spread medium type classification after learning process. After classification by RBFNN, the GAs can identify medium parameters precisely. The presented method for identification of complex Bragg Gratings demonstrated excellent performance providing precise agreement with full numerical simulations.

REFERENCES

1. M. Matsuhara, K. O. Hill, and A. Watanabe, “Optical-waveguide filters: Synthesis,” J. Opt. Soc. Am, 65, 2. 3. 4. 5. 6. 7. 8.

804-809,(1975). E. peral, J. Capmany, and J, Marti, “Iterative solution to the Gel'Fand-Levitan-Marchenko coupled equations and applications to synthesis of fiber gratings,” IEEE J. Quantum Electron. 32, 2078-2084 (1996). R. Feced, M. N. Zzervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of non uniform fiber Bragg gratings,” IEEE J. Quantum Electron., 35, 1105-1115 (1999). K. A. Winick and J. E. Roman, “Design of corruGAsted waveguide filters by Fourier Transform techniques,” IEEE J. Quaantom Electron., 26, 1918-1929 (1990). P. Roberts and G. Town, “Design ofmicrowave filters by inverse scattering,” IEEE Trans. Microwave Theory and Techniques, 43, 739-743 (1995). W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, and R. I. Laming,“Complex grating structures with uniform phase masks based on the moving fiber-scanning technique,” Opt. Lett., 20(20), 2051–2053 (1995). A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren, and R. A. H. Stubbe, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol., 15, 1419–1423 (1997). G. H. Song and S. Y. Shin, "Design of corrugated waveguide filters by the Gel "Fand-Levitan-Marchenko inverse-Scattering method," J. Opt. Soc. Am. A., 2, 1905-1985.


9. J. A. Dobrowolski and D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt., 17(19), 3039–3050 (1978).

10. B. G. Bovard, “Fourier transform technique applied to quarterwave optical coatings,” Appl. Opt., 27 (15),

3062–3063 (1988). 11. E. Peral, J. Capmany, and J. Marti, “Design of fiber grating dispersion compensators using a novel iterative solution to the Gel’fan-Levitan- Marchenko coupled equations,” Electron. Lett., 32(10), 918–919 (1996). 12. J. Skaar, B. Sahlgren, P. Y. Fonjallaz, H. Storoy, and R. Stubbe, “Highreflectivity fiber-optic bandpass filter designed by use of the iterative solution to the Gel’fan-Levitan-Marchenko equations,” Opt. Lett., 23(12), 933–935 (1998). 13. P. V. Frangos, D. J. Frantzeskakis, and C. N. Capsalis, “Pulse propaGAstion in a nonlinear optical fiber of parabolic index profile by direct numerical solution of the Gel’fan-Levitan integral equations,” Proc. Inst. Elect. Eng., pt. J, 140,(2), 141–149 (1993). 14. A. M. Bruckstein, B. C. Levy, and T. Kailath, “Differential methods in inverse scattering,” SIAM J. Appl. Math., 45(2), 312–335 (1995). 15. A. M. Bruckstein and T. Kailath, “Inverse scattering for discrete transmission-line models,” SIAM Rev., 29,(3), 359–389 (1987). 16. K. P. Bube and R. Burridge, “The one-dimensional inverse problem of reflection seismology,” SIAM Rev., 25(4), 497–559 (1983). 17. K. P. Bube, “Convergence of difference methods for one-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sensing, 22, 674–682 (1984). 18. J. Skaar and K. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave Technol.16, 1928–1932 (1998). 19. G. Cormier, R. Boudreau and S. Theriault, “Real-coded genetic algorithm for Bragg grating parameter synthesis,” J. Opt. Soc. Am. B, 18, 1771–1776 (2001). 20. A. Othonos and K. Kalli, “Fiber Bragg Gratings: fundamentals and applications in telecommunications and Sensing”, (Aetech House), 1999. 21. A. W. Snyder and J. D. Love, “Optical waveguide theory”, (Chapman and Hall, London), 542, (1983). 22. T. Erdogan, “Fibre grating spectra”, Journal of Lightwave Technology, 15(8), 1277-1294 (1997). 23. L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, “Ultrashort pulse reflection from fiber gratings: a numerical investigation”, Journal of Lightwave Technology, 15(8), 1503-1512 (1997). 24. M. T. Vakil-Baghmisheh and N. Pavesic, "Training RBF networks with selective backpropagation," Journal of Neurocomputing, 62, 39- 64 (2004). 25. J. H. Holland, Adaptation in Natural and Artificial Systems, MIT, Cambridge, MA, 2nd Edn., 1992. 26. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, 1989. 27. W. M. Spears, K. A. D. E. Jong, T. Baeck, and P. Bradzil “An overview of evolutionary computation,” Proceedings of European Conference on Machine Learning, Springer-Verlag, Berlin, 1993, 667, p. 442459.


Identification of complex Bragg Gratings based on optical transfer function estimation using Genetic Algorithm A. Rostamia, A. Yazdanpanah-Goharrizia, A. Yazdanpanah-Goharrizib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of Electrical Engineering, K. N. Toosi University of Technology

c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT In this paper an optical transfer function for description of the operation of complex fiber Bragg Gratings similar to electrical ones is presented ( H ( jω ) ). For this purpose and reconstruction of the transfer function, the Genetic Algorithm (GA) is used to find optimum number of poles and zeros from the measured reflection coefficient. After building the transfer function according to the developed algorithm in this paper, the reflection coefficient for this approximated system is obtained (simulated) and compared with measured values. The results obtained from the approximated transfer function in these cases are so close to real measured data. So, the presented method introduces an interesting approach for identification of the complex Bragg Gratings in frequency domain. Some of optical characteristics (both frequency domain and time domain parameters) of these systems can be extracted from the approximated transfer function easily. Keywords: Fiber Bragg Grating, Genetic Algorithm, Optical Transfer Function, Optical System Identification

1. INTRODUCTION Optical device and system design based on complex fiber Bragg Gratings is interesting for high-speed optical communication and computing, particularly within Optomechatronic systems. Complex fiber Bragg Gratings are very interesting but complex for synthesis in practice [1-5]. Investigation of the effect of the parameters of designed system and input waveform on output characteristics is extremely important in optomechatronic systems engineering and design optimization. Also, in optical engineering this subject is very necessary for device and system design and reliable tuning purposes. For this aim, introducing optical system transfer function illustrating all system parameters effects on output behavior in frequency domain is interesting for control and system analysis purposes, such as traditional methods in control system engineering tools. In this paper, a novel method for evaluating a transfer function for Fiber Bragg Gratings is examined. For this purpose a model for medium should be assumed and then optimized using numerical methods [6, 7]. As an example, in reconstruction of optical medium types based on the measured reflection coefficient, intelligence methods are used to obtain optimum medium parameters [8]. An analytical proposal for system input-output characteristic is also interesting from system identification point of view. In this case optical transfer function can provide excellent tool and successful inverse problem algorithms can be applied. In this paper, we try to present an efficient method to extract optimum transfer function for the mentioned structures. In this field there are some interesting reported works for managing inverse problem as follows. A nontrivial inverse problem consists in the derivation of such a modulation (Bragg Grating) from the knowledge of spectrum reflected (or transmitted) by grating. One of the simplest approaches to the solution of the inverse problem is Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740X, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684881

Proc. of SPIE Vol. 6374 63740X-1

based on the existence of a Fourier-transform relation between the spectral response and the grating coupling coefficient [9]. This relation is however exact only for weak gratings and its extension to high reflectivity has an approximate validity. An exact solution of the inverse problem can be obtained at least in principle by the coupled integral equations derived in scattering theory by Gelfand, Levitan and Marchenko (GLM) [10]. These equations, unfortunately, can easily be solved by numerical methods only when the reflection coefficient can be written as a rational function [11, 12]. This limitation was overcome by a method based on an iterative solution of GLM equations with the expense of increased mathematical complexity [10]. A recently proposed and efficient method for grating reconstruction is the layer peeling algorithm that provides a path integral solution to the inverse problem by use of causality arguments and by taking into account all the multiple reflections inside the grating [13]. The above-mentioned methods consider both the amplitude and the phase of the spectral response to recover the grating properties. In contrast, an integral relation was derived between the reflected intensity spectrum alone and the index modulation phase for a given modulation amplitude. In some experiments, this integral relation enabled determination of the non-uniform strain acting along the grating from the knowledge of the reflected intensity spectrum. Another related approach considers only the phase spectrum of the complex reflection coefficient. A measurement of this quantity makes it possible to derive the relative delays among the spectral components of the signal reflected from the strained grating and hence the applied strain. Both methods present some limitations. Here, we present an efficient method based on GAs [14] to find optimum number of poles and zeros for reconstruction of medium profile. Our method is as follows. Based on Least Square (LS) technique in system control engineering, we approximate the reflection coefficient in frequency domain in terms of some poles and zeros (optimum number of poles and zeros). Then a suitable transfer function in frequency domain can be considered for the reflected light from complex optical Grating systems. Also, our presented method is for complete and full scale range of the reflection coefficient. Finally we compare the presented method with complete numerical solution and we show that there is excellent agreement. The organization of the paper is as follows. In section 2, brief mathematical principle of Fiber Bragg Gratings is reviewed. Optical transfer function optimization using GAs is discussed in section 3. Simulation results is presented and discussed in section 4. Finally the paper ends with a conclusion.

2. FIBER BRAGG GRATINGS In this section, the Riccati equation for the reflection coefficient of the complex Bragg Gratings is reviewed. For these structures the index of refraction is given as follows [1]. ⎛ 2π ⎞ n( z ) = n0 + ∆ndc + A( z ) ∆nac cos ⎜ z + Φ (z )⎟ , ⎝ Λ ⎠

(1)

where n0 , ∆ndc , ∆nac , A(z ) , Λ , Φ (z ) and z are the refractive index of core, average refractive index of core, ac index of refraction, Apodization function, fixed period of Grating, arbitrary spatially varying phase, and the light propagation axis along the medium ( 0 ≤ z ≤ L , where L is the grating length) respectively. For these structures after some mathematical manipulation of the Maxwell’s equations, the coupled wave equations can be obtained [2-4]. Using these coupled wave equations, the Riccati equation for managing the reflection coefficient can be obtained as follows.

(

) (

)

dρ ( z, ω ) = ik ( z ) 1 + ρ 2 ( z, ω ) + i 2ω − Φ ' ( z ) ρ ( z , ω ) , dz

(2)

where ρ ( z , ω ), k ( z ) and ω are the reflection coefficient at given position ( z ) and frequency ( ω ), the coupling coefficient and the detuning frequency respectively. Now, the following relations can be used for the above-mentioned constants. ⎛ π ⎞ k ( z ) = ⎜⎜ ∆nac ⎟⎟ A( z ) = k 0 A( z ) , (3) λ ⎝ B ⎠


where λ B = 2neff Λ is the Bragg wavelength and neff is effective index of refraction, related to the frequency by the following equation.

ω=

2π

λ

neff −

π Λ

.

(4)

The Range-Kutta numerical method can be applied to Eq. (2) and using the following boundary condition the reflection coefficient for the proposed structures can be obtained.

ρ ( L, ω ) = 0 .

(5)

3. OPTICAL TRANSFER FUNCTION OPTIMIZATION In this section, we explain the complex curve fitting algorithm and find a continuous-time transfer function that corresponds to a given complex reflection coefficient. This algorithm can be used to convert the magnitude and phase information from given reflection coefficient to transfer function and returns the real numerator and denominator coefficients in vectors b and a of the transfer function. H ( s) =

b s + b2 s −1 + . . .bn +1s − n B( s) , = 1 A( s ) a1s + a 2 s −1 + . . .a m +1s − m

(6)

where s = jω is the Laplace domain variable. Here, we arrange the sampled frequency in a vector ω and the corresponding reflection coefficient in ρ (0, ω ) . Scalars n and m specify the desired orders of the numerator and denominator polynomials, respectively. The proposed algorithm is used to incorporate the conjugate ρ (0, ω ) at −ω to ensure the proper frequency domain symmetry for a real medium. Now, the proposed algorithm is explained in detail as follows. For the above purpose, a weighted least square type error (Eq. (7)) is used to identify the best model from the data as follows. The vectors b and a (of Eq. (6)) can be found by minimizing the error function defined in Eq. (7) and creating a system of linear equations and solving them numerically [5]. ⎛ p 2⎞ e = min⎜ ∑ wt K ρ (0, ω ) A(ω K ) − B(ω K ) ⎟ . ⎜ ⎟ ⎝ K =1 ⎠

(7)

where A(ω K ) , B(ω K ) , p and wt K are the Fourier transforms of the polynomials a and b at the frequency ω (K ) , the number of frequency points (the length of ρ (0, ω ) and ω ), and a vector of weighting factors respectively. The proposed algorithm in this work uses the nonlinear least squares Gauss-Newton method for iterative search [6] with the output of the first algorithm as the initial estimation. ⎛ p B (ω K ) e = min⎜⎜ ∑ wt K ρ (0, K ) − A(ω K ) ⎜ K =1 ⎝

2⎞

⎟ ⎟⎟ ⎠

(8)

