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0.954 1.5 =} 0.75 1.0796 => 0.5398 1.0642 => 0.5321
SFG, o+e =} 0 1.0642 + 0.5321 =} :::} 0.35473
XZ plane, e 1.3414 =} 0.6707
Oexp
[deg]
4.2 [3.5] 5.0 [3.9]
Otheor
[deg]
[3.2]
[3.5]
[3.6]
4.67
4.17
5.00
71
72
3 Properties of Nonlinear Optical Crystals
1.3188 :::} 0.6594 1.3 => 0.65 XZ plane, 4>
5.2 [3.2] 5.4 [3.9]
5.10 5.26
4.62 4.78
5.29 5.36
== 0°, () > Vz
In teracting wavelengths [Jlm]
(}exp
[deg]
(}theor
[3.2]
SHG, e+e => 0 1.3414 => 0.6707
86.3 86.6 86.0 86.1
1.3188 => 0.6594 1.3 => 0.65
[3.5] 86.47 [3.9] [3.2] 86.26 [3.9] 86.25
[deg] [3.5]
[3.6]
86.22
88.93
86.03 86.01
87.79 87.41
Note: The other sets of dispersion relations from [3.1, 18,3, 19,20,8,21,22, 23] show worse agreement with the experiment Best set of dispersion relations (A in urn, T == 20°C) [3.2]: 2
0.01125 2 A - 0.01135 0.01277 == 2.5390 + 2 A - 0.01189
nx == 2.4542 + 2
ny
n2
== 2.5865 +
z
A2
2
-
0.01388 A ,
-
0.01848 A ,
2
0.01310 _ 0.01861 A2 • - 0.01223
Calculated values of phase-matching and "walk-off" angles: XY plane, () == 90°
In teracting wavelengths [urn] SHG, 0 + 0 => e 2.098 => 1.049 1.1523 => 0.57615 1.0642 => 0.5321 0.6943 => 0.34715 0.5782 => 0.2891 SFG, 0 + 0 => e 1.0642 + 0.5321 :::} => 0.35473 1.0642 + 0.35473 => => 0.26605 1.3188 + 0.6594 :::} => 0.4396
¢Jpm [deg]
P3 [deg]
31.61 6.06 11.60 44.19 69.91
0.840 0.213 0.403 1.086 0.730
37.21
1.046
60.63
1.006
21.11
0.705
3.1 Basic Nonlinear Optical Crystals
73
yz plane, 4> == 90° In teracting wavelengths [J.!rn] SHG, 0 + e=}o 2.098 ==> 1.049 1.1523 ==> 0.57615 1.0642 ==> 0.5321 SFG, 0 +e => 0 1.0642 + 0.5321 => => 0.35473
XZ plane
(Jpm [deg]
P3 [deg]
72.90 9.28 20.45
0.307 0.169 0.348
42.19
0.533
4J == 0°, (J < Vz
In teracting wavelengths [urn] SHG, e + 0 =} e 1.3188 ==? 0.6594
XZ plane, 4>
(Jpm [deg] PI [deg]
0.248
5.10
P3 [deg]
0.262
== 0°, (J > Vz
In teracting wavelengths [J.!rn] SHG, e +e => 0 1.3188 =} 0.6594
Opm[deg]
PI [deg]
86.26
0.191
Calculated values of inverse group-velocity mismatch for the SHG process in LBO: XY plane, () == 90°
In teracting 4>pm [deg] wavelengths [urn]
SHG,
0
+0
1.2 =} 0.6 1.1 =} 0.55 1.0 =} 0.5 0.9 => 0.45 0.8 => 0.4 0.7 =} 0.35 0.6 =} 0.3
=}
f3
[fs/mm]
e
2.36 9.37 15.74 22.94 31.69 43.38 62.63
18 37 59 86 123 175 257
74
3 Properties of Nonlinear Optical Crystals
YZ plane,
l/J = 90
Interacting wavelengths [urn]
0
f}pm
[deg]
SHG, 0 + e=}o 1.1 =} 0.55 15.98 28.96 1.0 => 0.5 0.9 =} 0.45 45.36 0.8 =} 0.4 76.88
P [fs/mm]
82 106 139 186
Experimental values of NCPM temperature: along X axis Interacting T rC] wavelengths [urn] SHG, type I 1.25 =} 0.625 1.215 => 0.6075 1.211 =} 0.6055 1.2 =} 0.6 1.15 =} 0.575 1.135 =} 0.5675 1.11 =} 0.555 1.0796 => 0.5398 1.0642 =} 0.5321
1.047
=}
0.5235
-2.9 21 20 24.3 61.1 77.4 108.2 112 148 148.5 149 149.5 151 166.5 167 172 175 176.5 180 190.3
1.025 =} 0.5125 SFG, type I 1.908 + 1.0642 =} =} 0.6832 81 1.135 + 1.0642 => 112 => 0.5491
Ref
3.7, 8 3.8 3.2 3.7, 8 3.7, 8 3.10 3.7, 8 3.1 3.7, 8 3.24,25 3.10 3.26 3.17 3.27 3.28 3.29 3.30 3.31 3.32 3.7, 8
3.10 3.10
3.1 Basic Nonlinear Optical Crystals
75
Experimental values of internal angular, temperature and spectral bandwidths: along X axis Interacting wavelengths [urn]
1.047
=}
SFG, type I 1.908 + 1.0642 => =} 0.6832 1.135 + 1.0642 =} =} 0.5491
XY plane, 0
== 90
0
SHG, 0 + 0 =} e 1.0796 =} 0.5398 1.0642 =} 0.5321
0.886 0.870 0.78
=} =}
0.443 0.435
2.3
1.9
2.1
2.1
81
7.4
3.10
112
5.0
3.10
== 20 °C)
0.5675 1.0642 =} 0.5321
A > > >
10- 12 [W/m2]
0.4 0.6 0.6 1.0 470000(?) > 1.8
Ref.
Note
3.38 3.39 3.40 3.41 3.42 3.43
10 Hz
3.1 Basic Nonlinear Optical Crystals
A [urn]
Lp
[ns]
0.3547
10 10 8 7 0.03 0.03 0.015 0.018 0.025 0.5145 cw 0.5235 0.055 0.055 cw 0.5321 60 10 0.1 0.035 0.015 0.605 0.0002 0.616 0.0004 0.0004 0.0004 0.02 0.652 0.7--0.9 10 0.71--0.87 25 0.72-0.85 0.001 cw 1.0642 60 18 9 8 1.3 0.1 0.035 0.025 1.0796 0.04
Ithr X
10- 12 [W/rn2 ]
> 0.4 > 2.0 > 1.3 > 1.4 > 94 > 180 > 28 > 50 > 60 > 0.0003 > 11 > 50 > 0.004 > 0.7 > 2.2 > 45 > 31 > 44 > 250 310000 (?) 350000 (?) 380000 (?) > 8.1 > 0.3 11-14 > 80 > 0.01 > 0.6 >6 >9 >5 190 250 > 48 > 33 300
Thermal conductivity coefficient [3.58]: K
=
3.5W/rnK.
Ref. 3.12 3.44 3.19 3.45 3.46 3.47 3.14 3.13 3.48 3.49 3.32 3.50 3.26 3.51 3.9 3.52 3.24 3.20 3.53 3.42 3.54 3.55 3.21 3.11 3.34 3.56 3.26 3.51 3.43 3.57 3.17 3.33 3.1 3.24 3.48 3.42
Note
10 Hz 10 Hz
10 Hz 500 Hz 500 Hz 900 Hz 500 Hz
10 Hz 25 Hz
1333 Hz 10 Hz 10 Hz
10 Hz
77
78
3 Properties of Nonlinear Optical Crystals
3.1.2 KH 2P04 , Potassium Dihydrogen Phosphate (KDP) Negative uniaxial crystal: no > ne ; Point group: 42m; Mass density: 2.3383 g/cm 3 at 293 K [3.59]; Mohs hardness: 2.5; Transparency range at "0" transmittance level: 0.174 - 1.57 JlID [3.60, 59]; Transparency range at 0.5 transmittance level for a 0.8 em long crystal: 0.178 - 1.45 urn [3.60, 59]; Linear absorption coefficient a: A [Jlm]
a [cm"]
Ref.
0.212 0.25725
0.2 0.01-0.2 0.007 < 0.07 0.003 0.00005 0.01 0.01 0.05 0.058 0.02 0.1 0.3 0.1
3.61 3.62 3.63 3.64 3.65 3.62 3.66 3.67 3.66 3.65 3.65 3.68 3.69 3.68
0.3-1.15 0.3513 0.5145 0.5265 0.94 1.053 1.054 1.22 1.3152 1.32
Note e - wave, ..1 c e - wave, ..1 c e - wave, ..1 c wave 0 - wave
0-
wave o - wave e - wave, ..1 c 0 - wave 0-
e - wave, ..1 c
p:
Two-photon absorption coefficient A[urn]
px
0.216 0.2661
60±5 27 ± 8.1 40-80 0.59 ± 0.21
0.3547
1013 [m/W]
Ref. 3.70 3.71 3.72 3.71
Note
() == 410, 4> == 45° e - wave, .L c
Experimental values of refractive indices at T = 298 K [3.73]:
A [urn]
no
ne
A [)lID]
no
ne
0.2138560 0.2288018 0.2446905 0.2464068 0.2536519 0.2800869
1.60177 1.58546 1.57228 1.57105 1.56631 1.55263
1.54615
0.2980628 0.3021499 0.3035781 0.3125663 0.3131545 0.3341478
1.54618 1.54433
1.49824 1.49708 1.49667 1.49434 1.49419 1.48954
1.51586 1.50416
1.54117 1.54098
3.1 Basic Nonlinear Optical Crystals
0.3650146 0.3654833 0.3662878 0.3906410 0.4046561 0.4077811 0.4358350 0.4916036 0.5460740
1.52932 1.52923 1.52909 1.52341 1.52301 1.51990 1.51152
1.48432 1.48423 1.48409 1.48089 1.47927 1.47898 1.47640 1.47254 1.46982
0.5769580 0.5790654 0.6328160 1.0139750 1.1287040 1.1522760 1.3570700 1.5231000 1.5295250
1.50987 1.50977 1.50737 1.49535 1.49205 1.49135 1.48455
79
1.46856 1.46685 1.46041 1.45917 1.45893 1.45521 1.45512
Temperature derivative of refractive indices [3.74]:
A [Jlm]
dno/dT x 105 [K- 1] dne/dT x 105 [K- 1]
0.405 0.436 0.546 0.578 0.633
-3.27 -3.27 -3.28 -3.25 -3.94
-3.15 -2.88 -2.90 -2.87 -2.54
Temperature dependences of refractive indices upon cooling from room temperature to T [K]. for the spectral range 0.365 - 0.690 urn [3.75]:
no(T) == no(298) + 0.402 x 10- 4{[n o(298)]2 - 1.432}(298 - T) ne(T) == n e (298) + 0.221 x 10- 4{[n e(298)]2 - 1.105}(298 - T) for the spectral range 0.436 - 0.589 urn [3.76]:
no(T) == no(300) + 10-4(143.3 - 0.618T + 4.81 x 10-4 T 2 )
,
ne(T) == ne (300) + 10- 4(153.3 - 0.969T + 1.57 x 10- 3 T 2 )
.
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: In teracting wavelengths [urn] SHG, 0 + 0 =} e 0.517 =} 0.2585 0.6576 =} 0.3288 0.6943 =} 0.34715 0.8707 =} 0.43535 1.06 =} 0.53
(Jexp
[deg]
90 [3.74] 53.6 [3.69] 50.4 [3.79] 42.4 [3.80] 41 [3.81] 41 [3.82]
(Jtheor
[deg]
[3.73]
[3.77]
[3.78]K
no pm 53.6 50.6 42.8 41.2
no pm 53.6 50.6 42.7 41.0
73.6 53.2 50.4 42.8 40.9
80
3 Properties of Nonlinear Optical Crystals
44.3 [3.69] 1.3152 ==> 0.6576 SFG, o+o~e 1.415 + 0.22027 ~ ~ 0.1906 88.7 [3.83] 1.3648 + 0.6943 ~ 40.9 [3.80] ~ 0.46019 1.3152 + 0.6576 ~ ~ 0.4384 42.2 [3.69] 1.0642 + 0.2707 ~ 87.6 [3.84] ~ 0.21581 1.0642 + 0.5321 ~ =} 0.35473 47.3 [3.85] 1.06 + 0.53 ~ 47.5 [3.82] =* 0.35333 0.6576 + 0.4384 ~ ~ 0.26304 74 [3.86] SHG, e + 0 =} e 1.3152 =} 0.6576 61.4 [3.69] 1.06::::} 0.53 59 [3.82] SFG, e+o ~ e 1.0642 + 0.5321 ~ ==> 0.35473 58.3 [3.85] 1.06 + 0.53 =} =} 0.35333 59.3 [3.82]
44.6
44.7
44.1
83.7
83.6
54.3
41.7
41.7
41.6
42.1
42.1
42.0
87.5
87.3
62.9
47.3
47.3
47.1
47.4
47.4
47.3
75.2
75.4
68.6
61.8 59.0
61.8 58.8
60.7 58.6
58.2
58.3
57.9
58.5
58.5
58.1
Note: The other sets of dispersion relations from [3.74] and [3, 78]E show worse agreement with the experiment. [3.78]K ==> see [3.78], data of Kirby et al.; [3.78]E ==> see [3.78], data of Eimerl. Experimental values of NCPM temperature: T rOC]
Ref.
-13.7
-11 20 177 177
3.63 3.62 3.74 3.87 3.88
SFG, o+o~e -70 1.06 + 0.265 =} 0.212 1.0642 + 0.26605 =} 0.21284 -40 -35
3.61 3.89 3.90
Interacting wavelengths [)lID] SHG, 0+0 ~ e 0.5145 =} 0.25725 0.517 =} 0.2585 0.5321 ~ 0.26605
3.1 Basic Nonlinear Optical Crystals
Best set of dispersion relations (l in urn, T n2 = 2.259276
n
2
e
+ 13.00522A.2 + l2 _ 400
o
2 132 8 3.2279924l 66 + 2 l - 400
=.
= 20°C)
[3.74] :
0.01008956 l2 - (77.26408)-1 '
2
0.008637494 1 (81.42631)-
+l2 -
.
Temperature-dependent Sellmeier equations (l in urn, Tin K) [3.77] : 2
4
n2 o
=(1.44896 + 3.185 x 1O-5T) + (0.84181 - 1.4114 x 10- T)A. l2 _ (0.0128 - 2.13 x 10-7T) (0.90793 + 5.75 x 10- 7 T)l2 + l2 - 30 '
n2
=(1.42691 _ 1.152 x 10-5 T)
+
e
+
5
(0.22543 - 1.98 x 10- 7 T)l2 2
.
l - 30
Calculated values of phase-matching and "walk-off" angles:
Interacting wavelengths [Jlm] SHG, 0+0 ~ e 0.5321 ~ 0.26605 0.5782 ~ 0.2891 0.6328 ~ 0.3164 0.6594 ~ 0.3297 0.6943 ~ 0.34715 1.0642 ~ 0.5321 1.3188 ~ 0.6594 SFG, o+o~e 0.5782 + 0.5105 ~ 1.0642 + 0.5321 ~ 1.3188 + 0.6594 ~ SHG, e -} o ~ e 1.0642 ~ 0.5321 1.3188 ~ 0.6594 SFG, e+o~e 1.0642 + 0.5321 ~ 1.3188 + 0.6594 ~
0.27112 0.35473 0.4396
0.35473 0.4396
(}pm
2
(0.72722 - 6.139 x 10- T)A. l2 - (0.01213 + 3.104 x 10- 7 T)
[deg]
PI [deg]
P3 [deg]
76.60 64.03 56.15 53.43 50.55 41.21 44.70
0.808 1.391 1.611 1.657 1.687 1.603 1.549
72.46 47.28 42.05
1.025 1.712 1.657
58.98 61.85
1.149 0.922
1.404 1.269
58.23 49.42
1.166 1.104
1.521 1.634
81
82
3 Properties of Nonlinear Optical Crystals
Calculated values of inverse group-velocity mismatch for SHG process in KDP: In teracting wavelengths [J.1m]
SHG, 0 + 0 =} e 1.2 => 0.6 1.1 => 0.55 1.0 => 0.5 0.9 => 0.45 0.8 => 0.4 0.7 => 0.35 0.6 => 0.3 SHG, e + 0 => e 1.2 => 0.6 1.1 => 0.55 1.0 => 0.5 0.9 => 0.45 0.8 => 0.4
(}pm
[deg]
P[fs/mm]
42.45 41.38 41.22 42.24 44.91 50.14 60.40
42 17 9 40 77 128 208
59.54 58.87 59.75 62.97 70.71
89 67 89 118 158
Experimental values of internal angular and temperature bandwidths: Interacting wavelengths [urn]
SHG, 0 + 0 =} e 1.1523 =} 0.57615 1.0642 =} 0.5321 1.064 => 0.532 1.06 => 0.53 1.054 => 0.527 0.5321 =} 0.26605
0.53 => 0.265
SFG, 0 +0 => e 1.0642 + 0.5321 => => 0.35473 1.054 + 0.527 => => 0.35133 SHG, e + 0 =} e 1.0642 =} 0.5321 1.06 => 0.53
T rOC] 20 20 25 20 20 25 25 177 177 20 20
[deg]
A{fnt [deg]
41 41
0.074 0.070
41 41 41
0.069 0.063 0.060
(}pm
AT rOC]
23
90 90 77
77
1.7 1.9 2 0.059 0.066
5.5
25 25
48
0.046
25 20
59
0.129
Ref.
3.91 3.92 3.93 3.94 3.81 3.95 3.93 3.87 3.88 3.96 3.97
3.93 3.95
18.3
3.93 3.96
3.1 Basic Nonlinear Optical Crystals
1.054 => 0.527 SFG, e+ 0 => e 1.0642 + 0.5321 => :=} 0.35473 1.06 + 0.53 => :=} 0.35333 1.054 + 0.527 =} :=} 0.35133
25
3.95
0.126
59
25
5.2
3.93
20
59
0.062
3.97
25
59
0.059
3.95
Experimental values of spectral bandwidth: In teraeting wavelengths [um] SHG, 0 + 0 =} e 1.06 =} 0.53 0.53 =} 0.265 SHG, e + 0 =} e 1.06 =} 0.53
T
Bpm
L1v
Ref.
[OC] [deg] [cm"] 20 20
41 77
178 1.2
3.81 3.96
20
59
101.5
3.96
Temperature variation of phase-matching angle: Interacting wavelengths [urn] SHG, 0 + 0 =} e 1.0642 =} 0.5321 1.054 =} 0.527 0.5321 =} 0.26605 SFG,o+o=}e 1.0642 + 0.5321 =} 0.35473 1.054 + 0.527 =} 0.35133 SHG, e + 0 =} e 1.0642 =} 0.5321 1.06 =} 0.53 1.054 =} 0.527 SFG, e + 0 ~ e 1.0642 + 0.5321 =} 0.35473 1.054 + 0.527 =} 0.35133
T
rOC] 25 25 25 25 25 25 25 20 25 20 25 25 25 20
lJpm [deg]
dlJpm/dT Ref. [deg/K]
41
0.0028 0.0046 0.0382
3.93 3.95 3.93
0.0073 0.0046
3.93 3.95
0.0069 0.0069 0.0057 0.0086 0.0069
3.98 3.93 3.96 3.95 3.65
0.0106 0.0117 0.0152 0.0075
3.98 3.93 3.95 3.65
59 59 59 59 59 58 59 59
83
84
3 Properties of Nonlinear Optical Crystals
Temperature tuning of noncritical SHG [3.74]: Interacting wavelengths [JlmJ
dAI/dT [nmjKJ
SHG, 0 + 0 => e 0.517 => 0.2585
0.048
Temperature variation of birefringence for noncritical SHG process: Interacting wavelengths [um] 0.5145 => 0.25725 0.5321 => 0.26605
Ref. 3.99 3.87
1.745 1.2
Effective nonlinearity expressions in the phase-matching direction [3.100]:
d ooe == d36 sin 0 sin 2et> d eoe == d oee
,
== d 36 sin 20 cos 2cfJ .
Nonlinear coefficient [3.37]: d 36(1.064
,urn) == 0.39 pmjV ,
Laser-induced bulk-damage threshold: 't p
0.52 0.5265 0.527 0.53 0.5321 0.596 0.6943 1.053
1.054 1.06
1.064
[ns]
330 20 0.6 0.5 0.2 0.005 0.6 0.03 330 20 20 25 1 1 0.14 60 12-25 0.5 0.2 20 1.3
I thr
X
10- 12 [W1m2 ]
2 30 90 > 140 170 10000(?) > 80 300 2.4 30 >4 40 180 200 > 70 2 2.5 > 30 230 3-6 80
Ref. 3.101 3.66 3.66 3.102 3.103 3.104 3.72 3.105 3.101 3.101 3.106 3.66 3.66 3.107 3.108 3.109 3.81 3.110 3.103 3.111 3.33
3.1 Basic Nonlinear Optical Crystals
A [urn]
Lp
1.064
1 1 0.1
[ns]
Ithr X
10- 12 [Wjm 2 ]
30-70 50 70
Ref. 3.111 3.112 3.1
Thermal conductivity coefficient [3.59]: [WjmK], lie" [WjmK], -l c
T[K]
K
302 319
1.21 1.34
3.1.3 KD2P04 , Deuterated Potassium Dihydrogen Phosphate (DKDP) Negative uniaxial crystal: no > ne ; Point group: 42m; Mass density: 2.355 g/cm"; Mohs hardness: 2.5; Transparency range at "0" transmittance level: 0.2 - 2.1 urn [3.113, 114]; Linear absorption coefficient ex: [em-I]
A [um]
it
0.266 0.5321 0.82-1.21 0.94 1.0642 1.315 1.57 1.74
0.035 0.004-0.005 < 0.015 0.005 0.004-0.005 0.025 0.1 0.1
Ref. 3.115 3.116 3.67 3.67 3.116 3.117 3.68 3.68
Note 98-99 % deuteration
98-990/0 deuteration
o - wave, 950/0 deuteration e - wave, 950/0 deuteration
Two-photon absorption coefficient fJ: A [um]
f1
0.2661
2.0 ± 1.0 2.7 ± 0.7 0.54 ± 0.19
0.3547
x 1013 [mjW]
Ref.
Note
3.118 3.115 3.71
e - wave, .-L c
Experimental values of refractive indices at T = 298 K [3.95]:
0.4047 0.4078
1.5189 1.5185
1.4776 1.4772
85
86
3 Properties of Nonlinear Optical Crystals
A [urn] 1.5155 1.5111 1.5079 1.5063 1.5044 1.5022
0.4358 0.4916 0.5461 0.5779 0.6234 0.6907
1.4747 1.4710 1.4683 1.4670 1.4656 1.4639
Temperature derivative of refractive indices [3.74]:
0.405 0.436 0.546 0.578 0.633
-3.00 -3.37 -2.99 -3.00 -3.16
-1.86 -2.13 -1.95 -2.52 -2.03
Temperature dependences of refractive indices upon cooling from room temperature to T [K] for the spectral range 0.365 - 0.690 urn [3.75] :
no(T)
=
no(298) + 0.228 x 10- 4{[n o(298)]2 - 1.047}(298 - T)
ne(T) = ne(298) + 0.955 x 10- 5[n e(298)]2(298 - T) ; for the spectral range 0.436 - 0.589 urn [3.76]:
no(T) = no(300) + 10-4(85.2 - 0.0695 T - 7.25 x 10- 4T2 ) ne(T)
:=
ne(300) + 10-
4(21.8
- 0.445 T - 1.24 x 10-
3T2
,
) •
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [urn] SHG, 0 + 0 =} e 0.530 =} 0.265 0.6943 => 0.34715 1.062 =} 0.531 SHG, e + 0 =} e 1.3152 =} 0.6576
(Jexp
[deg]
(Jtheor
[deg]
[3.77]
[3.78]K [3.78]£
90 [3.119] 52 [3.79] 37.1 [3.120]
no pm 50.6 38.6
no pm 50.9 36.6
87.4 51.0 36.6
51.3 [3.69]
63.2
51.7
49.4
Note: The set of dispersion relations from [3.74] shows worse agreement with the experiment. [3.78]K ==> see [3.78], data of Kirby et al.;
3.1 Basic Nonlinear Optical Crystals
[3.78]E =} see [3.78], data of Eimerl. Experimental values of NCPM temperature: Interacting wavelengths [urn]
SHG, 0 + 0 =} e 0.528 =} 0.264 0.5321 =} 0.26605
0.536
=}
-30 42 45 46 49.8 60.8 100
0.268
Ref.
Note
3.119 3.89 3.87 3.90 3.121 3.122 3.119
99% deuteration 950/0 deuteration 99% deuteration > 95% deuteration 90% deuteration
Best set of dispersion relations (;, in urn, T n2
= 2.240921
+
o
2 _ 2 12 019 n - . 6 e
+
+
2.246956A? A? _ (11.26591)2 0.784404;,2
A? - (11.10871)
== 20°C) [3.78]K : 0.009676
A? _ (0.124981)2 '
2+
0.008578 2· ;,2 - (0.109505)
Temperature-dependent Sellmeier equations (A in urn, Tin K) [3.77] : n2 =(1.55934 + 3.3935 x 10-4 T)
+
o
4
(0.71098 - 4.1655 x 10- T)A? A2 - (0.01407 + 6.4904 x 10-6 T)
(0.67671 + 4.8281 x 10- 5 T)A? + - - - -2 - - - - - -
A
n2
-
30
=(1.68647 + 3.43 x 10-6 T)
e
+
(0.59614
+ 2.41
+
' 5
2
(0.46629 - 6.26 x 10- T)A. A2 - (0.01663 + 1.3626 x 10-6 T)
x 10- 7 T);,2
2
.
A - 30
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [Jlm]
(Jpm
SHG, 0 + 0 =} e 0.5321 =} 0.26605 0.5782 ::::} 0.2891 0.6328 ::::} 0.3164 0.6594 =} 0.3297 1.6943 ::::} 0.34715 1.0642 =} 0.5321 1.3188 =} 0.6594
86.20 66.87 57.53 54.31 50.86 36.60 36.36
[deg]
PI [deg]
P3 [deg] 0.225 1.197 1.467 1.522 1.558 1.450 1.412
87
88
3 Properties of Nonlinear Optical Crystals
SFG, 0 + 0 =} e 0.5782 + 0.5105 => 0.27112 1.0642 + 0.5321 => 0.35473 1.3188 + 0.6594 => 0.4396 SHG, e + 0 => e 1.0642 => 0.5321 1.3188 => 0.6594 SFG, e + 0 => e 1.0642 + 0.5321 => 0.35473 1.3188 + 0.6594 => 0.4396
77.88 46.82 39.18
0.595 1.580 1.515
53.47 51.70
1.286 1.222
1.427 1.420
59.38 47.70
1.174 1.254
1.378 1.527
Calculated values of inverse group-velocity mismatch for SHG process in
DKDP: Interacting wavelengths [urn]
Opm
SHG, 0 + 0 => e 1.2 => 0.6 1.1 => 0.55 1.0 => 0.5 0.9 =* 0.45 0.8 =* 0.4 0.7 =? 0.35 0.6 => 0.3 SHG, e + 0 => e 1.2 => 0.6 1.1 =* 0.55 1.0 =* 0.5 0.9 =? 0.45 0.8 =? 0.4
[deg]
P [fs/mm]
0.5321 0.5321 =? 0.26605 SHG, e+o =* e 1.0642 => 0.5321 1.06 =* 0.53
T rOC]
Opm
[deg]
L\oint [deg]
20 37 60.8 90 45 90
0.081
20 20 20
0.131 0.126 0.143
54 60
L\T rOC]
1.8 1.9
Ref.
3.92 3.122 3.87 3.123 3.124 3.96
3.1 Basic Nonlinear Optical Crystals
Experimental value of spectral bandwidth [3.96]: Interacting wavelengths [urn] SHG, e+o 1.06 ~ 0.53
(Jpm [deg]
~e
20
74.8
60
Temperature variation of phase-matching angle [3.96]: Interacting wavelengths [urn] SHG, e+o ~ e 1.06 ~ 0.53
20
(Jpm [deg]
d(Jpm/dT [deg/K]
60
0.0063
Temperature tuning of noncritical SHG [3.74]: Interacting wavelengths [Jlm] SHG, 0.519
0+0 ~ ~
dAI/dT [nm/K]
e
0.2595
0.068
Effective nonlinearity in the phase-matching direction [3.100]: d ooe
== d 36 sin (J sin 24> ,
d eoe
== d oee == d 36 sin 2(J cos 24> .
Nonlinear coefficient [3.37]: d 36(1.064Jlm)
== 0.37 pm/V.
Laser-induced bulk-damage threshold:
A [urn]
't
0.266 0.532
0.03 30 8 0.6 0.03 330 0.007 40 18 14 1 0.25 1
0.6 1.062 1.064
1.315
p [ns]
Ithr X
10- 12 [W/m2 ]
> 100 > 0.5 170
> 80 > 80 3
> 10 > 2.5 > 1.0 80 60 > 30 15
Ref. 3.115 3.122 3.125 3.72 3.118 3.101 3.120 3.122 3.116 3.125 3.124 3.116 3.69
89
90
3 Properties of Nonlinear Optical Crystals
Thermal conductivity coefficient [3.78]: K
== 1.86 Wm/K (II c) ,
K
== 2.09 Wrn/K (1- c) .
3.1.4 NU,,"2P04, Ammonium Dihydrogen Phosphate (ADP) Negative uniaxial crystal: no > ne ; Point group: 42rn; Mass density: 1.803 g/crn 3 at 293 K [3.59]; Mohs hardness: 2; Transparency range at "0" transmittance level: 0.18 - 1.53 urn [3.60, 126]; Transparency range at 0.5 transmittance level for a 0.8 em long crystal: 0.185 - 1.45 urn [3.60, 59] Linear absorption coefficient
A [urn]
(X
0.25725 0.265 0.266 0.3-1.15 0.5145 1.027 1.083 1.144
[em-I]
0.002 0.07 0.035 < 0.07 0.00005 0.086 0.208 0.150
(X:
Ref.
Note
3.62 3.127 3.115 3.64 3.62 3.67 3.67 3.67
e - wave, 1- c e - wave, 1- c
o - wave, ..L c
Two-photon absorption coefficient
A [urn]
p x 1013 [m/WJ Ref.
0.2661
6±1 11 ± 3 24±7 23 ± 5 0.68 ± 0.24
0.3078 0.3547
p:
Note
3.118 3.115 3.71 3.128 3.71
() == 42°, 4J == 45° e - wave, 1- c
Experimental values of refractive indices at T = 298 K [3.73, 129]:
A [Jlm]
no
ne
A [urn]
no
ne
0.2138560 0.2288018 0.2536519 0.2967278
1.62598 1.60785 1.58688 1.56462
1.56738 1.55138 1.53289 1.51339
0.3021499 0.3125663 0.3131545 0.3341478
1.56270 1.55917 1.55897 1.55300
1.51163 1.50853 1.50832 1.50313
3.1 Basic Nonlinear Optical Crystals
A [urn]
no
ne
A [urn]
0.3650146 0.3654833 0.3662878 0.3906410 0.4046561 0.4077811 0.4358350 0.4916036
1.54615 1.54608 1.54592 1.54174 1.53969 1.53925 1.53578
1.49720 0.5460740 1.52662 1.48079 1.49712 0.5769590 1.52478 1.47939 1.49698 0.5790654 1.52466 1.47930 0.6328160 1.52195 1.47727 1.49159 1.0139750 1.50835 1.46895 1.49123 1.1287040 1.50446 1.46704 1.48831 1.1522760 1.50364 1.46666 1.48390
91
ne
no
Temperature derivative of refractive indices [3.74]:
A [urn] dno/dT x 105 [K- 1] dne/dT x 105 [K- 1] 0.405 0.436 0.546 0.578 0.633
-4.78 -4.94 -5.23 -4.60 -5.08
~O
~O ~O ~O ~O
Temperature dependences of refractive indices upon cooling from room temperature to T [K]. for the spectral range 0.365 - 0.690 urn [3.75]:
no(T) == no(298) + 0.713 x 10- 2 {[no(298)J 2 - 3.0297 n o (298) + 2.3004} (298 - T) , ne(T) == ne(298) + 0.675 x 10-6(298 - T) ; for the spectral range 0.436 - 0.589 urn [3.76]:
no(T) == no(300)
+ 10-4(141.8 -
0.322 T - 5.02
ne(T) == ne(300) + 10-4(2.5 - 0.01763 T + 2.901 Experimental values of phase-matching angle (T between different sets of dispersion relations: In teracting wavelengths [urn]
SHG, 0 + 0 => e 0.524 => 0.262 0.530 => 0.265 0.6943 => 0.34715 0.7035 =>0.35175
(Jexp [deg]
90 [3.74] 81.7 [3.97] 51.9 [3.79] 50.5 [3.130]
10-4 T 2 )
X
=
X
10- 5 T 2 )
, .
293 K) and comparison
(Jtheor [deg] [3.73] [3.129]
[3.77]
[3.78]K
no pm 81.6 51.1 50.4
no pm 82.2 51.1 50.5
83.6 79.6 51.5 50.8
92
3 Properties of Nonlinear Optical Crystals
1.06 =* 0.53 SFG, 0 +0 => e 1.0642 + 0.5321 => => 0.35473 1.0642 + 0.2810 => =* 0.22230 0.81219 + 0.34715 => =* 0.24320 SFG, e + 0 => e 1.0642 + 0.5321 => => 0.35473
41.9 [3.79] 42 [3.81]
41.7
41.7
42.2
46.9 [3.85]
47.8
47.9
48.3
90 [3.84]
89.0
no pm 74.7
90 [3.131]
no pm no pm 81.1
60.2 [3.85]
59.9
60.0
60.4
Note: The other sets of dispersion relations from [3.74] and [3,78]£ show worse agreement with the experiment. [3.78]K =* see [3.78], data of Kirby et a1.: [3.78]E => see [3.78], data of Eimerl. Experimental values of NCPM temperature: In teracting wavelengths [urn] SHG, 0+0 =* e 0.4920 => 0.2460 0.4965 => 0.24825 0.5017 => 0.25085 0.5145 =* 0.25725
0.524 => 0.262 0.52534 =* 0.26267 0.53 => 0.265
0.5321 => 0.26605
0.548 =* 0.274 0.557 =* 0.2785 SFG, 0 + 0 => e 1.0642 + 0.26605 => 0.21284
T rOC]
Ref.