It is important to note that for the above strategy, we guess the initial values for m and n and evaluate the estimated transfer function H ( j ω ) at s = jω . Then, the absolute value of H ( jω ) is compared with the absolute value of the


reflection coefficient ( ρ (0, ω ) ), which is calculated by solving the Riccati equation. If these two spectrums ( ρ (0, ω ) and H ( j ω ) ) don’t match each other with an acceptable error, other values for m and n are guessed and the above steps are repeated. The effectiveness of the proposed methodology strongly depends on the values of m and n . Thus, for obtaining better performance the optimal values for m and n are calculated in this paper by using GAs. Here, our objective is to minimize system cost function f that measures the distance between the real reflection coefficient ρ (0, ω ) and the estimated one H ( jω ) . The simplest choice is a fitness function defined as ns

2

f = ∑ ρ (0, ωi ) − H ( jωi ) ,

(9)

i =1

where ωi are the sampled frequencies of the reflection coefficient whose total number is ns . Note that several alternatives exist for the definition of a fitness function [8], including the possibility that the contributions from different spectral regions could be weighted. In this case we want to obtain the optimal values for the degrees of numerator and denominator polynomials. Therefore, an individual is an unknown quantity ( {ni }{ , mi }, i = 1, . . .,V , where V is the possible solution for each individual in the initial population). In each generation the population size is kept as 50. The Roulette wheel is used as selection operator. For the population size of V the probability of selection of each fitness value f i (i.e., Pi ) is

i th individual with

f Pi = V i (i = 1,2,....,V ) . ∑ fm

(10)

m =1

Our crossover function is uniform crossover. In uniform crossover each bit of children are randomly picked from the parents with the crossover probability. Mutation operator is set uniform, so that a random real value makes a random change in a bit of the unknowns m, n . In each generation the cost function for minimization is checked. The GA process repeats until the specified maximum number of generations is reached. Explained algorithm is illustrated in Fig. 1.

n.m Trail value for

n, m

From initial population

ρ (0, ω )

Complex curve fitting algorithm For estimation of frequency response

H(ω) f = min

∑

H ( jω ) − ρ ( 0, ω )

2

New trail value for the unknown parameters (m, n) organized by Selection, Crossover and Mutation

Fig. 1. Schematic diagram of frequency domain identification using complex curve fitting and Genetic Algorithm.


In the next section the simulated results using the developed algorithm is illustrated. The accuracy and efficiency of the proposed method for identification of non-uniform fiber Bragg gratings (FBGs) in frequency domain such as apodized and chirped FBGs are shown and discussed.

4. SIMULATION RESULTS AND DISCUSSION In this section, using the above methodology frequency response of Apodization and chirped FBGs in frequency domain (poles and zeros) is estimated. In general case, the Riccati equation (Eq. (2)) has to be evaluated numerically. To make the numerical result more broadly applicable, it is convenient to introduce the normalized quantities such as z / L, δL, kL

and Φ ' L scaling to medium length. For the case study, we consider three Apodization functions and only one kind of chirp function as follows. 1. 2. 3. 4.

Gaussian apodization function Raised-cosine apodization function Quadratic apodization function Linear chirp function

3π . 4 1. Gaussian Apodization function- In this case the Gaussian Apodization profile is assumed as follows.

For all of our simulations the value of k 0 L is assumed to be

⎡ ⎛ z − 0.5L ⎞ 2 ⎤ A( z ) = exp ⎢ − a ⎜ ⎟ ⎥, L ⎠ ⎥ ⎢⎣ ⎝ ⎦

(11)

where a = 15 is the Gauss width parameter. For this Apodization function and given constant the real and estimated reflection coefficients are shown in Fig. 2. n=16,m=29,Gaussian 0.9 Real Estimation

0.8


0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8

10

Normalized Frequency

Fig. 2. The real and estimated reflection coefficients vs. normalized frequency.

The estimated poles and zeros are illustrated in Table 1.


Table 1: Estimated Poles and Zeros Gaussian Apodization 249.862 , 0.639 ± 54.175i, 14.227 ± 46.645i, 4.819 ± 48.153i, 16.748 ± 19.363i , -12.534533841755 , 9.744, 8.689 , -2.515, 1.679, -0. 03096 ± 0. 268

Zeros(16)

-6.335, 10

Poles(29)

−9

× (-721.20376, -28.93100 ± 635.553i, -106.60728 ± 620.60261i, -0.0243 ± 536.453i, -94.76511 ± 48.330347i, -39.824 ± 472.98i, -92.19 ± 396.265i, -90.876 ± 318.829i, -86.302 ± 248.115i, -81.684 ± 179.776i, -72.911 ± 112.648i, -57.754 ± 54.115i, -39.138 , -26.841 , -0.2955 ± 2.6653i, -16.161 )

2. Raised-cosine Apodization function- For this case the following Apodization function is adopted.

⎛ ⎛ z − 0.5L ⎞ ⎞ A( z ) = 0.5⎜⎜1 + cos⎜ π ( ) ⎟ ⎟⎟ , L ⎝ ⎠⎠ ⎝

(12)

For this Apodization function the real and estimated reflection coefficients are illustrated in Fig. 3. n=25,m=46,Raise−cosine 1 Real Estimated

0.9


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8

10


Fig. 3. The real and estimated reflection coefficients versus normalized frequency. The estimated poles and zeros are illustrated in Table 2. Table 2: Estimated Poles and Zeros Rise-cosine Apodization

Zeros(25)

-146.742 , -66.309, 54.422 ± 39.364i, -43.529 ± 24.751i, -0.096 ± 62.083i -12.431 ± 50.774i, -0.0474 ± 59.065i, -0.422 ± 54.4742i, 32.71899 ± 20.819i 41.632,-0.0923 ± 43.227i,-0.0891 ± 26.902i, 10.0689, -5.0009,1.856, .35659


-144.668 , -85.143 ± 78.126i, -31.264 ± 83.102i, -2.6597 ± 74.272i, -4.015 ± 70.944i, -0.0026 ± 59.177i, -7.376 ± 59.372i, -0.411 ± 54.48697i, -20.559 ± 56.2946i, -32.835 ± 49.0497i, -10.726 ± 51.770039i, -42.844 ± 35.808i, -44.9298 ± 27.390i, -49.096 ± 19.0146i, -49.870 ± 10.628i, -50.323 ± 3.506i, -13.071 ± 45.6424i, -13.854 ± 38.879i, -31.270 ± 23.334i, -20.3229 ± 24.1896i, -7.889 ± 22.976i, -18.787, -10.903, -4.966, -1.84998, -0.35148 ,

Poles(46)

3. Quadratic Apodization function- For the third case, the quadratic Apodization is considered. For simulation purpose, the Apodization parameter T = 6 is assumed. T z − 0.5L 2 ⎞ ⎛ +T( A( z ) = ⎜1 − ) ⎟, 12 L ⎝ ⎠

(13)

For this type of apodization, the real and estimated reflection coefficients are illustrated in Fig. 4.

n=29,m=29,Quadratic 1.4 Real Estimated


1.2

1

0.8

0.6

0.4

0.2

0

0

2

4

6

8

10


Fig. 4. The real and estimated reflection coefficients vs. normalized frequency. The estimated poles and zeros are illustrated in Table 3.


Table 3: Estimated Poles and Zeros Quadratic Apodization

Zeros(2 9)

Poles(2 9)

-57.741 ± 60.200i, -71.612, 2.286 ± 81.673i, -55.269 ± 15.354i, 53.919 ± 20.522i, 53.306, 23.753 ± 50.147i, -0.185 ± 60.917i, 0.252 ± 59.922i, -0.882 ± 54.058i, -2.649 ± 46.764i, 0.107 ± 40.787i, 0.117 ± 19.1098i, 15.756 , -10.1178, 4.214 , -2.0466898, 0.329,

-78.207, -11.0297 ± 77.991i , -33.72099 ± 62.438i , -55.822 ± 13.709i , -0.0366 ± 60.149i,-8.695 ± 59.761i,-23.867 ± 49.793i ,-37.4587 ± 29.6597i -0.8639 ± 54.054i, -2.649 ± 46.763i, -6.195 ± 39.864i, -3.3486 ± 18.664i, -29.0615, -18.503, -8.5158 , -5.20644 , -1.603 , -0.390 ,

4. Linear chirp function- For final simulation, the chirping case is considered. For this situation, the following linear chirp function is adopted. Φ ' ( z) =

2 F (z − 0.5L ) L2

,

(14)

where the chirp parameter (F ) is assumed to be π . For this given chip function, the real and estimated reflection coefficients are illustrated in Fig. 5. n=12,m=21,Linear chirp 1.4 Real Estimated


1.2

1

0.8

0.6

0.4

0.2

0

0

2

4

6

8

10


Fig. 5. The real and estimated reflection coefficient Vs. normalized frequency.

The estimated poles and zeros are illustrated in Table 4.


Table 4: Estimated Poles and Zeros Linear chirp Zeros(1 2) Poles(2 1)

5.568 ± 67.213i, 1.0278 ± 61.693i, 1.482 ± 42.582i, 2.439 ± 24.298i, 9.147 , 0.848 , 0.356 ± 0.442i, -59456.559,-1093.824,-10.402 ± 77.098i,-0.384 ± 63.328i, -16.972 ± 49.850i -7.694 ± 51.435i,-9.8297 ± 40.097i, -19.0889 ± 27.0676i, -5.6734 ± 22.624i -17.7278, -10.34798 , -0.8977 , -0.3167 ± 0.4768i,

In this section our proposed method for obtaining optimal number of poles and zeros has been investigated. We have shown that the optimum transfer function closely estimates the real reflection coefficient. Therefore, the proposed method can be an excellent method to implement and illustrate the optical systems in frequency domain.

5. CONCLUSION In this paper, GAs has been used to estimate an optimal transfer function to describe operation of complex fiber Bragg Gratings. For illustrating the ability of our method, useful examples have been considered. The simulated results have illustrated excellent agreementcompatibility between estimated and real functions. The presented results facilitate application of control system analysis to optical systems, covering both linear and especially nonlinear cases.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

T. Erdogan, “Fibre Grating spectra,” Journal of Lightwave Technology, 15(8), 1277-1294 (1997). Y. Sun, C. Yun, J. Lin, Y. Qian, B. Bai, Y. Yang and W. Qiu, “Study on the Apodized Function of chirped fibre grating for dispersion compensation,” Journal of Optoelectronics Laser, 10(3), 228-231 (1999). M. LeBlanc. S. Y. Huang, M. M. Ohn. R. M. Measures, A. Guemes, and A. Othonos, "Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis," Opt. Lett. 21, 1405-1407 (1996). H. Kogelnik, “Filter response of Non-uniform almost-periodic structures,” Bell Sys. Tech. J., 55, 109–126. J. Azana and L. R. Chen, “Synthesis of temporal optical waveforms by Fiber Bragg Gratings: a new approach based on space-to-frequency-to-time mapping,” J. Opt. Soc. Am. B, 19(11), Nov. 2002. J. E. Dennis, and R. B. Schnabel, “Numerical methods for unconstrained optimization and nonlinear equations,” Prentice-Hall, 1983. E. C. Levi, "Complex-Curve Fitting," IRE Trans. on Automatic Control, AC-4, 37-44 (1959). R. L. Haupt and S. Ellen Haupt, Practical Genetic Algorithms, John Wiley & Sons, 2004. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Sys. Tech. J., 55, 109–126 (1976), D. L. Jaggard and Y. Kim, “Accurate one-dimensional inverse scattering using a nonlinear renormalization technique,” J. Opt. Soc. Am., 2(11), 1922-1930 (1985). E. Peral, J. Capmany and J. Marti, “Iterative Solution to the Gelfand-Levitan-Marchenko Coupled equations and application to synthesis of fiber gratings,” IEEE J. Quantum Electronics, 37, 165-173 (2001). G. H. Song and S. Y. Shin, “Design of corrugated waveguide filters by the Gelfand-Levitan-Marchenko inverse scattering method,” J. Opt. Soc. Am. A, 2, 1905-1915 (1995). J. E. Roman, and K. A. Winick, “Waveguide Grating filters for dispersion compensation and pulse compensation,” IEEE J. Quantum Electronics, 32, 2078-2084, 1996.


14. J. Skaar, L. Wang and T. Erdogan, “On the Synthesis of fiber gratings by layer peeling,” IEEE J. Quantum Electronics, 37, 165-173 (2001). 15. J. Skaar and K. Magne Risvik, “A Genetic Algorithm for the inverse problem in synthesis of Fiber Gratings,” J. Lightwave Technology, 16(10), (1998).


Physical parameters identification of non-uniform fiber Bragg gratings using interpolation method A. Rostamia, A. Yazdanpanaha and F. Janabi-Sharifib a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3 E-mail: [email protected]

ABSTRACT The Interpolation method for identification of the Apodized and Chirped Fiber Bragg Gratings is used. For this purpose, the Riccati equation for obtaining the reflection coefficient is used and numerically solved. Then for various system parameters, the maximum reflection peaks, bandwidth of the reflection coefficient and the central frequency are determined. Then using interpolation technique, three analytical equations can be extracted for the above-mentioned quantities. Therefore using the obtained reflection coefficient there is a map from the reflection coefficient in frequency domain to real space (index of refraction space). Hence, for the measured reflection coefficient, one can determine the index of refraction profile including Apodized and Chirped functions. The proposed method is effective and can easily determine the index of refraction profile. Key words- Inverse Scattering, Interpolation method, Apodized and Chirped Fiber Bragg Grating

1. INTRODUCTION High speed optical fiber communication systems depend critically on the design of complex filters to perform various functions such as selection of wavelength multiplexed channels or compensation of the link dispersion. The technology of ultraviolet photo-induced fiber gratings has reached now the necessary maturity to implement these filters [1]. Several experiments have been demonstrated to fabricate nonuniform gratings, permitting an accurate control of both the local grating pith and the apodization profile along the structure [2, 3]. For design of these complex filters there are some interesting methods including: 1. Approximate Fourier Transform method [4-7]; 2. Exact Solution of the problem expressed in terms of integral equations [8-13]; and 3. Exact inverse scattering algorithms called differential or direct methods [14-17]. Since the design of optical complex systems is necessary for optical applications, identification of complex optical integrated systems and devices is very important for optimum optical integrated system design. In practice estimation of the implemented structure is critical for scaling of the output signal and relating the measured quantity to the physical parameters. There are some published works in this domain. But, all of the Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740Y, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.684886

Proc. of SPIE Vol. 6374 63740Y-1

presented methods are based on complex electro-optical setup [18-20]. However, arranging these complex setups need more careful tuning for precise measurement. Here, we present a novel algorithm based on interpolation technique to identify the system parameters of the complex Bragg gratings. In this method, we extract three distinguishable quantities such as maximum reflection peak, bandwidth of the reflection coefficient and the central frequency, which are interesting and easy to measure in practice. The proposed method can be easily implemented in all-optical domain. Therefore, the presented method will offer highspeed for reconstruction of the medium profile. The organization of the paper is as follows. In section II, the mathematical modeling of the complex Bragg Gratings is presented. Also, the Riccati equation is derived. In section III, interpolation relation and simulation result of the proposed method are illustrated. Finally the paper ends with a conclusion.

2. MATHEMATICAL MODELING OF COMPLEX BRAGG GRATINGS A fiber Bragg grating is a periodic perturbation structure of the refractive index in a waveguide. The Apodized and chirped index of refraction for the fiber Bragg gratings can be written as follows [21].

n( z) = n0 + ∆ndc +

A( z)∆nac i[( 2πΛN ) z +Φ( z )] (e + c.c.) , 2

(1)

where n0 , ∆ndc , ∆n ac , Φ (z ) , N , Λ and A(z ) are constant index of refraction, the average refractive index of the core, the modulated ac refractive index, an arbitrary spatially varying phase, an integer that signifies its harmonic order, the period of the perturbation, and the Apodization function respectively.

z Fig. 1. Refractive index change of the fiber Bragg grating.

Based on Helmholtz equation, the following electric field distribution can be considered for the Grating mentioned above as [21]

Et =

1 i (ω t − β µ z ) i (ω t + β µ z ) ( Aµ ξ µt e + B µ ξ µt e + cc ) 2

(2)

, Aµ , Bµ and β µ are the radial transverse field distribution of the µ

th

guided mode, the

amplitude of direct and indirect propagating modes and the propagation constant of µ Also the propagation constant can be defined as follows.

th

mode respectively.

Where ξ

µt

βµ =

2π

λ

n0 cos θ =

2π

λ

neff ,


(3)

where n0 , λ , and θ are the refractive index of the core, input wavelength and beam angle respectively. The appeared electric field amplitudes in Eq. (2) can be related together by the standard coupled-wave equations [22, 23] as follows.

∂Bµ ∂z ∂Aµ ∂z

= iK dc Bµ + iK ac Aµ e −i ( ∆βz −Φ ( z ))

= −iK dc Aµ − iK ac∗ Bµ ei ( ∆βz −Φ ( z )) ,

(4)

where the phase mismatch ∆β , as known as detuning, is given by Eq. (5), 2π 4π 2π 1 1 ∆β = 2 β − = n eff − = 4πn eff ( − ), λ λ λD Λ Λ

(5)

where λ D = 2neff Λ is the Bragg wavelength. The coupling dc coefficient can be calculated as follows.

K dc =

2π∆n ac

λ

.

(6)

Also the ac coupling constant K ac is given as follows:

K ac =

π ∆ n ac . λ

(7)

Now based on introducing the following variables [24], a new form of the coupled wave equations can be derived that is easy for extraction of physical quantities. i −( )[∆βz −Φ ( z ) ]

R = Aµ e

S = Bµ

2

i ( )[∆βz −Φ ( z ) ] e2 .

(8)

By substitution Eq. (8) into Eq. (4) the following set of coupled wave equation can be obtained.

1 dΦ ( z ) dR )]R = −iK ac∗ A( z ) S , + i[ K dc + (∆β − dz 2 dz dS 1 dΦ ( z ) − i[ K dc + (∆β − ]S = iK ac A( z ) R. 2 dz dz

(9)

Here, for simplicity we assume that both the ac coupling coefficient K ac A(z ) and the grating phase

Φ ( z ) are slowly varying functions of z , indicating the non-uniformity in the grating parameters. We assume that the structure has a length L and extends from z = 0 to z = L . The boundary conditions for our scattering problem are:

R ( 0 ) = 1, S ( L ) = 0 . Then a local reflection coefficient ρ ( z ) is defined as


(10)

ρ (z) =

S R

(11)

So, based on the above-mentioned definition and using coupled mode equations the following differential equation can be obtained that is Riccati equation. 4π 2π π .∆ n dρ dΦ ) A ( z )( 1 + ρ 2 ) + i ( )ρ = i( − n effnew − λ Λ dz λ dz

(12)

where n effnew = ∆ n dc + n eff .The boundary condition for this equation according to boundary conditions presented in Eq. (10) can be presented as ρ ( L ) = 0 . Based on exact or numerical solutions of the Riccati equation, the reflection coefficient and energy reflection can be extracted.

3. RESULTS AND DISCUSSION In this section the presented relations in section 2 is applied for two practical interesting cases. These cases are linear chirped Bragg Grating and Gaussian Apodization. Hence, we first consider the linear chirped Bragg Gratings. a) Linear Chirped Bragg Gratings- In this case linear chirped is considered. According to basic information about chirp concept the following relations can be used [25]. 1 dΦ z (13) = F 2 dz ( FWHM ) 2 where F is chirp parameter and defined as [26] F =

where FWHM and

( FWHM z2

)2

Φ ( z ) = − 4 π n eff

( FWHM

λ

2 D

)2 dλD dz

(14)

dλD are full-width-at-half-maximum of the Grating profile and rate of change of the dz

design wavelength with the position in the grating, respectively. Now based on the presented simulation results, three analytical relations based on interpolation technique are presented for three main parameters that were presented in introduction (the maximum reflection coefficient, bandwidth, and the central frequency) as follows. In this case, we consider four different values of modulated index of refraction, i.e., 0.0002, 0.0004, 0.0006 and 0.0009.


0.8 0.7 0.6

reflectivity

0.5

(a)

(b)

0.4 0.3 0.2 0.1 0 1.54

1.545

1.55 1.555 Weavelenght(micrometre)

1.56

1.565

Fig. 2. The reflection coefficient vs. incident wavelength for chirped Bragg grating dλ ∆n ac = 0.0004 , and (a) dλ D = −2.5 ; (b) D = 2.5 . dz dz

1

(a)

0.9 0.8

(b)

reflectivity

0.7 0.6

(c)

0.5 0.4

(d)

0.3 0.2 0.1 0 1.52

1.525

1.53

1.535 1.54 1.545 Weavelenght(micrometre)

1.55

1.555

Fig. 3. The reflection coefficient vs. wavelength for chirped Bragg grating

dλ D dλ D dλ D ∆nac = 0.0006 , (a) = −1, (b) = −2, (c) = −4, dz

dz d λ D (d) = −6. dz


dz

1

(d)

0.9 0.8

(c)

reflectivity

0.7

(b)

0.6 0.5 0.4 0.3

(a)

0.2 0.1 0 1.544

1.546

1.548

1.55 1.552 1.554 Weavelenght(micrometre)

1.556

1.558

Fig. 4. The reflection coefficient vs. wavelength for chirped Bragg grating

dλ D = −2.5 (nm/cm), ∆n ac = (a) 0.0002; (b) 0.0004; dz (c) 0.0006; (d) 0.0009.

1.1 1

maximum reflectivity

0.9 0.8

0.0009 0.0006 0 0006

0.0004

0.7 0.6 0.5

0.0002

0.4 0.3 0.2 0.1 −5

−4.5

−4 −3.5 −3 −2.5 −2 chirp variable(nonometre/centimetre)

Fig. 5. The maximum reflection vs.

−1.5

−1 −7

x 10

dλD with different modulated refractive index as parameter dz ∆n ac varies

Fig. (4) shows our simulations for four different modulated Index of refractions. In the following figures the lines show simulated results and circles show corresponding interpolated versions.


dλ D 3 dλ dλ ) + 9.97 × 1012 ( D ) 2 + 4.57 × 10 7 ( D ) dz dz dz dλ 11 dλ D 3 11 dλ D 2 = −1.30099 × 10 ( ) − 1.1345 × 10 ( ) + 1.47 × e 6 ( D ) dz dz dz d d d λ λ λ = −2.84 × 1018 ( D ) 3 − 3.2 × 1012 ( D ) 2 − 4.8 × 10 5 ( D ) dz dz dz d λ d λ dλ = 3.336969 × 1018 ( D ) 3 − 4.692 × 1011 ( D ) 2 − 3.3 × 10 5 ( D ) dz dz dz

1) ρ max = 7.92 × 1018 ( 2) ρ max 3) ρ max 4) ρ max

(15)

After interpolation of the maximum reflection coefficient, we consider the case for bandwidth. Using simulated results the following interpolated relations can be obtained for different modulated refractive indices of 0.0002, 0.0004, 0.0006 and 0.0009 for following cases 1 to 4 respectively. dλ D ) − 1.6 × 10 − 4 dz dλ 2)∆ω = 1.88 × 10 4 ( D ) + 1.6 × 10 − 4 dz 4 dλ D 3)∆ω = 1.85 × 10 ( ) + 5.3 × 10 − 4 dz dλ 4)∆ω = 1.85 × 10 4 ( D ) + 1.01 × 10 −3 dz

1)∆ω = 1.92 × 10 4 (

(16)

Here based on the interpolated relations the following figure show good agreement between complete simulations and our interpolations. As a final interpolation, we consider central frequency of the reflection coefficient. Our simulations show that in this case for different modulated refractive index really the central frequency approximately is unique and we can consider only one interpolated relation for the case. So, the following relation shows the central frequency in terms of system parameters. dλ dλ ⎡ ⎤ λ0 = ⎢4.4643 × 10 8 ( D ) 2 + 9.85 × 10 3 ( D )1 + 1.55⎥ . dz dz ⎣ ⎦

(17)

Using the interpolated relation, Fig. 7 shows complete simulation (two curves) and interpolated case (curve with circles) that follow each other closely. Using the interpolated relations for basic three factors, now in the following we consider two maps between the bandwidth and maximum reflection coefficient versus modulated refractive index that are shown in Figs. (7 and 8). Using these figures one can obtain the modulated refractive index in terms of the measured bandwidth and the maximum reflection coefficient. Now, we first present the interpolated relation as follows. (18) ∆ω = −2.525252 × 10 5 (∆nac ) 3 + 5.9 × 10 2 (∆nac ) 2 + 9.9 × 10 −1 (∆n ac )1 + 4.59 × 10 −3 Fig. (7) Shows the simulation results and interpolated curves (F=200) and illustrate close compatibility between them.


−3

x 10

10

0.0006

9

Bandwidth(micrometre)

8

0.0009

7 6

0.0002

5

0.0004

4 3 2 1

1

1.5

2

2.5 3 3.5 Chirp variable(nm/cm)

4

4.5

5 −7

x 10

Fig. 6. The 3dB bandwidth vs. dλ D with different modulated refractive index ∆n ac values. dz

central wavelenght(micrometre)

1.557

1.556

0.0002

1.555

0.0004 1.554

1.553

1.552

0.5

1

1.5

2 2.5 3 3.5 chirp variable(nm/cm)

4

4.5

5 −7

x 10

Fig. 7. The central wavelength vs. dλ D with different modulated refractive index ∆nac values.

dz


−3

6

x 10

5.5

200

Bandwidth(micrometre)

5 4.5

150

4 3.5

100

3 2.5 2

2

3

4

5 6 modulation index

7

8

9 −4

x 10

Fig. 8. The bandwidth vs. the modulated refractive index for different F values.