-116 -93.2 -68.4 -11.7 -10.2 -9.2 20 30 43 47 48 49.6 47.1 49.5 50 51.2 44.6 51-52 100 120
3.132 3.133 3.133 3.99 3.133 3.62 3.74 3.134 3.127 3.97 3.135 3.136 3.90 3.137 3.138 3.139 3.139 3.140 3.134 3.119
-55
3.141
Note
0.1-1 Hz 20 Hz
3.1 Basic Nonlinear Optical Crystals
Best set of dispersion relations (l in urn, T n2
= 2.302842 + 15.102464A? + ,12 _ 400
o
n2
0.011125165 ,12 - (75.450861)-1 '
2
= 2.163510 + 5.919896..1. + l2 _ 400
e
== 20°C) [3.73], [3.129] :
0.009616676 . l2 - (76.98751)-1
Temperature-dependent Sellmeier equations (A in 11m, T in K) [3.77] :
n2 = (1.6996 _ 8.7835 x 10-4 T)
+
o
4
(1.10624 - 1.179 x 10-4 T)l2 + ,{2 _ 30 '
n2 = (1.42036 _ 1.089 x 10- 5 T)
+
e
+
6
(0.74453 + 5.14 x 10- T);.2 l2 - (0.013 - 2.471 x 10- 7 T)
(0.42033 - 9.99 x 10- 7 T),1 2 2
.
l - 30
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [11m] SHG, 0 + 0 ~ e 0.5321 :::} 0.26605 0.5782 :::} 0.2891 0.6328 ::::} 0.3164 0.6594 =} 0.3297 0.6943 =} 0.34715 1.0642 =} 0.5321 1.3188 =} 0.6594 SFG, 0 + 0 ~ e 0.5782 + 0.5105 =} 0.27112 1.0642 + 0.5321 =} 0.35473 1.3188 + 0.6594 =} 0.4396 SHG, e + 0 ~ e 1.0642 =} 0.5321 1.3188 ::::} 0.6594 SFG, e + 0 ~ e 1.0642 + 0.5321 =} 0.35473 1.3188 + 0.6594 =} 0.4396
{}pm
[deg]
2
(0.64955 + 7.2007 x 10- T)A l2 - (0.01723 -1.40526 x 10- 5 T)
PI [deg] P3 [deg]
80.15 65.28 56.91 54.07 51.09 41.74 45.55
0.639 1.427 1.703 1.762 1.803 1.746 1.694
74.84 47.82 42.56
0.955 1.836 1.794
61.39 65.63
1.230 0.968
1.449 1.250
59.85 50.86
1.272 1.274
1.582 1.748
93
94
3 Properties of Nonlinear Optical Crystals
Calculated values of inverse group-velocity mismatch for SHG process in ADP: In teracting wavelengths [urn] SHG, 0 + 0 => e 1.2 => 0.6 1.1 => 0.55 1.0 => 0.5 0.9 => 0.45 0.8 => 0.4 0.7 => 0.35 0.6 => 0.3 SHG, e+o => e 1.2 => 0.6 1.1=>0.55 1.0 => 0.5 0.9 => 0.45 0.8 => 0.4
(}pm
[deg]
P [fs/mm]
43.10 41.94 41.71 42.68 45.34 50.67 61.39
49 21 8 42 85 142 233
62.50 61.39 62.02 65.24 73.80
105 78 95 127 173
Experimental values of internal angular and temperature bandwidths: In teracting wavelengths [urn] SHG, 0 + 0 => e 1.06 => 0.53 0.5321 => 0.26605 0.53 => 0.265
T
(}pm
~fint
~T
[OC]
[deg]
[deg]
[OC]
20 49.5 51 20 20 20
42 90 90 82 82 82
0.057 1.086 0.118 0.088 0.089
0.60 0.53
0.63
Experimental values of spectral bandwidth: Interacting wavelengths [prn]
T rOC]
(}pm
~v
[deg]
[cm']
SHG, 0 + 0 => e 1.06 => 0.53 0.53 => 0.265
20 20
42 82
178 1.2
Ref.
3.81 3.96
Ref.
3.81 3.137 3.139 3.103 3.96 3.97
3.1 Basic Nonlinear Optical Crystals
95
Temperature variation of phase-matching angle [3.97]: Interacting wavelengths [urn] SHG, 0 + 0 => e 0.53 => 0.265
T
Opm
rOC]
[deg]
dOpm/dT [degjK]
20 47
82 90
0.1418 1.1020
Temperature tuning of noncritical SHG [3.74]: Interacting wavelengths [J.lm]
dAl/dT [nmjK]
SHG, 0 + 0 => e 0.524 => 0.262
0.306
Temperature tuning of noncritical SFG [3.142]: Interacting wavelengths (J.lm]
dA3/dT [nmjK]
SFG, 0 + 0 => e 0.6943 + 0.39961 => 0.25363
0.171
Temperature variation of birefringence for (0.5145 urn => 0.25725 urn, 0 + 0 => e): d(n~ - n~)/dT
== 5.65
noncritical
SHG process
x 10- 5K- 1[3.99].
Effective nonlinearity expressions in the phase-matching direction [3.100]:
d ooe == d 36 sin 0 sin 2
0.23825 0.488 =:} 0.244 0.4965 => 0.24825 0.5145 => 0.25725 0.5321 => 0.26605
0.604 =:} 0.302 0.6156 =? 0.3078 0.70946 =:} 0.35473
1.0642 ==> 0.5321
Oexp
[deg]
90 [3.145] 90 [3.150] 82.8 [3.145] 79.2 [3.145] 57 [3.151] 54.5 [3.151] 52.5 [3.151] 49.5 [3.151] 47.3 [3.148] 47.5 [3.145] 47.5 [3.152] 47.6 [3.153] 47.6 [3.45] 48 [3.154] 40 [3.155] 39 [3.156] 32.9 [3.157] 32.9 [3.158] 33 [3.159] 33 [3.152] 33 [3.160] 33.1 [3.45] 33.3 [3.147] 33.7 [3.161] 22.7 [3.148] 22.8 [3.145] 22.8 [3.152] 22.8 [3.33] 22.8 [3.162] 22.8 [3.45] 22.8 [3.163]
SFG,o+o=>e 0.73865 + 0.25725 => =} 0.1908 81.7 [3.164] 0.72747 + 0.26325 => =:} 0.1933 76 [3.165] 0.5922 + 0.2961 => 88 [3.166] => 0.1974
Otheor
[deg]
[3.149]
[3.148] [3.145]
89.36 87.25 84.11 79.80 57.79 55.53 54.00 51.13 48.67
86.51 85.54 82.99 78.87 56.57 54.29 52.76 49.87 47.42
88.82 86.97 83.77 79.31 56.73 54.46 52.94 50.06 47.62
41.00 40.02 33.65
39.89 38.95 32.94
40.13 39.18 33.15
21.42
22.88
22.78
72.94
75.27
76.11
71.79
73.59
74.22
80.44
82.13
83.22
98
3 Properties of Nonlinear Optical Crystals
0.5964 + 0.2982 => 82.5 [3.167] => 0.1988 0.5991 + 0.29955 => 80 [3.166] => 0.1997 0.60465 + 0.30233 => 76.2 [3.167] => 0.20155 0.5321 + 0.32561 => 83.9 [3.145] => 0.202 0.6099 + 0.30495 => 73.5 [3.166] => 0.2033 0.5321 + 0.34691 => 71.9 [3.145] => 0.21 1.0642 + 0.26605 => 51.1 [3.145] => 0.21284 1.0642 + 0.35473 => 40.2 [3.145] => 0.26605 1.0642 + 0.5321 => 31.1 [3.148] => 0.35473 31.3 [3.145] 31.4 [3.161] 0.5782 + 0.5106 => 46 [3.168] => 0.27115 0.59099 + 0.5321 => 44.7 [3.169] => 0.28 2.68823 + 0.5712 => 21.8 [3.170] => 0.4711 1.41831 + 1.0642 => 21 [3.171] => 0.608
SHG, e+o => e 0.5321 ::::} 0.26605 0.70946 =} 0.35473 1.0642 => 0.5321
SFG, e + 0 => e 1.0642 + 0.35473 => => 0.26605 1.0642 + 0.5321 => => 0.35473
78.02
79.11
79.81
76.71
77.57
78.14
74.41
74.92
75.34
80.88
81.22
81.95
72.51
72.82
73.16
72.11
71.60
71.84
50.69
51.04
51.12
40.75
40.19
40.31
31.52
31.12
31.28
45.23
46.03
46.24
45.23
44.03
44.25
18.37
21.73
21.39
18.40
21.26
20.96
no pm 48.72
82.03 47.61
80.78 47.92
30.00
31.94
32.18
46.6 [3.145]
46.81
46.11
46.31
38.4 [3.148] 38.5 [3.145]
38.39
37.77
38.15
81 [3.145] 48 [3.159] 48.1 [3.152] 31.6 [3.172] 32.4 [3.148] 32.7 [3.152] 32.7 [3.33] 32.9 [3.145]
3.1 Basic Nonlinear Optical Crystals
SFG, 0 +e => e 1.0642 + 0.5321 =} =} 0.35473
59.8 [3.145]
59.46
58.91
99
58.89
Note: The sets of dispersion relations from [3.143, 154, 170] show worse agreement with the experiment. Best set of dispersion relations (2 in urn, T n2
== 2.7359 +
o
n2
== 2.3753 +
e
== 20°C) [3.145]:
A2
0.01878 - 0.013542 2 - 0.01822 '
A2
0.01224 - 0.01516.A? . - 0.01667
Calculated values of phase-matching and "walk-off" angles: In teracting wavelengths [urn]
SHG, 0+0 =? e 0.4880 =} 0.2440 0.5105 =} 0.25525 0.5145 =} 0.25725 0.5321 =} 0.26605 0.5782 =} 0.2891 0.6328 => 0.3164 0.6594 =} 0.3297 0.6943 =} 0.34715 1.0642 => 0.5321 1.3188 =} 0.6594 SFG,o+o=}e 1.3188 + 0.6594 => 0.4396 1.3188 + 0.4396 => 0.3297 1.3188 + 0.3297 => 0.26376 1.3188 + 0.26376 => 0.2198 1.0642 + 0.5321 => 0.35473 1.0642 + 0.35473 => 0.26605 1.0642 + 0.26605 => 0.21284 0.6943 + 0.34715 => 0.23143 0.5782 + 0.5105 => 0.27112 0.5145 + 0.4880 => 0.25045
(Jpm
[deg] P3 [deg]
54.46 50.66 50.06 47.62 42.46 37.87 36.05 33.96 22.78 20.36
4.757 4.861 4.869 4.879 4.782 4.571 4.457 4.306 3.189 2.881
25.39 31.19 37.40 44.52 31.28 40.31 51.12 55.00 46.12 52.17
3.515 4.205 4.897 5.588 4.132 4.941 5.497 4.882 4.872 4.831
100
3 Properties of Nonlinear Optical Crystals
In teracting wavelengths [urn]
(}pm
SHG, e + 0 => e 0.5321 => 0.26605 0.5782 => 0.2891 0.6328 => 0.3164 0.6594 => 0.3297 0.6943 => 0.34715 1.0642 => 0.5321 1.3188 => 0.6594 SPG, e + 0 => e 1.3188 + 0.6594 => 0.4396 1.3188 + 0.4396 => 0.3297 1.3188 + 0.3297 => 0.26376 1.0642 + 0.5321 => 0.35473 1.0642 + 0.35473 => 0.26605 1.0642 + 0.26605 => 0.21284 0.6943 + 0.34715 => 0.23143 0.5782 + 0.5105 => 0.27112 SFG, 0 + e => e 1.3188 + 0.6594 ==> 0.4396 1.3188 + 0.4396 ==> 0.3297 1.0642 + 0.5321 ==> 0.35473 0.5782 + 0.5105 ==> 0.27112
[deg] PI [deg] P2 [deg] P3 [deg]
80.78 65.08 55.98 52.77 49.25 32.18 28.77
1.252 3.068 3.773 3.941 4.070 3.840 3.632
30.88 35.71 41.38 38.15 46.31 56.96 72.50 70.05
3.773 4.013 4.140 4.078 4.108 3.666 2.254 2.555
45.50 78.68 58.89 84.64
1.252 3.068 3.773 3.941 4.070 3.840 3.632
1.446 3.460 4.163 4.310 4.408 3.940 3.663 3.947 4.444 4.973 4.441 4.913 5.048 2.860 2.951
4.164 1.556 3.619 0.737
4.312 1.640 3.831 0.842
Calculated values of inverse group-velocity mismatch for SHG process in BBO: Interacting wavelengths [urn] SHG, 0 + 0 => e 1.2 => 0.6 1.1 => 0.55 1.0 => 0.5 0.9 => 0.45 0.8 => 0.4 0.7 => 0.35 0.6 => 0.3 0.5 => 0.25 SHG, e+o => e 1.2 => 0.6 1.1 => 0.55 1.0 => 0.5
(}pm
[deg]
P[fs/rnm]
21.18 22.28 23.85 26.07 29.18 33.65 40.47 52.34
54 76 104 141 194 275 415 695
29.91 31.46 33.73
103 130 164
3.1 Basic Nonlinear Optical Crystals
0.9 0.8 0.7 0.6
=> => => =>
0.45 0.4 0.35 0.3
36.98 41.67 48.74 60.91
101
210 276 373 531
Experimental values of internal angular, temperature and spectral bandwidths at T == 293 K: Interacting wavelengths [J.lm] SHG, 0 + 0 => e 0.5321 => 0.26605 1.0642 => 0.5321
SFG,o+o=>e 1.0642 + 0.5321 => 0.35473 2.44702 + 0.5712 ~ 0.4631 2.68823 + 0.5712 => 0.4711 SHG,e+o=>e 1.0642 => 0.5321 SFG, e + 0 => e 1.0642 + 0.5321 ~ 0.35473 SFG, 0 +e => e 1.0642 + 0.5321 => 0.35473
L\l1llt
L\T rOC]
L\v Ref. [cm"]
4 37
9.7
Opm [deg]
[deg]
47.3 22.8 21.9 22.7
0.010 0.021 0.028 0.030
31.1 22.1 21.8
0.015 0.026 0.028
32.7 32.4
0.034 0.046
37
3.33 3.148
38.4
0.020
13
3.148
58.4
0.050
12
3.148
51 16
3.148 3.170 3.170
8.8
Temperature variation of phase-matching angle at T In teracting wavelengths [J.lm] SHG, 0 + 0 => e 0.5321 => 0.26605 1.0642 => 0.5321 SFG,o+o=>e 1.0642 + 0.5321 => 0.35473 SHG, e + 0 => e 1.0642 => 0.5321 SFG, e + 0 => e 1.0642 + 0.5321 => 0.35473 SFG, o+e => e 1.0642 + 0.5321 => 0.35473
3.148 3.33 3.154 3.148
== 293 K [3.148]:
lJpm [deg]
dOpm/dT [deg/K]
47.3 22.7
0.00250 0.00057
31.1
0.00099
32.4
0.00120
38.4
0.00150
58.4
0.00421
102
3 Properties of Nonlinear Optical Crystals
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
== d 31sin e- d 22 cos esin 3 0.5
Ref. 3.218 3.199 3.219 3.220 3.221 3.222 3.222 3.220 3.202 3.101 3.206 3.185 3.203 3.220 3.220 3.223 3.202 3.201 3.224
Note
25 Hz 1 Hz 12.5 Hz
10 pulses 500 pulses
100 Hz 1 kHz 50 Hz
Thermal conductivity coefficient [3.182]: K
== 1.47 W/mk
3.1.7 KTiOP0 4 , Potassium Titanyl Phosphate (KTP) Positive biaxial crystal: 2Vz == 37.4° at A == 0.5461 urn [3.225]; Point group: mm2 Assignment of dielectric and crystallographic axes: X, Y, Z =? a, b, C (Fig. 3.2) ; Mass density: 2.945 g/cm 3 [3.226, 227]; 3.023 g/cm 3 [3.228]; 3.03 g/cm 3 [3.229]; Mohs hardness: 5 [3.227]; Vickers hardness: 531 [3.228], 566 [3.230]; Knoop hardness: 702 [3.228];
107
108
3 Properties of Nonlinear Optical Crystals
Z(c)
light
optic axis
Fig. 3.2. Dependence of refractive index on light propagation direction and polarization (index surface) in the first octant of dielectric reference frame (X, Y, Z) of KTP crystal. Designations: ()is the polar angle, ¢ is the asimuthal angle, Vz is the angle between one of the optical axes and the Z axis
Transparency range at "0" transmittance level: 0.35 - 4.5 urn [3.231, 232]; Linear absorption coefficient rx : A [Jlm]
rx [cm"]
Ref.
Note
0.43-0.78 0.5145
< 0.004
2.233 3.186 3.186 3.186 2.233 3.234 3.235 3.186 3.186 3.186 3.229 3.235 3.234 3.186 3.186 3.186
oxygen annealing + cerium doping along a axis along b axis along c axis oxygen annealing along SHG direction
0.53-0.78 0.5321 0.6594
1.06 1.0642
0.013 0.027 0.026 < 0.005 0.04 < 0.02 0.0065 0.0087 0.0065 < 0.01 < 0.006 0.005 0.0002 0.0005 0.0004
along a axis along b axis along c axis
along along along along
SHG direction a axis b axis c axis
3.1 Basic Nonlinear Optical Crystals
A [um]
('J,
1.3188
[em-I]
Ref.
Note
0.0015 0.0004 0.001
3.186 3.186 3.186
along a axis along b axis along c axis
Experimental values of refractive indices: hydrothermally grown KTP [3.229]
A[urn]
nx
ny
nz
0.53 1.06
1.7787 1.7400
1.7924 1.7469
1.8873 1.8304
flux-grown KTP A [urn]
nx
ny
nz
Ref.
0.4047 0.4358 0.4916 0.5343 0.53975 0.5410 0.5461 0.5770 0.5790 0.5853 0.5893 0.6234 0.6328 0.6410 0.6939 0.6943 0.7050 1.0640 1.0642 1.0795 1.3414
1.8249 1.8082 1.7883 1.7780 1.7764
1.8410 1.8222 1.8000 1.7887 1.7869 1.7873 1.7860 1.7803 1.7798 1.7787 1.7780 1.7732 1.7714 1.7709 1.7652 1.7652 1.7642 1.7458 1.7454 1.7450 1.7387
1.9629 1.9359 1.9044 1.8888 1.8863 1.8869 1.8850 1.8769 1.8764 1.8749 1.8740 1.8672 1.8649 1.8641 1.8564 1.8564 1.8550 1.8302 1.8297 1.8291 1.8211
3.225 3.225 3.225 3.225 3.236 3.225 3.225 3.225 3.225 3.225 3.225 3.225 3.236 3.225 3.225 3.225 3.225 3.225 3.236 3.236 3.236
1.7767 1.7756 1.7703 1.7699 1.7689 1.7684 1.7637 1.7622 1.7617 1.7565 1.7564 1.7555 1.7381 1.7379 1.7375 1.7314
Temperature derivative of refractive indices [3.237] : dnx /dT x 105 == 0.1323 A- 3 - 0.4385 A- 2 + 1.2307 A-I + 0.7709 , dny/dT x 105 == 0.5014 A- 3 - 2.0030 A- 2 + 3.3016 A-I + 0.7498 , dnz/dT x 105 == 0.3896 A- 3 -1.3332 A- 2 +2.2762 A-I +2.1151 ,
where A in urn and dnx/dT, dny/dT, and dnz/dT are in K- 1.
109
110
3 Properties of Nonlinear Optical Crystals
Temperature derivative of refractive indices [3.237] :
0.5321 2.41 1.0642 1.65
4.27 3.40
3.21 2.50
Experimental values of phase-matching angle (T between different sets of dispersion relations: hydrothermally grown KTP XY plane, () = 90° In teracting wavelengths [urn]
0.5321
YZ plane,
4J
4Jexp
[deg]
4Jtheor
[deg]
[3.242] [3.232] [3.236] 23.0 23.2 23.3 24.1 25.0 25.2 25.2 25.2 25.3
[3.243] [3.225] [3.244] [3.245] [3.227] [3.231] [3.238] [3.246] [3.230]
21.12
24.59
22.89
= 90°
In teracting wavelengths [urn] SHG, o+e~ 0 1.0642 => 0.5321 1.068 => 0.534 1.182 => 0.591 1.3188 => 0.6594 1.5 => 0.75
Oexp
[deg]
Otheor
[deg]
[3.242] [3.232] [3.236] 69.0 69.2 67.8 57.4 50.0 44.6
[3.247] [3.238] [3.247] [3.247] [3.238] [3.247]
68.03
68.67
68.83
67.52 56.77 49.42 43.80
68.16 57.41 50.25 45.02
68.32 57.64 50.38 44.87
111
3 Properties of Nonlinear Optical Crystals
112
XZ plane, 1> == 0°, fJ > Vz fJexp [deg]
In teracting wavelengths [urn] SHG, o+e* 0 1.0796 * 0.5398
1.3414 * 0.6707 1.54 * 0.77 1.90768 * 0.95384 2.05 * 1.025 2.1284 * 1.0642 SFG, o+e* 0 1.3188 + 0.6594 :::} * 0.4396 1.338 + 0.669 * * 0.446 1.3414 + 0.6707 :::} * 0.44713 1.0642 + 1.90768 * =? 0.68333 1.0796 + 1.3414 :::} * 0.59817 1.54 + 0.78 =? =? 0.51776 1.90768 + 2.40688 =? * 1.0642 1.58053 + 1.54 * *0.78 1.90768 + 1.0642 * * 0.68333
[deg]
[3.242]
[3.232]
[3.236]
85.68
no pm
86.94
59.03
60.38
59.58
58.02 52.02 48.33 48.6 48.63
59.42 53.93 51.32 51.82 52.36
58.58 52.64 49.07 48.82 49.15
87.6 [3.238] 87.1 [3.241]
84.76
86.84
83.14
79.8 [3.241]
79.21
80.23
78.53
78.1 [3.252]
78.52
79.50
77.91
77.2 [3.249]
72.47
75.21
72.73
74.9 [3.236]
75.03
76.49
74.48
61 [3.253]
59.87
60.79
60.17
58.6 [3.249]
52.79
57.08
53.37
52.1 [3.253]
51.21
53.15
51.83
48.7 [3.249]
46.70
48.17
47.22
85.3 [3.248] 86.7 [3.236] 58.3 [3.238] 58.9 [3.249] 58.7 [3.236] 53 [3.250] 51.1 [3.249] 50.8 [3.249] 53.7 [3.251] 54 [3.249]
1.3188 * 0.6594
(}theor
Note: The other sets of dispersion relations from [3.225, 254, 255, 238] show worse agreement with the experiment. Best sets of dispersion relations (A in urn, T == 20°) hydrothermally grown KTP [3.239] : n2 x
= 2.1146 +
2
O.89188A ,1,2 _ (0.20861)2
-
O.01320A2
'
3.1 Basic Nonlinear Optical Crystals
= 2.1518 +
n2 Y
2
nz
- O.01327A?
O.87862A?
,12 _ (0.21801)2
== 2.3136 + 2
1.00012,12
A - (0.23831)
'
2 - 0.01679,1
2
.
flux-grown KTP [3.232] : n 2 == 3.0065
+
0.03901 - 0.01327A? ,12 - 0.04251 '
+
0.04154 - 0.01408,12 ,12 - 0.04547 '
+
0.05694 - 0.01682,12 . ,12 - 0.05658
x
n 2 == 3.0333 Y
n 2 == 3.3134 z
Calculated values of phase-matching and "walk-off" angles for flux-grown KTP: XY plane, () == 90° In teracting wavelengths [urn]
SHG, e+o ~ e 1.0642 =:} 0.5321
cjJpm [deg]
PI [deg] P3 [deg]
24.59
0.202
YZ plane, 4J == 90° In teracting wavelengths [urn]
SHG, o+e ~ 0 1.0642 =} 0.5321 1.1523 =} 0.57615 1.3188 =} 0.6594 2.098 1.049 2.9365 =} 1.46825 SFG, 0 +e 0 1.3188 + 0.6594 => 0.4396
*
*
{}pm
[deg]
P2 [deg]
68.67 59.59 50.25 43.01 57.95
1.829 2.314 2.544 2.481 2.225
65.14
2.210
*
0.268
113
114
3 Properties of Nonlinear Optical Crystals
XZ plane, 4J = 0°, () > V,
Interacting wavelengths [urn] SHG, 0 + e=>o 1.1523 => 0.57615 1.3188 => 0.6594 2.098 =} 1.049 2.9365 => 1.46825 SFG, 0 + e=>o 1.3188 + 0.6594 => => 0.4396
(Jpm
[deg]
P2 [deg]
72.01 60.38 52.13 67.36
1.747 2.487 2.671 1.928
86.84
0.362
Calculated values of inverse group-velocity mismatch for SHG process in flux-grown KTP: XY plane, (J = 90° Interacting wavelengths [urn] SHG, e + 0 => e 1.0=>0.5 1.05 => 0.525
o 1.0=>0.5 1.1 => 0.55 1.2 => 0.6 1.3 => 0.65 1.4 => 0.7 1.5 => 0.75 1.6 => 0.8 1.7 => 0.85 1.8=>0.9 1.9 => 0.95 2.0 => 1.0
[fsjmm]
3.1 Basic Nonlinear Optical Crystals
115
XZ plane, cP = 0°, () > Vz Interacting wavelengths [urn]
SHG, 0 + e=>o 1.1 => 0.55 1.2 => 0.6 1.3 => 0.65 1.4 => 0.7 1.5 => 0.75 1.6 => 0.8 1.7 =} 0.85 1.8 => 0.9 1.9 => 0.95 2.0 => 1.0
()pm
[deg]
80.31 67.47 61.25 57.32 54.70 52.99 51.94 51.42 51.32 51.57
P [fs/mm]
391 307 246 200 164 135 111 90 81 98
Experimental values of NCPM temperature and corresponding temperature bandwidth: hydrothermally grown KTP along X axis T [OC]
~T
1.3188 Y + 0.6594z => 0.4396 Y 1.338 Y + 0.660/ => 0.446Y along Yaxis
47 463
8.5 8.5
Interacting wavelengths [urn]
T (OC]
~T
20
175
3.256
20
122
3.257
T [OC]
~T
153(?) 63
20 30
Interacting wavelengths [urn]
[OC]
Ref.
SFG, type II
SHG, type II 0.9943x + 0.9943 z => 0.49715x SFG, type II 1.0642x + 0.800/ => 0.45961 x
3.241 3.241
(OC]
Ref.
flux-grown KTP along X axis Interacting wavelengths [urn]
[OC]
Ref.
SHG, type II 1.0796Y
+ 1.0796z => 0.5398 Y
SFG, type II 1.090Y + 1.030/ => 0.5321 Y
20 20
3.248 3.258 3.259 3.260
116
3 Properties of Nonlinear Optical Crystals
2.15Y + 1.04z => 0.70094Y 3.09Y + 1.38z => 0.95396Y 3.297Y + 1.571 z => 1.047Y 3.276Y + 1.530/ => 1.0642Y 1.3188 Y + 0.6594z => 0.4396Y 1.338 Y + 0.660/ => 0.446Y
20 20 20 20 60.2 484
3.261 3.261 3.262 3.262 3.241 3.241
8.5 8.5
along Yaxis Interacting wavelengths [Jlm]
T rOC] Ref.
SHG, type II 0.90/ + 0.90/ => 0.495x SFG, type II 1.0642x + O.8068 z => O.458~ 1.0642x + 0.808z => 0.45920/ 1.0642x + 0.9691 z => 0.5072x
20
3.254
20 20 20
3.254 3.238 3.254
Note: Superscripts of interacting wavelengths represent polarization directions Experimental values of internal angular, temperature, and spectral bandwidths: XY plane, () == 900 ( T == 20°C) Interacting wavelengths [urn]
l/>pm
[deg]
SHG, e + 0 => e 1.0582 => 0.5921 1.062 => 0.531 1.0642 => 0.5321
YZ plane, c/J
25 23 23.2 23.3 25 25.2 25.2 25.2
== 90
0(T
Al/>int
L\Oint
[deg]
[deg]
0.43 0.49 0.53 0.58 0.43
2.01 2.23
0.42 0.52
1.82
AT [OC]
Av [cm"]
25 20 24 20
4.9
3.263 3.229 3.243 3.225 3.244 3.227 3.231 3.246 3.230
4.0 6.2
25 17.5 25.7
2.52
Ref.
== 20°C)
In teracting wavelengths [urn]
()pm
A ()int
AljJint
[deg]
[deg]
[deg]
AT [Oe]
[cm"]
SHG, o+e => 0 0.9943 => 0.49715
90
2.96
5.70
175
7.1
Av
Ref.
3.256
3.1 Basic Nonlinear Optical Crystals
1.0642 => 0.5321 2.532 =} 1.266 SFG, type II I.0642x + O.80~ => =} 0.45961 x
XZ plane, 4>
== 0°
1 ()
100
69 69 56
0.11 0.20
90
2.72
6.13
T
()pm
~()int
[Oe]
[deg] [deg]
20 153
85.3 90
47 30.7
3.237 3.264 3.264
17.6(~v2)
3.257
117
> Vz
Interacting wavelengths [urn] SHG, 0 + e=}o 1.0796 =} 0.5398
0.34 1.70
Ref.
3.248 3.248
Note: Superscripts of interacting wavelengths represent polarization directions Effective nonlinearity in the phase-matching direction for three-wave interactions in the principal planes of KTP crystal [3.35, 36]: XYplane d eoe == d oee
== d 31sin2 c/J + d 32 cos 2 c/J ,
YZ plane d oeo == d eoo
== d 31sin () ,
XZ plane, () < Vz d ooe == d 32 sin () , XZ plane, () > Vz
d oeo == d eoo == d32 sin () . Effective nonlinearity for three-wave interactions in the arbitary direction of KTP crystal are given in [3.36] Nonlinear coefficients [3.265] : d31(1.0642,um)
== 1.4 pm/V,
d 32(1.0642,um)
== 2.65 pmjV ,
d 33(1.0642,um)
== 10.7 pmjV .
118
3 Properties of Nonlinear Optical Crystals
Laser-induced damage threshold: hydrothermally grown KTP A [urn]
Lp
[ns]
0.03 0.03 1.0642 125000 30 20 11
0.526
Ithr X
10- 12 [W/m 2 ]
300 300 0.01 1.5 > 1.5 20-30
Ref. 3.239 3.235 3.266 3.267 3.268 3.269
Note 10 Hz
10 Hz
flux-grown KTP
A [urn]
Lp
0.526 0.5291 0.5321
0.03 18 14 8 8 0.06 25 30 25
1.0582 1.0642
10- 12 [W/m 2 ]
Ref.
Note
100 0.8-1.0 0.5 14-22 20-32 > 18 1.8-2.2 > 3.3 >6
3.235 3.263 3.246 3.270 3.270 3.245 3.263 3.249 3.271
10 Hz surface damage 60 pulses 2 Hz, surface damage 2 Hz, bulk damage 5 Hz surface damage
25
>3
3.271
20 11 11 10 9 1.3 1 1
1.5 15-22 24-35 9-10 310 46 150 > 150
3.246 3.270 3.270 3.243 3.272 3.33 3.225 3.112
[ns]
Ithr X
250 000 pulses, bulk darkening 3 500 000 pulses, bulk darkening 60 pulses 2 Hz, surface damage 2 Hz, bulk damage 1 pulse, bulk damage surface damage 1 pulse
Thermal conductivity coefficient [3.235] : K
2
[W/mK], along a
K
3
[W/mK], along b
K
[W/mK], along c
3.3
3.1 Basic Nonlinear Optical Crystals
3.1.8 LiNb0 3 , Lithium Niobate
Negative uniaxial crystal: no > ne ; Point group: 3m; Mass density: 4.628 g/cm 3 [3.273]; Mohs hardness: 5 - 5.5; Transparency range at "0" transmittance level: 0.4 - 5.5 urn [3.274, 275]; Linear absorption coefficient a: A [urn]
0.5145
0.6594 1.0642
1.3188
(J.
[cm']
Ref.
0.025 0.019-0.025 0.035-0.045 0.0021-0.0044 0.0085-0.0096 0.0019-0.0023 0.0014-0.0019 0.0042 0.0028 0.0018-0.0044 0.0017-0.0110
3.276 3.186 3.186 3.186 3.186 3.186 3.186 3.277 3.277 3.186 3.186
Two-photon absorption coefficient A [11m]
0.5288 0.53 0.5321
px
1011 [m/w] Ref.
0.15 (?) 5.0 2.90 1.57
Note
3.278 3.279 3.188 3.188
II c e - wave, 1- c II c e - wave, 1- c II c e - wave, .L c II c ..lc
II c e - wave, 1- c
p:
Note
o-wave e-wave
Experimental values of refractive indices for lithium-rich lithium niobate, T = 293 K [3.280] : A [urn]
no
ne
A [urn]
no
ne
0.3250 0.4545 0.4579 0.4658 0.4727 0.4765
2.6360 2.3751 2.3719 2.3658 2.3604 2.3573
2.4670 2.2608 2.2584 2.2530 2.2489 2.2465
0.4880 0.4965 0.5017 0.5145 0.6328 1.0642
2.3495 2.3437 2.3405 2.3334 2.2878 2.2339
2.2398 2.2352 2.2329 2.2270 2.1890 2.1440
119
3 Properties of Nonlinear Optical Crystals
120
lithium niobate grown from stoichiometric melt (mole ratio Li/Nb = 1.000), T == 293 K [3.274] :
A [urn]
no
ne
A [urn]
no
ne
0.42 0.45 0.50 0.55 0.60 0.70 0.80 0.90 1.00 1.20 1.40 1.60
2.4089 2.3780 2.3410 2.3132 2.2967 2.2716 2.2571 2.2448 2.2370 2.2269 2.2184 2.2113
2.3025 2.2772 2.2457 2.2237 2.2082 2.1874 2.1745 2.1641 2.1567 2.1478 2.1417 2.1361
1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00
2.2049 2.1974 2.1909 2.1850 2.1778 2.1703 2.1625 2.1543 2.1456 2.1363 2.1263 2.1155
2.1306 2.1250 2.1183 2.1129 2.1071 2.1009 2.0945 2.0871 2.0804 2.0725 2.0642 2.0553
lithium niobate grown from congruent melt (mole ratio Li/Nb = 0.946), T = 293 K [3.281] :
A [urn]
no
ne
0.43584 0.54608 0.63282 1.1523 3.3913
2.39276 2.31657 2.28647 2.2273 2.1451
2.29278 2.22816 2.20240 2.1515 2.0822
T
=
297.5 K [3.282]:
A [urn]
no
ne
A [um]
no
ne
0.40463 0.43584 0.46782 0.47999 0.50858 0.54607 0.57696 0.57897 0.58756 0.64385
2.4317 2.3928 2.3634 2.3541 2.3356 2.3165 2.3040 2.3032 2.3002 2.2835
2.3260 2.2932 2.2683 2.2605 2.2448 2.2285 2.2178 2.2171 2.2147 2.2002
0.66782 0.70652 0.80926 0.87168 0.93564 0.95998 1.01400 1.09214 1.15392 1.15794
2.2778 2.2699 2.2541 2.2471 2.2412 2.2393 2.2351 2.2304 2.2271 2.2269
2.1953 2.1886 2.1749 2.1688 2.1639 2.1622 2.1584 2.1545 2.1517 2.1515
3.1 Basic Nonlinear Optical Crystals
A [11m]
no
ne
A [11m]
no
ne
1.28770 1.43997 1.63821 1.91125 2.18428
2.2211 2.2151 2.2083 2.1994 2.1912
2.1464 2.1413 2.1356 2.1280 2.1211
2.39995 2.61504 2.73035 2.89733 3.05148
2.1840 2.1765 2.1724 2.1657 2.1594
2.1151 2.1087 2.1053 2.0999 2.0946
Temperature derivative of refractive indices for lithium-rich niobate, T == 298 K [3.280] : ;t [11m]
dno/dT x 105 [K- 1]
dne/dT x 105 [K- 1]
0.3250 0.4545 0.6328 1.0642
8.71 1.93 0.522 0.141
12.9 6.22 4.31 3.85
stoichiometric melt (mole ratio Li/Nb = 1.000), ;t ==: 0.45 - 0.70 11m, T == 293 K) [3.283] : dno/dT == 2.0 x 10- 5 K- 1 5
dne/dT == 7.6 x 10- K-
1
,
;
Sellmeier equations (;t in urn, T == 20°C) for lithium-rich niobate [3.280] : n 2 == 4.91296
+
0.116275 - 0.0273;t2 ;t2 _ 0.048398 '
+
0.091649 - 0.0303;t2 . ;t2 - 0.046079 '
o
n 2 == 4.54528 e
stoichiometric melt (mole ratio Li/Nb = 1.000) [3.284] : n 2 == 4.91300
+
o
n 2 == 4.57906
+
e
0.118717 A,2 - 0.045932
- 0.0278;t2 '
0.099318 - 0.0224;t2 . ;t2 - 0.042286 '
congruent melt (mole ratio Li/Nb = 0.946) [3.281] : n 2 == 4.9048
+
0.117680 - 0.027169;t2 ;t2 - 0.047500 '
+
0.099169 - 0.021950;t2 . ;t2 - 0.044432
o
n 2 == 4.5820 e
121
122
3 Properties of Nonlinear Optical Crystals
Temperature-dependent Sellmeier equations (;, in urn, T in K) for lithium-rich lithium niobate [3.280] n~
==
4.913
+
+ 1.6 x
10- 8 (T2 - 88506.25) 8(T2
0.1163 + 0.94 x 10- 88506.25) _ 0.0273A? 2 8(T2 A - [0.2201 + 3.98 x 10- 88506.25)]2 '
n; == 4.546 + 2.72 x 10- (T 7
+
2
-
88506.25) 8
2
0.0917 + 1.93 x 10- (T - 88506.25) _ 0.0303A? . ;,2 _ [0.2148 + 5.3 x 10- 8(T2 - 88506.25)]2
stoichiometric melt (mole ratio Li/Nb = 1.000) [3.284] : n2 = 4.9130
+
o
8
= 4.5567 + 2.605 x
n2
2
0.1173 + 1.65 x 10- T _ 0.0278A? ;,2 _ (0.212 + 2.7 x 10- 8 T2)2 '
1O-7 T 2 +
e
8
2
- 0.0224A? 0.0970 + 2.70 x 10- T _ (0.201 + 5.4 x 10-ST2)2 '
;,2
congruent melt (mole ratio Li/Nb = 0.946) [3.285] : n~
= 4.9048 + 2.1429 x +
10- 8 (T2 - 88506.25) 8
n; = 4.5820 + 2.2971 x 10- (r 7
+
2
0.11775 + 2.2314 x 10- (T - 88506.25) _ 0.027153A,2 8(T2 - 88506.25)]2 ' ;,2 _ [0.21802 - 2.9671 x 102
-
88506.25) 8(T2
0.09921 + 5.2716 x 1O- 88506.25) _ 0.021940A,2 . ;,2 _ [0.21090 - 4.9143 x 10-8(T2 - 88506.25)]2
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: lithium-rich lithium niobate, T == 295 K Interacting wavelengths [urn] SHG, 1.0642
o+o~e ~
0.5321
(Jexp
[deg]
(Jtheor
[deg]
P3 [deg]
[3.280] 67.5 [3.280] 66.76
1.776
3.1 Basic Nonlinear Optical Crystals
stoichiometric melt (mole ratio Li/Nb = 1.000), T In teracting wavelengths [urn]
(Jexp
[deg]
(Jtheor
[deg]
P3 [deg]
[3.284]
SHG, 0 + 0 => e 1.118=>0.559 1.1523 => 0.57615 SFG, 0 + 0 => e 2.17933 + 0.8529 => 0.613 4.0 + 0.72394 =} 0.613
71.7 [3.284] 67.6 [3.284] 68 [3.274] 69 [3.286]
71.80 67.74
1.312 1.543
55 [3.287] 47.5 [3.287]
54.75 47.48
2.073 2.212
congruent melt (mole ratio Li/Nb = 0.946), T Interacting wavelengths [urn]
(Jexp
[deg]
= 293 K
(Jtheor
[deg]
P3 [deg]
[3.284]
SHG, 0 + 0 => e 1.1523 => 0.57615 2.12 => 1.06 2.1284 => 1.0642 SFG, 0 + 0 => e 1.95160 + 1.0642 => 2.57887 + 1.0642 => 3.22241 + 1.0642 => 4.19039 + 1.0642 =>
= 293 K
0.68867 0.75333 0.80000 0.84867
72 [3.286] 70.39 43.8 [3.288] 45.25 44.6 [3.289] 45.28 47 [3.290]
1.341 1.988 1.987
52.7 [3.291] 48.1 [3.291] 46.5 [3.291] 47 [3.291]
2.000 2.047 2.044 2.026
52.86 48.13 46.50 46.90
Note: The PM angle values are strongly dependent on melt stoichiometry Experimental values of NCPM temperature: lithium-rich lithium niobate In teracting wavelengths [urn] SHG, 0 + 0 => e 0.954 =} 0.477 1.0642 => 0.5321 1.3188 => 0.6594
T
[OC] Ref.
-62.5 233.7 238 520
3.280 3.277 3.280 3.280
123
3 Properties of Nonlinear Optical Crystals
124
stoichiometric melt (mole ratio Li/Nb = 1.000) In teracting wagelengths [urn] SHG, 0 + 0 =} e 1.029 =} 0.5145 1.058 =} 0.529 1.0642 =} 0.5321 1.084 ~ 0.542 1.118 ~ 0.559 1.1523 =} 0.57615
T [OCl
Ref.
15 0 43 72 97 153.5 193 208 211
3.292 3.293 3.294 3.295 3.296 3.284 3.293 3.284 3.295
congruent melt (mole ratio Li/Nb = 0.946) In teracting wavelengths [11m] SHG, 0+0 ~ e 1.029 ~ 0.5145 1.0576 ~ 0.5288 1.0642 ~ 0.5321
1.084
~
1.1523
0.542
~
0.57615
T [OCl
Ref.
-66 -14 -8 6 11.5 38 42 46 172 174
3.292 3.278 3.297 3.298 3.294 3.299 3.297 3.292 3.297 3.282
Note: The NCPM temperature values are strongly dependent on melt stoichiometry Experimental value of internal angular bandwidth [3.81]: Al1nt[deg]
Interacting wagelengths [Jlm] SHG, 0+0 1.06 ~ 0.53
~
e 0.040
Experimental values of temperature and spectral bandwidths: In teracting wavelengths [urn] SHG, 0+0 1.06 ~ 0.53
~
T rOC]
Bpm [deg]
20
68
A T [OC]
LiVI [em-I]
Ref.
3.2
3.81
e
3.1 Basic Nonlinear Optical Crystals
1.0642
=}
*
1.084
0.5321
0.542
1.1523 =} 0.57615 SFG, 0 + 0 ~ e 1.7 + 0.6943 0.493 0.4115 2.65 + 0.488
* *
51 234 38 46 172
90 90 90 90 90
0.72 0.52 0.74 0.74 0.66
70 90
90 90
1.6
125
3.300 3.277 3.292 3.299 3.297 7.9 2.9
3.301 3.302
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe = d 3 1 sin () - d 22 cos ()sin 34> ,
d eoe
= d oee = d 22 cos 2 () cos 31> .
Nonlinear coefficients: stoichiometric melt (mole ratio LijNb
=
1.000)
d22(1.058 urn] = 2.46 ± 0.23 pm/V [3.274,37] , d 31 (1.058 pm) = -4.64 ± 0.66 pmjV [3.274, 37] ,
d33(1.058 pm) = -41.7 ± 7.8 pmjV [3.274,37] . congruent melt (mole ratio LijNb = 0.946)
d 22(1.06 pm) = 2.10 ± 0.21 pmjV [3.303,37] , d31
(1.06 um) = -4.35 ± 0.44 pmjV [3.303,37],
d33(1.06 um) = -27.2 ± 2.7 pmjV [3.303,37] . Laser-induced surface-damage threshold: 'r p
0.53 0.5321 0.59-0.596 0.6943 1.06
1.0642
[ns]
0.007 0.002 ~ 10 25 30 30 10-30 30 0.006 20 30
Ithr X
10- 12 [Wjm 2 ]
> 100
> 700 > 3.5 1.5 1.2 1.7 3.0 12 > 100 >1 150-200
Thermal conductivity coefficient [3.64]: K
= 4.6 W /mK at T = 300 K .
Ref. 3.304 3.305 3.305 3.306 3.307 3.308 3.309 3.307 3.288 3.289 3.310
Note 10 Hz 10 Hz 1 pulse
bulk damage
with coating
126
3 Properties of Nonlinear Optical Crystals
3.1.9 KNb0 3 , Potassium Niobate Negative biaxial crystal: 2Vz = 66.78° at A = 0.5321 urn [3.311]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z ~ b,a,c (Fig. 3.3) Transparency range at "0" transmittance level: ~ 0.4- > 4flm [3.312,313]; Linear absorption coefficient ex:
< 0.05 0.015 0.0018-{).0025
0.42-1.06 0.82 1.0642
Ref.
Note
3.314 3.315 3.316
along b axis
Z(c)
optic axis
..... Y(a)
~-~------+-~
X(b) Fig. 3.3. Dependence of refractive index on light propagation direction and polarization (index surface) in the first octant of dielectric reference frame (X, Y, Z) of KNb0 3 crystal. Designations: (J is the polar angle, t/> is the asimuthal angle, Vz is the angle between one of the optical axes and the Z axis
Experimental values of refractive indices at T = 295 K [3.312]:
A [urn]
nx
0.430 0.488 0.514 0.633
2.4974 2.4187 2.3951 2.3296
nz
2.4145 2.3527 2.3337 2.2801
2.2771 2.2274 2.2121 2.1687
3.1 Basic Nonlinear Optical Crystals
A [~m]
nx
ny
nz
0.860 1.064 1.500 2.000 2.500 3.000
2.2784 2.2576 2.2341 2.2159 2.1981 2.1785
2.2372 2.2195 2.1992 2.1832 2.1674 2.1498
2.1338 2.1194 2.1029 2.0899 2.0771 2.0630
127
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: XY plane, () == 90 0
In teracting wavelengths [urn] SHG, e +e => 0.946 =:} 0.473
¢exp
~
[3.311]
[3.312]
[3.317]
30 [3.318]
26.88
29.97
30.43
[deg]
()theor
[3.311]
[3.312]
[3.317]
77.37 69.03 63.36 60.27 46.57
83.13 70.67 63.92 60.43 45.95
87.98 71.92 64.94 61.37 46.52
[3.311]
[3.312]
[3.317]
71.05
71.85
71.16
()exp
SHG, 0 + 0 ==> e 0.43 0.86 0.445 0.89 0.92 0.46 0.94 0.47 0.5321 1.0642
83.5 [3.319] 70.7 [3.319] 64 [3.319] 60.5 [3.319] ~ 47 [3.311]
*
== 0
0
Interacting wavelengths [urn] SHG, 0 1.0642
[deg]
0
In teracting wavelengths [~m]
XZ plane, 1>
¢theor
0
YZ plane, 4> == 90
* * * *
[deg]
, ()
[deg]
> Vz ()exp
[deg]
()theor
[deg]
+ 0 =* e
*
0.5321
70.4 [3.320] 71[3.311] 71 [3.314] 71 [3.317] ~
Note: The dispersion relations given in [3.321] show worse agreement with the experiment
3 Properties of Nonlinear Optical Crystals
128
Experimental values of NCPM temperature: along X axis In teracting wavelengths [urn] SHG, type I 0.972 ~ 0.486 0.982 => 0.491 0.986 =* 0.493 0.988 ~ 0.494 1.047 => 0.5235 1.0642 =* 0.5321
T rOC]
Ref.
-20 20 20 20 162 178 181 182 184 188
3.322 3.323 3.324 3.314 3.325 3.326 3.311 3.320 3.300 3.327
along Yaxis Tnteracting wavelengths [um] SHG, type I 0.8385 =} 0.41925 0.8406 => 0.4203 0.842 ~ 0.421 0.856 ~ 0.428 0.857 =* 0.4285 0.8593 ~ 0.42965 0.86 => 0.43 0.8615 ::::} 0.43075 0.862 ::::} 0.431 0.879 ~ 0.4395 0.9289 ~ 0.46445 0.95 :::} 0.475 SFG, type I 0.6764 + 1.0642 :::} 0.41355 0.6943 + 1.0642 => 0.42017
T [0 C]
Ref.
-34.2 -28.3 -22.8 15 20 20 22 30 34 70 158 180
3.328 3.329 3.330 3.331 3.332 3.328 3.324 3.333 3.334 3.334 3.328 3.324
-4 27.2
3.335 3.335
Best set of dispersion relations (A in urn, T == 22°C) [3.312]: n2 x
= 1+
1.44121874A? _ 0.07439136
A2
+
2.54336918A?
A2 - 0.01877036
- O.02845018A?
3.1 Basic Nonlinear Optical Crystals
n2
= 1 + 1.33660410,1.1 + 2.49710396,1.1 _ 0.02517432,1.2 A2
y
n2
= 1+
z
-
A2 - 0.01666505
0.06664629 2
1.04824955A A2 _ 0.06514225
+
2
2.37108379A A2 - 0.01433172
_
0.01943289A2
•
Temperature-dependent dispersion relations (A in urn, T in K) [3.336]: n2 x
= 1 + (2.5389409 + 3.8636303 x 10- 6 F)A2 A2 _ (0.1371639 + 1.767 x 10- 7 F)2 (1.4451842 - 3.909336 x 10- 6F - 1.2256136 x 10-4 G)A2
+------------------,-A? - (0.2725429 + 2.38 x 10- 7F - 6.78 x 10- 5 G)2 - (2.837
10- 2
X
1.22
-
X
10- 8F)A2
-
3.3 x 10- 10F A4
,
= 1 + (2.6386669 + 1.6708469 x 10- 6 F)A2 Y JL2 - (0.1361248 + 0.796 x 10- 7 F)2
n2
(1.1948477 - 1.3872635 x 10-6 F - 0.90742707
X
10-4 G)A2
+ -2- - - - - - - - - -7 - - - - -5- - A - (0.2621917 + 1.231 x 10- F - 1.82 X 10- G)2 - {2.513 X 10- 2 n2 = z
-
0.558
X
10-8 F)A2
-
4.4 x 10- 10F A4
,
2
1 + (2.370517 + 2.8373545 x 10- 6 F)A A2 _ (0.1194071 + 1.75 x 10- 7 F)2
{1.048952 - 2.1303781 x 10-6 F - 1.8258521
X
10-4 G)A2
+ -2- - - - - - - - - -------A - (0.2553605 + 1.89 x 10-7 F - 2.48 X 10-5 G)2 - (1.939 where F == T 2
-
X
10-2
-
0.27
X
10-8 F);? - 5.7 x 10- 10 F)..,4 ,
295.15 2 , and G == T - 293.15 .
Calculated values of phase-matching and "walk-off" angles: YZ plane, e 1.0642 => 0.5321 1.3188 => 0.6594
Opm
[deg] P3 [deg]
45.95 29.87
3.009 2.507
129
XZ plane, 1> == 0° () > Vz Interacting wavelengths film] SHG, 0 + 0 =} e 1.0642 =} 0.5321 1.3188 =} 0.6594
()pm
[deg] P3 [deg]
71.85 57.47
2.479 3.553
Experimental values of the internal angular bandwidth: XZ plane, 1> == 0° Interacting wavelengths [urn]
SHG, 0+0 =} e 1.0642 => 0.5321
T [OC] ()pm [deg]
20
A()int
[deg]
0.013-0.014
71
Ref.
3.323
along Yaxis Interacting wavelengths [urn]
SHG, type I 0.857 =} 0.4285
T [OC]
()pm
20
90
[deg]
[deg]
A()int
0.659
A1>int
[deg]
1.117
Ref.
3.323
Experimental values of temperature bandwidth: along X axis Interacting wavelengths [Jlm] SHG, type I 1.0642 =} 0.5321
T [OC] ()pm [deg]
181 182 184 188
90 90 90 90
AT [OC]
Ref.
0.27-0.32 0.28 0.28-0.29 0.34
3.311 3.320 3.300 3.327
along Yaxis Interacting wavelengths [urn] SHG, type I 0.8385 =} 0.41925 0.842 =} 0.421 0.855 =} 0.4275 0.92 =} 0.46 SFG, type I 0.6764 + 1.0642 =} 0.41355
-34.2 -22.8 26.4 (?) 163.5 (?) -4
90 90 90 90
0.27 0.30 0.265 0.285
3.328 3.330 3.314 3.314
90
0.35
3.335
3.1 Basic Nonlinear Optical Crystals
131
Temperature of noncritical SHG [3.323] along X axis
Al == 0.97604 + 2.53 x 10- 4 T + 1.146 X 10- 6 T 2 along Yaxis
Al == 0.85040 + 2.94 x 10-4 T + 1.234 X 10-6 T 2 where A.I in urn, and Tin °C. Temperature variation of birefringence for noncritical SHG process [3.314]: along X axis (1.0642 urn => 0.5321Jlm)
d[nz(2w) - ny(w)]/dT == 1.10 x 10- 4 K- I along Yaxis (0.92 urn => 0.46 um)
d[nz(2w) - nx(w)]/dT == 1.43 x 10- 4 K- 1
.
Effective nonlinearity expressions in the phase-matching direction for three.. wave interactions in the principal planes of KNb0 3 crystal [3.35], [3.36]: XYplane d eeo
== d 32 sin2 ljJ + d 3 I cos 2 ljJ ;
YZ plane d ooe == d 32 sin (); XY plane, 0
Vz d ooe == d 3I sin () . d oeo
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of KNb0 3 crystal are given in [3.36]. Nonlinear coefficients [3.323,37,313]:
== -11.9 pm/V, d 32(1.0642Jlm) == -13.7 prnjV , d 33(1.0642 urn) == -20.6 pmjV .
d31(1.0642Ilm)
Laser-induced surface-damage threshold: A [J.1m]
1:p
0.527
0.5 0.5 10 25 11
0.5321 1.047
[ns]
Ithr X
10- 12 [W/m 2)
88-94 120-150 0.55 1.5-1.8 > 0.3
Ref.
Note
3.337 3.337 3.326 3.300 3.325
along b axis, E II c along b axis, E ..l c
4 kHz, 2000 hours
132
3 Properties of Nonlinear Optical Crystals
A [urn]
[ns] Ithr
1:p
1.054
10- 12 [W/m2 ]
110 180 370 1.5-1.8 > 1000
0.7 0.7 0.7 25 0.1
1.0642
X
Ref.
Note
3.337 3.337 3.337 3.300 3.323
along a axis, E J.. c along b axis, E J.. c along b axis, E J.. c
Thermal conductivity coefficient: K
> 3.5 W/mK [3.316] .
3.1.10 AgGaS2' Silver Thiogallate Negative uniaxial crystal: no > ne (at A < 0.497 urn ne > no); Point group: 42m ; Mass density: 4.58 g/cm 3 [3.338] ; Mohs hardness: 3 - 3.5 ; Transparency range at "0" transmittance level: 0.47 - 13 urn [3.339] ; Linear absorption coefficient ex:
A [urn]
(X
[cm:']
< 0.1
0.5-13 0.6-0.65 0.6--12 0.633 0.9-8.5 1.064 4-8.5
0.04 < 0.09 0.05 < 0.9 0.01 < 0.04
Ref. 3.340 3.341 3.339 3.342 3.343 3.342 3.341
Experimental values of refractive indices [3.344]:
A [~m]
A [um]
no
0.490 0.500 0.525 0.550 0.575 0.600 0.625 0.650 0.675 0.700 0.750 0.800
2.7148 2.7287 0.850 2.6916 2.6867 0.900 2.6503 2.6239 0.950 2.6190 2.5834 1.000 2.5944 2.5537 1.100 2.5748 2.5303 1.200 2.5577 2.5116 1.300 2.5437 2.4961 1.400 2.5310 2.4824 1.500 2.5205 2.4706 1.600 2.5049 2.4540 1.800 2.4909 2.4395 2.000
ne
A [~m]
no
ne
2.4802 2.4716 2.4644 2.4582 2.4486 2.4414 2.4359 2.4315 2.4280 2.4252 2.4206 2.4164
2.4279 2.200 2.4192 2.400 2.4118 2.600 2.4053 2.800 2.3954 3.000 2.3881 3.200 2.3819 3.400 2.3781 3.600 2.3745 3.800 2.3716 4.000 2.3670 4.500 2.3637 5.000
no
ne
2.4142 2.4119 2.4102 2.4094 2.4080 2.4068 2.4062 2.4046 2.4024 2.4024 2.4003 2.3955
2.3684 2.3583 2.3567 2.3559 2.3545 2.3534 2.3522 2.3511 2.3491 2.3488 2.3461 2.3419
3.1 Basic Nonlinear Optical Crystals
133
A [urn]
no
ne
A [um]
no
ne
A [Jlm]
no
ne
5.500 6.000 6.500 7.000 7.500
2.3938 2.3908 2.3874 2.3827 2.3787
2.3401 2.3369 2.3334 2.3291 2.3252
8.000 8.500 9.000 9.500 10.00
2.3757 2.3699 2.3663 2.3606 2.3548
2.3219 2.3163 2.3121 2.3064 2.3012
10.50 11.00 11.50 12.00 12.50
2.3486 2.3417 2.3329 2.3266 2.3177
2.2948 2.2880 2.2789 2.2716
Optical activity [3.339, 345]: p == 522 degjmm at isotropic point (no == ne , A == 0.4973 J,1m) Temperature dependences of refractive indices (A in J,1m)[3.346] :
2 5 10[39.88A -2no x - A.2 _ 0.0676
dno/dT
==
dn dT
== -
e/
4
112.20A
+ -(A-2-_-0-.0-6-7-6)~2
]
'
10-5 [25.50A.2 45.72A,4] x + + Zn; A,2 - 0.107584 (A,2 - 0.107584)2
.
Note: Canarelli et al. [3.347] observed the discrepancy between these dispersion formulas and the experiment Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [um]
SHG, 0 + 0 =} e 3.3913 =} 1.69565 10.6 =} 5.3
SFG,o + 0 => e 11.538 + 1.17233 => 1.0642 9.9 + 1.19237 =} 1.0642 8.7 + 1.21252 =} 1.0642 6.24 + 1.28301 =} 1.0642 5.89 + 1.29888 =} 1.0642 4.8 + 1.36735 => 1.0642 4.0 + 1.44996 => 1.0642 3.09 + 1.62325 =:} 1.0642 2.53 + 1.83683 =:} 1.0642 6.85 + 1.0642 =} 0.92110 4.43 + 1.0642 =} 0.85807 6.6 + 0.77593 =} 0.6943
()exp
[deg]
8t heor [deg] [3.348]
[3.349]
[3.350]
33 [3.339] 67 [3.351] 67.5 [3.352] 68 [3.339] 70.8 [3.344]
34.1 70.7
33.2 73.3
33.5 71.7
34.7 [3.48] 35.9 [3.353] 37 [3.354] 41.1 [3.355] 42.1 [3.353] 44 [3.354] 47.7 [3.355] 51 [3.350] 53.4 [3.350] 42 [3.356] 55 [3.356] 60 [3.357]
35.9 36.4 37.3 40.9 41.7 44.7 47.7 51.9 54.4 43.9 57.1 60.5
35.3 35.6 36.4 39.8 40.5 43.4 46.1 50.0 52.4 42.7 55.3 60.4
35.7 36.2 37.0 40.4 41.2 44.1 46.9 50.9 53.4 43.6 56.7 61.8
134
3 Properties of Nonlinear Optical Crystals
4.8 + 0.81171 => 0.6943 11.66329 + 0.617 => 0.586 10.12478 + 0.622 => 0.586 SFG, e + 0 => e 10.9 + 1.17934 :::} 1.0642 8.8 + 1.21060 => 1.0642 7.0 + 1.25500 => 1.0642 5.2 + 1.33803 => 1.0642 10.6 + 1.0642 => 0.96711 9.6 + 1.0642 => 0.95800 10.6 + 0.6943 => 0.65162
75.5 [3.357] 64 [3.358] 70 [3.358]
79.5 58.9 64.2
79.0 67.0 75.4
83.9 63.4 70.1
38.3 [3.359] 40.3 [3.359] 43.6 [3.359] 50.6 [3.359] 39.8 [3.360] 41.5 [3.360] 55 [3.361]
38.3 40.2 43.7 50.6 39.7 41.0 54.0
37.5 39.1 42.4 48.7 38.8 40.0 55.3
38.0 39.9 43.2 49.9 39.5 40.8 55.8
Note: The other sets of dispersion relations from [3.348, 362, 48] show worse agreement with the experiment Best of dispersion relations (A in urn, T = 20°C) [3.350]. n2
o
= 3.3970 +
2.3982A? A2 _ 0.09311
+
2.1640A? A2 - 950.0 '
2
2
2 _ 3 5873 1.9533A 2.3391A n-. +2 +2 e A-0.II066 A-I030.7
.
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0 + 0 => e 10.6 => 5.3 9.6 => 4.8 5.3 => 2.65 4.8 => 2.4 2.9365 => 1.46825 2.1284 => 1.0642 SFG,o + 0 => e 10.6 + 3.533 => 2.65 10.6 + 2.65 => 2.12 10.6 + 1.0642 => 0.96711 10.6 + 0.6943 => 0.65162 SFG, e + 0 => e 10.6 + 5.3 => 3.533 10.6 + 1.0642 => 0.96711 10.6 + 0.6943 => 0.65162
(Jpm
[deg]
PI [deg]
P3 [deg]
71.68 58.15 32.00 31.04 37.27 54.23
0.76 1.15 1.17 1.15 1.24 1.18
37.40 34.79 37.31 52.85
1.25 1.21 1.21 1.04
58.15 39.52 55.76
1.18 1.32 1.23
1.15 1.23 1.00
3.1 Basic Nonlinear Optical Crystals
135
Experimental values of internal angular and spectral bandwidths at T = 293 K: In teracting wavelengths [urn] SHG, 0 + 0 => e 10.6 => 5.3 SFG,o + 0 => e 4.6 + 0.8177 => 0.6943 10.53 + 0.589 => 0.56589 6.24 + 1.283 => 1.0642 4.817 + 1.0642 => 0.87163 10.619 + 0.634 => 0.598 10.6 + 0.598 => 0.566 10.6 + 0.5968 => 0.565
Opm [deg]
L\Oint [deg]
67.5
0.41
3.339
82.7 90 41.1 52 90 90 90
0.42 2.34
3.357 3.349 3.355 3.356 3.341 3.363 3.364
i\Vl [cm'] Ref.
9.8 5.9 1.73 1.5 1.44
Temperature variation of phase-matching angle [3.360]: Interacting wavelengths [Jlm]
T [Oe]
Opm [deg]
dOpm /dT [deg/K]
SPG, e + 0 => e 10.6 + 1.0642 => 0.9671
20
39.8
0.03
Temperature tuning of noncritical SPG [3.347]: Interacting wavelengths [urn]
dAl/dT [nm/K]
SHG, 0 + 0 => e 7.8 + 0.65 => 0.6
~4
Experimental value of temperature bandwidth for the noncritical SPG process (10.6 urn + 0.598 urn => 0.566 urn, 0 + 0 => e): ~T
== 2.5 °C [3.346] .
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe = d 36 sin ()sin 24> ,
d eoe
=:
d oee
=:
d 36 sin 20 cos 24> .
Nonlinear coefficient: d 36(10.6 urn) == 0.134 x d 36(GaAs)
± 15%
=:
11.1 ± 1.7 pm/V [3.344], [3.37] , d 36(10.6 urn] == 0.15 x d 36(GaAs) ± 20% 12.5 ± 2.5 pm/V [3.351], [3.37] .
==
136
3 Properties of Nonlinear Optical Crystals
Laser-induced surface-damage threshold: A [um]
'tp
0.59 0.598 0.625 0.6943
500 3 500 30 10 10 35 20 17.5 15 12 0.023 0.025 0.002 0.021 0.020 150 150 220
1.06 1.0642
10.6
[ns]
I thr
X
10- 12 [W/m 2 ]
0.2 0.15 0.25--0.36 0.006 0.1 0.2 0.2--0.25 0.1 > 0.12 0.2 0.35 > 0.75 >7 > 10 > 20 30 0.1 0.2 0.25
Ref.
Note
3.358 3.363 3.358 3.361 3.357 3.348 3.348 3.350 3.365 3.352 3.359 3.366 3.48 3.367 3.355 3.353 3.349 3.368 3.365
10 pulses 10 pulses 1 Hz, 1000 pulses 100 pulses
10 Hz 1000 pulses 10 Hz 10 Hz 10 Hz
1000 pulses
Thermal conductivity coefficient at T == 293 K [3.58]: K
[W/mK],
II
c
1.4
K
[W/mK], 1- c
1.5
3.1.11 ZnGeP2 , Zinc Germanium Phosphide Positive uniaxial crystal: ne > no ; Point group: 42m ; Mass density: 4.12 g/cm 3 [3.338] ; Mohs hardness: 5.5 ; Transparency range at "0" transmittance level: 0.74 - 12 urn [3.369,370] Linear absorption coefficient a: A [urn]
a [cm"]
Ref.
1.9 2.15 2.5-8 2.5-8.3
0.8--0.95 0.6 < 0.1 < 0.2
3.371 3.372 3.373 3.374
Note
3.1 Basic Nonlinear Optical Crystals
A [urn]
~ [cm"]
Ref.
2.5-8.5 2.8-8.3 3-8 3.5-3.9 3.5 3.8 4.5-8 4.65
< 0.1 < 0.1 < 0.1
3.375 3.376 3.377 3.378 3.379 3.371 3.380 3.381 3.382 3.383 3.378 3.374 3.379 3.373 3.381 3.382 3.383 3.384 3.372 3.379 3.378
0.41 0.4 0.1-0.18 0.03 0.4 0.1-0.2 0.16 0.32 < 0.3
4.8 5.3-6.1 8.3-9.5 9 9.28 9.3
~
1
0.4 0.8 0.4-0.5 0.56 0.42 0.6 0.9 0.83
9.6 10.3 10.4 10.6
Note
o - wave, SFG direction
best samples
e - wave, SFG direction
e - wave, SFG direction
Experimental values of refractive indices [3.369]:
A [um]
no
ne
0.64 0.66 0.68 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.60 1.80 2.00 2.20
3.5052 3.4756 3.4477 3.4233 3.3730 3.3357 3.3063 3.2830 3.2638 3.2478 3.2232 3.2054 3.1924 3.1820 3.1666 3.1562 3.1490 3.1433
3.5802 3.5467 3.5160 3.4885 3.4324 3.3915 3.3593 3.3336 3.3124 3.2954 3.2688 3.2493 3.2346 3.2244 3.2077 3.1965 3.1889 3.1829
A [urn] 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.50 4.70 5.00 5.50 6.00 6.50 7.00 7.50
no
ne
3.1388 3.1357 3.1327 3.1304 3.1284 3.1263 3.1257 3.1237 3.1223 3.1209 3.1186 3.1174 3.1149 3.1131 3.1101 3.1057 3.1040 3.0994
3.1780 3.1745 3.1717 3.1693 3.1671 3.1647 3.1632 3.1616 3.1608 3.1595 3.1561 3.1549 3.1533 3.1518 3.1480 3.1445 3.1420 3.1378
137
138
3 Properties of Nonlinear Optical Crystals
A [~m]
no
ne
A [flm]
no
ne
8.00 8.50 9.00 9.50 10.00
3.0961 3.0919 3.0880 3.0836 3.0788
3.1350 3.1311 3.1272 3.1231 3.1183
10.50 11.00 11.50 12.00
3.0738 3.0689 3.0623 3.0552
3.1137 3.1087 3.1008 3.0949
Temperature derivative of refractive indices [3.369]: A [urn] dno/dT x 105 [K- 1]
dne/dT x 105 [K- 1]
A [um] dn.Jd T x 105 [K- 1]
0.64 0.66 0.68 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20
37.58 37.34 32.53 31.82 28.26 26.43 25.39 24.61 24.26 23.01 22.08 20.51 20.12 16.55 16.75 14.40 15.29 15.28 15.49 16.80 16.05 13.96 16.28
3.40 3.60 3.80 4.00 4.20 4.50 4.70 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50 12.00
35.94 31.23 29.52 28.63 26.22 24.69 24.12 22.34 21.32 21.18 20.11 18.63 16.84 15.34 15.10 13.20 14.19 14.60 14.14 15.13 15.48 13.26 14.94
14.40 15.58 14.58 14.26 13.57 15.31 15.51 15.05 14.49 14.58 15.60 12.85 18.15 16.10 15.16 15.56 16.27 16.53 15.40 15.25 14.74 14.24
dne/dT x 105 [K- 1]
15.46 16.29 16.53 15.02 15.14 16.60 16.71 16.43 15.42 16.30 16.13 15.01 18.59 17.43 17.37 17.50 17.11 18.41 16.84 16.34 18.32 16.59
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: In teracting wavelengths [urn] SHG, e + e=}o 3.8 ~ 1.9 4.34 ~ 2.17 4.64 ~ 2.32
f}exp
[deg]
57.8 ±0.3 [3.371] 55.8 ±0.2 [3.372] 47.5 [3.386]
Otheor
[deg]
[3.362]
[3.385]
59.8 52.5 50.1
59.7 52.4 49.9
3.1 Basic Nonlinear Optical Crystals
9.2 => 4.6 9.3 => 4.65
9.5 => 4.75
9.6 => 4.8 10.2 => 5.1 10.3 => 5.15 SFG, e + e=}o 10.668 + 4.34 => 3.085 9.74 + 4.2039 => 2.9365 SFG,o + e ::::} 0 6.74 + 5.2036 => 2.9365 6.45 + 5.3908 => 2.9365 6.25 + 5.5389 => 2.9365 6.15 + 5.6199 => 2.9365 6.29 + 5.0173 => 2.791 6.19 + 5.0828 => 2.791 6.06 + 5.1739 => 2.791 6.015 + 5.207 => 2.791 5.95 + 5.2569 => 2.791 5.90 + 5.2965 => 2.791 10.6 + 1.0642 => 0.9671
63.8 [3.387] 61.3 [3.375] 61.3 [3.385] 62.7-64.4 [3.382] 64 [3.381] 62.1 [3.375] 62.1 [3.385] 66.8 [3.387] 64.9 [3.382] 72 [3.375] 74.3 [3.384]
64.4 65.5
64.0 65.1
67.9
67.6
69.3 81.6 86.9
69.0 81.3 86.4
54.3 ± 0.2 [3.372] 51.5 49.6 [3.370] 49.5
51.3 49.3
76 [3.388] 79.2 [3.374] 84.0 [3.374] 85.5 [3.374] 76 [3.376] 77.6 [3.376] 80.5 [3.376] 84 [3.389] 83.4 [3.376] 87 [3.376] 84 [3.379]
74.9 78.8 83.3 89.0 76.5 78.0 80.5 81.6 83.6 85.8 83.4
Best set of dispersion relations (A in urn, T n2
= 4.47330 +
2 _
ne -
5.26576..1.1
+
A? - 0.13381
o
== 20°C) [3.385]:
1.49085..1.1
A? - 662.55 '
2
4 63 18 5.34215A + 2 . 3 A - 0.14255
75.9 80.1 85.9 no pm 77.4 79.1 82.0 83.3 86.1 no pm 83.0
139
2
+
1.45795A 2 A - 662.55
.
dispersion relation for T = 93 K, 173 K, 373 K, 473 K, and 673 K are given in [3.390], for T = 343 K in [3.391]. Calculated values of phase-matching and "walk-off" angles: In teracting wavelengths [urn]
(Jpm
SHG, e + e :::} 9.6 => 4.8 5.3 => 2.65
68.95 47.08
[deg]
PI [deg]
P2 [deg]
0.49 0.70
0.49 0.70
0
3 Properties of Nonlinear Optical Crystals
140
4.8 =* 2.4
SFG, e + e=}o 10.6 + 2.65 =} 2.12 9.6 + 2.4 =} 1.92 10.6 + 1.0642 :::} 0.96711 9.6 + 1.0642 =} 0.958 SFG,o + e=>o 10.6 + 5.3 =} 3.533 9.6 + 4.8 =} 3.2 10.6 + 1.0642 :::} 0.96711
48.97
0.69
0.69
50.11 51.08 72.54 82.66
0.72 0.71 0.42 0.18
0.66 0.69 0.47 0.21 0.20 0.46 0.19
81.66 69.74 83.31
Experimental values of internal angular bandwidth: Interacting wavelengths [urn] SHG, e+e =} 0 3.8 =} 1.9 4.34=>2.17 5.3 =? 2.65 9.3 :::} 4.65 9.6 =} 4.8 10.2 =} 5.1 10.3 =} 5.15
~oint
[deg]
Ref.