Now, the maximum reflection coefficient can be considered. The following relations show the interpolated relations for the maximum reflection coefficient versus modulated refractive index for different chirp parameters 100, 150 and 200 respectively. 1) ρ max = 3.896 × 10 9 (∆nac ) 3 − 8.37 × 10 6 (∆nac ) 2 + 5.89 × 10 3 (∆n ac )1 − 3.58 × 10 −1 (19) 2) ρ max = 1.787 × 10 9 (∆n ac ) 3 − 4.95 × 10 6 (∆n ac ) 2 + 4.4469 × 10 3 (∆nac )1 − 2.97 × 10 −1 3) ρ max = 1.829 × 10 9 ( ∆n ac ) 3 − 2.212 × 10 7 (∆n ac ) 2 + 3.193 × 10 4 (∆n ac )1 − 2.28 The following figure shows simulated and interpolated (blue curves) cases and illustrates good compatibility in different values of the chirp parameter.

maximum reflectivity

1.4

1.2

100

1

150

0.8

0.6

200

0.4

0.2

0

1

2

3

4 5 6 7 refractive index modulation

8

9

10 −4

x 10

Fig. 9. The maximum reflection coefficient vs. the modulated refractive index for different values of the chirp parameter F.using both simulation and interpolation methods.

b) Gaussian Apodization- In this case we consider the Gaussian Apodization as follows.


L ⎤ ⎡ (z − )2 ⎥ ⎢ , 2 A ( z ) = exp ⎢ − a ⎥ , z ∈ [0 , L ] L ⎢ ⎥ ⎣ ⎦

(20)

where a is Gauss width parameter [27]. Using the simulated results the following relation can give a suitable interpolated relation for the maximum relation versus Gauss parameter.

ρ max = −5.49 × 10 −7 (a) 3 + 1.142 × 10 −6 (a) 2 − 2.07 × 10 −6 (a) + 0.9999996 .

(21)

Fig. (9) shows the simulated result and interpolated case. Interpolated curve is shown with blue curve that is compatible with real case that is illustrated with red curve. These curves are hardly distinguishable. 1

1

maxreflectance

1

1

1

0.9999

0.9999

0

0.5

1

1.5

2 2.5 3 Gauss width parameter

3.5

4

4.5

5

Fig. 10. The maximum reflection coefficient vs. the Gauss width parameter

∆nac = 0.0004 . 4. CONCLUSION In this paper a novel method based on interpolation technique for identification of complex Bragg Gratings has been developed. Here, three main factors, which are critical, interesting and easy for measurement have been considered for interpolation. Our proposed analytical relations are greatly compatible with complete numerical simulations. Also, our proposed method provides a map from frequency domain to position to identify medium optical characteristics. The proposed method is easy for practical engineering and can be extended for more complex cases. REFERENCES 1. 2.

G. Meltz, W. W. Morey, and W. H. Glen, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett., vol. 14, no. 15, pp. 823–825, Aug. 1989. W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, and R. I. Laming, “Complex grating structures with uniform phase masks based on the moving fiber-scanning technique,” Opt. Lett., vol. 20, no. 20, pp. 2051–2053, Oct. 1995.


3.

A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren, and R. A. H. Stubbe, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol., vol. 15, pp. 1419–1423, Aug. 1997. 4. K. I. Hopcraft and P. R. Smith, “An introduction to electromagnetic inverse scattering.” Dordrecht, The Netherlands: Kluwer, 1992. 5. J. A. Dobrowolski and D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt., vol. 17, no. 19, pp. 3039–3050, Oct. 1978. 6. B. G. Bovard, “Fourier transform technique applied to quarterwave optical coatings,” Appl. Opt., vol. 27, no. 15, pp. 3062–3063, Aug. 1988. 7. K. A. Winick and J. E. Roman, “Design of corrugated waveguide filters by Fourier-transform techniques,” IEEE J. Quantum Electron., vol. 26, pp. 1918–1929, Nov. 1990. 8. I. M. Gel’fand and B. M. Levitan, “On a determination of a differential equation from its spectral function,” Amer. Math. Soc. Trasl., Ser. 2, vol. 1, pp. 253–304, 1955. 9. G. L. Lamb, Jr, “Elements of soliton theory.” New York: Wiley, 1980. 10. A. M. Bruckstein, B. C. Levy, and T. Kailath, “Differential methods in inverse scattering,” SIAM J. Appl. Math., vol. 45, no. 2, pp. 312–335. Apr. 1995. 11. P. V. Frangos and D. L. Jaggard, “A numerical solution to the Zakharov- Shabat inverse scattering problem,” IEEE Trans. Antennas Propagat., vol. 39, pp. 74–79, Jan. 1991. 12. B. Gopinath and M. M. Sondhi, “Inversion of the telegraph equation and the synthesis of nonuniform lines,” Proc. IEEE, vol. 59, pp. 383–392, Mar. 1971. 13. P. V. Frangos and D. L. Jaggard, “The reconstruction of stratified dielectric profiles using succesive approximations,” IEEE Trans. Antennas Propagat., vol. 35, pp. 1267–1272, Nov. 1987. 14. I. Kay, “The inverse scattering problem when the reflection coefficient is a rational function,” Commun. in Pure Appl. Math., vol. 13, pp. 371–393, 1960. 15. G. H. Song and S. Y. Shin, “Design of corrugated waveguide filters by the Gel’fan-Levitan-Marenko inversescattering method,” J. Opt. Soc. Amer. A, vol. 2, no. 11, pp. 1905–1915, Nov. 1985. 16. J. E. Roman and K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron., vol. 29, pp. 975–982, Mar. 1993. 17. E. Peral, J. Capmany, and J. Marti, “Design of fiber grating dispersion compensators using a novel iterative solution to the Gel’fan-Levitan- Marchenko coupled equations,” Electron. Lett., vol. 32, no. 10, pp. 918–919, May 1996. 18. “Iterative solution to the Gel’fan-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings,” IEEE J. Quantum Electron., vol. 32, pp. 2078–2084, Dec. 1996. 19. J. Skaar, B. Sahlgren, P. Y. Fonjallaz, H. Storoy, and R. Stubbe, “Highreflectivity fiber-optic bandpass filter designed by use of the iterative solution to the Gel’fan-Levitan-Marchenko equations,” Opt. Lett., vol. 23, no. 12, pp. 933–935, June 1998. 20. P. V. Frangos, D. J. Frantzeskakis, and C. N. Capsalis, “Pulse propagation in a nonlinear optical fiber of parabolic index profile by direct numerical solution of the Gel’fan-Levitan integral equations,” Proc. Inst. Elect. Eng., pt. J, vol. 140, no. 2, pp. 141–149, Apr. 1993. 21. R. Kashayap, Fiber Bragg Gratings, Academic, Londan, 1999. 22. A.Yariv, “Coupled-mode Theory for guided-wave optics,” IEEE J.Quantum Electron ., QE-9 (September 1973) , pp.919-913. 23. H. Kogelnik, “Theory of Dielectric waveguides,” in Integrated optics , ed . T . Tamir , Heidelberg : Springer , 1975 . 24. E. Kreyszig, Advanced Engineering Mathematics , 5 th Ed. , p .345, Wiley , New York, 1992. 25. T. Erdogan, “Fiber grating spectra,”, Journal of Lightwave Technology , vol. 15, no.8, 1997, pp. 1277-1294. 26. H.Kogelnik , “Filter response on nonuniform almost-periodic structures.” Bell system Technical Journal, vol.55, no.1, 1976, pp. 109-126. V. Tzolov, D. Feng, S. Tanev, and Z.Jakubczyk, “Modeling tools for integrated and fiber optical devices,” Proc. Integrated Optics Devices ΙΙΙ , Photonics West 99, San Jose, CA,1999, pp. 23-29.


Circuit modeling of Multiple Quantum Well Lasers optimized by carrier tunneling A. Rostamia, H. Rasoolib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Department of Electrical Engineering, Islamic Azad University of Tabriz, Tabriz, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT In this paper, the effect of carrier tunneling between wells on multiple-quantum well (MQW) laser characteristics is investigated. Based on the rate equations developed for 3-levels (carrier transport between 3-D, 2-D and quasi 2-D states) including carrier tunneling effect, a circuit model is proposed. According to simulation results with change of tunneling time three interesting regions of operation are obtained. The operation of the proposed laser doesn’t change for tunneling time larger than a threshold value (0.1 nsec). For the tunneling time smaller than another threshold value (0.01 nsec) the operation of the laser strongly degraded. For the tunneling time between the two thresholds values the operation of the laser can be optimized, which in this paper it is done for obtaining low turn-on delay time, leading to suitable operation from simultaneous filling of the wells, high output intensity and large bandwidth points of view. Keywords- Multiple Quantum Well Laser, Carrier Tunneling, Spice Circuit Modeling

1. INTRODUCTION Nowadays high speed optical communication and computing are basic demands in industry and biology. For this purpose, high speed laser diodes, broadband optical fibers and high speed photo-detectors are necessary. Recently it is illustrated that Multiple Quantum Well Lasers (MQWL) has inherent properties such as lower threshold current and low temperature dependency, high differential gain and higher bandwidth. Also, it is demonstrated that MQWL has faster dynamics [1]. These effective properties are excellent to introduce MQWL for high speed optical communication and computing. For analysis of the quantum well lasers first one level rate equation was presented [2]. In this model the interaction between quantum wells confined states and photon population has been considered. This method had some problems for description of dynamic response such as low frequency roll off degradation [3]. So, for description of this problem, two levels model was presented [3]. In this model transportation of carriers across optical confinement layer (OCL) was considered and it was shown that the origin of the problem is related to this phenomenon. This model had good ideas about transportation of carriers across OCL but it couldn’t illustrate clearly quantum coupling between OCL (3-D) states and confined (2-D) states in well [4]. The capturing and escaping between 3-D and 2-D states is so important for exact modeling of high speed

Optomechatronic Actuators, Manipulation, and Systems Control, edited by Yukitoshi Otani, Farrokh Janabi-Sharifi, Proc. of SPIE Vol. 6374, 63740Z, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.683990

Proc. of SPIE Vol. 6374 63740Z-1

laser diodes. For introducing suitable model to incorporate this phenomenon, the three levels rate equations proposed by [5]. For building of this model the gateway states has been added to two levels rate equations [6]. For MQWL there is another interesting phenomenon related to transportation of carriers across the barriers. For handling of this phenomenon, there are two basic events including thermionic emission and carrier tunneling [7]. For solving of the obtained equations in each of mentioned above models the transmission line method (TLM) [8], full numerical self consistent methods based on finite difference (FD) and finite element (FE) and circuit models have presented [6]. From simulation point of view the circuit modeling is interesting especially there is a little problem about convergence compared other methods. Also, this type of simulation can help to total system evaluation. In this direction the circuit model for single quantum well lasers using three levels rate equations was presented by B. P. C. Tsou et al [6]. Also, for MQWL the circuit modeling based on three levels rate equations was presented by G. Rossi et al [9]. For integrated laser diodes such as MQWL the tunneling effect between wells is possible. In this paper, we try to incorporate the tunneling effect to these circuit models and investigate it properties. We like study the tunneling effect on output intensity, turn on delay time, transient behavior, inhomogeneous wells filling up and bandwidth of the MQWL. In this study the tunneling time based on optimum laser operation will be adopted. So, in our treatment generally different tunneling time for each well should be considered. The organization of this paper is as follows: In section II the mathematical modeling based on three levels including the tunneling effect is considered. The circuit model is presented in section III. In section IV simulation results and discussion will be presented. Finally the paper ends with a conclusion.

2. MATHEMATICAL MODELING In this section the operation of MQWL based on the 3-levels rate equation is explained as follows [7]. Fig. 1 shows carrier transportation processes and light emission in MQWL. According to the 3-levels rate equations fundamental there are four sets of equations for carriers including left and right OCLs , the quasi 2-D states (gateway) and confined states (wells) and one equation for photon density variation. In this analysis the ambipolar model is used [7]. I Dout

thff]$!©=©

da-ajff]si© th©,]li©rn SCH

tlu bt

1qui-2D]

çui-2D] 1qui-2D]

L_° L_° cT HIT LIT J/ — J/

Clathhng I OCL L_&to&

Lan.r

QW3

cui-2D)

cui2D1

______

______

OCL

LIT LIT _)Stthd

Cladding

QW4

P-side

N-side

Fig. 1. Schematics of Multiple Quantum Wells Laser.