1.33 1.05 0.69 0.74-0.80 1.15 0.8 1.35 1.20
3.371 3.372 3.386 3.382 3.381 3.382 3.375 3.384
1.23
3.372
0.55
3.379
SFG, e + e=}o 10.668
+ 4.34
:::} 3.085
SFG,o + e=>o 10.6 + 1.064 =} 0.967
Experimental values of spectral bandwidth: Ref.
Interacting wavelength [urn] SHG, e + e :::}
0
7.9 4.9
4.34 =} 2.17 10.2 => 5.1
3.372 3.375
Experimental value of temperature bandwidth for SHG process =} 5.1 urn, e + e :::} 0);
(10.2 urn ~T
== 50°C
[3.375] .
3.1 Basic Nonlinear Optical Crystals
Temperature variation of phase-matching angle: In teracting wavelengths [um] SHG, e+e => 0 9.2 => 4.6 10.3 => 5.15 10.6 => 5.3 SFG,o + e=>o 10.6 + 1.0642 => 0.9671
dOpm/dT [deg/K]
Ref.
0.014 0.072 0.107
3.387 3.375 3.375
0.007
3.379
Effective nonlinearity expressions in the phase-matching direction [3.100]:
deeo == d36 sin 20 cos 2ifJ, doeo == deoo
:::::
d36 sin ()sin 2ifJ.
Nonlinear coefficient: d36(10.6Ilm) == 0.83 x d 36(GaAs) ± 15% == 68.9 ± 10.3 pm/V [3.369], [3.37] , d36(9.6Ilm) :::: 75 ± 8 pm/V [3.383] .
Laser-induced surface-damage threshold: A [urn]
Lp
[ns]
1.064
30 10 2.79 0.15 0.1 0.11 2.94 0.11 cw 5.3-6.1 cw 9.28 2 9.3-10.6 125 125 9.3 100r 9.6 129 10.2-10.8 105 - 107 cw cw 10.6 cw
Ithr X
10- 12 [W/m 2 ]
> 0.03 0.03 300 350 300 300 > 0.0001 0.0025 12.5 0.3-0.4 0.25 0.12 0.78 0.6 > 0.00001 > 0.0000001 0.002
Ref.
Note
3.392 3.369 3.376 3.389 3.388 3.370 3.386 3.378 3.373 3.384 3.384 3.381 3.383 3.375 3.375 3.392 3.378
12.5 Hz
Thermal conductivity coefficient at T = 293 K [3.58]: K
[W/mK],
36
II
c
K
[W/rnK] , 1- c
35
2 Hz 20 Hz 100 Hz
1500 Hz
141
142
3 Properties of Nonlinear Optical Crystals
3.2 Frequently Used Nonlinear Optical Crystals 3.2.1 KBsOs . 4H 20, Potassium Pentaborate Tetrahydrate (KB5) Positive biaxial crystal: 2Vz == 126.3° at A = 0.5461 urn [3.393]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z => a,b,c (Fig. 3.4); Molecular mass: 1.74 g/cm 3 [3.394]; Mohs hardness: 2.5 [3.394]; Transparency range at "0" transmittance level: 0.162 - 1.5 urn [3.395]; z(c)
X(a) Fig. 3.4. Dependence of refractive index on light propagation direction and polarization (index surface) in the first octant of dielectric reference frame (X, Y, Z) of KB5 crystal. Designations: (J is the polar angle, 0.434 => 0.217
cPexp
[deg]
cPtheor
293 K) and comparison
[3.401]
[3.402]
81.6
no pm
0
90 [3.400]
144
3 Properties of Nonlinear Optical Crystals
0.4342 =} 0.2171 0.4384 =} 0.2192 0.50 => 0.25 0.630 =} 0.315 SFG, e + e=}o 0.5435 + 0.3511 =} 0.2133 0.6943 + 0.3472 =} 0.2314 0.5737 + 0.3345 =} 0.2113 0.6522 + 0.3261 =} 0.2174 0.6219 + 0.3110 =} 0.2073 0.6943 + 0.30519 => 0.2120 0.6943 + 0.28409 => 0.2016 1.06415 + 0.26604 => 0.2128 0.78971 + 0.26604 => 0.1990 0.75322 + 0.26604 => 0.1966 0.79737 + 0.25725 => 0.1945 0.79235 + 0.25725 => 0.1942 0.9 + 0.23287 => 0.185
YZ plane,
¢
90 [3.403] 80.5 [3.86] 52.8 [3.400] 31 [3.403]
81.3 77.3 53.8 33.0
no pm 80.4 54.1 32.8
90 [3.404] 57 [3.405] 90 [3.404] 68 [3.398] 90 [3.398] 70 [3.406] 90 [3.406] 53 [3.397] 75 [3.407] 90 [3.407] 84 [3.408] 90 [3.408] 90 [3.409]
78.9 56.3 77.9 65.7 76.9 66.2 74.2 48.5 67.5 72.5 70.0 70.7 68.4
87.3 57.9 87.2 68.8 no pm 70.5 no pm 52.1 76.1 no pm 83.3 85.6 no pm
== 90°
In teracting wavelengths [urn] SHG, 0 + 0 => e 0.4346 => 0.2173 0.4690 => 0.2345 0.4796 => 0.2398 SFG,o + 0 => e 0.5634 + 0.3511 ==> 0.2163 0.5948 + 0.3345 ==> 0.2141 0.6264 + 0.3132 ==> 0.2088 0.7621 + 0.26604 => 0.1972
¢exp
[deg]
¢theor
[deg]
[3.401]
[3.402]
90 [3.405] 17 [3.405] o [3.403]
69.1 no pm no pm
83.4 12.8 no pm
63 63 68 68
49.2 47.0 52.2 38.5
59.9 59.8 72.0 75.3
[3.404] [3.404] [3.398] [3.407]
Best set of dispersion relations (revised data of [3.401], given in [3.402], A in urn, T == 293 K): ,12 2 n == 1 + x 0.848117,12 - 0.0074477 ' ,12 2 n == 1 + y 0.972682,12 - 0.0087757 ' ,12 n~ == 1 + 2 . 1.008157,1 - 0.0094050
3.2 Frequently Used Nonlinear Optical Crystals
145
Calculated values of phase-matching and "walk-off" angles: XY plane, f) = 90°
Interacting wagelengths [urn]
cjJpm [deg]
SHG, e+e => 0 0.5105 => 0.25525 51.62 0.532075 => 0.26604 47.19 39.57 0.5782 => 0.2891 25.83 0.6973 => 0.34715 SFG, e + e=>o 1.06415 + 0.532075 => 0.35473 20.65 36.35 1.06415 + 0.35473 => 0.26604 52.12 1.06415 + 0.26604 => 0.21283 57.93 0.6943 + 0.34715 => 0.23143 0.5782 + 0.5105 :::} 0.27112 45.17
PI [deg]
P2 [deg]
2.037 2.073 2.020 1.585
2.037 2.073 2.020 1.585
1.324 1.946 2.015 1.889 2.017
1.332 1.979 2.078 1.918 2.075
Experimental values of NCPM temperature: along b axis Interacting wavelengths [urn]
T roC]
Ref.
SFG, type I 0.6943 + 0.28334 => 0.20122 0.6943 + 0.28361 => 0.20136 0.6943 + 0.28405 => 0.20158 0.6943 + 0.28449 => 0.20180 0.79202 + 0.25725 => 0.19418 0.79344 + 0.25725 => 0.19427
-15 0 20 35 25 40
3.406 3.406 3.406 3.406 3.408 3.408
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of KB5 crystal; [3.35, 36]: XYplane d eeo
= d 3I sin 2 4J + d 32 cos 2 4J
YZ plane
= d 31 sin f) ; XZ plane, () < V» d oeo = d eoo = d 32 sin f) XZ plane, f) > Vz d ooe
d ooe = d32 sin f)
;
.
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of KB5 crystal are given in [3.36].
Nonlinear coefficients [3.37]: d31 (0.5321 um] = 0.04 pm/V ,
d 32 (0.5321 urn) = 0.003 pmjV , d33(0.5321 um) = 0.05 pm/V .
Laser-induced surface-damage threshold: A [Ilm]
't p
0.2661
8 0.03 10 8 7 10 10 30 12
0.311 0.3472 0.45 0.622 0.6943 0.74-0.91 1.0642
[ns]
Ithr X
10- 12 [Wjm 2 ]
> > > >
0.43 4.8 0.13 0.9 10 > 0.4 > 0.8 > 0.5 > 0.85
Ref.
Note
3.397 3.410 3.398 3.393 3.405 3.398 3.393 3.409 3.397
10 Hz 1 Hz 10 Hz 15 Hz 10 Hz
10 Hz
3.2.2 CO(NH2)2, Urea Positive uniaxial crystal: ne > no; Point group: 42m; Mass density: 1.318 g/cm'; Mohs hardness: < 2.5 ; Transparency range at 0.5 transmittance level for a 0.5 em long crystal cut at f) == 74° : 0.2 - 1.43 urn [3.411]; Linear absorption coefficient ex [3.411]:
A [urn]
rx [cm"]
Note
0.213 0.266 1.064
0.10 0.04 0.02
o - wave, FIHG direction e - wave, FIHG direction e - wave, FIHG direction
The graph of no and n« dependences versus wavelength is given in [3.412, 413]. Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: In teracting wavelengths [urn] SHG, e+e => 0.476 => 0.238 0.500 => 0.250 0.550 => 0.275 0.600 => 0.300
f)exp
[deg]
f)theor
[deg]
[3.414]
[3.415]*
[3.416]
82.2 67.5 54.2 46.5
no pm 76.7 55.9 46.5
no pm 72.2 55.2 46.5
0
90 [3.414] 67.6 [3.414] 54 [3.414] 46.6 [3.414]
3.2 Frequently Used Nonlinear Optical Crystals
SFG, e + e ~ 0 0.6943 + 0.34715 => => 0.23143 1.0642 + 0.26605 => => 0.21284 SHG, 0 + e=>o 0.597 => 0.2985 0.650 => 0.325 0.700 => 0.350 SFG,o + e=>o 1.0642 + 0.29146 => 0.2288 1.0642 + 0.29668 => 0.2320 1.0642 + 0.30656 => 0.2380 1.0642 + 0.42792 => 0.3052 1.0642 + 0.63501 => 0.3977 0.720 + 0.53764 => 0.3078 0.646 + 0.58793 => 0.3078 0.62875 + 0.5321 => 0.2882 0.63980 + 0.5321 ::::} 0.2905 0.66406 + 0.5321 => 0.2954 SFG, e + 0 => 0 1.0642 + 0.50787 => 0.3438 1.0642 + 0.53 => 0.3538 1.0642 + 0.575 => 0.3733 1.0642 + 0.63195 => 0.3965
77 [3.411]
81.5
no pm
no pm
72 [3.411]
86.7
no pm
no pm
90 [3.414] 63.6 [3.414] 55.6 [3.414]
no pm 65.4 56.6
no pm 63.5 54.6
no pm 64.6 55.6
90 [3.414] 80 [3.414] 70.4 [3.414] 47.5 [3.414] 37.7 [3.414] 63 [3.417] 69 [3.418] 90 [3.414] 80.5 [3.414] 73.4 [3.414]
no pm 83.6 75.0 49.9 39.1 64.7 71.6 no pm 85.1 75.3
no pm 80.9 70.0 48.8 37.1 63.1 70.0 no pm 84.3 74.3
76.6 72.8 67.8 47.0 37.6 62.7 70.3 no pm 81.5 73.1
90 [3.414] 72.2 [3.414] 62.5 [3.414] 53.5 [3.414]
79.2 70.9 61.4 53.9
84.5 72.3 61.5 53.4
no pm 74.8 63.0 54.5
*with correction given in [3.419]. Best set of dispersion relations (A. in urn, T == 293 K) [3.415, 419]: n 2 == 2.1548
+
o
2-25527 n-. e
0.01310 0.0318'
A? -
0.01784 A. - 0.0294
+2
+
147
O.0288(A-l.5) 2 (A - 1.5) + 0.03371
.
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn]
(Jpm
SHG, 0 +e => 0 0.6118 => 0.3059 0.6328 => 0.3164 0.6594 => 0.3297 0.6943 => 0.34715
75.95 68.01 61.49 55.40
[deg]
PI [deg]
P2 [deg]
2.31 3.35 3.98 4.34
148
3 Properties of Nonlinear Optical Crystals
SFG,o + e=>o 1.0642 + 0.5321 =? 1.3188 + 0.6594 =? SFG, e + 0 => 0 1.0642 + 0.5321 => 1.3188 + 0.6594 =>
0.35473 0.4396
41.10 30.46
0.35473 0.4396
71.63 48.98
4.52 3.82 2.69 3.97
Experimental value of internal angular bandwidth [3.411]: In teracting wavelengths (flm] FIHG, e + e=>o 1.064 + 0.266 => 0.213
~f)int
[deg]
0.017
Temperature tuning for noncritical SHG [3.414]: In teracting wavelengths [urn] SHG, e + 0 => e 0.597 :::} 0.2985
dAIIT [nm/K]
-0.013
Effective nonlinearity expressions in the phase-matching direction [3.100]: deeo
== d36 sin 20 cos 2fjJ,
doeo == deoo == d36 sin 0 sin 2fjJ. Nonlinear coefficient: d36(0.6 um) ~ 3 x d 36(KDP) = 1.17 pm/V [3.412,37], d 36(O.597 urn) == 2.4 x d36(ADP) ± 80/0 == 1.13 ± 0.09 pm/V [3.419,37] .
Laser-induced bulk-damage threshold:
A [Jlm]
Lp
0.266 0.355
10 10 10 10 10
0.532 1.064
[ns]
Ithr X
5 14 1.5 30 50
10- 12 [W/m2 ]
Ref.
Note
3.420 3.420 3.421 3.420 3.420
single pulse single pulse 3000 pulses single pulse single pulse
3.2 Frequently Used Nonlinear Optical Crystals
149
3.2.3 CsH 2As04 , Cesium Dihydrogen Arsenate (CDA) Negative uniaxial crystal: no > ne ; Point group: 42m ; Mass density: 3.53 gjcm 3 ; Transparency range at 0.5 transmittance level for a 17.5 mm long crystal cut at f) = 90°, 1J = 45° : 0.26 - 1.43 urn [3.422] ; UV edge of transmission spectrum at "0" transmittance level: 0.2161lm [3.113] ; IR edge of transmission spectrum at "0" transmittance level: 1.871lm for 0 - wave, 1.671lm for e - wave [3.78] ; Linear absorption coefficient lJ. : Ref. 0.35-1.4 1.062 1.064
0.6 0.041 0.041
3.113 3.120 3.422
Two-photon absortion coefficient fJ( f) = 90°, 1J = 45°) [3.71]:
fJ 0.355
X
1013 [mjW]
Note e - wave
2.81
Experimental values of refractive indices [3.422]: A [um]
no
ne
0.3472 0.5321 0.6943 1.0642
1.6027 1.5733 1.5632 1.5516
1.5722 1.5514 1.5429 1.5330
Temperature derivative of refractive indices [3.74]:
0.405 0.436 0.546 0.578 0.633
-3.15 -3.05 -2.59 -2.76 -2.80
-1.89 -2.09 -2.12 -2.39 -2.56
150
3 Properties of Nonlinear Optical Crystals
Experimental values of phase-matching angle (T between different sets of dispersion relations: Interacting wavelengths [urn]
[deg]
Oexp
=
Otheor
293 K) and comparison
[deg]
[3.74]
[3.78]K
[3.78] E
59.8 59.7 59.0
no pm
no pm
no pm no pm
no pm no pm
58.6
no pm
88.7
58.3
88.2
86.5
SHG, o+o:::::} e 1.05 ~ 0.525 1.052 => 0.526 1.06 =* 0.53
90 [3.119] 90 [3.74] 87 [3.423] 87 [3.96] 83.5 [3.424] 83.5 [3.425] 84.2 [3.422] 84.4 [3.426]
1.0642 => 0.5321
1.068 => 0.534
Note: [3.78] K => see [3.78], set of Kirby et al. ; [3.78] E =* see [3.78], set of Eimerl. Experimental values of NCPM temperature: Interacting wavelengths [urn]
T roC]
Ref.
20 20 31 40.3 41 42 43 44.5 45 46 48 39.6 49.2 61 100
3.119 3.74 3.423 3.427 3.425 3.428 3.426 3.90 3.120 3.424 3.422 3.422 3.429 3.428 3.119
Note
SHG, 0+0 =* e 1.05 => 0.525 1.052 ==> 0.526 1.06 => 0.53 1.0642 => 0.5321
1.073 ==> 0.5365 1.078 => 0.539
10 Hz
12.5 Hz 0.1-1 Hz 20 Hz 10 Hz
Best set of dispersion relations (A. in urn, T = 293 K) [3.78]E:
n~ = 1.8776328 -
O.03602222A?
+ O.00523412U4 +
2
O.550395U?
A. - (0.1625700)
2'
3.2 Frequently Used Nonlinear Optical Crystals
n; = 1.6862889 - O.01372244A? + O.003948463A.
4
+
2
O.669457U 2 A - (0.1464712) 2
Calculated values of phase-matching and "walk-off" angles: In teracting wavelengths [urn]
Opm
SHG, 0 +0 =} e 1.0642 => 0.5321 1.3188 => 0.6594
[deg]
P3 [deg]
0.035 0.384
88.72 74.52
Experimental values of internal angular and temperature bandwidths: In teracting wavelengths [urn] SHG, 0 + 0 => e 1.06 => 0.53
1.062 => 0.531 1.0642 => 0.5321
T[OC]
22 31 20 63 (?) 45 40.3 24 46 20 48 20 43
fJpm [deg]
87 90 87 90 90 90 83.5 90 84.2 90 84.4 90
Arfnt
AT[OC] Ref.
[deg] ~O.4 ~
3.8 0.43 3.03 2.85 0.86 3.2 0.70 2.91 0.70
~3
6.5 6.8 rv8
6
~3
3.423 3.423 3.96 3.96 3.120 3.427 3.424 3.424 3.422 3.422 3.426 3.426
Temperature variation of phase-matching angle: In teracting wavelengths [urn] SHG, 0 + 0 => e 1.06 => 0.53 1.0642 => 0.5321
151
T [OC]
fJpm [deg]
dfJpm/dT [deg/K]
Ref.
20 63(?) 24 20 35 39 41
87 90 83.5 84.4 86.5 87.6 88.3
0.085 0.481 0.129 0.131 0.194 0.251 0.537
3.96 3.96 3.424 3.426 3.426 3.426 3.426
.
152
3 Properties of Nonlinear Optical Crystals
Temperature tuning of noncritical SHG [3.74]: In teracting wavelengths [urn]
dAI/dT [nm/K]
SHG, 0 + 0 => e 1.052 :=} 0.526
0.308
Temperature variation of birefringence for (1.0642 urn ~ 0.5321 urn, 0 + 0 => e): d(n~ - nf)/dT
noncritical SHG process
== 7.2 x 10- 6 K- 1 [3.427] ,
d(ni - n1)/dT == (8.0 ± 0.2) x 10-6 K- 1 [3.422] . Effective nonlinearity expressions in the phase-matching direction [3.100]:
== d36 sin 8 sin 24>, d eoe == d oee = d36 sin 28 cos 24> . dooe
Nonlinear coefficient: d36(1.0642 urn) == 0.40
± 0.05 pm/V
[3.422] .
Laser-induced bulk-damage threshold:
A [urn] 0.532 1.062 1.064
'tp
[ns]
10 0.007 12 10 18
Ithr
x 10- 12 [W/m 2]
>3 > 40 > 2.6 3.5 4
Ref.
Note
3.429 3.120 3.422 3.424 3.427
10-20 Hz 12.5 Hz 2-50 Hz
3.2.4 CsD2As04 , Deuterated Cesium Dihydrogen Arsenate (DCDA) Negative uniaxial crystal: no > n.: Point group: 42m ; Transparency range at 0.5 transmittance level for a 13.5 mm long crystal cut at 8 == 90°, t/J == 45° : 0.27 - 1.66 urn [3.422] IR edge of transmission spectrum at "0" transmittance level: 2.03 urn for 0 - wave, 1.78 urn for e - wave [3.78] ;
3.2 Frequently Used Nonlinear Optical Crystals
Linear absorption coefficient
A [Ilm]
(J.
1.062 1.064
0.01 0.02
[em-I]
153
lJ. :
Ref. 3.120 3.422
Two-photon absorption coefficient fJ(8
A [urn] fJ x 1013 [m/W]
Note
0.355
0 - wave e - wave
8.0 5.1
= 90°,4> = 45°) [3.71]:
Experimental values of refractive indices [3.422]: A [urn]
no
ne
0.3472 0.5321 0.6943 1.0642
1.5895 1.5681 1.5596 1.5503
1.5685 1.5495 1.5418 1.5326
Temperature derivative of refractive indices [3.74]:
0.405 0.436 0.546 0.578 0.633
-2.26 -2.26 -2.47 -2.31
-1.77 -1.51 -1.64 -1.71 -1.70
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [urn] SHG, 0+0 =* e 1.034 =* 0.517 1.037 =* 0.5185 1.046 =* 0.523
8exp [deg]
90 [3.119] 90 [3.74]
8theor
[deg]
[3.74]
[3.78]K [3.78]E
65.2 64.8 63.7
no pm no pm no pm no pm 88.4 88.1
154
3 Properties of Nonlinear Optical Crystals
1.0642 ==> 0.5321
79.35 [3.422] 80.8 [3.426]
61.8
82.4
82.3
[3.78]K =:} see [3.78], data of Kirby et al. ; [3.78]E =:} see [3.78], data of Eimerl.
Note:
Experimental values of NCPM temperature: In teracting wavelengths [flm] SHG, 0 + 0 =:} e 1.034 =:} 0.517 1.037 => 0.5185 1.0642 => 0.5321
T [OC]
Ref.
20 20 102 102 112.3 109.8 96.4 108
3.119 3.74 3.428 3.425 3.422 3.422 3.426 3.119
Note
90% deuteration, < 1 Hz 90% deuteration, 20 Hz 70 % deuteration
Best set of dispersion relations (A in urn, T n~
== 1.6278496 - 0.018220310A2 +0.000281333U4 +
n~
== 293 K) [3.78]E :
0.7808170;,2 A2 - (0.1407699)2 '
== 1.6236063 - 0.009338692A? + 0.001965413014 +
0.7249589A?
.
A? - (0.1414850)2
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [Ilm]
SHG,
0
fJpm [deg] P3 [deg]
+ 0 => e
1.0642 =:} 0.5321 1.3188 =:} 0.6594
82.32 69.54
0.188 0.449
3.2 Frequently Used Nonlinear Optical Crystals
Experimental values of internal angular and temperature bandwidths: In teracting wavelengths [urn] SHG,o+o=:}e 1.0642 =:} 0.5321
T [OC]
Opm [deg]
L\Oint [deg]
L\T [OC]
20 112.3 20 96.4
79.35 90 80.8 90
0.41 2.90 0.50
6.1
~3.5
Ref.
3.422 3.422 3.426 3.426
Temperature variation of the phase-matching angle [3.426]: Interacting wavelengths [urn]
T
[OC]
SHG, 0 + 0 =:} e 1.0642 =:} 0.5321 20 66.3 80 87.7
Opm [deg]
dOpm/dT [deg /K]
80.8 84.3 86.4 88.1
0.042 0.081 0.270 0.533
Temperature tuning of noncritical SHG [3.74]: Interacting wavelengths [Ilm] SHG, 0 + 0 =:} e . 1.037 =:} 0.5185
dA,l/dT [nm/K] 0.317
Temperature variation of birefringence for noncritical SHG process (1.0642Ilm =:} 0.5321Ilm, 0 + 0 =:} e) :
d(n~; n1) = (7.8 ± 0.2)
x 10-6 K- 1 [3.422] .
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe = d36 sin 0 sin 2¢ , d eoe
= d oee = d 36 sin 20 cos 2¢ .
Nonlinear coefficient: d36(1.0642Ilm) = 0.40
± 0.05 pm/V
[3.422] .
Laser-induced bulk-damage threshold:
A [urn] !p [ns]
Ithr X
1.064
>2.6 >2.5
12 12
10- 12 [W/m 2 ] Ref. 3.422 3.139
Note 10-20 Hz 0.1-20 Hz
155
156
3 Properties of Nonlinear Optical Crystals
3.2.5 KTiOAs0 4 , Potassium Titanyl Arsenate (KTA) Positive biaxial crystal: 2Vz == 34.5° at A == 0.5321 urn; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z::::} a,b,c;
Transparency range at "0" transmittance level: 0.35 - 5.3 urn [3.430, 431]; Linear absorption coefficient a [3.432] :
A [Jlm]
rJ,
4.0 5.0
0.2 1.0
[em-I]
Experimental values of refractive indices [3.433]:
A [urn]
nx
nr
nz
0.6328
1.8083
1.8142
1.9048
Experimental values of phase-matching angle (T == 293 K) and comparison between different sets of dispersion relations: XY plane, f}
== 90°
Interacting wavelengths [um] SHG, e + 0 => e 1.053 => 0.5265 1.0642 :::} 0.5321 SFG, e + 0 =:} e 1.3188 + 0.6594 =:} =? 0.4396 1.0642 + 1.5791 =:} =? 0.6358 YZ plane,
¢exp
[deg]
[deg]
¢theor
[3.433]
[3.434]
65 [3.434] no pm 57.8 [3.434] no pm
64.97 57.58
47.8 [3.434] 68.84
47.79
19.8 [3.434] 16.64
19.63
4J == 90°
Interacting wavelengths [urn] SHG, 0 + e=>o 1.0642 =* 0.5321 1.1523 =* 0.57615
f}exp
[deg]
f}theor
[deg]
[3.433] 76.3 [3.434] no pm 64 [3.434] 69.30
[3.434] 76.28 63.94
3.2 Frequently Used Nonlinear Optical Crystals
1.3188 =} 0.6594 SFG, 0 + e=}o 1.3188 + 0.6594 =} =} 0.4396 1.0642 + 1.5791 =} =} 0.6358 4.15 + 1.0642 =} =} 0.847
XZ plane,
55.9 [3.433] 56.22
53.09
71.2 [3.434] 82.37
71.15
67.3 [3.434] 73.04
67.29
30.3 [3.431] 31.19
31.87
4J == 0°, 0 >
Interacting wavelengths [Ilm]
Vz
(}exp
[deg]
(}theor
[deg]
[3.433]
SHG, 0 + e=}o 1.1523 =} 0.57615 1.3188 =} 0.6594 SFG, 0 +e =} 0 1.5791 + 0.6358 =} =} 0.4533
[3.434]
82.9 [3.434] 80.61 64.2 [3.434] 63.28
83.00 64.25
73.7 [3.434] 72.82
73.74
Best set of dispersion relations (A in urn) [3.434]: n2 x
n2
== 3.1533 + == 3.1775 +
Y
n2 z
== 3.4487 +
0.04029
- 0.01320,12
0.04353
- 0.01444,12
.,t2 _ 0.04932
A? - 0.05640
'
'
0.06334 _ 0.01646 A2 A2 - 0.05887
.
Calculated values of phase-matching and "walk-off" angles: XY plane, 0 == 90°
Interacting wavelengths [urn]
SHG, e + 0 =} e 1.0642 =} 0.5321 SFG, e + 0 => e 1.3188 + 0.6594 => =} 0.4396
(jJpm [deg]
PI [deg]
P3 [deg]
57.58
0.211
0.337
47.79
0.217
0.511
157
158
3 Properties of Nonlinear Optical Crystals
YZ plane, ¢
= 90
0
In teracting wavelengths [urn]
SHG, 0 + e =* 0 1.0642 =* 0.5321 1.1523 =} 0.57615 1.3188 =} 0.6594 2.098 =} 1.049 2.9365 =} 1.46825 SFG, 0 + e =* 0 1.3188 + 0.6594 =} =} 0.4396
XZ plane, ¢ = 0
0,0
Interacting wavelengths [urn] SHG, 0 + e=}o 1.1523 =} 0.57615 1.3188 =} 0.6594 2.098 =} 1.049 2.9365 =} 1.46825
Opm [deg]
P2 [deg]
76.28 63.94 53.09 44.71 59.80
1.179 1.978 2.344 2.345 2.042
71.15
1.708
> Vz Opm [deg]
P2 [deg]
83.00 64.25 53.50 69.37
0.676 2.119 2.445 1.657
Experimental values of internal angular and temperature bandwidths: XY plane, 0 = 90 0
Interacting wavelengths [urn]
SHG, e+o =} e 1.053 =} 0.57615 1.0642 =} 0.5321
yz plane,
4> = 90
Interacting wavelengths [11m] SHG, 0 +e =} 0 1.3188 =} 0.6594
4Jpm [deg]
AcjJint [deg]
AT rOC]
Ref.
65 57.8
0.4 0.37
10.4
3.430 3.434
Opm [deg]
AOint [deg]
Ref.
55.9
0.093
3.433
0
3.2 Frequently Used Nonlinear Optical Crystals
159
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of KTA crystal [3.35, 36]: XY plane
d eoe == d oee == d31 sirr' ¢
+ d 32 cos 2 ¢
;
yz plane d oeo == d eoo == d 31sin () ; XZ plane, ()
< Vz
d ooe == d 32 sin () ;
XZ plane, ()
> Vz
d oeo == d eoo == d32 sin () . Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of KTA crystal are given in [3.36] Nonlinear coefficients: d 31(1.0642Ilm) == 2.5 ± 0.3 pm/V [3.434] , 2.8
d32(1.0642Ilm)
± 0.3
pm/V [3.433] ;
== 4.2 ± 0.4 pm/V [3.433] , 4.5 ± 0.5 pm/V [3.434] ;
d33(1.06421lffi) == 16.2 ± 1.0 pru/V [3.433] . Laser-induced surface-damage threshold:
A [urn]
'r p
0.85 1.0642
2 8
[ns]
Ithr X
>10 >12
10- 12 [W/m 2 ]
Ref.
Note
3.431 3.432
20 Hz, 1000 pulses
3.2.6 MgO : LiNb03, Magnesium-Oxide-Doped Lithium Niobate (5 mole % MgO) Negative uniaxial crystal: no > ne ; Point group: 3m ; Transparency range at "0" transmittance level: Linear absorption coefficient ex:
0.5321 1.0642
0.02 0.96711 10.6 + 0.6943 => 0.65162 SFG,o+e*e 10.6 + 5.3 * 3.533 9.6 + 4.8 =} 3.2
*
* *
PI [deg]
P2
[deg]
P3 [deg]
22.13 19.90 14.71 15.01 21.02 29.46
3.42 3.17 2.50 2.56 3.45 4.44
19.57 25.28
3.39 4.52
30.28 27.27 29.45 42.46
3.84 3.70 4.21 4.77
4.19 3.97 4.32 4.96
19.78 18.70 20.29 25.83
2.87 2.81 2.93 3.49
3.19 3.06 3.49 4.59
28.65 26.89
4.06 3.93
4.13 3.99
Experimental values of internal angular bandwidth: Interacting wavelengths [urn] AOint [deg] Ref.
*
SHG, 0+0 e 10.6 =} 5.3 9.2 =} 4.6 SFG, e + 0 =} e 10.6 + 0.6943 =} 0.6516
0.098 0.082
3.450 3.452
0.031
3.467
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe == d eoe
d 31 sin
0-
d22
cos 0 sin 34> , 2
== doee == d 22 cos 0 cos 3lfJ .
Nonlinear coefficients [3.455, 37]: jd22(10.6 Jlm)j == (0.2 ± 0.03) x jd36(GaAs)j = 16.6 ± 2.5pmjV ,
165
166
3 Properties of Nonlinear Optical Crystals
Id31(10.6 Jlm)1
± 0.1)-1 X Id22(Ag3AsS3)I 10.4 ± 2.2 pmjV .
== (1.6 ==
Laser-induced surface-damage threshold: A [Jlm]
't p
[ns]
106 14 1.0642 cw 18 2.098 200 10.6 190 150 0.6943
Ithr X
10- 12 [Wjm 2 ]
0.00006 0.03 0.000001 >0.12 >0.1 >0.46 0.53
Ref. 3.469 3.365 3.469 3.365 3.365 3.365 3.450
3.2.8 GaSe, Gallium Selenide Negative uniaxial crystal: no > n e ; Point group: 62m; Mass density: 5.03 gjcm 3 [3.338]; Mohs hardness: ~ 0; Transparency range at "0" transmittance level: 0.62 - 20 urn [3.388]; Linear absorption coefficient ex: ex [em-I]
A [urn]
0.65-18 0.7 1.06
n e (at A < 0.804 urn ne > no) ; Point group: 42m; Molecular mass: 5.71 g/cm 3[3.338] ; Mohs hardness: 3 - 3.5 ; Transparency range at "0" transmittance level: 0.71 - 19 urn [3.477, 478]; Linear absorption coefficient (:J. :
A [11m] 1 1.3 2.0
2.05 2.1 2.2 5-11 10.6
a
[em-I]
5.15 6:::}3 5.2 => 2.6 4.1 => 2.05
55.3 53.7 53.1 42.2 40.3 49.7
SFG, 0 + 0 => e 12.15 + 10.63 => 5.67 10.63 + 5.33 => 3.55 5.515 + 3.3913 => 2.1 4.84 + 3.55 =} 2.0479 5.13+2.685=> 1.763 6.00 + 2.586 => 1.807 7.43 + 2.484 => 1.862 9.93 + 2.384 => 1.923 6.95 + 1.66 =} 1.34 7.4 + 1.604 =} 1.318 8.8 + 1.550 =} 1.318 12.3 + 1.476 => 1.318
[3.488] 54.7 [3.488] 53.1 [3.488] 52.5 [3.488] 39.5 [3.488] 41.5 [3.483] 50.6
61 [3.488] 42.7 [3.488] ~48 [3.478] 49.2 [3.483] 61.3 [3.474] 56 [3.474] 49.5 [3.474] 45.8 [3.474] ~78 [3.483] 80 [3.477] 70 [3.477] 60 [3.477]
56.7 54.9 54.3 39.4 40.8 48.3
57.4 55.7 55.1 40.1 41.3 48.6
63.5 42.7 46.2 48.0 53.3 51.7 46.6 42.9 68.6 no pm 69.8 69.0 61.2 58.2 53.1
63.6 43.3 46.5 48.2 53.5 51.9 46.9 43.1 69.2 70.4 61.7 53.4
60.7 42.1 48.1 50.1 57.1 54.9 49.0 44.6 83.1
Best set of Sellmeier equations (2 in urn, T == 293 K) [3.488]: n2
= 3.9362 +
o
n2
= 3.3132 +
e
+ 1.7954-1.2
2.9113-1.2 22 _ (0.38821)2
22 - 1600 '
+
3.3616 -1.2 ,12 _ (0.38201)2
1.7677 -1.2 . A2 - 1600
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0 + 0 =} e 10.6 =} 5.3 9.6 =} 4.8 5.3 => 2.65 4.8 =} 2.4 SFG,o+o=>e 10.6 + 2.65 =} 2.12 9.6 + 2.4 => 1.92 SHG, e + 0 =} e 5.3 =} 2.65
Opm
[deg]
PI [deg]
P3 [deg]
55.02 49.00 41.10 43.63
0.68 0.71 0.69 0.68
43.71 46.36
0.67 0.66
72.03
0.42
0.40
171
172
3 Properties of Nonlinear Optical Crystals
SFG, e + 0 => e 10.6 + 5.3 => 3.533 9.6 + 4.8 => 3.2
55.60 55.36
0.68 0.70
0.66 0.67
Experimental values of internal angular bandwidth Interacting wavelengths [Jlm]
SHG, 0 + 0 => e 10.25 =::} 5.125 SFG, 0 + 0 => e 5.515 + 3.3913 ==> 2.1
~oint [deg]
Ref.
0.84
3.486
0.54
3.478
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe == d36 sin () sin 24J , d eoe == d oee == d 36 sin 20 cos 24J .
Nonlinear coefficient: d 36(10.6 Jlm ) == 33pmjV [3.37] , d 36(9.5 urn) == 32 ± 4pmjV [3.489] .
Laser-induced surface-damage threshold: A [JlID] 1.064
2.0
2.05 2.1
9.5 10.25 10.6
'r p
[ns]
23 35 35 30 30 20-30 50 50 180 180 30 75 150
Ithr X
10- 12 [Wjm 2 ]
Ref. 3.483 3.488 3.488 3.481 3.481 3.482 3.483 3.478 3.485 3.485 3.489 3.486 3.368
0.13--0.4 0.3 0.11 0.083 no ; Point group: 6mm; Mass density: 5.81 g/cm 3 [3.338]; Mohs hardness: 3.25 [3.59]; Transparency range at "0" transmittance level: 0.75 - 25 urn [3.490, 59]; Linear absorption coefficient fY. :
A [urn]
fY.
[em-I]
0.75-20 2.87 15.96 + 2.28 =} 1.995 14.1 + 3.604 =} 2.87 13.7 + 2.8492 =} 2.3587 10.6 + 2.72 => 2.1646 10.361 +2.227 =} 1.833 9.871 + 2.251 =} 1.833 9.776 + 2.256 =} 1.833 8.278 + 4.3 ==> 2.83 8.253 + 4.4 ==> 2.87 8.236 + 4.5 ==> 2.91 7.88 + 3.36 ==> 2.3587 7.86 + 3.37 =} 2.3587
[deg]
f}theor
73.7 [3.493] 62.2 [3.498] 70.9 [3.493] 65 [3.499] 70.5 [3.491] 78 [3.500] 84 [3.500] 90 [3.500] 84 [3.492] 84 [3.492] 84 [3.492] 90 [3.499] 90 [3.490]
[3.362]
71.3 64.2 68.9 65.2 70.4 78.7 83.9 85.8 81.4 82.4 83.6 no pm no pm
72.4 64.6 69.7 65.5 70.5 78.5 83.5 85.1 81.9 83.0 84.5 no pm no pm
== 20°C) [3.362]:
= 4.2243 + 1.7680A? + 3.1200A?
o 2 _ 4 2009 n-.
e
[deg]
[3.468]
Best set of dispersion relations (A in urn, T n2
== 293 K) and comparison
,1.2 _ 0.2270 1.8875,1.2
+2
A - 0.2171
,1.2 - 3380 '
3.6461 ,1.2
+2
A - 3629
.
dispersion relations for the temperatures 73 K, 173 K, 373 K, 573 K are given in [3.390]. Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn]
f}pm
SFG, 0 + e==>o 22 + 2.9365 =} 2.5907 20 + 2.9365 =} 2.5605 15 + 2.9365 => 2.4557 10 + 2.9365 => 2.2699 9 + 2.9365 =} 2.2141
83.2 74.0 66.0 71.6 77.6
[deg]
P2 [deg] 0.11 0.24 0.34 0.27 0.19
3.2 Frequently Used Nonlinear Optical Crystals
15 + 3.6513 =} 10 + 4.1573 =} 20 + 3.2437 =} 15 + 3.4290 =} 10 + 3.8715 =}
71.5 73.3 80.9 69.3 71.8
2.9365 2.9365 2.791 2.791 2.791
0.27 0.25 0.14 0.30 0.27
Experimental value of internal angular bandwidth [3.491]: Interacting wavelengths [Jlm]
~()int [deg]
SFG,o+e=}o 10.6 + 2.72 =} 2.1646
1.24
Experimental value of spectral bandwidth [3.491]: Interacting wavelengths [Jlm]
~v
SFG, 0 +e =} 0 10.6 + 2.72 =} 2.1646
15
[em-I]
Effective nonlinearity expression in the phase-matching direction [3.100]: d oeo
== d eoo == d31 sin () .
Nonlinear coefficients [3.37]: d31(10.6Jlm)
== -18pmjV ,
d 33( 10.6 urn)
== 36pmjV .
Laser-induced surface-damage threshold: A [urn]
1"p
[ns]
Ithr X
10- 12 [W/m2 ]
0.3 >0.5 0.5 0.6
1.833 200 1.995 20 2.36 35 200 10.6
Ref. 3.494 3.498 3.490 3.365
Thermal conductivity coefficient at T == 293 K [3.58]: K
[WjmK],
6.9
II
c
K
[WjmK], -.L c
6.2
175
176
3 Properties of Nonlinear Optical Crystals
3.2.11 CdGeAs2 , Cadmium Germanium Arsenide Positive uniaxial crystal: ne > no ; Point group: 42m; Mass density: 5.60 g/cm 3 [3.338]; Mohs hardness: 3.5-4 ; Transparency range at "0" transmittance level: 2.4 - 18 urn [3.501]; Linear absorption coefficient (X :
A [urn]
T [K]
(X
[cm'] Ref.
3.39 4-18 5.3
300 5.7 300 + d32 cos2 4> ;
YZ plane
d ooe = d31 sin fJ ;
< Vz d oeo = d eoo == d32 sin fJ ; plane, fJ > Vz
XZ plane, fJ
XZ
d ooe = d32 sin fJ .
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of DKB5 crystal are given in [3.36]. Nonlinear coefficients [3.395, 37]: d31 2:: d 31(KB5)
::=
0.04 pm/V ,
180
3 Properties of Nonlinear Optical Crystals
d 32
2 d 32(KB5)
= 0.003 pm/V.
Laser-induced bulk-damage threshold [3.395, 405]:
A [J.1m]
Lp
0.43
7
[ns]
I thr
X
10- 12 [W/rn2 ]
10
3.3.2 CsB30S ' Cesium Triborate (CBO) Negative biaxial crystal: 2Vz = 97.3° at A = 0.5321 urn [3.507]; Point group: 222 ; Mass density: 3.357 g/cm 3 ; Transparency range at "0" transmittance level: 0.167 - 3.0 J.1m [3.507] ; Experimental values of refractive indices [3.507]:
A [J.1m]
nx
ny
nz
0.3547 0.4765 0.4880 0.4965 0.5145 0.5321 0.6328 1.0642
1.5499 1.5370 1.5367 1.5362 1.5349 1.5328 1.5294 1.5194
1.5849 1.5758 1.5736 1.5716 1.5690 1.5662 1.5588 1.5505
1.6145 1.6031 1.6009 1.5996 1.5974 1.5936 1.5864 1.5781
Dispersion relations (A in J.1m, T = 20 DC) [3.507]:
n2
= 2.2916 +
x n 2 = 2.3731
+
y
n2 = 2.4607 Z
+
0.02105
A2 + 0.06525 0.03437
A2 + O.11600 0.03202
A2 + 0.08961
- 3.1848 x 10- 5 A?
. '
_ 7.2632 x 10- 5 A2
.
'
- 5.6332 x 10- 5 A2
.
Note: The dispersion relations in [3.507] are given with a mistake. The numerator of the second term in the equation for n} should be 0.03437 instead of 0.3437
3.3 Other Inorganic Nonlinear Optical Crystals
181
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angles: XZ plane, 4> == 0° , 8 > Vz In teracting wavelengths [urn]
SHG, e + e :::} 0 1.0642 =} 0.5321 SFG, e + e :::} 0 1.0642 + 0.5321 =} 0.35473
[deg]
8theor [deg] [3.507]
PI [deg]
P2 [deg]
62 [3.507]
67.53
1.54
1.54
76 [3.507]
76.31
1.01
1.08
8 exp
Experimental value of internal angular bandwidth [3.507]: XZ plane, 4> == 0° Interacting wavelengths [um]
SHG, e + e :::} 0 1.0642 =} 0.5321
Opm
[deg]
A8int [deg]
0.064
62
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of CsB 30S' crystal [3.35]: XY plane d eoe
== d oee == dl 4 sin 24J ;
YZ plane
== d 14 sin 28 ; XZ plane, 8 < Vz d eoe == d oee == d 14 sin 28 ; XZ plane, (j > Vz d eeo == d 14 sin 28 . d eeo
Nonlinear coefficient: d I4(1.064 urn) == 0.648xd22 (BBO) == 1.49 pm/V [3.507,37] .
Laser-induced damage threshold [3.507]:
A [urn] 1.053
Lp
[ns]
I thr
260
X
10- 12 [W/m 2 ]
182
3 Properties of Nonlinear Optical Crystals
3.3.3 BeS04 . 4820, Beryllium Sulfate Negative uniaxial crystal: no > ne ; Point group: 42m; Mass density: 1.713 g/cm 3[3.508] ; Mohs hardness: > 2.5 [3.509] ; Transparency range at "0" transmittance level: 0.17 - 1.58 J.1m [3.508, 510] Linear absorption coefficient (X : (X
0.3164 0.6328 0.187-1.3
[cm"] Ref.
0.6 0.17 e 1.1523 => 0.5762 0.6328 => 0.3164 0.5400 => 0.2700 0.5340 => 0.2670 0.5321 => 0.2661 0.5266 => 0.2633 SHG, e+o ~ e 1.1523 => 0.5762 0.7606 => 0.3803
f}exp
[deg]
== 293 K) and comparison
f}theor
[deg]
[3.510]
[3.511]
30.4 59.9
42.9 56.2
79.0 81.9 83.1
76.7 80.1 81.5
42 [3.508] 55 [3.508] 60 [3.509] 77 [3.511] 80 [3.511] 81.5 [3.510] 81.6 [3.511] 90 [3.511]
no pm* no pm#
64 [3.508] 90 [3.511]
43.7 78.3
65.3 89.3
3.3 Other Inorganic Nonlinear Optical Crystals
SFG, 0 +0 => e 1.0642 + 0.5321 => 1.0642 + 0.3547 => 0.9070 + 0.3547 => 0.8468 + 0.3547 => 0.8209 + 0.3547 =>
47.4 [3.511] 62.4 [3.511] 72.3 [3.511] 80 [3.511] 90 [3.511]
0.3547 0.2661 0.2550 0.2500 0.2477
183
47.4 62.5 72.4 80.0 89.5
47.8 59.4 67.3 71.8 74.2
* NCPM corresponds to the SHG with Al = 0.5271 J.1m; # NCPM corresponds to the SHG with Al = 0.52681Jll1.
Best set of dispersion relations (A in J.1m, T = 20 DC) [3.511]: n2 == 2.1545
+
o
n2
== 2.0335 +
e
0.00835
A2 - 0.01606 A2
- 0.03573 A2 '
0.00806 - 0.01970 A2 - 0.01354
.
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [J.1mJ SHG, 0 + 0 => e 1.0642 ==> 0.5321 0.6943 ==> 0.34715 0.5782 ==> 0.2891 0.5321 ==> 0.26605 SFG, 0 + 0 => e 1.0642 + 0.3547 => 0.26605 0.5782 + 0.5105 => 0.2711 SHG, e + 0 => e 1.0642 ::::} 0.5321 SFG, e + 0 => e 1.0642 + 0.5321 => 0.3547
(}pm
[degJ PI [deg]
P3 [deg]
41.88 50.32 64.99 81.46
1.59 1.60 1.25 0.48
62.50 75.34
1.36 0.80
64.07
1.11
1.23
60.87
1.20
1.37
Experimental values of internal angular, temperature, and spectral bandwidths at T = 293 K: Interacting wavelengths [J.1m] SHG, 0 + 0 => e 0.5321 ::::} 0.2661
(}pm
81.5 81.6
[deg]
Atfnt [deg]
AT [DC]
Av [cm'] Ref.
0.09 0.11
1.45
4.9
3.510 3.511
184
3 Properties of Nonlinear Optical Crystals
Temperature variation of phase-matching angle [3.511]: Interacting wavelengths [J.1m]
TrCJ
Opm [degJ dOpmj dT [deg jKJ
20
81.6
*
SHG, 0+0 e 0.5321 0.2661
*
0.077
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
:::::
d 36 sin 0 sin 21> ,
d eoe
:::::
d oee == d 36 sin 20 cos 24> .
Nonlinear coefficient: d36(0.5321 J.1m)
== 0.62 x d 36(DKDP) ± 10% == 0.23 ± 0.02 pmjV [3.510, 37] .
Laser-induced surface-damage threshold:
0.2661 0.5321
8 8
1 >2.2
Ref.
Note
3.510 3.511
10 Hz 3 Hz
3.3.4 MgBaF4, Magnesium Barium Fluoride Negative biaxial crystal: 2Vz == 117.5° at ,1== 0.5321 J.1m [3.512]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z b,c,a; Transparency range: 0.17 - 8 J.1m [3.513]; Experimental values of refractive indices [3.512]:
*
A [J.1m] nx
nz
ny
0.5321 1.4508 1.4678 1.4742 1.0642 1.4436 1.4604 1.4674
== 20°C) [3.512]:
Sellmeier equations (A in J.1m, T n2
x
== 2.0770 + 0.00760
2 _ 2 1238 n y -.
,12 - 0.0079 '
+
0.00860 ,12
'
n~ == 2.1462 + 0.00736 Z
,12 - 0.0090
.
3.3 Other Inorganic Nonlinear Optical Crystals
185
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XY plane, ()
== 90°
In teracting wavelengths [urn] SHG, 0+0
*
¢
1.0642
*
¢theor
[deg]
P3 [deg]
[3.512]
9.2 [3.512]
9.65
0.223
== 0° , () < Vz
Interacting wavelengths [urn] SHG, e+o
[deg]
e
1.0642 => 0.5321
XZ plane,
¢exp
*
()exp
[deg]
()theor
[deg]
PI [deg]
P3 [deg]
0.525
0.516
[3.512]
e 18.9 [3.512]
0.5321
17.39
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of MgBaF4 crystal [3.35], [3.36]: XY plane
== d31 cos ¢ ;
dooe
yz plane
== deoo == d32 cos () ; XZ plane, () < Vz d oeo
== d eoe == d 31 sirr' () + d 32 cos 2 () XZ plane, () > Vz d oee
deeo
== d 31 sirr' () + d 32 COS 2 ()
;
.
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of MgBaF 4 crystal are given in [3.36]. Nonlinear coefficient: d31
(1.0642 urn) == ±0.057 x d 36 (KDP) ± 23%
== ±0.022 ± 0.005 pmjV [3.512, 37] , d 32 ( 1.0642 um)
== ±0.085 x
d 36
(KDP) ± 12%
== ±0.033 ± 0.012 pmjV [3.512, 37] ,
186
3 Properties of Nonlinear Optical Crystals
d33(1.0642 um) = ± 0.023 X d36 (KDP) ± 14% = ± 0.009 ± 0.001 pm/V [3.512, 37] . Laser-induced surface-damage threshold [3.513]:
[nsJ
A [llmJ
'rp
1.0642
~20
Ithr X
10- 12 [W/m 2J
>10
3.3.5 NH 4D2P04 , Deuterated Ammonium Dihydrogen Phosphate (DADP) Negative uniaxial crystal: no > ne ; Point group: 42m; IR edge of transmission spectrum (at "0" transmittance level): 1.9 urn [3.78]; Linear absorption coefficient: rx < 0.013cm- 1 in the range 0.78 - 1.03 urn [3.67]; Experimental values of refractive indices:
A [urn] no
ne
Ref.
0.3472 0.4358 0.53 0.5461 0.6943 1.06
1.4923 1.4831 1.4784 1.4759 1.4737 1.4712
3.126 3.126 3.79 3.126 3.126 3.79
1.5414 1.5278 1.5198 1.5194 1.5142 1.5088
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [urn]
(}exp
[deg]
(}theor
[deg]
[3.78]K
[3.78]E
*
SHG, 0+0 e 90 [3.119] 82.2 0.264 0.528 0.34715 47 [3.514] 50.3 0.6943
* *
Note: [3.78]K [3.78]E
no pm (?) no pm (?)
* see [3.78], data of Kirby et al.; * see [3.78], data of Eimerl
Experimental values of NCPM temperature [3.119]: Interacting wavelengths [Jlm] SHG, 0.516
0+0
*
*
0.258
T rOC]
e -20
3.3 Other Inorganic Nonlinear Optical Crystals
o
0.524 => 0.262 0.528 => 0.264 0.554 => 0.277
20 100
Best set of dispersion relations (A in urn, T = 20°C) [3.78]K: n2 = 2.279481
+
n2
+
1.215879 A? ,12 _ (7.614168)2
o
= 2.151161 +
+
1.199009 A? ,12 _ (11.25169)2
e
0.010761 ,12 - (0.115165)2 '
0.009652
.
,12 - (0.098550)2
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0+0 * e 0.5321 ==} 0.26605 0.5782 ==} 0.2891 0.6328 ==} 0.3164 0.6594 ==} 0.3297 0.6943 ==} 0.34715 1.0642 ==} 0.5321 1.3188 ==} 0.6594 SFG, 0 + 0 => e 0.5782 + 0.5105 * 1.0642 + 0.5321 * 1.3188 + 0.6594 * SHG, e+o * e 1.0642 ==} 0.5321 1.3188 ==} 0.6594 SFG, e+o *e 1.0642 + 0.5321 * 1.3188 + 0.6594 *
0.27112 0.35473 0.4396
0.35473 0.4396
(}pm
[deg] PI [deg]
P3 [deg]
79.53 65.24 56.61 53.58 50.31 36.93 37.18
0.652 1.357 1.611 1.664 1.700 1.599 1.569
74.57 46.44 39.29
0.930 1.728 1.659
54.47 53.55
1.411 1.339
1.547 1.533
59.17 48.09
1.308 1.399
1.504 1.668
Effective nonlinearity expressions in the phase-matching direction [3.100]:
d ooe = d36 sin (} sin 2et> , d eoe = d oee = d 36 sin 2(} cos 2et> . Nonlinear coefficient:
d36(0.6943 um) = 1.10 x d 36(K DP) ± 15% = 0.43
± 0.06pmjV [3.514, 37] .
187
188
3 Properties of Nonlinear Optical Crystals
3.3.6 RbH2P04, Rubidium Dihydrogen Phosphate (RDP)
Negative uniaxial crystal: no > n.; Point group: 42m; Mass density: 2.805 g/crrr': Transparency range at 0.5 transmittance level for a 15.3 mm long crystal cut at () == 50°,
== 45°) [3.71]:
Note e - wave
Experimental values of refractive indices: Ref. 0.3472 0.4358 0.4765 0.4880 0.4965 0.5017 0.5145 0.5321 0.5468 0.5893 0.6328 0.6943 1.0642
1.5284 1.5165 1.5140 1.5132 1.5126 1.5121 1.5116 1.5106 1.5082 1.5053 1.4976 1.5020 1.4926
1.4969 1.4857 1.4861 1.4832 1.4827 1.4825 1.4820 1.4811 1.4790 1.4765 1.4775 1.4735 1.4700 Ref.
0.4699 1.5148 3.518 0.4950 1.5128 3.518
3.516 3.516 3.517 3.517 3.517 3.517 3.517 3.517 3.516 3.516 3.517 3.516 3.517 Ref. 0.4658 1.4851 3.518 0.4780 1.4845 3.518
3.3 Other Inorganic Nonlinear Optical Crystals
0.5120 0.5329 0.5851 0.5980 0.6245 0.6474 0.6662
1.5117 1.5104 1.5074 1.5069 1.5056 1.5047 1.5042
3.518 3.518 3.518 3.518 3.518 3.518 3.518
0.4950 0.5324 0.5577 0.5878 0.6165 0.6521 0.6640
1.4833 1.4810 1.4798 1.4787 1.4776 1.4766 1.4763
189
3.518 3.518 3.518 3.518 3.518 3.518 3.518
Temperature derivative of refractive indices [3.74]:
A [urn] dno/dT x 105 [K- 1] 0.405 0.436 0.546 0.578 0.633
dne/dT x 105 [K- 1]
-2.67 -2.76 -2.54 -2.80 -2.89
-3.69 -3.86 -3.72 -3.72 -3.72
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: In teracting wavelengths [urn] SHG, 0+0 * e 0.626 ~ 0.313 0.627 => 0.3135 0.6275 * 0.31375 0.6294 => 0.3147 0.6328 * 0.3164 0.6386 * 0.3193 0.6550 * 0.3275 0.6700 * 0.3350 0.6943 => 0.34715 1.0642 => 0.5321
1.1523 * 0.57615 SHG, e+o * e 1.0642 * 0.5321 1.1523 * 0.57615 THG, 0+0 *e 1.0642 + 0.5321 => 0.3547
(}exp
[deg]
(}theor
[deg]
[3.517]
[3.74]
[3.78]K
[3.78]E
90 [3.74] 90 [3.119] 90 [3.519] 86.6 [3.519] 83.2 [3.520] 78.9 [3.519] 73.9 [3.519] 70.8 [3.519] 66 [3.516] 50.8 [3.521] 50.8 [3.515] 50.9 [3.425] 51 [3.520]
no pm no pm no pm no pm no pm no pm no pm no pm no pm 52.5
no pm no pm no pm no pm no pm no pm no pm 81.3 72.9 39.4
85.8 84.9 84.5 83.1 81.3 78.9 74.1 70.9 67.0 51.1
no pm no pm no pm no pm no pm 84.3 76.5 72.5 67.9 51.0
48.4
36.0
51.7
51.3
83.1 [3.521] 77.1 [3.520]
no pm 74.6
61.3 54.4
85.3 82.0
84.6 80.0
61.2 [3.515]
75.5
62.1
60.9
61.4
190
3 Properties of Nonlinear Optical Crystals
Note: [3.78]K ---+ see [3.78], data of Kirby et al.; [3.78]E ==> see [3.78], data of Eimerl Experimental values of NCPM temperature: Interacting wavelengths [flm] T [DC]
Ref.
SHG, 0 + 0 ~ e 0.627 :::} 0.3135 0.6275 :::} 0.31375 0.635 => 0.3175 0.637 :::} 0.3185
[3.425, 119] [3.519] [3.425, 119] [3.519]
20 20 100 98
Best set of dispersion relations (A in urn, T = 20°C) [3.78]K: n2
= 2.249885 +
n2
3.688005
A?
+
,12 _ (11.27829)2
o
= 2.159913 +
e
A2
0.988431 A? _ (11.30013)2
;? -
+
0.010560 (0.088207)2 ' 0.009515
.
A2 - (0.092076)2
Calculated values of phase-matching and "walk...off" angles: Interacting wavelengths [urn]
SHG, 0 + 0 :::} e 0.6328 => 0.3164 0.6594 => 0.3297 0.6943 => 0.34715 1.0642 :::} 0.5321 1.3188 => 0.6594 SFG, 0 + 0 :::} e 1.0642 + 0.5321 :::} 0.35473 1.3188 + 0.6594 :::} 0.4396 SHG, e + 0 :::} e 1.0642 :::} 0.5321 SFG, e + 0 :::} e 1.3188 + 0.6594 :::} 0.4396
(}pm
(deg]
PI (deg]
P3 (deg]
81.31 73.05 66.96 51.08 55.49
0.357 0.664 0.853 1.093 0.994
60.86 52.53
1.008 1.114
85.26
0.141
0.182
62.54
0.567
0.938
Experimental values of internal angular bandwidth at T = 293 K: Interacting wavelengths [flm]
Opm
SHG, 0 + 0 :::} e 0.6275 :::} 0.31375 0.6943 :::} 0.34715 1.0642 :::} 0.5321
90 66 50.8
[deg]
L\Oint
1.73 0.14 0.10
[deg]
Ref.
3.519 3.522 3.521
3.3 Other Inorganic Nonlinear Optical Crystals
1.0642 :::} 0.5321 SHG, e + 0 :::} e 1.0642 :::} 0.5321
THG, 0+0 => e 1.0642 + 0.5321 :::} 0.3547
50.8
0.11
3.515
83.1
0.40 0.54
3.523 3.521
61.2
0.08
3.515
191
Temperature tuning of noncritical SHG: Interacting wavelengths [Jlm]
dAl/dT [nm/K] Ref.
SHG, 0 + 0 =} e 0.626 =} 0.313 0.6275 :::} 0.31375
0.12 0.123
3.74 3.519
Experimental value of temperature bandwidth for noncritical SHG process (0.6275 urn :::} 0.31375 urn, 0 + 0 :::} e): ~T == 2.5 ± 0.3 °C [3.519].
Temperature variation of birefringence for (0.6275 urn :::} 0.31375 urn, 0 + 0 :::} e):
noncritical SHG process
d(n~ - n~)/dT == (1.1 ± 0.1) x 10- 5K - 1 [3.519].
Effective nonlinearity expressions in the phase-matching direction [3.100]:
d ooe == d 36 sin () sin 24> , d eoe == d oee == d36 sin 2() cos 2¢ .
Nonlinear coefficient:
d36(0.6943 urn) == 1.04 x d 36(K DP) ± 15% == 0.41 ± 0.06 pm/V [3.514, 37], d36(0.6943 urn) == 0.92 x d 36 (KDP) ± 10% == 0.36 ± 0.04 pm/V [3.198, 37]. Laser.. induced bulk-damage threshold:
0.6281 0.6943 1.0642
330 10 12
5.5 > 1.8 > 2.6
3.101 3.522 3.521
10-20 Hz
192
3 Properties of Nonlinear Optical Crystals
3.3.7 RbD 2P04 , Deuterated Rubidium Dihydrogen Phosphate (DRDP) Negative uniaxial crystal: no > n e; Point group: 42m; IR edge of transmission spectrum (at "0" transmittance level): 1.66 urn [3.78]; Best set of dispersion relations (A. in urn, T == 20°C) [3.78]K: n2
= 2.235596 +
o 2 _ 2 1 2727 n-.5 +
e
+
2.355322 A?
0.010929
;? _ (11.26298)2 ;? - (0.0376136)2 ' 0.691253 A? 0.010022 2+ 2 2· ;? _ (11.27007) A - (0.037137)
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0+0 * e 0.6328 * 0.3164 0.6594 * 0.3297 0.6943 * 0.34715 1.0642 * 0.5321 1.3188 * 0.6594 SFG,o+o*e 1.0642 + 0.5321 * 0.35473 1.3188 + 0.6594 * 0.4396 SHG, e+o * e 1.0642 * 0.5321 1.3188 * 0.6594 SFG, e+o * e 1.3188 + 0.6594 * 0.4396
(Jpm
[deg] PI [deg]
P3 [deg]
81.66 73.26 66.98 47.19 47.35
0.319 0.610 0.793 1.054 1.021
60.01 50.09
0.955 1.064
75.61 70.09
0.427 0.502
0.502 0.648
61.81
0.654
0.894
Effective nonlinearity expressions in the phase-matching direction [3.100]:
== d 36 sin (J sin 24> . d eoe == d oee == d36 sin (J cos 24> . d ooe
Nonlinear coefficient: d36 ~
0.38 pmjV [3.78].
3.3.8 KH2As04' Potassium Dihydrogen Arsenate (KDA) Negative uniaxial crystal: no > ne ; Point group: 42m; Calculated mass density: 2.872 gjcm 3 ;
3.3 Other Inorganic Nonlinear Optical Crystals
193
Transparency range at "0" transmittance level: 0.213-1.82 urn [3.113, 524, 78]; Linear absorption coefficient a:
0.35-1.45 0.3-0.9
3.113
Two-photon absorption coefficient fJ (() == 90°, ¢ == 45°) [3.71]:
A [um]
fJ x 1013 [m/W]
Note
0.355
4.84
e - wave
Experimental values of refractive indices [3.517]: A [J.1m]
no
ne
0.4861 0.5460 0.5893 0.6563
1.5762 1.5707 1.5674 1.5632
1.5252 1.5206 1.5179 1.5146
Temperature derivative of refractive indices [3.74]:
A [urn] dno/dT x 105 [K- 1] 0.436 0.546 0.578 0.633
dne/dT x 105 [K- 1]
-2.31 -2.13 -2.51 -2.12
-3.64 -4.07 -3.98 -4.09
Experimental values of the phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [urn] SHG, 0+0 *e 0.596 =? 0.298 0.616 * 0.308 0.6943 * 0.34715 1.0642 * 0.5321
()exp
[deg]
90 [3.74] 59 [3.514] 40.5 [3.425]
()theor
[deg]
[3.74]
[3.78]K
[3.78]E
70.7 65.0 51.7 29.2
74.2 68.7 56.5 40.0
no pm 88.3 60.1 41.9
Note: [3.78]K * see [3.78], data of Kirby et al.; [3.78]E * see [3.78], data of Eimerl
194
3 Properties of Nonlinear Optical Crystals
Experimental values of NCPM temperature [3.425]: Interacting wavelengths [Jlrn]
T rOC]
SHG, 0 + 0 :::} e 0.594 :::} 0.297 0.601 :::} 0.3005
20 100
Best set of dispersion relations (A in urn, T
== 20°C) [3.78]E:
A? + 0.01409368 -1,4 +
0.4430935 -1,2 ,12 _ (0.1710929)2 '
0.03195326 -1,2 + 0.01217516 -1,4 +
0.2681806 -1,2 . ,12 _ (0.1925064)2
n 2 = 1.988413 _ 0.05826141 o
n2
= 2.011142 _
e
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0 + 0 :::} e 0.6328 :::} 0.3164 0.6594 :::} 0.3297 0.6943 :::} 0.34715 1.0642 :::} 0.5321 1.3188 :::} 0.6594 SFG, 0 + 0 :::} e 1.0642 + 0.5321 :::} 1.3188 + 0.6594 :::} SHG, e + 0 :::} e 1.0642 :::} 0.5321 1.3188 :::} 0.6594 SFG, e + 0 :::} e 1.0642 + 0.5321 :::} 1.3188 + 0.6594 :::}
0.35473 0.4396
0.35473 0.4396
(Jpm
[deg] PI [deg]
P3 [deg]
74.64 66.48 60.09 41.89 38.82
0.986 1.423 1.688 1.860 1.762
54.29 43.32
1.859 1.926
61.38 53.50
1.298 1.334
1.541 1.698
71.12 51.93
0.939 1.356
1.182 1.855
Temperature tuning for noncritical SHG [3.74]: Interacting wavelengths [urn]
d,1I/dT [nm/K]
SHG, 0 + 0 :::} e 0.596 :::} 0.298
0.077
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
== d 36 sin (J sin 24> ,
d eoe
== d oee == d 36 sin 2(J cos 24> .
3.3 Other Inorganic Nonlinear Optical Crystals
195
Nonlinear coefficient:
d36(0.6943 urn] == 0.70 x d36 (KDP) ± 15% == 0.27 ± 0.04 pm/V [3.514, 37] , d 36(1.064 urn) == 1.06 x d 36 (KDP) ± 5°/6
== 0.41 ± 0.02 pm/V [3.525, 37].
Laser-induced bulk-damage threshold [3.101]:
A [urn]
Lp
0.6
330
[ns]
Ithr
x 10- 12 [W1m2 ]
0.12
3.3.9 KD2As04 , Deuterated Potassium Dihydrogen Arsenate (DKDA) Negative uniaxial crystal: no > ne ; Point group: 42m; Transparency range at "0" transmittance level: 0.22 - 2.3 urn [3.524]; Two-photon absorption coefficient f3 (() == 90°, 4> == 45°)
A [Jlrn]
f3 x 1013 [m/W]
Note
0.355
2.66
e - wave 3.71
Ref.
Experimental values of NCPM temperature [3.425]: Interacting wavelengths [urn]
SHG, 0 + 0 :::} e 0.609 :::} 0.3045 0.615 :::} 0.3075
20 100
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
== d 36 sin () sin 24> ,
d eoe
== d oee == d 36 sin 2Bcos 24> .
Nonlinear coefficient:
d36
~
d 36 (KDP) == 0.39 pmjV [3.78, 37].
Laser-induced bulk-damage threshold [3.101]:
A [11m]
'p
0.61
330
[ns]
Ithr
x 10- 12 [W1m2]
0.24
196
3 Properties of Nonlinear Optical Crystals
3.3.10 NH4H2As04' Ammonium Dihydrogen Arsenate (ADA) Negative uniaxial crystal: no > ne; Point group: 42m; Transparency range at "0" transmittance level: 0.218 - 1.53 urn [3.526, 78] Two-photon absorption coefficient f3 (0 == 90°,4> == 45°) [3.71]:
A [urn]
f3 x 1013 [m /W] Note
0.355
3.53
e - wave
Temperature derivative of refractive indices [3.74]:
A [Jlm]
dno/dT x 105 [K- 1]
dne/dT x 105 [K- 1]
0.436 0.546 0.578 0.633
-4.85 -4.39 -4.53 -4.45
+ 1.27 + 1.31 + 1.24 + 1.19
Experimental values of phase-matching angle (T between different sets of dispersion relations: In teracting wavelengths [urn]
SHG, 0 + 0 :::} e 0.58 :::} 0.29 0.582 :::} 0.291 0.584 :::} 0.292 1.0642 :::} 0.5321
Oexp
[deg]
90 [3.425] 90 [3.74] 41.3 [3.425]
0theor
=
293 K) and comparison
[deg]
[3.74]
[3.78]K
[3.78]E
76.5 75.8 75.1 32.8
no pm no pm 87.3 41.7
no pm no pm no pm 41.7
Note: [3.78]K :::} see [3.78], data of Kirby et al.; [3.78]E :::} see [3.78], data of Eimerl Experimental values of NCPM temperature: Interacting wavelengths [Jlm]
T [OC]
Ref.