The following sets of equations are presented to describe the operation of MQWL [9]. In these equations the tunneling effect is inserted in Eq. (8) considering carrier flow due to this phenomenon. (1) RS ,B,W = AS ,B,W nS ,B,W + BS , B,W nS2,B,W + CS , B,W nS3,B,W


I inj dn S1 I = − R S1 − D , qV S 1 dt qV S1

(2)

VS 1nS 1 − VW nB1 , τD

(3)

dn S 2 I D ( N QW ) − I DOut n V nW ( N QW ) = − RS 2 − [ S 2 − W ], dt qV S 2 τ C VS 2 τ e

(4)

ID =

VS 2 nS 2 , τD I −I n n = D ( j ) D ( j +1) − RB − [ B ( j ) − W ( j ) ] , τC τe qVW I Dout =

dnB ( j ) dt

I D( j ) = dnW ( j ) dt

=[

n B( j )

τC

−

VW nB ( j ) − VW nB ( j −1)

nW ( j )

τe

τB

G[nW ( j ) ] 1+ ∈ s

G[nW ( j ) ] = G0 [1 + ln

(6)

,

(7)

] − RW ( j ) −ν g G[nW ( j ) , S ]S +

G[nW ( j ) , s ] =

(5)

nW ( j −1)

τ Tun ( j −1)

−

nW ( j )

τ Tun ( j )

,

nW ( j ) N0

(8) (9)

],

τ−p1 = [α + ln( Rm−1 ) / LC ] / vg , K dS K s = ∑ Γ ( j ) vg G[nW ( j ) , s ]s + ∑ Γ ( j )β( j ) RSp [nW ( j ) ] − , τ dt j =1 j =1 p

R=

,

τC 2 = R0 + R1 J inj , τe

(10)

(11) (12)

(13)

where A, B, C, n Sj , nW ( j ) , n B ( j ) , RSj , RWj , RBj ,VSj ,VWj , I inj , I D , I D , I D ( j ) , G , G0 , N 0 ,τ p , LC , , τ D ,τ C ,τ e ,τ B ,τ Tun ( j ) , ε Out

Γ, β , R, S , α , Rm , vg , Rsp and N QW are the recombination coefficients, the carrier density of left (j=1) and right (j=2) OCL, carrier density in quantum wells, carrier density in quasi 2-D states, recombination rates for left and right OCLs, recombination rates for wells, recombination rates for quasi 2-D states, the volume of OCLs, the volume of Wells, injected current from p-side (left) OCL, drift-diffusion current from left OCL to the first quasi states, outgoing current from right OCL, drift-diffusion current between two adjacent quasi states, optical Gain for each Well, parameter extracted from characterization of real device, parameter extracted from characterization of real device, photon life time in the cavity, cavity length, effective space transport time [7], carrier capture time, carrier escape time, diffusion time across the barriers, the tunneling time, gain suppression factor, optical confinement factor, spontaneous emission factor, the ratio of capture to


escape times, photon density, internal loss, mirror reflection coefficient, group velocity, spontaneous emission rate and the total number of quantum wells respectively. In these sets of equations Eqs. (2), (4), (6), (8), and (12) are the carrier rate equations for left and right OCLs, the carrier rate equations for quasi 2-D states, carrier rate equations for the wells and the photon density equation respectively. Also, in these equations we let the density of carriers in each well change with the tunneling effect between wells. For this purpose, there is a possibility to change the density of carriers inside each well with incoming rate of carriers from left and outgoing to the right well. In this calculation, the tunneling time from left and to the right can be different. Also, in this paper the tunneling effect is assumed completely stochastic and Eq. (8) can show this effect.

3. CIRCUIT MODELING For solution of these coupled equations mentioned above in section II, we try to present circuit model that can be solved by SPICE simulation software. For this purpose, the following sets of equations that are based on the rate equations can be arranged.

VS 1

d (qnS 1 ) = I inj − I Sric1 − I D , dt I Sric1 = qVS1 RS 1 , vS 1 = qnS 1

(14)

,

CS 1 = vS 1 dv CS 1 S 1 = I inj − I Sric1 − I D , dt CB

CW ( j ) =

dvB ( j ) dt

dvW ( j ) dt

= [ I D ( j ) − I D ( j +1) ] − I Bric( j ) − [ I C ( j ) − I e ( j ) ] ,

= [ I C ( j ) − I e ( j ) ] − I Wric( j ) − I stm ( j ) + I tun ( j −1) − I tun ( j ) ,

(15) (16) (17)

I Bric,W = qV B ,W RB ,W ,

v B ,W = qn B ,W , C B ,W = VB ,W , I Tun ( j −1) = qVW ( j −1)

nW ( j −1)

I Tun ( j ) = qVW ( j ) CW ( j ) =

dvW ( j ) dt

I c = qVB

,

τ Tun ( j −1) nW ( j )

τ Tun ( j )

,

(18) (19)

= [ I C ( j ) − I e ( j ) ] − IWric( j ) − I stm ( j ) ,

(20)

nB Rn , I e = qVW W , τC τC

(21)


C fm

dv fm dt

=

N QW

∑Γ j =1

NQW

I

( j ) stm ( j )

+ ∑ Γ ( j ) I sp ( j ) − j =1

v fm R fm

,

I stm ( j ) = qVW vg G[nW ( j ) , s ]s ,

(22) (23)

I sp ( j ) = qVW β( j ) Rsp [nW ( j ) ] ,

(24)

hv , qVW qV = W , hv

R fm = τ p C fm

S

I

So, based on electrical passive component relations and circuit principles such as KCL and KVL, the following figure shows the circuit model for describing the laser operation. For example Eq. (16) shows a capacitor, which variation of the current of this element is controlled by some current sources connected to the node.

Fig. 2. Circuit model for MQWL including Tunneling effect (CPL and CPR are constants depending on device geometry and parameters).

Also, Eq. (15)-(17) and Eq. (22) show the circuit model for left OCL, quasi 2-D states, confined states (Wells) and photon density respectively. The tunneling effect on circuit modeling is introducing two current incoming and outgoing sources for each well, which is shown in Eq. (17).


4. SIMULATION RESULTS AND DISCUSSION In this section for simplicity the circuit modeling is done for 5 wells of InGaAsP laser diode. This laser is tuned for 1.55µm to apply to optical communication. Also, the active layer of the laser diode includes two OCLs

In0.13 Ga 0.87 As 0.45 P0.55 ( 1000A 0 ) with density of impurity at level 5 × 1017 cm −3 , 5 wells

In0.27 Ga 0.73 As 0.75 P0.25 ( 90A 0 ) and 4 barriers In0.13 Ga 0.87 As 0.45 P0.55 ( 96A 0 ).The simulation parameters are given in Table 1. In this section the circuit model presented in section 3 is simulated using SPICE software. The static, transient and frequency response are illustrated. It is shown that using optimal tunneling time for each well (generally different from together) some of interesting quantities such as the output intensity, bandwidth and turn-on delay time are improved. Therefore, the tunneling effect can be engineered to introduce better operation for MQWL in high speed optical communication. Table 1. Simulation parameters. Name Symbol Number of well NQW Spontaneous emission factor Β Optical confinement factor Г (mean value for one well) Trap aided recombination coefficient A Radiative recombination coefficient B Auger recombination coefficient C Ambipolar Diffusivity Da Barrier width LB Well width LW Active region width W Gain coefficient G0 Gain carrier weighting coefficient N0 Gain suppression factor ε Capture time τc Capture to escape time ratio eq(2-13) R0 Capture to escape time ratio eq(2-13) R1 Internal losses α Facet reflectivity Rm Parasitic capacitance Cp Parasitic series resistence Rp

Value 5 0.0001 0.0235 ~108 s-1 ~10-11 s-1cm3 ~10-28 s-1cm6 ~1s-1 cm2 9.6 nm 9 nm 2.3 µm 980 cm-1 2.5*1018 cm-3 5*10-17 1 ps 0.01 30*10-12 (cm2/A)2 30 cm-1 0.32 7 pF 3.5 Ω

In Fig. 3 the carrier distribution without tunneling in wells is illustrated. As it can be seen the population is decreased from first to fifth wells. On the other hand the population for left hand side well is highest and for right hand side is lowest between all wells (nonuniform population distribution). Hence, population is inhomogeneous and the output intensity is low.


Lc Inmi T loCi

B

Ohhoi tunneling eIc1e)

B

ci B

4

co uJ

3 =

0 2 C)

U U

IU

2U

3U

4U

BU

BU

7U

8U

9U

IUU

Current [mA]

Fig. 3. Nonuniform distribution of carriers in Wells (without Tunneling).

Fig. 4 shows the case for nonzero tunneling effect. As it can be seen the population is more uniform than previous case. This is related to the tunneling possibility between wells that make another way for carrier transportation between wells. Therefore the population in all wells near together.

Lc Inmi T loCi

B

sfth tunneling eIc1e)

B

ci B

4

co uJ

3 =

0 2 C)

U U

IU

2U

3U

4U

BU

BU

7U

8U

9U

IUU

Current [mA]

Fig. 4. Distribution of carriers in Wells (with Tunneling) ( τ Tun −1 = τ Tun − 2 = 0.2 n sec,τ Tun −3 = 0.3 n sec,τ Tun − 4 = 0.5 n sec ).

Output power in terms of bias current for both cases is illustrated in Fig. 5. In this simulation for given parameters the output power for nonzero tunneling case is more than zero tunneling case. This can be related to uniform population distribution in wells that is related to tunneling effect.


T20 [oC]

Lc200 [nm] 10

9-

——

8- _______________ — — —without tunneling effects

/ -:'

withtunneling effects

7

--

__ —

,_ —

8-

-

8

0-4-

-

-

3-

/

-

///, -7/

ft

-

20

30

:7 U

ID

-

-

;.

40

;.

80

80

70

80

90

lOU

Current [mA]

Fig. 5. Output Optical Power Vs. current of the LD ( τ Tun −1 = τ Tun − 2 = 0.2 n sec,τ Tun −3 = 0.3 n sec,τ Tun − 4 = 0.5 n sec ).

Now the transient behavior for current pulse including 2 × I th amplitude and 3 nsec pulse width is investigated for both cases. Fig. 6 and Fig. 7 are for without and with tunneling effect respectively. One can conclude that the transient behavior for nonzero tunneling times is more uniform than zero tunneling case from amplitude point of view and has low turn-on delay time. Especially from rise-time point of view, the situation is better for nonzero tunneling case. In this case, wells approximately fill up simultaneously. Also fall-time for this case is approximately close to previous one.

Lc Inmi T loCi

3.6

wfthoi tunneling eIc1e

3

V1 2.6

6

co

1.6

C)

0.6

U U

1000 2000 3000 4000 6000 6000 7000 8000 9000 10000 Time [ps]

Fig. 6. Carrier Density Transient behavior (without Tunneling).


Lc Inmi T loCi

2.6

wfth tunneling eIc1e

2

ci 6 co

1.6

=

0 C)

0.6

U

1000 2000 3000 4000 6000 6000 7000 8000 9000 10000

U

Time [ps]

Fig. 7. Carrier Density Transient behavior (with Tunneling).

Now the transient behavior of the output power is illustrated for both cases in Fig. 8. For considering the tunneling case, there are advantages such as lowering the turn-on delay time near to 55 Psec, increasing the amplitude of output power, decreasing the relaxation-time and decreasing the fall-time. These improvements in the transient characteristic are related to the tunneling process, which make faster transport of carriers between wells. Therefore, the tunneling possibility and selection of suitable tunneling time constant for each well can improve efficiency of the MQWL. Lc.Thnm

--

ThZ ccl

Ir2Ith

———without tunneling effects

with tunneling effects

U

US

IS

26

3

Time Ens]

Fig. 8. Transient Behavior of the LD.

Finally our simulation is concentrated on the frequency response of the laser diode. In this case with considering tunneling effect the bandwidth is increased more than 2 GHz. This is clearly related to faster dynamics made by the tunneling effect.


Lc200 ]nm]

T20 [oC]

ID

IUU288IUi8i82, Frequency ]GHz]

Fig. 9. Relative intensity vs. frequency.

In this section our simulations including the tunneling effect have been considered. It has shown that with considering the tunneling process, the output intensity is increased that is related to the effect of tunneling on static characteristic (uniform population distribution in wells) of the laser diode. Also, the modulation bandwidth (large and small signals point of views) of the laser is increased. This is related to faster dynamics of carrier transport due to the tunneling effect.

5. CONCLUSION In this paper the effect of tunneling process between wells in MQWL has been investigated. It has been shown that in presence of tunneling, the output intensity and modulation bandwidth can be improved. The circuit model including tunneling effect has been proposed. Our simulations have shown that there is a band for the tunneling time ( 0.01 n sec < τ Tun < 0.1 n sec ) for obtaining better characteristics for MQWL. Our proposal for improving the laser diode performance will be more visible as the number of wells increases.

REFERENCES 1. 2. 3. 4. 5. 6.

Y. Suematsu and A. R. Adams, Handbook of Semiconductor Laser and Photonic Integrated Circuits, London, U.K.: Chapman & Hall, 1994, pp. 1–22. L. V. T. Nguyen, A. J. Lowery, P. C. R. Gurney, and D. Novak, “A time-domain model for high-speed quantumwell lasers including carrier transport effects,” IEEE J. Select. Topics Quantum Electron., vol. 1, pp. 494–504, 1995. R. Nagarajan, T. Fukushima, M. Ishikawa, J. E. Bowers, and R. S . Geels, “Transport limits in high-speed quantumwell lasers: experiment and theory,” IEEE Photonics Technology Letters, vol. 4, no. 2, Feb. 1992. D. McDonald and R. F. O’Dowd, “Comparison of two- and three-level rate equations in the modeling of quantumwell lasers,” IEEE J. Of Quantum Electronics. vol. 31, no. 11, Nov. 1995. J. A. Brum and G. Bastard, “Resonant carrier capture by semiconductor quantum wells,” Phys. Rev. B, vol. 33, pp. 1420-1423, Jan. 1986. B. P. C. Tsou and D. L. Pulfrey, “A versatile SPICE model for quantum-well lasers,” IEEE J. Of Quantum Electronics, vol. 33, no. 2, Feb. 1997.