SHG, 0 + 0 :::} e 0.568 :::} 0.284 0.572 :::} 0.286 0.58 :::} 0.29 0.586 :::} 0.293 0.606 :::} 0.303 0.611 :::} 0.3055 0.619 => 0.3095
-30 -10 20 25 80 100 120
3.119 3.425 3.425 3.527 3.101 3.425 3.119
3.3 Other Inorganic Nonlinear Optical Crystals
Best set of dispersion relations (A in urn, T n2
== 20°C) [3.78]K:
= 2.443449 +
2.017752 .f + 0.016757 A2 _ (7.604942)2 A2 - (0.135177)2 '
2 27 962 + . 5
1.598260 .1.2 0.014296 2+ 2 2 . A - (11.26433) A - (0.128689)
o
2 _ -
ne
2
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0 + 0 =} e 0.6328 :::} 0.3164 0.6594 :::} 0.3297 0.6943 :::} 0.34715 1.0642 :::} 0.5321 1.3188 :::} 0.6594 SFG, 0 + 0 :::} e 1.0642 + 0.5321 => 0.35473 1.3188 + 0.6594 => 0.4396 SHG, e + 0 :::} e 1.0642 =} 0.5321 1.3188 :::} 0.6594 SFG, e + 0 :::} e 1.0642 + 0.5321 =} 0.35473 1.3188 + 0.6594 =} 0.4396
Opm
[deg] PI [deg] P3 [deg]
67.42 62.69 58.05 41.71 42.58
1.544 1.764 1.928 2.023 1.964
53.05 44.31
2.065 2.087
62.22 61.26
1.423 1.315
1.640 1.627
69.20 53.77
1.139 1.497
1.402 1.968
Temperature tuning of noncritical SHG [3.74]: Interacting wavelengths [urn]
SHG,
0
+0
:::}
dAI/dT [nm/K]
e
0.582 :::} 0.291
0.359
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
== d 36 sin 0 sin 24> ,
d eoe
== d oee == d 36 sin 20 cos 24> .
Nonlinear coefficient: d 36(ADA) == d 36(ADP) == 0.45 pm/V [3.414, 419, 37]. Laser-induced bulk-damage threshold [3.101]:
A (Jlm]
Lp
0.581 0.606
330 330
[ns]
Ithr X
6.1 4.8
10- 12 [W/m 2 ]
197
198
3 Properties of Nonlinear Optical Crystals
3.3.11 NIlaD 2As04 , Deuterated Ammonium Dihydrogen Arsenate (DADA) Negative uniaxial crystal: no > ne ; Point group: 42m; Experimental value of the phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: In teracting wavelengths [Jlm] SHG, 0 + 0 :::} e 0.585 :::} 0.2925
(Jexp
[deg]
(Jtheor
90 [3.119]
[deg]
[3.78]K
[3.78]E
no pm
86.6
Note: [3.78]K :::} see [3.78], data of Kirby et al.; [3.78]E :::} see [3.78], data of Eimerl Experimental values of NCPM temperature: Interacting wavelengths [Jlm] T rOC]
Ref.
SHG, 0 + 0 :::} e 0.585 => 0.2925 0.592 :::} 0.296
3.119 3.101
20 25
Best set of dispersion relations (A, in urn, T = 20°C) [3.78]E: n~
== 1.5985275 - 0.02238475 _ 0.0003971065 ;,4 +
A,2
0.8226489 ;,2 A,2 _ (0.1402481)2 '
n; = 0.8036475 - 0.0002608396 A,2 + 0.0037782240 ;,4 +
1.4554770 ;,2
.
A,2 - (0.1025233)2
Calculated values of phase-matching and "walk-off" angles: Interacting wavlengths [urn] SHG, 0 + 0 :::} e 0.6328 :::} 0.3164 0.6594 => 0.3297 0.6943 :::} 0.34715 1.0642 => 0.5321 1.3188 => 0.6594 SFG, 0 + 0 :::} e 1.0642 + 0.5321 :::} 0.35473
(Jpm
[deg] PI [deg]
P3 [deg]
68.11 63.26 58.39 39.04 37.59
1.453 1.666 1.827 1.893 1.818
52.89
1.968
3.3 Other Inorganic Nonlinear Optical Crystals
1.3188 + 0.6594 ~ 0.4396 SHG, e+o ~ e 1.0642 =? 0.5321 1.3188 =? 0.6594 SFG, e + 0 :::} e 1.0642 + 0.5321 ~ 0.35473 1.3188 + 0.6594 :::} 0.4396
42.71
199
1.971
55.91 50.00
1.488 1.342
1.762 1.827
68.13 50.56
1.098 1.336
1.392 1.923
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
== d 36 sin ()sin 24> ,
d eoe
== d oee == d 36 sin 28 cos 24> .
Laser-induced bulk-damage threshold [3.101]:
A [J.1m]
'Lp
0.592
330
[ns]
Ithr X
10- 12 [W1m2 ]
2.4
3.3.12 RbH2As04, Rubidium Dihydrogen Arsenate (RDA) Negative uniaxial crystal: no > ne ; Point group: 42m; Mass density: 3.28 gjcm 3 ; Transparency range at "0" transmittance level: 0.22 - 1.82 urn [3.528]; Transparency range at 0.5 transmittance level for a 14.8 mm long crystal cut at 8 == 50°,4> =:: 45° : 0.26 - 46 urn [3.529]; IR edge of transmission spectrum (at "0" transmittance level): 1.65 urn for 0 - wave, 1.87 urn for e - wave [3.78]; Linear absorption coefficient ex: A [J.1m]
ex [em-I]
Ref.
Note
0.3-1.4 0.3547 0.5321 1.0642
0.1-0.2 0.051 0.031 0.036
3.113 3.529 3.529 3.529
8 == 50°, 4> == 45° () == 50°, 4J == 45° 8 == 50°, 4> == 45°
Two-photon absorption coefficient A [J.1m]
f3 x 1013 [m/W] Note
0.355
4.99
e - wave
f3 CO == 90°,
0.342 0.6943 :::} 0.34715 1.0642 => 0.5321 THG, 0 + 0 => e 1.0642 + 0.5321 => 0.3547
()exp
[deg]
()theor
90 [3.74] 80 [3.514] 80.3 [3.530] 48.8 [3.425] 50.1* [3.529]
66.2* [3.529]
[3.74]
[3.78]K
[3.78]E
79.8 76.1
83.4 79.1
13.8(?) 13.6(?)
40.4
49.5
10.3(?)
63.8
67.4
12.8(?)
= 298 K Note: [3.78]K :::} see [3.78], data of Kirby et al.; [3.78]E => see [3.78], data of Eimer/. Experimental values of NCPM temperature:
SHG, 0 + 0 :::} e 0.679 :::} 0.3395 0.684 :::} 0.342 0.6943 :::} 0.34715
0.695 :::} 0.3475 0.698 :::} 0.349
293 K) and comparison
[deg]
*T
Interacting wavelengths [11m]
=
T roC]
Ref.
-10 20 92 92.6 96.5 97.4 100 110
3.425 3.425 3.425 3.531 3.530 3.198 3.119 3.425
3.3 Other Inorganic Nonlinear Optical Crystals
Best set of dispersion relations (A in urn, T = 293 K) [3.78]K:
+
3.487176 A? + 0.015513 ,12-(11.25899)2 A2 - (0.134582)2 '
= 2.275570 +
0.720099 A? + 0.013915 . ,12 _ (11.25304)2 ,12 - (0.120800)2
n 2 = 2.390661 o
n2 e
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0 + 0 =} e 0.6943 =} 0.34715 1.0642 =} 0.5321 1.3188 =} 0.6594 SFG, 0 + 0 =} e 1.0642 + 0.5321 =} 0.35473 1.3188 + 0.6594 =} 0.4396 SHG, e + 0 =} e 1.0642 =} 0.5321 1.3188 =} 0.6594 SFG, e + 0 =} e 1.3188 + 0.6594 =} 0.4396
(Jpm
[deg] PI [deg] P3 [deg]
79.06 49.52 49.53
0.558 1.367 1.309
67.35 53.38
1.064 1.372
81.77 72.53
0.314 0.543
0.385 0.748
65.46
0.718
1.073
Experimental values of internal angular and temperature bandwidths: In teracting wavelengths [urn]
T
[DC]
SHG, 0 + 0 =} e 0.6943 =} 0.34715 20 20 92.6 96.5 97.4 1.0642 =} 0.5321 25 THG, 0+0 =} e 1.0642 + 0.5321 =} 0.3547 25
(}pm
[deg]
A(jnt [deg] AT [DC]
Ref.
0.126 0.13
80.3 80 90 90 90 50.1
0.08
3.530 3.531 3.531 3.530 3.198 3.529
66.2
0.057
3.529
~2
1.57
Temperature tuning of noncritical SHG [3.74]: Interacting wavelengths [urn]
dAI/dT [nm/K]
SHG, 0 + 0 =} e 0.684 =} 0.342
0.136
3.3 3.4
201
202
3 Properties of Nonlinear Optical Crystals
Temperature variation of birefringence for (0.6943 urn :::} 0.3472 urn, 0 + 0 :::} e): d(n~ - n1)/dT
noncritical
SHG process
== (9.3 ± 0.4) x 10-6K- 1 [3.530]
Effective nonlinearity in the phase-matching direction [3.100]: d ooe
== d 36 sin fJ sin 2¢ ,
d eoe == d oee == d 36 sin 2fJ cos 24> . Nonlinear coefficient:
d 36(0.6943 urn] == 1.04 x d 36(KDP) ± 10% == 0.41 ± 0.04 pmjV [3.198,37], d 36(0.6943 urn)
== 0.39 ± 0.04 pmjV [3.530] .
Laser-induced bulk-damage threshold:
A [urn]
't p
0.684 0.6943
330 20
[ns]
Ithr X
10- 2 [W1m2] Ref. 3.101 3.530
1.2 3.5
3.3.13 RbD 2As04 , Deuterated Rubidium Dihydrogen Arsenate (DRDA) Negative uniaxial crystal: no > n e; Point group: 42m; Transparency range at "0" transmittance level: 0.22 - 2.3 urn [3.528]; IR edge of transmission spectrum (at "0" transmittance level): 2 urn for 0 - wave, 2.3 urn for e - wave [3.78]; Experimental value of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [Jlm]
fJexp
[deg]
SHG, 0 + 0 :::} e 90 [3.425] 0.698 :::} 0.349 0.700:::} 0.350
fJtheor
[deg]
[3.78]K [3.78]E no pm no pm 86.9 no pm
Note: [3.78]K :::} see [3.78], data of Kirby et al.; [3.78]E =} see [3.78], data of Eimerl
3.3 Other Inorganic Nonlinear Optical Crystals
Experimental values of NCPM temperature [3.425]: Interacting wavelengths [J.lm]
T [Oe]
SHG, 0 + 0 :::} e 0.698 :::} 0.349 0.714 :::} 0.357
20 100
Best set of dispersion relations (;, in urn, T = 20°C) [3.78]K: n 2 = 2.373255
+
1.979528
A,2
+
0.015430
o
;,2 _ (11.26884)2
2 _ 2 27 806 . 0 +
0.013592 0.275372 ;,2 2+ 2 ;,2 _ (7.621351) ;,2 - (0.126357)
n e
;,2 _ (0.125845)2 '
.
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn]
SHG, 0 + 0 :::} e 1.0642 :::} 0.5321 1.3188 :::} 0.6594 SFG, 0 + 0 :::} e 1.0642 + 0.5321 :::} 0.35473 1.3188 + 0.6594 :::} 0.4396 SHG, e + 0 :::} e 1.0642 :::} 0.5321 1.3188 :::} 0.6594 SFG, e + 0 :::} e 1.3188 + 0.6594 :::} 0.4396
8pm [deg]
PI [deg]
P3 [deg]
46.62 42.98
1.278 1.242
69.79 52.14
0.875 1.272
77.09 63.77
0.484 0.821
0.547 0.973
66.99
0.744
0.935
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe
== d 36 sin () sin 24> ,
d eoe
== d oee == d36 sin 28 cos 24> .
Nonlinear coefficient: d 36
~
0.31 pmjV [3.78]
Laser-induced bulk-damage threshold [3.101]:
;, [urn]
Lp
0.7
330
[ns] 0.21
203
204
3 Properties of Nonlinear Optical Crystals
3.3.14 LiCOOH· H 20, Lithium Formate Monohydrate (LFM) Negative biaxial crystal: 2Vz == 123.8° at A == 0.5321 urn [3.532]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y, Z => a, b, c; Mass density: 1.46 g/cm 3 [3.532]; Transparency range at "0" transmittance level: 0.23 - 1.56 urn [3.532, 533]; Linear absorption coefficient r:J. (0 == 90°, 4J == 10°) [3.534]:
[cm"]
A (flm]
r:J.
0.3547 0.5321 1.0642
0.025 0.012 0.017
Experimental values of refractive indices [3.535]:
A [flm] nx 1.3810 1.3791 1.3777 1.3767 1.3758 1.3748 1.3729 1.3714 1.3705 1.3696 1.3686 1.3677 1.3666 1.3657 1.3647
0.35 0.36 0.37 0.38 0.39 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58
ny
nz
A [flm] nx
1.5073 1.5051 1.5034 1.5017 1.4999 1.4981 1.4955 1.4928 1.4902 1.4880 1.4862 1.4845 1.4827 1.4813 1.4804
1.5540 1.5510 1.5484 1.5458 1.5432 1.5405 1.5367 1.5332 1.5301 1.5279 1.5257 1.5236 1.5219 1.5200 1.5187
0.60 0.62 0.64 0.66 0.68 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
Sellmeier equations (A in urn, T n2
x n2
=
1.4376
+ +
=
1.6586
=
1.6714 +
y n2
z
A2
-
=
1.3643 1.3638 1.3633 1.3628 1.3625 1.3623 1.3614 1.3604 1.3595 1.3590 1.3587 1.3585 1.3583 1.3581
20°C) [3.535]:
0.4045 ..1.2 - 0.0005 0.01692601
A2
0.5006 ..1.2 - 0.0127 A2 - 0.023409
A2
-
A?
0.5928 ..1.2 - 0.0153 A2 0.02534464
'
.
ny
nz
1.4796 1.4787 1.4778 1.4768 1.4760 1.4751 1.4729 1.4711 1.4694 1.4675 1.4658 1.4644 1.4630 1.4617
1.5174 1.5161 1.5152 1.5144 1.5135 1.5126 1.5099 1.5077 1.5055 1.5032 1.5011 1.4987 1.4970
3.3 Other Inorganic Nonlinear Optical Crystals
205
Comparison between experimental and theoretical values of phase-matching angle: XY plane, == 90 0
e
In teracting wavelengths [urn]
4Jexp
SFG, e + 0 => e 1.0642 + 0.5321 => 0.3547
XZ plane,
4J
== 0
[deg]
4Jtheor [deg] [3.535]
8.2 [3.534]
9.5
0
In teracting wavelengths [urn]
Oexp
SHG, 0 + 0 => e 0.486 => 0.243 1.0642 => 0.5321 SHG, 0 + e=>o 1.0642 => 0.5321
[deg]
Otheor [deg] [3.535]
38.5 [3.536] 55.1 [3.532]
36.8 56.0
82.0 [3.532]
80.4
Calculated values of phase-matching and "walk-off" angles: XY plane, == 90 0
e
In teracting wavelengths [urn] SHG, e + 0 => e 0.5105 => 0.25525 0.5321 => 0.26605 0.5782 => 0.2891 0.6943 => 0.34715 SFG, e + 0 =::} e 0.5782 + 0.5105 => 0.27112 1.0642 + 0.5321 => 0.35473 SFG, 0 + e =::} e 0.5782 + 0.5105 => 0.27112 1.0642 + 0.5321 => 0.35473
XZ plane,
4J
== 0
0 ,
47.94 44.15 37.38 24.96
4.639 4.689 4.574 3.683
5.783 5.712 5.368 4.103
40.23 9.49
4.637 1.545
5.641 1.786 4.705 4.442
44.78 33.34
0 < Vz [deg] P3 [deg]
Interacting wavelengths [flm]
Opm
SHG, 0 + 0 => e 0.5105 => 0.25525 0.5321 => 0.26605 0.5782 => 0.2891 0.6943 => 0.34715
39.44 41.38 44.69 50.00
7.722 7.603 7.341 6.784
5.631 4.780
206
3 Properties of Nonlinear Optical Crystals
1.0642 ~ 0.5321 1.3188 =} 0.6594 SFG, 0 + 0 => e 0.5105 + 0.5782 =} 0.27112 1.0642 + 0.5321 =} 0.35473 1.3188 + 0.6594 => 0.4396 XZ plane, ¢
== 0
0 , ()
55.98 56.86
5.937 5.731
46.42 51.41 54.66
7.721 6.705 6.209
> Vz
In teracting wavelengths [urn]
epm
SHG, 0 + e=}o 1.0642 =} 0.5321 1.3188 => 0.6594
80.42 76.68
[deg] P2 [deg] 2.087 2.759
Experimental value of internal angular bandwidth [3.534]: XY plane, e ~ 90 0 Interacting wavelengths [flm]
cjJpm
SFG, e + 0 => e 1.0642 + 0.5321 ::::} 0.3547
8.2
[deg] ~ Vz XZ plane,
d oeo
~
d eoo
= d 32 sin e.
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of LFM crystal are given in [3.36] Nonlinear coefficients [3.37]: d 31(1.0642 urn) == 0.13 pm/V , d 32(1.0642 urn) == -0.60 pm/V , d 33(1.0642 urn) == 0.94 pm/V ,
3.3 Other Inorganic Nonlinear Optical Crystals
207
Laser-induced surface-damage threshold:
A [urn]
't p
0.475 0.488 0.490
330 cw 330
[ns]
I thr
X
10- 12 [W1m2 ]
Ref. 3.101 3.532 3.101
1.5
> 0.00001 1.5
3.3.15 NaCOOH, Sodium Formate
Negative biaxial crystal: 2Vz == 92.5° at A == 0.54 urn [3.533] ; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y, Z =} a, b, c; Transparency range at "0" transmittance level: 0.23-2.2 urn [3.533] ; Linear absorption coefficient (l (along X axis) [3.537]:
0.3547 0.5321 1.0642
0.013 0.003 0.010
The graph of nx, nr, nz dependences versus wavelength is given in [3.533] (nx < nv < nz). Sellmeier equations (A in urn, T = 20°C) [3.533]: n2
=
1.2646 +
x n2
= 1.2589 +
y
n2 = 1.2515 +
A2
-
A2
-
0.6381 -1.2 _ 0.0011 -1.2 0.01212201 '
0.8423 -1.2 - 0.0005 -1.2 0.01447209 ' 1.0729 -1.2
- 0.0013 -1.2 .
A2 - 0.01726596 Experimental and theoretical values of phase-matching angle and calculated values of "walk-off' angle: XY plane, () == 90° z
Interacting wavelengths [Jlrn] SFG, 0 +e =} e 1.0642 + 0.5321 =} 0.3547
4Jexp
[deg]
2.2 [3.537]
4Jtheor [deg] [3.533]
P2 [deg]
P3 [deg]
4.61
0.512
0.559
208
3 Properties of Nonlinear Optical Crystals
Experimental values of internal angular band-width [3.537]: XY plane, () == 90° Interacting wavelengths [flm]
cjJpm [d~g]
~4Jint [deg]
~(Jint [deg]
SFG, 0 +e =* e 1.0642 + 0.5321 ~ 0.3547
2.2
0.75
1.8
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of NaCOOH crystal [3.35, 36]: XYplane d eoe
== d oee == d31 sirr' 4J + d32 cos 2 4J ,
YZ plane
== deoo == d 31 sin (J , XZ plane, (J < Vz dooe == d32 sin {}, XZ plane, (J > Vz d oeo == deoo == d 32 sin (J . d oeo
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of NaCOOH crystal are given in [3.36] Nonlinear coefficients:
Id 32 (1.0642 urn + 0.5321 urn ~ 0.3547 == 1.2 x
d36(KDP)
flm)1
± 200/0 == 0.47 ± 0.09 pm/V [3.537, 515, 37];
d 31(1.0642 pm)
~
d 32 ( 1.0642 11m)
== -0.47 ± 0.09 pm/V [3.537,515, 198,37];
d3 3 (1.0642
0.047 pm/V [3.533,537,515, 198,37];
urn) ~ 0.70 pm/V [3.533,537,515, 198,37].
Laser-induced surface-damage threshold [3.537]:
A [urn]
Tp
0.3547 0.5321 1.0642
8 10 12
[ns]
Ithr X
> 1.2 > 1.4 > 1.2
10- 12 [W1m2]
Note 10 Hz 10 Hz 10 Hz
3.3 Other Inorganic Nonlinear Optical Crystals
209
3.3.16 Ba(COOH)2' Barium Formate Positive biaxial crystal: 2Vz == 101.3° at A == 0.5321 urn [3.512]; Point group: 222; Assignment of dielectric and crystallographic axes: X, Y, Z =* a, b, c; Transparency range: 0.245 - 2.2 urn [3.512]; Experimental values of refractive indices [3.512]: nz
ny
0.5321 1.6407 1.6019 1.5773 1.0642 1.6214 1.5819 1.5585 Sellmeier equations (A in urn, T = 20°C) [3.512]: 2 0.0177 nx == 2.619 + A2 _ 0.039 ; n 2 == 2.491 + y
0.0184 . - 0.035 '
A2
n 2 == 2.421 + 0.0160 . A2 - 0.042 z
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XZ plane, Vz d'~oe ==
d oee == d 14 sin 20 .
210
3 Properties of Nonlinear Optical Crystals
Nonlinear coefficient:
= 0.27 x d 36 (K DP) ± 15%
d14(1.064 urn)
= 0.105 ± 0.016 pm/V [3.512,37]
3.3.17 Sr(COOH)2' Strontium Formate Positive biaxial crystal: 2Vz == 78.8° at A = 0.532 urn [3.94]; Point group: 222; Assignment of dielectric and crystallographic axes: X, Y, Z =} c, a, b ; Mass density: 2.69 g/cm'; Transparency range at "0" transmittance level: 0.25 - 1.7 urn [3.94]. Linear absorption coefficient ~ [3.94]:
A [JlmJ
~
0.235 0.250
2
[em-I)
> 15
Experimental values of refractive indices [3.94]:
0.266 0.3547 0.532 1.064
1.613 1.569 1.545 1.528
ny
nz
1.635 1.587 1.560 1.543
1.675 1.612 1.583 1.563
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: YZ plane, 4J = 90° Interacting wavelengths [urn] SHG, e +e => 1.064 => 0.532 XZ plane,
fJexp
[deg]
fJtheor
[deg]
PI [deg]
0
26 [3.94]
18.60#
0.442
4J = 0°, fJ > Vz
Interacting wavelengths [urn] SHG, e+e ==> 1.064 => 0.532
fJexp
[deg]
fJtheor
[deg]
PI [deg]
0
72.5 [3.94]
73.25#
0.730
#derived from experimental data on refractive indices [3.94].
3.3 Other Inorganic Nonlinear Optical Crystals
211
Experimental value of internal angular bandwidth [3.94]: YZ plane, 4J == 90° Interacting wavelengths [urn] SHG, e +e =*
epm
[deg]
~eint
[deg]
0
1.064 =* 0.532
0.204
26
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes on Sr(COOH)2 crystal [3.35]: XYplane d eoe == d oee == d 14 sin 24J ;
YZ plane deeo == d 14 sin 2e;
e
Vz
XZ plane,
deeD == d 14 sin 2e .
Nonlinear coefficient: d I 4(1.064 um) == 1.25 x d 36 (KDP)
± 160/0
== 0.49
± 0.08 pm/V [3.94,37].
Laser-induced damage threshold [3.94]: A [Jlm]
!p
[ns]
Ithr X
1.064
~
20
> 1.5
10- 12 [W1m2 ]
3.3.18 Sr(COOH)2 . 2H 20, Strontium Formate Dihydrate Negative biaxial crystal: 2 Vz == 64.6° at A == 0.532 urn [3.94]; Point group: 222; Assignment of dielectric and crystallographic axes: X, Y, Z =* a, b, c; Mass density: 2.25 g/cm! [3.94]; Transparency range at "0" transmittance level: 0.25 - 1.4 urn [3.94]; Linear absorption coefficient ~ [3.94]:
A [Jlm]
~
0.235 0.250
2
[em-I]
> 15
212
3 Properties of Nonlinear Optical Crystals
Experimental values of refractive indices [3.94]:
A [urn]
nx
ny
nz
0.266 0.3547 0.532 1.064
1.621 1.570 1.542 1.525
1.598 1.553 1.526 1.509
1.543 1.509 1.488 1.477
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off' angle: YZ plane, 4J == 90 0 Interacting wavelengths [urn]
Oexp
SHG, e + 0 =} e 1.064 =} 0.532 SFG, e+o =} e 1.064 + 0.532 ==> =} 0.35467 XZ plane, 4J
== 0
0 ,
0
Interacting wavelengths [urn]
Otheor
[deg]
PI [deg] P3 [deg]
46 [3.94]
38.56#
1.203#
1.405#
58.5 [3.94]
53.60#
1.165#
1.559#
> Vz Oexp
SHG, e + 0 => e 1.064 ==> 0.532
[deg]
[deg]
71 [3.94]
Otheor
[deg]
65.07#
PI [deg] P3 [deg]
1.372#
1.525#
#derived from experimental data on refractive indices [3.94]: Experimental value of internal angular bandwidth [3.94]: YZ plane, 4J == 90 0
In teracting wavelengths [flm]
Opm
SHG, e + 0 => e 1.064 =} 0.532
46
[deg]
L\Oint
[deg]
0.142
Effective nonlinearity in the phase-matching direction for three-wave interactions in the principal planes of Sr(COOH)2 . 2H20 crystal [3.35]: XYplane d eeo
== d 14 sin 24J ;
YZ plane d eoe
== d oee == d 14 sin 20;
3.3 Other Inorganic Nonlinear Optical Crystals
213
< Vz
XZ plane, ()
deeo == d 14 sin 2();
> Vz d eoe == d oee == d 14 sin 28 .
XZ plane, ()
Nonlinear coefficient: dI4(1.064 urn) == 0.8 x d 36 (KDP) ± 25%
== 0.31 ± 0.08 pm/V [3.94,37].
Laser-induced damage threshold [3.94]:
1.064
't"p
[ns]
~
20
> 1.5
3.3.19 LiGa02, Lithium Gallium Oxide Negative biaxial crystal: 2Vz == 74.5° at A == 0.5 urn [3.538]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y, Z => b, C, a [3.538] ; Mass density: 4.187 g/cm 3 [3.64]; Mohs hardness: 7.5 [3.64] Transparency range: 0.3 - 5 11m [3.539] Experimental values of refractive indices:
A [urn]
nx
0.41 0.47 0.50 0.54 0.58 0.62 0.66 0.70 0.80 0.90
1.7702 1.7534 1.7477 1.7407 1.7351 1.7311 1.7289 1.7268 1.7218 1.7185
ny
nz
1.7835 1.7768 1.7683 1.7626 1.7589 1.7578
1.7852 1.7791 1.7708 1.7653 1.7617 1.7604
Ref.
A [urn]
nx
3.539 3.538 3.538 3.538 3.538 3.538 3.538 3.539 3.539 3.539
1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60
1.7160 1.7122 1.7095 1.7070 1.7045 1.7025 1.7005 1.6978 1.6955
nr nz Ref. 3.539 3.539 3.539 3.539 3.539 3.539 3.539 3.539 3.539
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of LiGa02 crystal [3.35, 36]: XYplane dooe == d31
cos 4J ;
214
3 Properties of Nonlinear Optical Crystals
YZ plane
d oeo == d eoo == d 32 cos 0; XZ plane, 0 < Vz
== d eoe == d 31sirr' 0 + d 32 cos2 0; XZ plane, e > Vz d oee
deeD
== d31 sin 2 (} + d32 cos 2 (}.
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of LiGa02 crystal are given in [3.36]. Nonlinear coefficients: d31(1.0642 urn)
== ±0.17 x d36 (KDP) ± 10% == ±0.066 ± 0.007 pm/V [3.539, 37] ,
d 32(1.0642 urn)
== =F0.37 x d 36 (KDP) ± 10% == =F0.144 ± 0.014 pm/V [3.539,
d33(1.0642 urn)
37],
== ±1.45 x d36 (KDP) ± 10% == ±O.566 ± 0.057 pm/V [3.539, 37].
3.3.20 ex-UI03 , ee-Iodic Aeid Negative biaxial crystal: 2Vz == 47° [3.540]; Point group: 222; Assignment of dielectric and crystallographic axes: X, Y, z-s ». c, a,· Mass density: 4.63 gjcm 3 [3.540]; Transparency range at "0" transmittance level: 0.32 - 1.7 urn (II c), 0.32 - 2.3 urn (1- c) [3.540]; Linear absorption coefficient a : < 0.3 cm' in the range 0.35 - 1.3 urn [3.541]; Experimental values of refractive indices at T = 293 K [3.542]:
A [urn] nx
ny
nz
A [urn]
nx
ny
nz
0.35 0.36 0.37 0.38 0.39 0.40 0.41
2.1265 2.1077 2.0917 2.0782 2.0662 2.0545 2.0465
1.9612 1.9474 1.9360 1.9257 1.9154 1.9086 1.9020
0.42 0.44 0.46 0.48 0.50 0.52 0.54
2.0637 2.0494 2.0378 2.0292 2.0194 2.0126 2.0065
2.0394 2.0246 2.0119 2.0026 1.9926 1.9883 1.9829
1.8952 1.8847 1.8753 1.8685 1.8624 1.8562 1.8522
2.1485 2.1330 2.1171 2.1053 2.0929 2.0808 2.0715
3.3 Other Inorganic Nonlinear Optical Crystals
A [urn]
nx
ny
nz
A [urn]
nx
ny
nz
0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.80 0.85
2.0010 1.9960 1.9918 1.9884 1.9854 1.9821 1.9791 1.9763 1.9668 1.9634
1.9763 1.9712 1.9665 1.9632 1.9589 1.9560 1.9529 1.9506 1.9409 1.9377
1.8476 1.8436 1.8405 1.8388 1.8368 1.8348 1.8328 1.8311 1.8248 1.8222
0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60
1.9602 1.9569 1.9541 1.9486 1.9436 1.9390 1.9348 1.9310
1.9346 1.9314 1.9286 1.9260 1.9229 1.9206 1.9180 1.9157 1.9132
1.8202 1.8184 1.8150 1.8114 1.8088 1.8063 1.8038 1.8018 1.7998
215
Optical activity at T = 300 K [3.540]:
A [um]
p [deg/mm]
0.4360 0.5461
74.5 58.7
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: YZ plane, 4> == 90° In teracting wavelengths [urn] SHG, e+o::::} e 0.976 ::::} 0.488 1.029 ::::} 0.5145 1.0642 ::::} 0.5321 1.065 ::::} 0.5325
XZ plane, 4>
Oexp
[deg]
57.9 [3.544] 52.7 [3.544] 50.4 [3.545] 52 [3.540]
f)theor
[deg]
[3.458]
[3.542]
[3.543]
56.9 51.9 49.3 49.3
57.5 52.5 49.8 49.8
58.1 52.9 49.9 49.9
== 0°, 0 > Vz
In teracting wavelengths [Jlm] SHG, e+o::::} e 0.976 ::::} 0.488 1.029::::} 0.5145 1.06::::} 0.53 1.065 ::::} 0.5325
Oexp
[deg]
72.2 [3.544] 66.1 [3.544] 64.9 [3.199] 66 [3.540]
Otheor
[deg]
[3.458]
[3.542]
[3.543]
71.2 65.0 62.4 62.1
71.4 65.4 62.9 62.5
72.4 66.3 63.6 63.2
216
3 Properties of Nonlinear Optical Crystals
Best set of Sellmeier equations (A in 11m, T == 293 K) [3.543]: n 2 == 3.739 +
A2
0.07128 - 0.05132 '
A2
0.06721 - 0.04234 '
A2
-
x n 2 == 3.654 + y
n2
== 3.239 +
z
0.05353 . 0.017226
Calculated values of phase-matching and "walk-off" angles: YZ plane, 4> == 90° In teracting wavelengths [urn]
Opm
SHG, e + 0 => e 1.0642 => 0.5321 1.3188 => 0.6594
49.92 34.55
[deg]
PI [deg]
P3 [deg]
3.416 3.324
3.725 3.484
PI [deg]
P3 [deg]
3.224 4.058
3.557 4.278
XZ plane, 4> == 0°, 0 > Vz Interacting wavelengths [urn]
(Jpm
SHG, e + 0 => e 1.0642 =? 0.5321 1.3188 => 0.6594
63.21 49.22
[deg]
Experimental values of internal angular and spectral bandwidths [3.96]: XZ plane, 4> == 0°, 0 > Vz Interacting wavelengths [Jlm]
Opm
SHG, e + 0 =? e 1.06 => 0.53
66
[deg]
L\Oint
[deg]
0.035
Av [em-I] 3.38
Temperature tuning of critical SFG process [3.544]: XZ plane, 4> == 0° Interacting wavelength [urn]
Opm
SHG, e + 0 => e 1.9226 + 0.654 => 0.488
50
[deg] dA2/dT [nm/K] 0.055
3.3 Other Inorganic Nonlinear Optical Crystals
217
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of a-HI0 3 crystal [3.35]: XYplane deeo = d 14 sin 2¢ ;
YZ plane
= d oee = d 14 sin 20 XZ plane, 0 < Vz d eoe
;
deeD = d 14 sin 20 ;
XZ plane, 0 > Vz d eoe = d oee = d1 4 sin 20 .
Nonlinear coefficient:
± 25%
d1 4 (1.064 urn) = 20 x d ll(Si02 ) = 6.0
± 1.5 pm/V [3.540], [3.37] ,
d1 4 (1.1523 urn) = 10.9 x d36(ADP) ± 14% = 5.1 ± 0.7 pm/V [3.546, 37] . Laser-induced surface-damage threshold:
A [Jlm] 0.488 0.528 0.53 0.532
!p
[ns]
cw 0.007 15 0.006 0.03 0.03 0.035 0.035
Ithr X
10- 12 [W/m 2 ]
Ref. 3.540 3.68 3.199 3.547 3.548 3.549 3.222 3.222
>0.0025 >70 0.55 >8 >8 >55 80-100 40-50
Note 2Hz
25 Hz
1 Hz 12.5 Hz
3.3.21 K2La(N03)s . 2H20, Potassium Lanthanum Nitrate Dihydrate (KLN) Negative biaxial crystal: 2Vz = 111 at A = 0.5461 urn [3.550] Point group: mm2; Assignment of dielectric and crystallographic axes: 0
X, Y,Z::::} b,c,a;
Transparency range at "0" transmittance level: 0.335 - > 1.1 urn [3.550]; Linear absorption coefficient: a < 0.03 crn- 1 at A = 1.064 urn [3.550];
218
3 Properties of Nonlinear Optical Crystals
Experimental values of refractive indices [3.550]: A [JlID]
nx
ny
nz
0.3650 0.4005 0.4872 0.5461 0.6476 0.7500 0.8500 0.9500 1.0500
1.5297 1.5201 1.5062 1.5008 1.4950 1.4915 1.4891 1.4872 1.4857
1.5820 1.5702 1.5530 1.5456 1.5387 1.5341 1.5306 1.5285 1.5269
1.6063 1.5936 1.5760 1.5682 1.5601 1.5556 1.5518 1.5496 1.5475
Sellmeier equations (A in urn, T n2
:=:
2.20094 +
:=:
0.0142619 _ 0.00617543 A2 - 0.0313420 '
A2
0.0200108 - 0.00586460A 2 - 0.0247406 '
A2
0.0208525 - 0.00873084 A2 - 0.0269388
2.31901 +
y
n2
:=:
2.38504 +
Z
20°C) [3.550]:
A2
x n2
:=:
.
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XY plane, 0 :=: 90° Interacting wavelengths [um] SHG, 0+0 => e 1.0642 => 0.5321 SFG, 0+0 => e 1.0642 + 0.5321 =} 0.35473
YZ plane,
1>
1>exp
[deg]
1>theor
[deg]
P3 [deg]
[3.550] 0.8 [3.550]
4.17
0.26
42.6 [3.550]
41.64
1.94
== 90°
In teracting wavelengths [urn] SHG, o+e => 0 1.0642+0.5321 =} 0.35473
Oexp
[deg]
Otheor
[deg]
P2 [deg]
[3.550] 42.1 [3.550]
41.69
0.81
3.3 Other Inorganic Nonlinear Optical Crystals
219
XZ plane, ¢ == 0°, (J < Vz In teracting wavelengths [urn]
(Jexp [deg]
(Jtheor [deg]
PI [deg]
P3 [deg]
1.48
1.60
[3.550]
SHG, e+e => 0 1.0642 => 0.5321
19.8 [3.550]
20.42
Experimental values of internal angular bandwidth [3.550]: XY plane, (J == 90° Interacting wavelengths [urn] ¢pm[deg] ~¢int[deg] SHG, 0+0 ~ e 1.0642 => 0.5321
0.8
1.107
XZ plane, ¢ == 0°, (J < Vz Interacting wavelengths [urn] (Jpm [deg] ~(Jint [deg] SHG, e+o => e 1.0642 => 0.5321
19.8
0.123
Effective nonlinear expressions in the phase-matching direction for three-wave interactions in the principal planes of KLN crystal [3.35,36]: XYplane d ooe == d31 cos ¢ ;
YZ plane d oeo == d eoo == d 32 cos () ;
XZ plane,
(J
Vz
deeo == d 31 sirr'
(J +
d 32 cos 2 (J •
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of KLN crystal are given in [3.36] Nonlinear coefficients [3.550]:
d31(1.0642Jlm) == =f1.13
±
0.15pmjV ,
220
3 Properties of Nonlinear Optical Crystals
d32(1.0642 11m) = ±l.lO ± O.lOpm/V,
Id33 (1.0642 Jlm)1
= 0.13
±
0.10pmjV .
3.3.22 CsTiOAs04 , Cesium Titanyl Arsenate (CTA) Positive biaxial crystal: 2Vz = 52.9° at A = 0.5321 urn [3.551]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z =* a,b,c; Transparency range at "0" transmittance level: 0.35 - 5.3 Jlm[3.551]; Sellmeier equations (A in um, T = 20°C) [3.551]; n2
x
= 2.34498 +
1.04863;.1 - 0.01483 _ (0.22044)2 2
2 ny
== 2.74440 +
2
== 2.53666 +
nz
A2
0.70733 A
'
2
2
A - (0.26033)
2 -
O.01526A ,
2 -
0.01711 A .
2
1.10600 A 2
A?
2
A - (0.24988)
Experimental and theoretical values of phase-matching angle and calculated values of "walk off" angle: XY plane, () == 90° In teracting wavelengths [urn]
¢exp
[deg]
¢theor
[deg]
PI [deg]
P3 [deg]
0.378
0.369
[3.551]
SHG, e+o =* e 1.3188 =* 0.6594
64.5 [3.551]
62.85
Experimental value of internal angular bandwidth [3.551]: XY plane, 0 == 90° Interacting wavelengths [Jlm]
cPpm
[deg]
A¢int
SHG, e+o => e 1.3188 => 0.6594
64.5
0.5
[deg]
3.3 Other Inorganic Nonlinear Optical Crystals
221
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of CTA crystal [3.35,36]: XYplane
+ d 32 cos2 ¢ ;
d eoe == d oee == d31 sin2 ¢
YZ plane d oeo == deoo == d 31 sin 0 ; XZ plane, 0 < Vz
dooe == d32 sin (J ; XZ plane, 0 > Vz
d oeo == deoo == d 32 sin 0 .
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of CTA crystal are given in [3.36] Nonlinear coefficients [3.551]: d31(I.0642Jlm)
==
2.1 ± O.4pmjV ,
d 32(1.0642Jlm) == 3.4 ± 0.7pmjV , d33(1.0642Jlm) == 18.1
± 1.8pmjV .
3.3.23 NaN0 2 , Sodium Nitrite
Positive biaxial crystal: 2Vz == 62.5° at A == 0.5325 urn [3.552]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z:::::} a,c,b;
Mass density: 2.168 g/cm'; Transparency range: 0.35 - 3.4 urn with the window in 5 - 8 urn range [3.553,554]; Experimental values of refractive indices:
A [urn]
nx
ny
nz
Ref.
0.5325 0.5762 1.0650 1.1523 1.3673 1.5295 1.7109
1.3475 1.3455 1.3395 1.3353
1.4147 1.4125 1.4036 1.4029 1.4018 1.4010 1.4010
1.6643 1.6547 1.6365 1.6319 1.6214 1.6160 1.6136
3.552 3.553 3.552 3.553 3.554 3.554 3.554
222
3 Properties of Nonlinear Optical Crystals
A [urn]
nx
ny
nz
Ref.
1.3997 1.3980 1.3950 1.3907 1.3880
1.6102 1.5933 1.5400 1.4950 1.4626
3.554 3.554 3.554 3.554 3.554
2.2500 3.4000 4.4000 5.4000 6.0000
Sellmeier equations (A in urn, T n2
== 1 + _0_.7_2_74_5_4_A2 _ A2 _ (0.108759)2 '
x n2
== 293 K) [3.553J:
2
== I + _0_.9_7_8_10_8_A__
y
A2-(0.105970)2'
2 1 A? + -1.616683 ---zA? - (0.149021)2 .
n -
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XZ plane, 4> == 0°, () < Vz Interacting wavelengths film] SHG, e+o =* e 1.1523 => 0.57615
XZ plane, 4>
(}exp
[deg]
Otheor
[deg]
PI [deg]
P3 [deg]
8.309#
8.531#
[3.553] 27.1 [3.553]
27.60# 34.35*
== 0°, f) < Vz
In teracting wavelengths [urn] SHG, e+e::::} 0 1.1523 => 0.57615
(}exp
[deg]
(}theor
[deg]
PI [deg]
[3.553] 34.6 [3.553]
34.56# 39.34*
9.801#
#derived from experimental data on refractive indices; *derived from Sellmeier equations.
3.3 Other Inorganic Nonlinear Optical Crystals
223
Experimental values of internal angular bandwidth [3.553]: XZ plane, 4> == 0°, 0 < Vz Interacting wavelengths [urn]
Opm [deg]
AOint [deg]
SHG, e+o ==> e 1.1523 => 0.57615
27.08
0.407
Interacting wavelengths [Jlm]
8pm [deg]
Aunt
SHG, e+e => 0 1.1523 => 0.57615
34.60
0.22
XZ plane, 4>
== 0°, 0 > Vz [deg]
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of NaNO z crystal [3.35, 36]: XYplane d ooe
== d 32 cos 4> ;
YZ plane
== d eoo == d31 cos 0 ; XZ plane, 0 < Vz d oeo
== d oee == d32 sin2 0 + d31 cos2 0 ; XZ plane, (J > Vz d eoe
deeD
== d32 sin 2 0 + d 31 cos2 0 .
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of NaN0 2 crystal are given in [3.36] Nonlinear coefficients: d31
(1.1523 urn) == 0.174 x d36 (KDP) ± 28% == 0.068 ± 0.019pmjV [3.553, 37J ,
d32(1.1523
urn) == -3.367 x
d36
(KDP)
± 0.5%
== -1.313 ± 0.004pmjV [3.553, 37J , Id33(1.06 Jlm)1
== 0.24 x d36 (KDP) ± 250/0 == 0.094 ± 0.023 pmjV [3.553, 37J .
224
3 Properties of Nonlinear Optical Crystals
3.3.24 Ba2NaNbsOlS, Barium Sodium Niobate ("Banana") Negative biaxial crystal: 2Vz = 13° [3.555]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z =} a, b, c; Mass density: 5.4076 g/cm 3 [3.555], 5.42 g/cm 3 [3.556]; Transparency range at "0" transmittance level: 0.37 - 5 urn [3.555, 557]; Linear absorption coefficient oc: A [urn]
oc [cm"]
0.5321
0.04 0.051-0.067 1.0642 Vz In teracting wavelengths [pm] SHG, 0+0 =} e 1.0642 =} 0.5321
f}exp
[deg]
75.4 [3.555]
f}theor
[deg]
[3.458]
[3.555]
74.6
75.3
Note: The PM angle values are strongly dependent on melt stoichiometry Experimental values of NCPM temperature and temperature bandwidth: along a axis
T [OC] In teracting wavelengths [urn] SHG, 0+0 => e 1.0642 =} 0.5321
1.08
=}
85 85 86-87 89
0.54
~T
[OC]
Ref.
0.45--0.47
3.558 3.559 3.300 3.555 3.560
0.45 0.5 0.42
along b axis Interacting wavelengths [urn] SHG, 0+0 =} e 1.0642 =} 0.5321
T rOC]
~
97 101
0.5
T rOC]
Ref.
3.561 3.555
Note: The NCPM temperature values are strongly dependent on melt stoichiometry
226
3 Properties of Nonlinear Optical Crystals
Best set of Sellmeier equations (l in urn, T= 293 K) [3.555]: 2 3.9495 l2 nx == 1 + l2 _ 0.04038894 '
n
2 y
3.9495 l2 == 1 + l2 _ 0.04014012 ' 3.6008 l2
1
2
nz
== + l2 _ 0.03219871 .
Calculated values of phase-matching and "walk-off" angles; YZ plane, 4J == 90° Interacting wavelengths [urn]
epm
SHG, 0+0 => e 1.0642 => 0.5321 1.3188 => 0.6594
75.03 53.44
XZ plane,
[deg]
P3 [deg] 1.384 2.442
4J == 0°, e > Vz
Interacting wavelengths [urn]
epm
SHG,o +0 => e 1.0642 :::} 0.5321 1.3188 => 0.6594
75.31 53.63
[deg]
P3 [deg] 1.372 2.450
Temperature variation of birefringence for noncritical SHG process [3.555]: along b axis (1.0642 urn :::} 0.5321 urn)
d[nz(2w) - nx(w) ]/dT == 1.05 x 10-4 K- 1
.
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of Ba2NaNbsOlS crystal [3.35,36]: XYplane d eeo == d 31sin2 4J + d 32 cos2 4J ; YZ plane d ooe == d31 sin e ;
XZ plane, d oeo
e
Vz
d ooe == d 32 sin e .
3.3 Other Inorganic Nonlinear Optical Crystals
227
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of Ba2NaNbsOlS crystal are given in [3.36]. Nonlinear coefficients: d31(1.0642Jlm)
== 40 x dl1(Si0 2 ) ± 5°A. == 12 ± 0.6pmjV[3.555, 37]
d32(1.0642 um)
== 40 x dII (Si02) ± 10% == 12 ± 1.2 pmjV [3.555, 37] ,
d 33 (1.0642 urn] == 55 x d II (Si0 2) ± 7%
== 16.5 ± 1.2 pmjV[3.555, 37] . Laser-induced damage threshold: A [urn]
't"p
0.5321
cw 450 0.05 450 0.08
1.0642
[ns]
Ithr X
10- 12 [Wjm2 ]
>0.0005 0.002 0.72 0.04 >0.025
Ref.
Note
3.561 3.562 3.563 3.562 3.558
2 kHz I kHz 2 kHz 500 MHz
Thermal conductivity coefficient [3.556]:
,,== 3.5W jmK . 3.3.25 K2Ce (N0 3)s · 2820, Potassium Cerium Nitrate Dihydrate (KCN) Negative biaxial crystal: 2Vz == 115.2° at A == 0.5461Jlm [3.550]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y, Z :::} b, C, a; Transparency range at "0" transmittance level: 0.39 - > 1.1 urn [3.550]; Linear absorption coefficient: ex < 0.03 cm- 1 at A == 1.064Jlm[3.550]; Experimental values of refractive indices [3.550]:
A [Jlm]
nx
ny
nz
0.3650 0.4005 0.4872 0.5461
1.5340 1.5238 1.5099 1.5041
1.5912 1.5775 1.5597 1.5524
1.6142 1.5999 1.5811 1.5732
228
3 Properties of Nonlinear Optical Crystals
A [urn]
nx
ny
nz
0.6476 0.7500 0.8500 0.9500 1.0500
1.4983 1.4947 1.4924 1.4905 1.4890
1.5443 1.5398 1.5365 1.5343 1.5324
1.5653 1.5603 1.5567 1.5542 1.5519
Sellmeier equations (A in urn, T == 20 °C)[3.550]: n 2 == 2.21109
x
+
n 2 == 2.33882 + y
n2 == 2.40514 +
z
A2
0.0140950 - 0.0063894 A2 - 0.0345830 '
A2
0.0193380 - 0.0079345 A2 - 0.0333504 '
A2
0.0194084 - 0.0135716 A2 - 0.0371520
.
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XY plane, f) == 90° Interacting wavelengths [Jlm] SHG, 0+0 =} e 1.0642 =} 0.5321
XZ plane,
4J ==
0°, f)
In teracting wavelengths [urn] SHG, e+o =} e 1.0642 =} 0.5321
4Jexp
[deg]
4Jtheor
[deg]
P3 [deg]
[3.550] 10.2 [3.550]
0.74
11.74
< Vz f)exp
[deg]
f)theor
[deg]
PI [deg]
P3 [deg]
1.63
1.78
[3.550]
21.5 [3.550]
22.58
Experimental value of internal angular bandwidth [3.550]: XY plane, f) == 90° Interacting wavelengths [Jlm]
4Jpm
SHG, 0+0 =} e 1.0642 =} 0.5321
10.2
[deg]
~4Jint [deg]
0.152
3.3 Other Inorganic Nonlinear Optical Crystals
229
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of KCN crystal [3.35,36]: XYplane
dooe == d 31cos
4J ;
YZ plane d oeo == deoo
== d 32 cos () ;
XZ plane, () < Vz d oee == d eoe == d31 sin
2
()
+ d32 cos 2 ()
;
XZ plane, () > Vz deeD
== d 31sin 2 () + d 32 cos 2 ()
.
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of KCN crystal are given in [3.36] Nonlinear coefficients [3.550]: d 31( 1.0642 Jlm )
== =fl.13 ± 0.15pmjV ,
d 32(1.0642 Jlm )
== ±1.10±0.10pmjV ,
Id33(1.0642 Jlm)1 == 0.13 ± 0.10pmjV . 3.3.26 K3Li2NbsOlS, Potassium Lithium Niobate Negative uniaxial crystal: no > n e ; Point group: 4mm; Mass density: 4.3 gjcm 3 [3.273]; Transparency range: 0.35 - 5 urn [3.564, 3151; Linear absorption coefficient:
a
== 0.004 cm " at A == 1.064 urn [3.315J
Experimental values of refractive indices at T = 303 K [3.517]:
A [urn]
no
ne
0.4500 0.4750 0.5000 0.5250 0.5321 0.5500 0.5750 0.6000 0.6250
2.4049 2.3751 2.3546 2.3349 2.3260 2.3156 2.3016 2.2899 2.2799
2.2512 2.2315 2.2144 2.2010 2.1975 2.1900 2.1801 2.1720 2.1645
230
3 Properties of Nonlinear Optical Crystals
l [urn]
2.2770 2.2711 2.2361 2.2080
0.6328 0.6500 0.6750 1.0642
2.1630 2.1586 2.1529 2.1120
Sellmeier equations (l in urn, T = 303 K) [3.517]: 2
n = o
n2 e
1
2
3.708l + --l2 - 0.04601
= 1+
3.349A.2
'
.
l2 - 0.03564
Experimental and theoretical values of phase-matching angle: In teracting wavelengths [urn]
fJexp
[deg]
fJtheor
[deg]
[3.517]
SHG, 0+0 => e 0.82 => 0.41
90 [3.315]
no pm
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn]
fJpm
SHG, 0+0 => e 2.9365 => 1.46825 2.098 => 1.049 1.3188 => 0.6594 1.0642 => 0.5321 1.053 => 0.5265 1.047 => 0.5235
[deg]
22.64 32.07 54.03 75.45 77.46 78.69
P3 [deg]
1.75 2.30 2.73 1.54 1.35 1.23
Effective nonlinearity expression in the phase-matching direction [3.100]:
d ooe = d31 sin fJ. Nonlinear coefficients: d 31(0.8Jlm)
= 11.8 pm/V [3.315] ,
d 31(1.0642 urn] = 19.3 x d ll (Si02 ) ± 20 %
= 5.8 ± 1.2 pm/v [3.565, 37] , d33(1.0642 urn] = 35 x d ll (Si0 2 )
± 15%
= 10.5 ± 1.5 pm/V [3.565,37] .
3.3 Other Inorganic Nonlinear Optical Crystals
3.3.27 HgGa2S4, Mercury Thiogallate Negative uniaxial crystal: no > ne ; Point group: 4; Mass density: 4.95 g/cm 3 [3.338]; Mohs hardness: 3 - 3.5; Transparency range at "0" transmittance level: 0.55 - 13 urn [3.566]; Linear absorption coefficient oc: A [urn] oc [em-I] Ref.
Note
0.53 8 11 0.96 0.25 1.06 0.1 0.25 1.2 10.6
e - wave, SHG direction
3.567 3.566 3.568 3.567 3.568 3.568
e - wave, o - wave, o .- wave, o - wave,
SFG direction SHG direction SFG direction SFG direction
Experimental values of refractive indices at T= 293 K [3.569]: A [urn]
no
ne
0.5495 0.5747 0.6009 0.6328 0.6500 1.0760 1.1500 2.6500 3.5400 7.1500 8.7300 10.400 11.000
2.6592 2.6334 2.6112 2.5890 2.5796 2.477 2.472 2.444 2.439 2.414 2.400 2.380 2.369
2.5979 2.5748 2.5549 2.5349 2.5264 2.432 2.428 2.403 2.398 2.372 2.358 2.337 2.329
Sellmeier equations (A in urn, T = 20°C) [3.569]: n2 =
6.20815221
n2 =
e
+ 63.70629851 + A2
o
6.00902670
_
225
+ 63.28065920 + A2
_
225
0.23698804
A2 - 0.09568646 ' 0.21489656
A2 - 0.09214633
.
231
232
3 Properties of Nonlinear Optical Crystals
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0+0 =} e 9.6 :::} 4.8 5.3 :::} 2.65 4.8 :::} 2.4 2.9365 =} 1.46825 2.1284 =} 1.0642 SFG, 0+0 =} e 10.6 + 1.0642 =} 0.9671 SHG, e+o =} e 5.3 :::} 2.65 4.8 :::} 2.4 2.9365 =} 1.46825 SFG, e+o =} e 10.6 + 5.3 =} 3.533 9.6 + 4.8 =} 3.2 10.6 + 1.0642 =} 0.9671
Opm
[deg]
PI [deg]
P3 [deg]
68.38 31.80 31.53 42.22 64.40
0.66 0.89 0.88 1.00 0.80
41.62
1.05
47.95 47.39 70.02
0.97 0.97 0.62
0.97 0.98 0.64
70.21 54.49 43.93
0.63 0.94 1.01
0.61 0.92 1.06
Effective nonlinearity expressions in the phase-matching direction [3.100]:
d ooe = d36 sin 8 sin 24J + d 3I sin 8 cos 24J , deoe
= doee == d36 sin 2fJ cos 21J - d31 sin 2fJ sin 21> .
Nonlinear coefficients: Id36(1.064 Jlm)1 = 80 x d ll (Si02) ± 30% = 24.0 ± 7.2 pm/V [3.566, 37] , Id36(1.064 Jlm)1 = 1.08 x d36(AgGaS2) ± 15% = 20.0 ± 3.0 pm/V [3.567, 344, 37] , Id3I(I.064 umj] = 0.33 x Id36(H gGa 2 S4)I = 6.7 ± 1.0pm/V [3.576,344,37] . Laser-induced surface-damage threshold [3.568]: A [urn]
't"p
1.064 10.6
30 cw
[ns] 0.6
> 0.00000016
3.3 Other Inorganic Nonlinear Optical Crystals
3.3.28 HgS, Cinnibar Positive uniaxial crystal: ne > no; Point group: 32; Mass density: 8.10 gjcm 3 [3.64]; Mohs hardness: 2 - 2.5 [3.64], 3 [3.338]; Transparency range at "0" transmittance level: 0.62 - 13 urn [3.570]; Linear absorption coefficient (X [3.571]: Note 0.6328 0.6729 5.3 10.6
oeoe-
1.7 1.4 0.032 0.073
wave, wave, wave, wave,
DFG direction DFG direction SHG direction SHG and DFG directions
Experimental values of refractive indices [3.570]: A [urn] no
ne
0.62 0.65 0.68 0.70 0.80 0.90 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60
3.2560 2.80 3.2064 3.00 3.1703 3.20 3.1489 3.40 3.0743 3.60 3.0340 3.80 3.0050 4.00 2.9680 5.00 2.9475 6.00 2.9344 7.00 2.9258 8.00 2.9194 9.00 2.9146 10.00 2.9108 11.00 2.9079
2.9028 2.8655 2.8384 2.8224 2.7704 2.7383 2.7120 2.6884 2.6730 2.6633 2.6567 2.6518 2.6483 2.6455 2.6433
A [urn] no
2.6414 2.6401 2.6387 2.6375 2.6358 2.6353 2.6348 2.6267 2.6233 2.6156 2.6112 2.6066 2.6018 2.5914
ne 2.9052 2.9036 2.9017 2.9001 2.8987 2.8971 2.8963 2.8863 2.8799 2.8741 2.8674 2.8608 2.8522 2.8434
Optical activity [3.194]:
A [urn]
p [degjmm]
A [urn]
p [degjmm]
0.6058 0.6131 0.6278 0.6424 0.6571 0.6681 0.6770
447 393.5 319 270.5 237.5 218 200
0.7281 0.7789 0.8296 0.8757 0.9196 0.9527 0.9967
145 113.5 92.5 74.5 65.5 59 51.5
233
234
3 Properties of Nonlinear Optical Crystals
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: Interacting wavelengths [urn] SHG, e+e:::} 10.6 =} 5.3 SFG, e+e =} 10.6 + 0.6729
(}exp
[deg]
(}theor
[deg]
[3.458] [3.362] [3.543]
0
23.0
21.3
25.3 [3.571] no pm 25.8
25.7
20.8 [3.571] 21.2 21.5 [3.572] 0 =}
0.6328
Best set of dispersion relations (A in urn, T == 20°C) [3.543]:
n2 == 7.8113 o 2 _
9 3139
n-. e
+
0.3944
A2 _ 0.1172
+2 0.5870
A -0.1166
+
604.5
A2 - 682.5 '
+2 542.6
A -540.8
.
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, e+e:::} 0 10.6 =} 5.3 9.6 =:} 4.8 5.3 =} 2.65 4.8 =} 2.4 2.65 =} 1.325 2.4 =} 1.2 SHG, o+e:::} 0 10.6 =} 5.3 9.6 =} 4.8 5.3 =} 2.65 4.8 =} 2.4 2.65 =} 1.325 2.4 =} 1.2 SFG, o+e =} 0 10.6 + 5.3 => 3.533 9.6 + 4.8 =} 3.2 SFG, e+o :::} 0 10.6 + 5.3 => 3.533 9.6 + 2.4 =} 1.92
(}pm
[deg]
21.32 19.09 14.42 14.82 23.44 26.00
PI [deg]
P2 [deg]
3.19 2.93 2.32 2.38 3.61 3.93
3.19 2.93 2.32 2.38 3.61 3.93
30.68 27.36 20.54 21.12 33.85 37.78
4.22 3.93 3.19 3.27 4.69 4.98
19.75 18.65
3.08 2.94
28.96 27.16
4.18 4.00
Effective nonlinearity expressions in the phase-matching direction [3.100]: d eeo
== d 11 cos 2() sin 34J ,
3.3 Other Inorganic Nonlinear Optical Crystals
d oeo
235
== d eoo == d 11 COS () cos 31> .
Nonlinear coefficient: d 11(10.6Jlm)
== 50± 16pmjV [3.365]:
Laser-induced surface-damage threshold [3.365]: A [Jlm]
'r p
1.06
17
[ns]
Ithr X
10- 12 [Wjm 2 ]
0.4
3.3.29 Ag3SbS3, Pyrargyrite Negative uniaxial crystal: no > ne ; Point group: 3m; Mass density: 5.83 gjcm 3 [3.64]; Mohs hardness: 2 - 2.5 [3.64]; Transparency range at "0" transmittance level: 0.7-14 urn [3.573]; Linear absorption coefficient ~:
A [Jlm] ~ [cm"] Ref. 0.967 1.064 10.6
13.5
~
0.7 0.7 ~ 0.7 0.5 0.34 0.08 0.09 >0.46
3.3.30 Se, Selenium Positive uniaxial crystal: ne > no; Point group: 32; Mass density: 4.79 g/cm3 [3.59]; Mohs hardness: 2 [3.59]; Transparency range at "0" transmittance level: 0.7 - 21 urn [3.577, 578]; Linear absorption coefficient a:
5.3 10.6
1.40 ± 0.05 1.09 ± 0.02
Ref.
Note
3.579 3.579
II
/I c c
3.3 Other Inorganic Nonlinear Optical Crystals
2.8 ± 0.5 50± 5
14 28
Ref.
Note
3.580 3.580
0 0 -
wave, 1.. c wave, 1.. c
Experimental values of refractive indices at 296 K [3.581]:
A [pm]
no
1.064 1.1523 3.3913 10.6
1.790 ± 2.737 ± 2.650 ± 2.640 ±
ne
0.008 0.008 0.01 0.01
3.608 ± 3.573 ± 3.460 ± 3.410 ±
0.008 0.008 0.01 0.01
Optical activity: A [urn] p [deg/rnm]
Ref.
0.70 0.79 0.91 1.00 1.14 3.39 10.6
3.582 3.582 3.582 3.582 3.582 3.579 3.579
440 ± 20 300 ± 15 200 ± 15 150 ± 10 100 ± 10 4.8 ± 0.5 2.5 ± 0.5
Experimental values of phase-matching angle: Interacting wavelengths [urn]
SHG, e+e => 10.6 => 5.3
(Jpm
[deg]
0
5.5 ± 0.3 [3.579] 6.5 [3.577] ~ 10 [3.583]
Effective nonlinearity expressions in phase-matching direction [3.100]: deeo
== d 11 COS 2 (J sin 3¢
d oeo
== deoo == d 11 cos (J cos 3¢
Nonlinear coefficient: d 11(10.6 urn] == 97 ± 25 pm/V [3.579]
Thermal conductivity coefficient [3.584]: T [K]
K
273 298
4.81 4.52
[WjmK],
II
c
K
[WjmK], 1.. c
1.37 1.31
237
238
3 Properties of Nonlinear Optical Crystals
3.3.31 TI3AsS3 , Thallium Arsenic Selenide (TAS) Negative uniaxial crystal: no > ne ; Point group: 3m; Mass density: 7.83 [3.585]; Mohs hardness: 2 - 3 [3.586]; Transparency range at 0.5 transmittance level for a 6 mm long crystal: 1.28 - 17 urn [3.586]; Linear absorption coefficient a:
A [urn]
< 0.02 0.082 0.038
2-12 10.6
Ref.
Note
3.585 3.454 3.586
SHG direction
Experimental values of refractive indices at 300 K [3.587]:
A [urn] no
ne
2.056 3.059 4.060 5.035 5.856 6.945 7.854 9.016 9.917 10.961 12.028
3.227 3.190 3.177 3.171 3.168 3.164 3.162 3.158 3.155 3.152 3.147
3.419 3.380 3.364 3.357 3.354 3.349 3.345 3.340 3.336 3.331 3.327
Temperature derivative of refractive indices at A == 2 - 10.6 urn (T
== 80 - 300 K) [3.587] :
~7 = -4.52 x 1O-5K- 1 ; ~~ = + 3.55 X
10- 5 K- 1
.
Sellmeier equations (A in urn, T
1
2
n
2
e
10.210 A? 0.197136
+ A2 _
no == 1
== +
2
8.993 A
27°C) [3.587]:
==
0.522 A? 625 '
+ A2 -
2
0.308 A
+~-A2-O.197136 A2-625·
3.3 Other Inorganic Nonlinear Optical Crystals
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn] SHG, 0+0 =* e 10.6 =* 5.3 9.6 =* 4.8 5.3 =* 2.65 4.8 =* 2.4 2.9365 =* 1.46825 SFG, 0 +0 =* e 10.6 + 2.65 =* 2.12 9.6 + 2.4 =* 1.92 SHG, e+o =* e 10.6 =* 5.3 9.6 =* 4.8 5.3 =* 2.65 4.8 =* 2.4 SFG, e+o =* e 10.6 + 5.3 =* 3.533 9.6 + 4.8 =* 3.2 SFG,o+e=*e 10.6 + 5.3 =* 3.533 9.6 + 4.8 =* 3.2
fJ pm [deg]
PI [deg]
P2
[deg]
P3
[deg]
19.10 18.54 24.79 27.26 48.74
2.12 2.07 2.60 2.77 3.26
25.21 27.65
2.64 2.81
26.79 26.03 35.77 39.78
2.65 2.62 3.16 3.25
2.72 2.67 3.18 3.27
23.81 25.06
2.45 2.55
2.52 2.62
34.84 36.84
3.13 3.19
3.14 3.20
Experimental values of internal angular bandwidth: Interacting wavelengths [urn]
AfJint [deg] Ref.
SHG, 0+0 =* e 9.6 =* 4.8 10.6 =* 5.3
0.27 0.30
3.588 3.589
Effective nonlinearity expressions in the phase-matching direction [3.100]: d ooe d eoe
== d 31 sin fJ - d 22 cos fJ sin 34J , == d oee == d 22 cos 2 fJ cos 34J .
Nonlinear coefficient: d+(10.6 urn) == (3.47 ± 1.04) x d+(Ag 3AsS 3 )
== 67.5 ± 31.3 pm/V [3.586,455, 37] , d+(10.6 urn) == (3.3 ± 1.0) x d+(Ag 3SbS 3 )
== 36.5 ± 12.5 pm/V [3.586, 576, 37] .
239
240
3 Properties of Nonlinear Optical Crystals
Laser-induced surface-damage threshold:
A [urn]
Lp
9.6 10.6 10.6
70 150 200
[ns]
Ithr X
10- 12 [W1m2]
> 0.054 0.1-0.17 0.16
Ref. 3.588 3.368 3.586
3.3.32 Te, Tellurium Positive uniaxial crystal: ne > no; Point group: 32; Mass density: 6.25 g/cm' [3.59]; Mohs hardness: 2 - 2.5 [3.59]; Transparency range at "0" transmittance level: 3.5 - 36 urn [3.590, 578, 591]; Linear absorption coefficient ~:
A [urn]
a
[em-I]
Ref.
Note
5.3 10.6
1.32 0.96 0.5-1.0 0.2-0.6 1.1 ± 0.4 4.4±0.04
3.451 3.451 3.576 3.592 3.580 3.580
oeeeoo-
14 28
wave, SHG direction wave, SHG direction wave, SHG direction wave, SHG direction wave, .L c wave, .L c
Two-photon absorption coefficient f3 [3.593]: Wavelengths of absorbed photons [um] 5.3 5.3
+ 5.3 + 10.6
f3 x
109 [m/W]
8 2
Experimental values of refractive indices:
A [urn] no
ne
Ref.
A [urn] no
ne
Ref.
4.0 5.0 6.0 7.0 8.0 8.5 8.8 9.3 9.7 10.2
6.372 6.316 6.286 6.257 6.253 6.260 6.258 6.255 6.252 6.249
3.578 3.578 3.578 3.578 3.578 3.590 3.590 3.590 3.590 3.590
10.6 10.8 11.4 12.0 12.8 13.7 14.0 14.7 15.9 17.2
6.247 6.246 6.243 6.240 6.235 6.231 6.230 6.227 6.222 6.216
3.590 3.590 3.590 3.590 3.590 3.590 3.590 3.590 3.590 3.590
4.929 4.864 4.838 4.821 4.809 4.801 4.799 4.798 4.795 4.793
4.792 4.791 4.789 4.785 4.781 4.776 4.775 4.772 4.767 4.761
3.3 Other Inorganic Nonlinear Optical Crystals
A [urn]
no
ne
Ref.
A [urn]
no
ne
Ref.
18.9 20.8 23.4
4.753 4.744 4.734
6.210 6.203 6.196
3.590 3.590 3.590
26.3 28.0 30.3
4.722 4.716 4.706
6.188 6.183 6.180
3.590 3.590 3.590
241
Optical activity [3.594]:
A [)lm]
p [deg/mm]
3.94 4.34 5.00 5.76 7.02
140 93.3 55.6 37.1 23.4
Experimental values of phase-matching angle (T = 293 K) and comparison between different sets of dispersion relations: In teracting wavelengths [urn] SHG, e + e=>o 10.6 => 5.3
23.4=> 11.7 26.6 => 13.3 28.0 => 14.0 SHG, 0 + e => e 10.6 => 5.3
(}exp
[deg]
[deg]
(}theor
[3.543] [3.362]# [3.362]* 14.17 [3.595] 14.83 [3.596] 14.07 [3.590] 14.75 [3.597] 12.19 [3.362] 13.33 [3.362] 14.07 [3.362]
14.28
14.22
15.28
6.12 5.36 5.09
9.14 9.56 9.82
12.49 13.53 14.07
20.42 [3.598]
20.22
20.13
21.64
Note: [3.362]# - a set for 4.0-14.0 urn spectral range; [3.362]* - a set for 8.5-30.3 urn spectral range. Best set of dispersion relations for 4.0-14.0 urn spectral range (A in urn, T = 293 K) [3.362]: n 2 = 18.5346 + o
2
4.3289A? + 3.7802 A2 _ 3.9810 A2 - 11813 ' 2
n2 e
2
= 29.5222 + 9.30682 + 9.2352 A2 _ 2.5766 A2 - 13521
.
242
3 Properties of Nonlinear Optical Crystals
Calculated values of phase-matching and "walk-off" angles: Interacting wavelengths [urn]
Opm
[deg] PI [deg]
P2 [deg]
SHG, e + e=}o 28 =* 14 14 =* 7 10.6 =} 5.3 9.6 =} 4.8
9.82 10.90 14.22 15.90
SHG, 0 + e=}o 28 =* 14 14 =* 7 10.6 =} 5.3 9.6 =} 4.8 SFG,o+e=}o
13.89 15.43 20.13 22.52
5.58 6.19 7.93 8.77
28 + 14 =} 9.333
11.32
4.59
3.98 4.42 5.72 6.36
3.98 4.42 5.72 6.36
SFG, e+o =} 0 28
+ 14 =} 9.333
16.09
6.44
Experimental values of internal angular bandwidth: Interacting wavelengths [urn] SHG, e + e=}o 10.6 =} 5.3
Opm
[deg]
14.17 14.5
~
L\oint [deg]
Ref.