7.

A. D. Vandermeer and D. T. Cassidy, “A rate equation model of asymmetric multiple quantum-well lasers,” IEEE J. Quantum Electronics, vol. 41, no. 7, July 2005. 8. R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “High speed quantum-well lasers and carrier transport effects,” IEEE J. Quantum Electron., vol. 28, pp. 1990–2007, 1992. 9. L. V. T. Nguyen, A. J. Lowery, P. C. R. Gurney, and D. Novak, “A time-domain model for high-speed quantumwell lasers including carrier transport effects,” IEEE J. Select. Topics Quantum Electron., vol. 1, pp.494–504, 1995. 10. G. Rossi, R. Paoletti, and M. Meliga, “SPICE simulation for analysis and design of fast 1.55 m MQW laser Diodes,”IEEE, J. Of Lightwave Technology, vol. 16, no. 8, Aug. 1998.


A Micro Optical Electromechanical System (MOEMS) for high precision displacement sensor design using ring resonator array A. Rostamia,b, A. Ghanbarib and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Center of Excellence of Mechatronics, University of Tabriz, Tabriz, Tabriz 51664, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

ABSTRACT An efficient method for high precision displacement measurement based on micro scale ring resonator and MOEMS is presented. The proposed structure can be used as discrete and integrated sensor in engineering applications. Photo-elastic effect is used to convert the physical displacement to the index of refraction variation in the ring resonator array. Analytical relation for description of system transfer function is derived. Single and multiple ring resonators are examined for increase of the system sensitivity. It is shown that an array of multiple ring resonators (array) is better than single ring case. Effects of optical and geometrical parameters of the proposed structure on sensitivity are studied. Keywords- MOEMS, High Precision Displacement Sensor, Ring Resonator, Photo-elastic Effect.

1. INTRODUCTION In recent years, fiber optical sensors and optical micro-mechatronic systems have moved out of the laboratory and assumed a significant role in sensing, measurement, and control of Optomechatronic systems. These optical techniques are important to a broad range of applications, including biomedicine, environmental sensing, mechanical and industrial measurement and art preservation. Optical techniques have been used for sensors and especially high-precision sensors design [1]. Among all integrated optical elements optical ring resonators are interesting elements for integrated applications from sensors to signal conditioners [2-5]. In this paper, displacement sensor design based on ring resonators is examined. In this paper a micro optical electromechanical system (MOEMS) for high-precision displacement measurement is presented. The proposed method has many advantages over other proposed methods. First, an integrated sensor doesn’t require any alignment while it can be used for wide applications. Second, integrated sensors are suitable due to their compactness, simplicity and potential for mass production. It should also be mentioned that integrated sensors such as piezo-resistive sensors have less sensitivity than external sensors such as optical levers. Using an integrated optical sensor, we expect to achieve sensitivity as high as that of external sensors. Integrated optical devices can be inexpensive and they can be used in harsh environments such as ultra-high vacuum (UHV) systems and electromagnetically active environments. Recently there have been several studies on integrated optic pressure sensors, biosensors, temperature sensors and strain sensors. These sensors consist of an integrated optical device, such as MachZehnder interferometer, a directional coupler and a ring resonator, with transmission characteristics changes due to external effects. In this paper an interesting displacement sensor based on array of ring resonators is investigated. Coupled mode theory for extracting input-output transfer function is used. It is shown that applied displacement introduces stress on the implemented ring resonators and then the changed index of refraction will change the output intensity and frequency response. Based on the output profile and related important characteristics high precision displacement can be measured. For the proposed structure sensitivity in the range of (10−4 − 10−5 ) Ao can be obtained.



2. MATHEMATICAL MODELING High-precision micro optical electromechanical displacement sensor is illustrated in Fig. 1. As it is shown N ring resonators coupled together are implemented on the cantilever surface and all coupled to main optical waveguide. External force applies vertical displacement to cantilever that introduces stress in the surface. If material of the ring resonators implemented on the cantilever has high photo-elastic coefficient, thus displacement through applied force will change the index of refraction of the ring resonators. Variation in the index of refraction causes variations in the output intensity and after calibration one can treat inversely and determine displacement based on the output intensity. Now, based on the proposed structure, we will try to evaluate relation between displacement and variation of the index of refraction in the following lines.

Fig. 1: Schematic of the proposed Displacement Sensor (MOEMS high-precision Displacement Sensor). For the proposed structure maximum stress on the surface of the base of the cantilever as a function of tip displacement, z, can be written as

σ max =

3Et z, 2 L2

(1)

where E, t and L are the Young’s Modulus of the cantilever material, thickness and the length of the cantilever respectively. Due to the photo-elastic effect, the index of refraction changes ( neff ) due to the applied stress is as follows.

neff = n0 + ∑ C iσ i ,

(2)

i

where C i and

σ i are the stress optic constants of the ring resonator waveguide and the local stress respectively. Usually

the longitudinal stress in the proposed structure is much larger than transverse stress, and hence it can be neglected. Also, for GaAs longitudinal and transverse stress optic coefficients are 1.7 × 10 −11 Pa −1 and 1 × 10 −11 Pa −1 respectively. Therefore, the index of refraction variation can be approximated as follows.

∆n max = C l σ l ≅ where

3C l Et z, 2L 2

(3)

σ l = σ max and C l are longitudinal stress and stress optics constant respectively.

Here, because of small ring radius, we assume that the applied stress is uniform on the ring resonator. However, in general applied stress would not be uniform for large ring dimensions. In those cases finite element and difference methods can be used for determining stress distribution numerically.


In this paper we assume that stress distribution is uniform and the following analytical relations can be used for extraction of output intensity. Fig. 2 shows the coupling of some ring resonators with a main optical single mode waveguide. Using coupled mode theory the following relations manage the field near to the coupling regions.

E1 K1 E2

Fig. 2. Detail information about the proposed displacement sensor from coupling point of view

E 2 = 1 − γ 1 [ 1 − k 1 E 1 + j k 1 E 4 ],

(4)

E 3 = 1 − γ 1 [ 1 − k 1 E 4 + j k 1 E 1 ],

(5)

α

E4 = E6 e

− πr 2

α

E5 = E3 e

− πr 2

e − jKπr ,

(6)

e − jKπr ,

(7)

E 6 = 1 − γ 2 [ 1 − k 2 E 5 + j k 2 E 7 ],

(8)

E 8 = 1 − γ 2 [ 1 − k 2 E 7 + j k 2 E 5 ],

(9)

α

− πr 2

e − jKπr ,

(10)

− πr 2 e − jKπr .

(11)

E 7 = E9 e

α

E10 = E8 e

where K 1 , K 2 , γ 1 , γ 2 , α , r , E i and K are the coupling coefficient of first coupler, the coupling coefficient for the second coupler, the coupler loss of first and second couplers, optical loss in ring resonator, radius of the rings, Electric fields in different points, and the propagating wave vectors respectively. These relations should be extended to include N coupled ring resonators. In the following transfer function for the proposed structure can be concluded for different numbers of ring resonators. For single ring resonator, the following relation shows transfer function of the system.

E2 = 1− γ1 [ E1

1 − K 1 − 1 − γ 1e

α

− 2π r 2

1 − (1 − γ 1 )(1 − K 1 )e

e − jK 2π r

α

− 2π r 2

e

],

(12)

− jK 2π r

Also, for double ring resonators coupled together the following relation can be extracted for the transfer function of the system.


E2 = 1 − γ1 [ 1 − K 1 − E1

K 1 (1 − γ 1 )(1 − γ 2 )[ 1 − K 2 − 1 − γ 2 e 1 − (1 − γ 2 )(1 − K 2 )e

α

− 2π r 2

α

− 2π r 2

e − jK 2π r ]e

α

− 2π r 2

e − jK 2π r

e − jK 2π r − (1 − γ 1 )(1 − K 1 )(1 − γ 2 )(1 − K 2 ) + (1 − γ 2 ) (1 − K 1 )(1 − γ 1 )e

α

− 2π r 2

]

,

(13)

e − jK 2π r

This method can be generalized for N ring resonators coupled together. In the next section, we simulate the extracted relations and illustrate the operation of the proposed sensor.

3. SIMULATION RESULTS AND DISCUSSION In this section based on derived relations for single and doubles ring resonators operation of the optical displacement sensor is demonstrated. For this purpose some simulations are presented and discussed. Transmission coefficient for single ring resonator with and without displacement is illustrated in Fig. 3. As it is illustrated the displacement affects the intensity and frequency response of output, so they can be used for displacement sensing. It is observed that the small coupling coefficient introduces very narrowband and high variation in the amplitude of the output and is excellent for sensor operation. High output signal is a good point for high sensitivity.

0.9

08 07 0.6 0.5 0.4 0.3 0.2 0.1

1.54

1.545

1.55

1.555

\Vavelengtli

1.56

1.565

x

Io

Fig. 3. Transmission coefficient for single ring resonator Vs. Wavelength for without (blue) and with (red) displacement

In the following double ring resonators is examined as displacement sensor. Also, the transmission coefficient for this structure is simulated and illustrated in Fig. 4. We observed that in double ring resonators the sensitivity of the system is increased near to two times. This subject is hold both in amplitude and wavelength shifting. So, it is interesting to see that with increase of the number of rings the sensitivity of the proposed structure is increased. Also, in double ring resonators case there are two transmission forbidden bands occurred around 1.55 um that the single ring case is designed for this wavelength. In this sensor the coupling factor has critical effect on sensitivity, so tuning of this parameter is important.


0.9 0.8 0.7 0. 6

0. 5 0. 4

0.3 0. 0.

1.53

1.54

1.55

1.56

1.57

1.58

I0

a ci en gti I

Fig. 4. Transmission coefficient for double ring resonator Vs. Wavelength for without (blue) and with (red) displacement

The effect of coupler loss on the transmission coefficient of single and double ring resonators based optical displacement sensor is illustrated in Fig. 5. It is observed that effect of the coupler loss on double ring resonators is so critical compared single ring case.

0.9 0.8 0.7

0.6 0.5 0.4 0.3

Coupler Loss=O.1

Coupler Loss=O.O1 0.2 0.1

1.52

1.53

1.54

1.55

1.56

\Vaveleugtli

1.57

1.58

x I0

Fig. 5. Transmission coefficient for single and double ring resonator Vs. Wavelength including the effect of the coupler loss (blue and red related to double and black related to single ring resonator)


In double ring case the amplitude is decreased considerable and it is broadened. In the following figure effect of different coupling coefficient on transmission coefficient is investigated and illustrated. It is observed that the first coupling coefficient is critical in operation of the sensor. So, it is constructive to hold the first coupling coefficient in small values. Change of the first coupling coefficient introduces small wavelength shift but considerable decreasing in amplitude. Changes of the second coupling coefficient don’t change the amplitude and only shift the wavelength.

0.9 0.8 0.7 0. 6

0. 5

04 0.3 0.2

1.54

1.545

1.55

1.555

1.56

a ci en gti I

1.565

.57

x I0

Fig. 6. Transmission coefficient for single and double ring resonator Vs. Wavelength including the effect of the different coupling coefficients

As a final simulated result, we considered effect of different coupling coefficient and applied displacement. These are against together. So, it should be considered in sensitivity calculation that these are opposite together.


(0

P

co

P P

05

P

P P A

Traiinioii Coefficient

P

P Fig. 7. Transmission coefficient for single and double ring resonator Vs. Wavelength including the effect of the different coupling coefficients as well as displacement

4. CONCLUSIONS In this paper a novel optical displacement sensor based on ring resonator implemented on cantilever has been investigated. Transfer function of the proposed sensor was derived analytically. Effect of all parameters on output intensity and frequency response can be analyzed and some of them were considered. We observed that the sensitivity of the proposed sensor with increase of the number of rings is increased. So, the proposed sensor structure is enough flexible for tuning of the sensitivity and one can make trade off between complexity and sensitivity.

REFERENCES 1. W. Suh, O. Solgaard and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” Journal of Applied Physics Letters, 98, 033102, 2005. 2. A. Rostami and G. Rostami, “Full optical analog to digital converter based on kerr–like nonlinear ring resonator,” Optics Communications, 228 (2003) 39–48. 3. G. Rostami and A. Rostami, “All Optical Integrated Coding System for Optical Analog to Digital (A/D) Converter,” J. Laser Phys. Lett. Vol. 1, No. 8, 1-5 (2004). 4. A. Rostami and G. Rostami, “Integrated Delay Line Using Cross Phase Modulation,” Proc. of IST2003, Isfahan Iran, August 16-18, 2003. 5. A. Rostami and G. Rostami, “All-Optical Implementation of Tunable Lowpass, Highpass and Bandpass Optical Filters Using Ring Resonator,” IEEE Journal of Lightwave Technology, Vol. 23, No. 1, Jan. 2005.


Tunable dispersion management using thermo optical effect in ring resonator G. Rostamia, b, A. Rostamia and F. Janabi-Sharific a) Photonics and Nanocrystals Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran Tel/Fax: +98 411 3393724 E-mail: [email protected] b) Optical Communication Group, Communication Technology Institute, Iran Telecommunication Research Center (ITRC), Tehran, Iran c) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada M5B 2K3

Abstract In optical and optomechatronics applications including hybrid and integrated cases, there are some inherent phenomena such as dispersion, loss and many others that must be critically removed for performance improvement. Among the others, one of the most quantities is dispersion. Dispersion is important in most optical applications such as optical communications including all accessories and optical sensors. Optical pulse broadening and chirping are main disadvantages of dispersion effect. Dispersion cancellation in these applications is crucial. Dispersion compensators are widely spread with many methods for realization of that. In this paper a novel dispersion compensator and management system based on thermo optical effect is introduced. Thermo optical effect and the index of refraction changes due to temperature in ring resonator are used to manipulate dispersion quantity. Thermal source is generated in this case with application of electrical potential on metallic layer coated on ring resonator. Introduced idea is realized using ring resonators and results are presented.

Keywords: All-pass Optical Circuits, Optical Delay Lines, Tunable Dispersion, Optical Filters, Thermo Optic Effect, Ring-Resonator, Tunable Delay Lines

1. INTRODUCTION Dispersion compensators provide an optical block for signal processing in communication and have been considered in several different contexts in Optomechatronic systems. In optical time division multiplexed (OTDM) communication systems and dense wavelength division multiplexing (DWDM), dispersion compensation is required for synchronization purposes and large distance transmission [1]. Also in full optical analog-to-digital (A/D) converter based on nonlinear ring resonator and optical coding system for synchronization between most significant bit (MSB) and least significant bit (LSB) bits delay lines are necessary that can be implemented by this block [2, 3]. For example, in OTDM demultiplexers, optical (A/D) converter, optical coding system, optical logic gates, and local control signals need to be overlapped in time with incoming data signals. Another example that highlighted request for optical tunable delay and dispersion is optical buffering [1]. For any of these applications, it is advantageous to develop a programmable optical delay and dispersion system, where true time delay and dispersion quantities can be varied continuously over large ranges [4, 5].



In the area of radio frequency (RF) photonics, broadband phased arrays require true time delay. Phased arrays can create very directional beams, which can be steered by changing the relative phase fed to the different array elements. If these phases are frequency dependent, then different spectral components of broadband transmission will point in different directions, causing degradation of the signal. This phenomenon (known as beam squinting) can be avoided if delays rather than phases are adjusted [6]. In this case, the RF signal is on optical carrier and the delay line is an optical one. In nonlinear optical systems, employing an enhanced delay is also desirable since it increases the effective nonlinear interaction length or interaction time. For example, it has been shown that the effective nonlinearity is enhanced in periodic structures when the propagation is near the stop band, where the group velocity can become very small [7]. In nonlinear cavities, the effective nonlinear length is enhanced due to the large number of roundtrips in the cavity [8, 9]. Single-mode optical fiber is an attractive delay medium for processing microwave frequency signals due to its extremely low loss (0.1 dΒ / µs ) and large available time-bandwidth product. Recent progress in the efficient trapping of light from single-mode fibers has made it possible to construct recirculation and nonrecirculating (tapped) delay-line structures that can perform a variety of important signal processing functions. These functions include coded sequence generation, convolution, correlation, matrix-vector multiplication, and frequency filtering [10]. Also, there are some interesting methods for delay line design based on Integrated Resonance-Enhanced [11], optical filters [12] and cross-phase modulation [13]. However, the presented techniques are so hard for integration and tunability. Most of the presented ideas introduce significant complexity for implementation. For example, in most of the proposed ideas, Fiber Bragg Gratings or optical filters made from Gratings were used that introduces reflection signals. The reflected signals are hard from optical system implementation point of views in practice and forces some additional blocks for compensation. Therefore, a proposal for optical dispersion compensators including large and tunable properties is excellent for integrated optical system designers. The proposed idea uses ring resonator element that has been studied extremely [2, 3, 13-19]. For this purpose, in this paper, we discuss tunable dispersion management using thermo optic phenomenon in integrated and wave optics. With application of electrical signal to metal plate, because of power dissipation, it starts to warm up and increases temperature of the metal and sub optical layers. Therefore, the index of refraction of optical waveguide changes due to applied variable temperature. With change of the refractive index, the group delay can be varied and, hence, tunable group delay and dispersion are introduced. Organization of this paper is as follows. In section 2, we will introduce the mathematical modeling of ring-resonator and its role in the optical dispersions. Simulation results of the proposed system are illustrated in section 3. Finally, the paper ends with a short conclusion.

2. THEORETICAL ANALYSIS OF THE PROPOSED DISPERTION ELEMENT In this section, mathematical background for investigation of the input-output transfer function as well as the effect of control signal is presented. The introduced and applied control signal is electrical that leads to variable temperature that causes variable refractive index and ring resonator length. Special implementation of the method based on ring resonator is illustrated in Fig. (1-a). Finally for more visual conception 3-D and cross sectional view of the idea is demonstrated in Fig. (1-b). Now, after introducing our proposed architecture, the coupled mode theory and Transfer Matrix Method (TMM) developed for ring resonators are used, and based on these methods, an analytical formalism for derivation of interesting quantities are proposed.


A

a

IiI

a

2

N

N

EDED - ED Ii!

2!

C1

(II

(b)

4 Metal Layer EulTer Layer Optwal Waveguide

layer

(c) Fig. 1. Schematic of the proposed integrated dispersion compensator. (a) Array of ring resonator as a tunable all-optical dispersion; and (b) 3-D and cross sectional illustration of delay line.

Therefore, according o the explained analytical methods and using light propagation in linear medium and matrix formulation, the following relations can be used for the proposed structure. For simplicity, first we present the mathematical relations to manage single ring resonators as well as two main waveguides coupled to the ring. b1 = (1 − γ 1 ) [ 1 − K1 a1 + j K1 a1′ ], a ′ = (1 − γ ) [ 1 − K a + j K b ], 1

1

1 1

1 1

where b1, γ 1, K1, a1 and a1′ are the outgoing and propagating electric field to the right hand side from upper coupler, the dissipation coefficient of the upper coupler, the coupling coefficient, the electric field inside ring near to the upper coupler from left hand and the electric field inside ring near to the upper coupler from right hand sides respectively. Also, one can write


c1 = (1 − γ 2 ) [ 1 − K 2 d1 + j K 2 a2 ], a2′ = (1 − γ 2 ) [ 1 − K 2 a2 + j K 2 d1 ],

where c1, γ 2 , K 2 , a2 and a2′ are outgoing electric field to the left hand side from the bottom coupler, the dissipation coefficient of the bottom coupler, the coupling coefficient, the electric field inside ring near to the bottom coupler from right hand and the electric field inside ring near to the upper coupler from left hand sides respectively. Also, the following equations are given for inside ring electric fields components. α

L

α

L

− L − jK n 2, a2 = a1′e 4 e − L − jK n 2, a1 = a2′e 4 e

where α i and K n =

2π

λ

n are the ring attenuation coefficient and propagating wave vector inside ring respectively.

Eqs. (1, 2) based on above mentioned basic relations are presented to demonstrate light propagation through the couplers between ring and two main optical waveguides. α

b1 =

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

− L 2 e − jK n L

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 (1 − γ 1 )(1 − γ 2 ) K1K 2

− L ) e 2 e − jK n L

K α − L −j nL 4 e e 2

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2

− L ) e 2 e − jK n L

a1 −

(1)

d1,

α

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

c1 =

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 (1 − γ 1 )(1 − γ 2 ) K1K 2

−

2π

λ

− L ) e 2 e − jK n L

K α − L −j nL 4 e e 2

α

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2

where γ i , K i , L, α i and K n =

− L 2 e − jK n L

− L ) e 2 e − jK n L

d1 −

(2)

a1,

n are loss in the couplers, the coupling coefficient, ring length, the attenuation

coefficient of the ring and the traveling wave vector (n is the refractive index inside ring) respectively. For simplification of the relations and matrix formulation the following definitions can be made. b TTransmission1 = 1 , a1 d1 = 0

(3)

c R1 = 1 . a1 d1 = 0

(4)


where TTransmission1 and R1 are transmission and reflection coefficients respectively. Now based on definitions presented above and using matrix formalism, the following relation is presented for transport matrix for the light propagation through the proposed structure.

⎡a1 ⎤ 1 ⎢c ⎥ = ⎣ 1 ⎦ TTransmission1

− R1

⎡1 ⎢ ⎢⎣ R1

2 Transmission1

T

⎤ ⎡b1 ⎤ , ⎥ − R ⎥⎦ ⎣⎢d 1 ⎦⎥ 2 1

(5) Now for generalization of the presented relation, the distance between first and second rings should be incorporated in the calculations. α

Λ

b1 = e 2 e jK n Λ a2 ,

(6)

α

d1

− Λ = e 2 e − jK n Λ c

2,

where Λ is distance between rings. As in a conventional grating, for constructive interference of the reflected waves from each ring to occur within the pass-band, we require that the periodic spacing Λ to be equal to an odd multiple of a quarter wavelengths Λ = ( 2 M + 1)

where nW and

λ0

λ0 4nW

, ( M = 0,1,...) ,

(7)

are the optical waveguide refractive index and central wavelength respectively. Transfer Matrix

formulation of an array of N ring resonators can be derived as follows. ⎡bN ⎤ ⎡a1 ⎤ N ⎢c ⎥ = ∏ (TDi TPi ) ⎢d ⎥, ⎣ 1 ⎦ m =1 ⎣ N⎦

(8)

where TDi =

1 TTransmissioni

TTransmissioni = Ri =

⎡1 ⎢ ⎢⎣ Ri

− Ri ⎤ ⎥, Ti2 − Ri2 ⎥⎦

bi , ai d i = 0

ci , ai d i = 0

⎡ αΛ ⎢ e 2 e jK n Λ 0 TPi = ⎢ α ⎢ − Λ ⎢⎣ 0 e 2 e − jK n Λ

(9) ⎤ ⎥ ⎥. ⎥ ⎥⎦

After some simplification applied on Eq. (8), the matrix formulation of the light propagation through array of ring resonators can be explained in terms of a 2 × 2 matrix as follows.


⎡bN ⎤ ⎡a1 ⎤ ⎢ c ⎥ = H ⎢ d ⎥, ⎣ 1⎦ ⎣ N⎦

⎛ h11 H = ⎜⎜ ⎝ h21

h12 ⎞ ⎟, h22 ⎟⎠

(10) System intensity transfer functions including the transmission and reflection coefficients can be obtained as follows. TTransmission = R=

bN , a1 d N = 0

c1 , a1 d N = 0

(11) In the following, effect of temperature on transfer function quantities is investigated. For this purpose the following definition are done. Therefore, there is a linear relation between temperature and controlling signal. L = L0 +

∂L (T − T0 ), ∂T T0

(12)

∂n n = n0 + (T − T0 ), ∂T T0

Using electrical equivalent circuit of metal plate on buffer layer, generated temperature is function of applied voltage and circuit parameters that is illustrated in the following. Tem. = f (VControl (t )),

(13)

Therefore, the following relation is calculated that is an important part of the derived relations incorporating temperature effect on transfer function. Θ = K n L = [ K n0 L0 + ( K n0

2π ∂n 2π ∂n ∂L ∂L + L0 )(T − T0 ) + ( )( )( )(T − T0 ) 2 ], λ ∂T λ ∂T ∂T ∂T

(14)

As an especial case, we consider in the following single stage two port ring resonator. Using developed transfer matrix formalism, the transmission ( TTransmission ), reflection ( R ) coefficients, phase difference ( Φ Transmission , Φ R ) and the group ( τ DT ,τ DR ) delay are derived analytically as follows. −

TTransmission =

α

−

L

α

L

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e 2 cos(Θ) + j (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e 2 sin( Θ) , −

α

−

L

α

L

1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e 2 cos(Θ) + j (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e 2 sin(Θ)

R=

− (1 − γ 1 )(1 − γ 2 ) K1K 2 e 1 − (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e

−

α 2

L

−

α 4

L

Θ Θ (cos( ) − j sin( )) 2 2

cos(Θ) + j (1 − γ 1 )(1 − K1 )(1 − γ 2 )(1 − K 2 ) e


, −

α 2

L

sin( Θ)

(16)

(15)

(1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

Φ Transmission = tan −1[

−

α 2

L

sin(Θ)

(1 − γ 1 )(1 − K1 ) − (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e tan −1[

(1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

−

1 − (1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

Θ Φ R = π − − tan −1[ 2

α 2 −

L

α 2

sin(Θ) L

α 2

]− L

cos(Θ)

(17)

],

cos(Θ)

(1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

−

α

1 − (1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

τ DT = −

−

2 −

L

α 2

sin(Θ) L

],

(18)

cos(Θ)

∂Φ Transmission , ∂ω ∂Φ τ DR = − R . ∂ω

(19)

(20)

For calculation of these quantities, the following relations are defined. P1 = (1 − γ 1 ) (1 − γ 2 )(1 − K 2 ) e

−

α 2

L

,

P2 = (1 − γ 1 )(1 − K1 ) , P3 = (1 − γ 1 )(1 − γ 2 )(1 − K1 )(1 − K 2 ) e

(21) −

α 2

L

,

So, using Eq. (15) and Eq. (16), we can write Φ Transmission = tan −1[

P1 sin(Θ) P sin(Θ) ] − tan −1[ 3 ], P2 − P1 cos(Θ) 1 − P3 cos(Θ)

P sin(Θ) Θ Φ R = π − − tan −1[ 3 ]. 2 1 − P3 cos(Θ)

(22)

The following final relations for group delay of the reflection and transmission coefficients can be obtained using Eq. (22). ∂Φ ∂Θ τ DT = − T ⋅ , ∂Θ ∂ω (23) ∂Φ R ∂Θ τ DR = − , ⋅ ∂Θ ∂ω where Φ T , Φ R and Θ are defined as follows. ⎡ P 2 − P1P2 cos Θ ⎤ ∂Φ Transmission P32 − P3 cos Θ ⎥ = −⎢ 2 1 2 + , ⎢ P + P2 − 2 P1 cos Θ 1 + P32 − 2 P3 cos Θ ⎥ ∂Θ ⎣ 1 ⎦ ∂Φ R − 1 ⎡ 1 − P3 cos Θ ⎤ = ⎢ ⎥, ∂Θ 2 ⎢⎣ 1 + P32 − 2 P3 cos Θ ⎦⎥


(24)

∂Θ 1 ∂L ∂n ∂n ∂L = ( )[n0 L0 + ( n0 + L0 )(T − T0 ) + ( )( )(T − T0 ) 2 ]. ∂ω c ∂T ∂T ∂T ∂T

(25)

Based on the proposed relations for delay times, dispersion quantities can be obtained easily ( D = ∂τ ). In the ∂ω following sections simulation results of the introduced system of equations are discussed. Also, based on the proposed relations other interesting quantities such as dispersion relations and group velocity can be extracted that can be used for special applications. In the next section, based on the obtained relations numerical evaluations are presented and discussed.

3. SIMULATION RESULTS In this section, the proposed device with single and two stages is investigated from the control of delay time perspective. First general behavior of the proposed structure and it dependency to the structural parameters is considered. Figs. (2-5) show the transmission and reflection coefficients versus wavelength for the different coupling and loss coefficients. With decrease of the coupling and loss coefficients, the obtained filter will be sharp with small bandwidth. This is acceptable, because with increase of the coupling coefficient, most part of incident power couples to the ring and with change of the incident wavelength there is small sensitivity for the variation of the output power. For simulation, we considered GaAs as basic material for implementation of the proposed ring resonators and optical waveguides. For GaAs and InP the index of refraction and the temperature ( T ) coefficients are given in Table 1. For other materials also the parameters can be used from handbooks. Table 1. Simulation parameters of GaAs and InP. n ∂n ∂T

Matter

3 .6 3 .4

GaAs InP

2.17 × 10 −4 / 0 C

∂L ∂T 6 × 10 −6 / 0 C

2.19 × 10 −4 / 0 C

4.56 × 10 −6 / 0 C

1

k1=k2=0.01 k1=k2=0.05 k1=k2=0.2 k1=k2=0.5

0.9

Transmission Coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.555

1.56

1.565

1.57

1.575

1.58

λ

1.585

1.59 -6

x 10

Fig. 2. Transmission (absolute value) coefficient vs. wavelength (single Ring) ( 1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.05, 3 − K1 = K 2 = 0.2,4 − K1 = K 2 = 0.5 ).


Also, the effects of the dissipation in the couplers on the transmission and reflection coefficients are illustrated in Fig. (3, 5). With increase of the dissipation coefficient, as it is described for the coupling coefficient, the designed filter is broadened. 1

γ1=γ2=0 γ1=γ2=0.05 γ1=γ2=0.2 γ1=γ2=0.5

0.9

Transmission Coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.555

1.56

1.565

1.57

1.575

1.58

1.585

λ

1.59 -6

x 10

Fig. 3. Transmission (absolute value) coefficient vs. wavelength (single Ring). (Effect of the attenuation coefficient of the coupler) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.05, 3 − γ 1 = γ 2 = 0.2, 4 − γ 1 = γ 2 = 0.5) 1 k1=k2=0.01 k1=k2=0.05 k1=k2=0.2 k1=k2=0.5

0.9

Reflection Coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.552

1.554

1.556

1.558

1.56

λ

1.562

1.564 -6

x 10

Fig. 4. Reflection (absolute value) coefficient vs. wavelength (single Ring) ( 1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.05, 3 − K1 = K 2 = 0.2,4 − K1 = K 2 = 0.5 )


1

γ1=γ2=0 γ1=γ2=0.05 γ1=γ2=0.1 γ1=γ2=0.3

Reflection Coefficient

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.55

1.552

1.554

1.556

1.558

1.56

λ

1.562

1.564 -6

x 10

Fig. 5. Reflected (absolute value) coefficient vs. wavelength with attenuation coefficient of the coupler (for single Ring) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.05, 3 − γ 1 = γ 2 = 0.1, 4 − γ 1 = γ 2 = 0.2) .

The variation of the phase difference for the transmission coefficient is demonstrated in Fig. 6. The phase variation is changed suddenly near to the resonance wavelength with decrease of the coupling coefficient. Because in small coupling coefficient, small part of incident light is coupled to the ring, outgoing light is governed by the incident light not by combination of incident light and light coupled from ring to the upper waveguide. Hence, the phase of the outgoing light is nearly uniform. But in resonance wavelength because of sudden coupling of the incident light to the ring, the output light phase changes suddenly. The following graphs show that the phase difference can be controlled with the coupling parameter and coupler dissipation. 3.5

Transmitted Phase

3

k1=k2=0.01 k1=k2=0.05 k1=k2=0.1 k1=k2=0.3

2.5

2

1.5

1

0.5

0 1.551 1.5512 1.5514 1.5516 1.5518 1.552 1.5522 1.5524 1.5526 1.5528 1.553

λ

-6

x 10

Fig. 6. Phase difference of transmitted light vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.05, 3 − K1 = K 2 = 0.1, 4 − K1 = K 2 = 0.3) .

Also, the group delay time of the designed device is illustrated in Fig. 7. It shows that the group delay time can be controlled with the coupling parameter and coupling dissipation coefficient, but control of the coupling parameter is hard from practical point of view. Also if the coupler dissipation parameter can be controlled, a tunable optical delay line is achieved.

Proc. of SPIE Vol. 6374 637411-10

-10

x 10

k1=k2=0 k1=k2=0.05 k1=k2=0.03 k1=k2=0.1

3.5 3

Group Delay

2.5 2 1.5 1 0.5 0 1.5513

1.5514

1.5515

1.5516

1.5517

λ

1.5518 -6

x 10

Fig. 7. Delay time of transmission coefficient vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.03, 3 − K1 = K 2 = 0.05, 4 − K1 = K 2 = 0.1)

Also, the group velocity of the designed device is illustrated in the Fig. 8. It shows that the group velocity can be controlled with the coupling parameter and the coupler dissipation coefficient. 13

4

x 10

k1=k2=0.01 k1=k2=0.03 k1=k2=0.05 k1=k2=0.1

3.5

Group Velocity

3 2.5 2 1.5 1 0.5 0 1.551 1.5512 1.5514 1.5516 1.5518 1.552 1.5522 1.5524 1.5526 1.5528 1.553

λ

-6

x 10

Fig. 8. Normalized group velocity of transmission coefficient vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.03, 3 − K1 = K 2 = 0.05, 4 − K1 = K 2 = 0.1) .

Proc. of SPIE Vol. 6374 637411-11

13

4

Group Velocity

3.5 3

x 10

γ1=γ2=0 γ1=γ2=0.01 γ1=γ2=0.02 γ1=γ2=0.03

2.5 2 1.5 1 0.5 0 1.551 1.5512 1.5514 1.5516 1.5518 1.552 1.5522 1.5524 1.5526 1.5528 1.553

λ

-6

x 10

Fig. 9. Normalized group velocity of transmission coefficient vs. wavelength with attenuation coefficient of the coupler (for single Ring) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.01, 3 − γ 1 = γ 2 = 0.02, 4 − γ 1 = γ 2 = 0.03) .

Also, the dispersion factor of the designed device is illustrated in Figs. (10, 11). The results show that dispersion factor can be controlled with the coupling coefficient and the coupler dissipation coefficient. High level variation of the dispersion factor is obtained by small coupling and dissipation parameters. Also, the coupling and dissipation coefficients have same effect on the dispersion factor. Near to the resonance wavelength, anomalous dispersion is observed. k1=k2=0.01 k1=k2=0.015 k1=k2=0.02 k1=k2=0.025

20 15

Dispersion Factor

10 5 0 -5 -10 -15 -20 1.5515

1.5515

1.5516

1.5516

1.5517

λ

1.5517 -6

x 10

Fig. 10. Dispersion of transmission coefficient vs. wavelength with coupling parameter (for single Ring) (1 − K1 = K 2 = 0.01, 2 − K1 = K 2 = 0.015, 3 − K1 = K 2 = 0.02, 4 − K1 = K 2 = 0.025) .

Proc. of SPIE Vol. 6374 637411-12

γ1=γ2=0 γ1=γ2=0.01 γ1=γ2=0.015 γ1=γ2=0.02

20

Dispersion Factor

15 10 5 0 -5 -10 -15 -20 1.5515

1.5515

1.5516

1.5516

1.5517

1.5517

λ

1.5518 -6

x 10

Fig. 11. Dispersion of transmission coefficient vs. wavelength with attenuation coefficient of the coupler (for single Ring) (1 − γ 1 = γ 2 = 0 , 2 − γ 1 = γ 2 = 0.01, 3 − γ 1 = γ 2 = 0.015, 4 − γ 1 = γ 2 = 0.02)

With control of the electrical signal on the bottom layer, temperature in optical waveguide is tuned. The effect of temperature on transfer function in frequency domain is illustrated in Fig. 12. With increase of temperature, the transfer function is shifted to higher wavelengths. Hence, this characteristic of the proposed structure can be used for implementation of tunable delay time. -10

x 10

dT=0 dT=0.3 dT=0.5 dT=1

3.5

Group Delay

3 2.5 2 1.5 1 0.5 0 1.5514 1.5515 1.5515 1.5516 1.5516 1.5517 1.5517 1.5518 1.5518 1.5519

λ

-6

x 10

Fig. 12. Delay time of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for single Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.3 0C , 3 − ∆T = 0.5 0C , 4 − ∆T = 1 0C .

Also, in the following figure, normalized group velocity is illustrated and the effect of control signal on this curve is demonstrated. Tunable dispersion factor due to temperature variation is illustrated in Figs. (13, 14). It is shown that with increase of the applied control signal, generated temperature dispersion curve is shifted to the higher wavelengths.

Proc. of SPIE Vol. 6374 637411-13

dT=0 dT=0.1 dT=0.2 dT=0.3

20 15

Dispersion Factor

10 5 0 -5 -10 -15 -20 -25 1.5514

1.5515

1.5515

1.5516

1.5516

1.5517

1.5517

λ

1.5518

1.5518 -6

x 10

Fig. 13. Dispersion of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for single Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.1 0C , 3 − ∆T = 0.2 0C , 4 − ∆T = 0.30C . dT=0 dT=0.1 dT=0.5 dT=1

20 15

Dispersion Factor

10 5 0 -5 -10 -15 -20 -25 1.5515 1.55151.5516 1.55161.55171.5517 1.55181.5518 1.55191.5519

λ

-6

x 10

Fig. 14. Dispersion of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for single Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.1 0C , 3 − ∆T = 0.5 0C , 4 − ∆T = 10C .

Finally the effect of temperature on delay time for two ring resonators is illustrated in Fig. 15. It is shown that with increase of the number of ring resonators, wavelength shift raises and finally the sensitivity of the proposed structure is increased. On the other hand with low value of the control signal, tuning in a wide range can be readily done.

Proc. of SPIE Vol. 6374 637411-14

-9

x 10

dT=0 dT=0.1 dT=0.3 dT=0.5

Delay Time for Two Ring Resonators

7 6 5 4 3 2 1

0 1.5512 1.5513 1.5514 1.5515 1.5516 1.5517 1.5518 1.5519 1.552 1.5521

λ

-6

x 10

Fig. 15. Delay time of transmission coefficient vs. wavelength with controlling signal that changes temperature parameter (for two cascode Ring) 1 − ∆T = 0 0C , 2 − ∆T = 0.1 0C , 3 − ∆T = 0.3 0C , 4 − ∆T = 0.5 0C .

4. CONCLUSION The realization of a ring-resonator fiber-optical delay line filter for synchronization of optical signal processing systems and dispersion compensation has been presented. The group delay and dispersion value of the device can be easily controlled by applying control signal to top layer of the proposed device. The easy integration in a transmission system is a benefit that is not obtained by planar or bulk-optic components. In further investigations, the capability of the device has to be proven in system experiments. The sensitivity of the proposed structure can be increased using a large number of ring resonators.

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