0.19 0.20
3.595 3.451
Effective nonlinearity expressions in the phase..matching direction [3.100]: deeo
d oeo
== d11 COS 2 0 sin 3cjJ, == deoo == d 11 cos 0 cos 3cjJ.
Nonlinear coefficient: d 11(10.6 urn) == 7.2 x d36(GaAs) ± 40/0 == 598 ± 25 pm/V [3.576,37] ,
d 11(10.6Jlm)
== 670±209 pm/V [3.599] ,
d ll (28 urn) == 570 ± 190 pm/V (3.590] .
Laser-induced surface-damage threshold:
10.6
cw 190 150
0.0000015 0.1-0.6 0.02 - 0.04
3.599 3.365 3.599
3.4 Other Organic Nonlinear Optical Crystals
243
Thermal conductivity coefficient [3.584]: T
[K]
K
273 298
[W/mK], II
K
C
3.60 3.38
[W/mK], 1- C
2.08 1.97
3.4 Other Organic Nonlinear Optical Crystals 3.4.1
C12H22011,
Sucrose (Saccharose)
Negative biaxial crystal: 2Vz == 132.3° at A == 0.5321 urn [3.600]; Point group: 2; Assignment of dielectric and crystallographic axes: Y II b, the axes a and c lie inXZ plane, the angle between them is p == 103.5°, the angle between the axes Z and c is a == 23.5° (Fig. 3.5) [3.600]; Mohs hardness: > 2.5 [3.600]; Transparency range at "0" transmittance level: 0.19 - 1.42 urn [3.600]; Experimental values of refractive indices [3.600]:
A [urn] nx
ny
nz
0.5321 1.5404 1.5681 1.5737 1.0642 1.5278 1.5552 1.5592
z
c
x a
Sellmeier equations (A in urn, T n2 x
=
1.8719 + 0.4660 A? A2 - 0.0214
=
Fig. 3.5. Dielectric (X, Y, Z) and crystallographic (a, b, c) axes of sucrose crystal. The Y axis is parallel to the b axis and normal to the plane of the figure
20° C) [3.600]:
_ 0.0113;.2
244
3 Properties of Nonlinear Optical Crystals
= 1.9703 +
n2 Y
n2
= 2.0526 +
Z
0.4502A.2 - 0.0101 A.2
A? -
0.0238
'
0.3909 A.2 - 0.0187 A.2 0.0252
A? -
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XY plane, f) == 90° In teracting wavelengths [urn]
SHG, e + 0 => e 1.0642 => 0.5321 XZ plane,
l/J == 0°, f)
e 1.0642 => 0.5321
[deg]
;
dooe
yz plane
d eeo == d 25 sin(20) d oeo == d eoo == d 21 cos 0 ; XZ plane, 0 < Vz
d eoe == d oee == d 21 cos 2 0 + d 23 sin 2 0 XZ plane, 0
>
d25
sin 20 ;
Vz
d eeo == d 21 cos 2 f) + d 23 sin 2 fJ -
d25
sin 2fJ .
Laser-induced surface-damage threshold [3.600]:
A [Jlm]
Lp
1.06
10
[ns]
Ithr X
>5
10- 12 [W1m2 ]
3.4 Other Organic Nonlinear Optical Crystals
245
3.4.2 L-Arginine Phosphate Monohydrate (LAP) Negative biaxial crystal: 2Vz == 141.3° at A == 0.5321 urn [3.112]; Point group: 2; Assignment of dielectric and crystallographic axes: Y II b, the axes a and c lie in XZ plane, the angle between them is f3 == 98°, the angle between the axes Z and c is a == 35° (Fig. 3.6) [3.112]; Transparency range at "0" transmittance level: 0.23 - 1.25 urn [3.112]; Linear absorption coefficient a:
A [urn]
a [cnr ']
Ref.
0.1 0.01 < 0.01 0.032 0.055 0.051 1.040 0.113 0.219 0.315 1.053 0.09 1.0642 0.097 0.145 0.184
3.601 3.66 3.112 3.112 3.112 3.112 3.112 3.112 3.112 3.66 3.112 3.112 3.112
0.230 0.5265 0.5321 0.910
Note
along X along Y along Z along X along Y along Z along X along Y along Z
Z c
x a
Fig. 3.6. Dielectric (X, Y, Z) and crystallographic (a, b, c) axes of LAP and DLAP crystals. The Yaxis is parallel to the b axis and normal to the plane of the figure
Sellmeier equations (A in urn, T == 25°C) [3.112]: n2
x
== 2.2439 +
A2
0.0117 - 0.0111 A2 - 0.0179 '
246
3 Properties of Nonlinear Optical Crystals
n2
== 2.4400 +
Y
n2
I
== 2.4590 +
Z
0.0158 - 0.0212 A? 0.0191 '
;? -
0.0177
;? _ 0.0226
- 0.0162 A,2 '
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XY plane, 0 == 90° In teracting wavelengths [urn] SHG, 0 + 0 => e 0.5321 => 0.26605 1.0642 => 0.5321 SFG, 0 + 0 => e 1.0642 + 0.5321 => =} 0.35473 SHG, e + 0 => e 1.0642 => 0.5321 SFG, e + 0 => e 1.0642 + 0.5321 => => 0.35473
XZ plane,
4J
[deg] PI [deg]
4Jtheor
P3 [deg]
[3.112] 60 [3.112] 25.5 [3.112]
61.65 24.02
2.498 1.919
35.4 [3.112]
35.73
2.618
40.8 [3.112]
40.00
2.290
2.485
43.2 [3.112]
46.28
2.302
2.711
== 0°, f) < Vz
Interacting wavelengths [prn]
SHG, e + 0 => e 1.0642 ==> 0.5321 SFG, e + 0 => e 1.0642 + 0.5321 0.35473
~
[deg]
4Jexp
Oexp
[deg]
Otheor
[deg] PI [deg]
P3 [deg]
[3.112] 40 [3.112]
40.59
2.568
2.774
34.8 [3.112]
33.86
2.381
2.891
~
Effective nonlinearity expressions in the phase-matching direction [3.35]: XY plane
d ooe d eoe
== d 23 cos 4J , == d oee = d25 sin2¢;
yz plane
deeo == d25 sin 28 ,d oeo == d eoo == d 2I cos 0 ;
XZ plane, 0 < Vz
== d oee == d 21cos2 0 + d23 sin2 0 - d 25 sin 20 ; XZ plane, 0 > Vz d eoe
d eeo
== d 21cos 2 0 + d 23 sin2 0 - d 25 sin 20 .
Nonlinear coefficients [3.112, .37]:
== 0.40 pm/V , d 22(1.0642 urn) == 0.37 pm/V, d 23(1.0642 um) == -0.84 pm/V, d 25(1.0642 um) == -0.58 pm/V. d21(1.0642 um)
Laser-induced damage threshold:
A [urn]
Lp
[ns]
0.5265
20 0.6 1.053 25 1 1.0642 1
Ithr X
10- 12 [W/m 2 ]
Ref. 3.66 3.66 3.66 3.66 3.112
300 600 130 630 100-130
Thermal conductivity coefficient [3.602]: K == 0.59 W /mK. 3.4.3 Deuterated L-Arginine Phosphate Monohydrate (DLAP)
Negative biaxial crystal: 2Vz == 142.6° at A == 0.5321 urn [3.112]; Point group: 2; Assignment of dielectric and crystallographic axes: Y II b, the axes a and c lie in XZ plane, the angle between them is f3 == 98°, the angle between the axes Z and c is a == 35° (Fig. 3.6) [3.112]; Mass density: ~ 1.5 g/crrr' [3.603]; Transparency range at "0" transmittance level: 0.22 - 1.30 urn [3.112]; Linear absorption coefficient a:
A [urn]
a [cm"] Ref.
0.074 0.131 0.184 0.3547 0.025 0.053 0.039 0.5265 0.01 0.5321 < 0.01 0.910 0.028 0.037 0.266
3.112 3.112 3.112 3.112 3.112 3.112 3.66 3.112 3.112 3.112
Note along along along along along along
X Y
Z X Y
Z
along X along Y
A [urn] 1.040
1.053 1.064
1.180
a [em-I] Ref.
Note
0.044 0.012 0.014 0.009 0.02 0.012 0.014 0.009 0.385 0.394 0.557
along along along along
3.112 3.112 3.112 3.112 3.66 3.112 3.112 3.112 3.112 3.112 3.112
Z X Y
Z
along X along Y along Z along X along Y along Z
Temperature derivative of refractive indices [3.604]: A [11m] dnx/dT x 105 [K- 1]
dny/dT x 105 [K- 1]
dnz/dT x 105 [K- 1]
0.5321 -3.64 1.0642 -3.73
-5.34 -5.30
-6.69 -6.30
Sellmeier equations (2 in J.1m, T = 25°C) [3.112]: n2 x n2
:=
:=
2.2352 + 2.4313 +
y
n 2 =2.4484+
z
0.0118
;? _ 0.0146
_ 0.00683 A2
'
0.0151 _ 0.0143 A2 0.0214 '
;? 22
0.0172 -O.Ol15A? _ 0.0229
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XY plane, 0 == 90° In teracting wavelengths [um] SHG, 0 + 0 => e 1.0642 => 0.5321 SHG, e + 0 => e 1.0642 => 0.5321
.xz plane, 4> =
4>exp
[deg]
4>theor
[deg] PI [deg] P3 [deg]
[3.112] 22.2 [3.604]
22.98
1.852
37.5 [3.604]
37.81
2.290
Otheor [degJ [3.112]
PI [deg] P3 [degJ
43.34
2.588
2.446
0°, 0 < Vz
Interacting wavelengths [urn] SHG, e + 0 => e 1.0642 => 0.5321
Oexp
[deg]
42.8 [3.604]
2.785
3.4 Other Organic Nonlinear Optical Crystals
249
Experimental values of internal angular, temperature and spectral bandwidths
(T == 20°C) [3.603]: XY plane, 0 == 90° In teracting wavelengths [urn] SHG,
0
= 90°
[deg]
Interacting wavelengths [pm]
()pm
SHG, 0 + 0 =} e 1.0642 =} 0.5321
8 [3.611]
3.4 Other Organic Nonlinear Optical Crystals
l/J == 0°, () < Vz
XZ plane,
Interacting wavelengths [Jlm] SHG, 1.0642
0
+0
=}
255
=}
(}pm
[deg]
e
0.5321
42 [3.611]
Experimental value of internal angular bandwidth [3.611]: YZ plane, 4> == 90° Interacting wavelengths [Jlm] SHG, 1.0642
0
+0
=}
=}
(}pm
[deg]
L\(}int
[deg]
e
8
0.5321
0.098
Effective nonlinearity expressions in the phase-matching direction in the principal planes of BAMB crystal [3.35, .36]: XY plane d eeo
== d31 sin2 4> + d32 cos2 4> ;
yz plane
d ooe
== d31 sin () ;
XZ plane, () < Vz d oeo
== d eoo == d32 sin () ;
XZ plane, () > Vz
d ooe == d32 sin () ; Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of BAMB crystal are given in [3.36] Nonlinear coefficients [3.611, .37]: d31 (1.0642 um) == 0.95 x d36(KDP) ± 20% == 0.37 ± 0.07 pm/V, d32(1.0642 um) == 2.45 x d36(KDP) ± 20% == 0.96 ± 0.19 pm/V, d 33(1.0642 urn) == 1.8 x d36(KDP) ±200iO == 0.70±0.14 pm/V .
Laser-induced surface-damage threshold [3.611]:
1.06
40
2
256
3 Properties of Nonlinear Optical Crystals
3.4.8 3-Methoxy-4-hydroxy-benzaldehyde (MHBA)
Positive biaxial crystal: 2Vz == 89.5° at A. == 0.5461 um [3.612]; Point group: 2; Assignment of dielectric and crystallographic axes: X, Y,Z =} a,b,c; Calculated mass density: 1.34 g/cm! [3.613]; Mohs hardness: 1.67 [3.613]; Transparency range at "0" transmittance level: 0.37 - 2.2 urn [3.612]; Linear absorption coefficient rx [3.612]:
A [urn]
rx [em-I)
0.415 0.532 0.830 1.064
1.42 0.95 0.53 0.53
Experimental values of refractive indices [3.612]: A. [urn]
nx
0.4047 0.4358 0.4471 0.5461 0.5875 0.5893 0.6563 0.6678 0.7057
1.63352 1.60345 1.59644 1.55840 1.55143 1.55127 1.53996 1.53673
ny
nz
1.89349 1.70018 1.69045 1.69039 1.68352 1.67963 1.67668
1.80896 1.79235 1.77105 1.76812
The Sellmeier equations given in [3.612] are incorrect. Experimental values of the phase-matching angle: == 90°
XY plane, ()
Interacting wavelengths [urn]
1>pm
SHG, 0 + 0 =} e 0.83 =} 0.415 1.0642 =} 0.5321 SHG, e + 0 =} e 0.83 =} 0.415
16 [3.612] 11 [3.612]
[deg]
58 [3.612]
3.4 Other Organic Nonlinear Optical Crystals
yz plane,
== 0°, (J
Interacting wavelengths [~m]
(Jpm
[deg]
L\(Jint
[deg]
SHG, e + e=}o 1.0642 =} 0.5321
68
0.052
Effective nonlinearity expressions in the phase-matching direction [3.35]: XY plane d ooe
== d 23 cos 4> ;
d eoe == d oee == d 25 sin 24> ;
yz plane d eeo
== d 25 sin 2(J
;
d oeo == d eoo == d 21 cos () ; XZ plane, (J < Vz
d eoe == d oee == d 21cos 2 () + d23 sin 2 (J - d25 sin 2{) XZ plane, (J > Vz d eeo ==
d 21 cos
2
(J
+ d23 sin 2 (J -
d25
sin 2(J .
;
257
258
3 Properties of Nonlinear Optical Crystals
Nonlinear coefficients [3.612, 37]: d2l (1.0642 urn) == 3.9 ± 0.8 pm IV
,
d22(1.0642 urn) == 9.8 ± 1.0 pm/V, d23(1.0642 urn) == 13.0 ± 1.3 pm/V,
== 3.2 ± 0.6 pm/V
d2s(I.0642 urn)
.
Laser-induced damage threshold [3.612]: A. [~m]
Lp
[ns]
1.064 10
10- 12 [W1m2 ]
[the X
20
3.4.9 2-Furyl Methacrylic Anhydride (FMA) Positive uniaxial crystal: ne > no; Point group: 4mm; Transparency range at "0" transmittance level: 0.38 - 1.1 urn [3.614]; Experimental values of refractive indices [3.614]: A. [~m] no
ne
0.4305 0.4535 0.4880 0.5145 0.5321 0.6328 0.8330 1.0642 1.1523
2.137 2.064 2.007 1.983 1.958 1.887 1.841 1.821 1.811
1.751 1.721 1.691 1.685 1.671 1.641 1.619 1.612 1.617
Sellmeier equations (A. in urn, T = 20°C) [3.614]: n2 o
n2
=
1.804 + 0.6884,1.2 + 0.0527 ,1.2 A.2 - 0.08301 '
= 2.097 +
e
2
1.l090.-t
A.
2
-
0.10172
-
0.008748.-t 2
.
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: Interacting wavelengths [urn]
SHG, e + 0 =:;> 0 1.0642 =:;> 0.5321
(}exp
[deg]
(}theor
[deg]
PI [deg]
[3.614] 51.2 [3.614] 50.80
6.766
3.4 Other Organic Nonlinear Optical Crystals
Experimental values of NCPM temperature [3.614]: Interacting wavelengths [urn] SHG, e + 0 =} 0 0.9038 =} 0.4519 0.9076 =} 0.4538 0.9108 =} 0.4554
o 19 38
Experimental value of internal angular bandwidth [3.614]: In teracting wavelengths [pm] SHG, e + 0 =} 0 1.0642 =} 0.5321
Opm [deg] AOint [deg]
0.031
51.2
Temperature tuning of noncritical SHG [3.614]: Interacting wavelengths [J.lm]
dAI/dT [nm/K]
SHG, e + 0 =} e 0.9076 =} 0.4538
0.18
Effective nonlinearity expression in the phase-matching direction [3.100]: d oeo
== d eoo == d 31 sin 0 .
Nonlinear coefficients [3.614, 37]: d 31 (1.0642 11m) == 12 pm/V,
d33(1.0642 J.1m) == 18 pm/V. 3.4.10 3-Methyl-4-nitropyridine-l-oxide (POM) Positive biaxial crystal: 2Vz =: 68.87° at A == 0.5461 urn [3.615]; Point group: 222; Assignment of dielectric and crystallographic axes: X, Y,Z =} c,a,b; Transparency range: 0.4 - 2.3 urn [3.615]; Linear absorption coefficient a: A [J.lm] ex [em-I] Ref.
0.5321 1.88 1.2 1.0642 0.77
3.615 3.616 3.615
259
3 Properties of Nonlinear Optical Crystals
260
Experimental values of refractive indices [3.615]: A [urn]
nx
ny
nz
0.435 0.468 0.480 0.509 0.532 0.546 0.579 0.644 1.064
1.717 1.690 1.682 1.668 1.660 1.656 1.648 1.637 1.625
1.809 1.793 1.766 1.750 1.742 1.728 1.709 1.668
2.114 2.082 2.028 1.997 1.981 1.953 1.915 1.829
Sellmeier equations (A in urn, T = 20°C) [3.615]: n2
= 2.4529
+
x
0.1641 ;,.1 - 0.1280 '
A2
n2 = 2.4315 + 0.3556 ;,.2
A2
y
n2 = 2.5521
+
Z
-
_ 0.0579 ;,.2
0.1276 2
0.7962.-t
2-O.1289
_
0.0941.-t 2
.
A
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: .xz plane, 4> == 0°, () > Vz Interacting wavelengths [urn] SHG, e+e ~ 0 1.0642 => 0.5321 1.3188 => 0.6594 1.34
~
0.67
()exp
[deg]
()theor
[deg] PI [deg]
[3.615]
54.3 [3.615] 44.2 [3.617] 43.8 [3.617]
6.640 6.010 5.943
54.12 45.28 44.90
Experimental values of internal angular bandwidth: XZ plane, 4> = 0° Interacting wavelengths [urn]
()pm
[deg]
A()int
[deg]
Ref.
SHG, e + e=>o 1.0642 ~ 0.5321 1.3188 =} 0.6594 1.34 =} 0.67
54.3 44.2 43.8
0.025 0.021 0.020
3.615 3.617 3.617
3.4 Other Organic Nonlinear Optical Crystals
261
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of POM crystal [3.35]: XY plane
d eoe
:=:
d oee
:=:
d 14 sin 24> ;
YZ plane
deeo
:=:
d 14 sin 20 ;
XZ plane, 0 < Vz d eoe
:=:
d oee
:=:
XZ plane, () >
deeo
:=:
d 14 sin 2()
;
Vz
d 14 sin 2()
;
Nonlinear coefficients [3.615,37]: d I4(1.064 urn) :=: 20 x dll(Si0 2 ) ± 15%
:=:
d I 4(1.064 urn) :=: 13.5 x d36(KDP) ± 10%
6 ± 0.9 pm/V, :=:
5.3 ± 0.5 pm/V ,
Laser-induced damage threshold: A [urn]
'r p
[ns]
15 0.02 0.025 0.5927 1 0.62 0.0001 1.0642 0.02 0.5321
Ithr X
10- 12 [W1m 2]
0.5 > 1.5 > 2.7 1 10000 (?) > 20
Ref. 3.616 3.615 3.616 3.618 3.619 3.615
3.4.11 Tbienylchalcone (T-17)
Positive biaxial crystal: 2Vz :=: 82.6° at A :=: 0.5321 urn [3.230]; Point group: 2; Assignment of dielectric and crystallographic axes: Y /I b, the axes a and c lie in XZ plane, the angle between them is p :=: 109.9°, Z II a (Fig. 3.7) [3.230]; Mass density: 1.27 g/cm! [3.230]; Vickers hardness: 17 [3.230]; Transparency range at "0" transmittance level: ~ 0.4 - 1.06 um [3.230];
262
3 Properties of Nonlinear Optical Crystals Fig.3.7. Dielectric (X, Y, Z) and crystallographic (a, b, c) axes of T-17 crystal. The Y axis is parallel to the b axis and normal to the plane of the figure
Z(a)
x c
Sellmeier equations n2 == 2.6311
+
X
n 2 == 2.8265 +
(A,
in urn, T = 20° C) [3.230]:
0.059014 A,2 - 0.121160
0.037232
+ 0.25553
x 10- 5 A,2
'
- 3.02020 x 10- 5 A,2
A,2 - 0.098256
Y
n 2 == 3.0468
+
Z
0.078174
' - 0.61590 x 10- 5 A,2 .
A,2 - 0.098845
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XZ plane, 4> == 0°, e > Vz Interacting
{}exp
wavelengths [urn] SHG, e+e 1.6042
~
[deg]
{}theor
[deg] PI [deg]
[3.230]
~ 0
0.5321
61.6 [3.230] 63.87
3.532
Experimental values of internal angular and temperature bandwidths [3.230]: == 0°, {} > Vz
XZ plane,
Interacting wavelengths SHG, e+e 1.0642
~
(Jpm
[deg] Atf°t [deg] Atf°t [deg] AT [deg]
[~m] ~ 0
0.5321
61.6
0.030
0.690
2.2
3.4 Other Organic Nonlinear Optical Crystals
Effective nonlinearity expressions in the phase-matching direction [3.35]: XYplane dooe
= d23 cos<jJ ,
d eoe = d oee
d25
::=
sin 24> ,
YZ plane deeo d oeo
= d25 sin 2f) , = deoo ::= d21 cosf) ,
XZ plane, f) > Vz d eoe
::=
d oee
== d21 cos 2f) + d23 sin 2 f) -
d25
sin 2f) ;
XZ plane, f) > Vz deeo
::=
2
d21 COS ()
+ d23
sin 2 () -
d 25
sin 2() .
Nonlinear coefficients [3.230, 37]: XZ plane, >
o r.
d eeo ( I.0642
=}
0.5321 urn) ::= 0.226
X d 21
+ 0.774
X d23 -
0.837
= 6.3pmjV.
3.4.12 5-Nitrouracil (5NU)
Positive biaxial crystal: 2Vz ::= 92.9° at A. ::= 0.546 urn [3.620]; Point group: 222; Assignment of dielectric and crystallographic axes: X, Y,Z =} b,c,a ; Transparency range: 0.41 - 2.4 urn [3.620]; Experimental values of refractive indices [3.620]: A.[~m]
nx
ny
nz
0.435 0.468 0.480 0.509 0.518 0.546 0.579 0.589 0.636 0.644 1.0642 1.3188
2.0051 1.9737 1.9668 1.9537 1.9411 1.9315 1.9190 1.9135 1.9014 1.9010 1.8517 1.8362
1.7797 1.7566 1.7500 1.7441 1.7375 1.7242 1.7176 1.7156 1.7070 1.7050 1.6799 1.6719
1.6351 1.6113 1.6065 1.5958 1.5894 1.5850 1.5787 1.5758 1.5694 1.5670 1.5341 1.5248
X d25
263
264
3 Properties of Nonlinear Optical Crystals
Sellmeier equations (A, in urn, T == 20°C) [3.620]: n 2 = 2.390 x
+
= 1.892
+
n2
1.033 A?
A,2 - 0.0700
0.870
-
0.0549
A?
'
A?
A,2 - 0.0599 '
Y
n 2 = 2.098
z
+
0.290
A? -
0.0485
A,2 - 0.0947
A? .
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XZ plane, ¢ == 0°, () < Vz Interacting wavelengths [J.lm]
()exp
()theor
[deg] PI [deg]
[3.620]
SHG, e + e=}o 1.0642 =} 0.5321 1.338 =} 0.669 XZ plane, ¢
[deg]
37.2 [3.620] 40.2 [3.620]
34.41 36.79
10.46 10.58
== 0°, () > Vz
Interacting wavelengths [urn] SHG, 0 + e =} e 1.0642 => 0.5321 1.338 =} 0.669 1.907 =} 0.9535
(Jexp
[deg]
(Jtheor
[deg] PI [deg]
P3 [deg]
[3.620] 67.7 [3.620] 60.0 [3.620] 61.2 [3.620]
67.60 59.05 56.57
6.56 8.52 9.12
6.91 8.74 9.02
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of 5-NU crystal [3.35]: XYplane d eeo
== d l 4 sin 2¢ ;
YZ plane
d eoe == d oee == d 14 sin 2() ; XZ plane, () < Vz
== d 14 sin 2() ; XZ plane, () > Vz d eoe == d oee == d 14 sin 2() . d eeo
3.4 Other Organic Nonlinear Optical Crystals
265
Nonlinear coefficient: d I 4(1.064Jlm)
== 8.4± 1.3pm/V [3.620] .
Laser-induced damage threshold [3.620]:
A [urn]
!p
0.532 0.593 1.0642 1.338
6 9 10 0.16
I thr
[ns]
X
10- 12 [W1m2 ]
10 10 30 68
3.4.13 2-(N-Prolinol)-5-nitropyridine (PNP) Negative biaxial cyrstal: 2Vz == 64.6° at A = 0.58 urn [3.621]; Point group: 2; Assignment of dielectric and crystallographic axes of PNP is given in [3.622]; Transparency range at "0" transmittance level [3.621]: 0.49 - 2.08 urn along X, Y axes; 0.466 - 2.3 urn along Z axis; Experimental values of refractive indices [3.621]:
A [um] nx
ny
nz
0.4880 0.5145 0.580 0.600 0.6328 1.0642
1.929 1.873 1.813 1.801 1.788 1.732
1.477 1.474 1.468 1.468 1.467 1.456
2.239 2.164 2.040 1.990 1.880
Sellmeier equations (A in urn, T n2
= 2.3454 +
x n2
= 2.5658 +
y
n2
z
= 2.0961 +
= 20°C) [3.621]:
1.029757 A? _ (0.3830)2 '
A2
0.375380 A?
A2 - (0.4006)2 ' 0.029386 A? A2 _ (0.4016)2
.
Experimental and theoretical values of phase-matching angle and calculated value of "walk-off" angle:
266
3 Properties of Nonlinear Optical Crystals
< Vz
XZ plane, ¢ = 0°, (J
Interacting wavelengths [prn] SHG,e+e=}o 1.0642 =} 0.5321
(Jexp
[deg]
(Jtheor
[deg]
PI [deg]
[3.621] 21 [3.621] 11.92
7.349
Effective nonlinearity expressions in the phase-matching direction [3.35]: XYplane d eeo = d 25 sin 2¢ , d oeo
= d eoo = d23 cos ¢ ;
YZ plane d ooe == d 21 cos () , d eoe
== d oee = d25 sin 2(J ;
XZ plane, (J < Vz d eeo = d21
cos 2 () + d23 sin 2 () -
XZ plane, () > d eoe
== d oee =
d25
sin 20 ;
Vz d21
cos 2 () + d23 sirr' ()-
d 25
sin 2() .
Nonlinear coefficients [3.622]: d21
(1.064 urn) == 48 ± 11 pm/V,
d22(1.064J,!m) = 17±4pm/V.
3.4.14 2-Cyclooctylamino-5-nitropyridine (COANP) Positive biaxial crystal: 2Vz == 36.13° at A = 0.547 urn (at A == 0.497 urn COANP becomes uniaxial) [3.623]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z =} c,a,b ; Mass density: 1.24 g/cm' [3.624]; Transparency range at 0.5 transmittance level for 0.9 mm long crystal: 0.47 - 1.5 urn (along a axis) [3.624]; Linear absorption coefficient a [3.624]:
A [J.lm]
a [em-I]
0.532 1.064 1.35
3 0.8 o 1.0642 => 0.5321
63.6 [3.624]
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of COANP crystal [3.35, 36]: XYplane d ooe ==
d32
sin 4J ;
YZ plane d eeo
== d 32 sirr' (J + d 31 cos2 ()
;
XZ plane, () < Vz
== d31 cos () ; XZ plane, () > Vz d oeo == d eoo == d 31 cos () . d ooe
Effective nonlinearity expressions for three-wave interactions in the aribitrary direction of COANP crystal are given in [3.36] Nonlinear coefficients [3.624, 623, 37]: d 31(1.0642Jlm)
== 11.3 ± 1.5pmjV ,
d32(1.0642Jlm)
== 24± 12pmjV ,
d 33(1.0642 urn) == 10.8 ± 1.5 pm/V .
Laser-induced damage threshold [3.624]:
A [urn]
7:p
1.064
250
[ns]
Ithr X
10- 12 [Wjm 2 ]
> 0.015
268
3 Properties of Nonlinear Optical Crystals
3.4.15 L-N-(5-Nitro-2-pyridyl)leucinol (NPLO) Positive biaxial crystal: 2Vz == 43° at A == 0.514 urn [3.625]; Point group: 2; Assignment of dielectric and crystallographic axes: Y II b, the axes a and c lie in XZ plane, the angle between them is the angle between the axes Z and c is rx == 56° (Fig. 3.8) [3.625]; Mass density: 1.24 g/cm" [3.625]; Vickers hardness: 18 [3.625]; Transparency range at "0" transmittance level: 0.47 - > 1.06 um; Experimental values of refractive indices [3.625]:
A [J.lm]
nx
0.4880 1.470 0.5145 1.463 0.6328 1.457 1.0642 1.451
ny
nz
1.712 1.681 1.631 1.598
2.218 2.116 1.933 1.812
p ==
110.4°,
Sellmeier equations (A in um , T == 20°C) [3.625]: n2 ==2.1240+
x
n2 == 2.5607 + y
n2 == 3.2123 + Z
0.0011
A2 - 0.2108 0.0257
A2 - 0.1700 A2
-0.0174A2
' _ 0.0299 A2 '
0.1302 _ 0.0559 A2 - 0.1625
.
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle:
z c
x
a
Fig. 3.8. Dielectric (X, Y, Z) and crystallographic (a, b, c) axes of NPLO crystal. The Y axis is parallel to the b axis and normal to the plane of the figure
3.4 Other Organic Nonlinear Optical Crystals
XZ plane, ¢ == 0°, (J < Vz In teracting wavelengths [urn]
(Jexp
SHG, e + e=}O 1.0642 => 0.5321
(Jtheor [deg] PI [deg] P3 [deg] [3.625]
[deg]
33 [3.625]
30.52
9.811
14.123
XZ plane, ¢ == 0° , (J > Vz
«;
Interacting wavelengths [J.lm] SHG, e+e => 0 1.0642 => 0.5321
(Jtheor [deg] PI [deg] [3.625]
[deg]
12.496
51.7 [3.625] 55.30
Experimental values of the internal angular bandwidth [3.625]: XZ plane, ¢ == 0°, (J < Vz Interacting wavelengths [J.lm]
(Jpm
SHG, e+o => e 1.0642 => 0.5321
33
[deg] ~(Jint [deg] 0.12
XZ plane, ¢ == 0° , (J > Vz Interacting wavelengths [urn]
SHG, e+e =>
(Jpm
[deg] ~(Jint [deg]
51.7
0.11
0
1.0642 => 0.5321
Effective nonlinearity expressions in the phase-matching direction [3.35]: XYplane
d ooe == d23 cos ¢ , d eoe
== d oee == d 25 sin2¢ ;
YZ plane d eeo == d25 sin 2(J ,
== d eoo == d21 XZ plane, (J < Vz
cos () ;
d eoe
== d oee == d21 XZ plane, (J > Vz
cos 2 () + d23 sin
d eeo == d21 cos 2 ()
+ d23
d oeo
sin 2 f)
-
2
() -
d 25 sin 2()
d25 sin 2() .
;
269
270
3 Properties of Nonlinear Optical Crystals
Nonlinear coefficients [3.625, 37]: XZ plane, () < Vz d eoe(I.0642:::} 0.5321 urn) = d oee(I.0642 :::} 0.5321 urn) = 0.703 x d 21 + 0.297
X d23 -
0.914
X d25
X d23 -
0.935
X d25
= 2.7pm/V; XZ plane,
f}
> Vz
d eeo(I.0642 :::} 0.5321J.lm) = 0.322 x d 21 + 0.678 =
33.2 pm/V.
Laser-induced surface-damage threshold [3.625]: 10- 12 [W/m2]
A [Jlm]
Lp
1.064
8
3.4.16
C~4(N02)2' m-Dinitrobenzene
[ns]
Ithr X
60
(MDNB)
Negative biaxial crystal: 2Vz = 51.15° at A = 0.5321J.lm [3.611]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z:::} a,b,c ; Mass density: 1.57 g/cm': Transparency range at "0" transmittance level: 0.48 - 1.57 urn [3.611]; Experimental values of refractive indices [3.611]: ny
0.436 0.492 0.532 0.546 0.577 0.579 0.589 0.633 1.064 1.153
1.8025 1.7731 1.7592 1.7553 1.7480 1.7476 1.7456 1.7381 1.7093 1.7072
1.7361 1.7104 1.6983 1.6950 1.6886 1.6882 1.6865 1.6798 1.6539 1.6520
1.5072 1.4964 1.4912 1.4896 1.4869 1.4865 1.4859 1.4827 1.4707 1.4698
3.4 Other Organic Nonlinear Optical Crystals
271
Experimental values of phase-matching angle: XZ plane, 4> == 0°, (J > Vz Interacting wavelengths [J.lm]
(Jpm
[deg]
SHG,o + 0 =} e 1.0642 =} 0.5321 1.1523 =} 0.57615
35 [3.611] 34.75 [3.626]
Experimental value of internal angular bandwidth [3.611]: XZ plane, 4> == 0° Interacting wavelengths [urn]
(Jpm
SHG, 0 + 0 =} e 1.0642 =} 0.5321
35
[deg] ~(Jint [deg] 0.029
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of MDNB crystal [3.35, 36]: XYplane d eeo
== d 31 sin2 4> + d32 cos 2 4> ;
YZ plane d ooe
== d31 sin (J
;
XZ plane, () < Vz
== d eoo == d 32 sin (J XZ plane, (J > Vz d ooe == d 32 sin () . d oeo
;
Effective nonlinearity expressions for three-wave interactions in the arbitrary direction of MDNB crystal are given in [3.36] Nonlinear coefficients [3.611, 37]: d 31(1.0642J.lm)
=:
2.75
X
d 36 (KDP) ± 20%
d32(1.0642 urn) == 5.5 x d36 (KDP) d33(1.0642 um)
== 1.1 ± 0.2pmjV ,
± 20% == 2.1 ± 0.4pmjV ,
== 1.7 x d 36 (KDP) ± 250/0 == 0.7 ± 0.2 pm/V.
Laser-induced surface-damage threshold [3.611]:
A [J.lm]
Lp
1.06
40
[ns]
Ithr X
2
10- 12 [Wjm2 ]
272
3 Properties of Nonlinear Optical Crystals
3.4.17 4-(N ,N- Dimethylamino)-3-acetamidonitrobenzene (DAN) Positive biaxial crystal: 2Vz == 81.7° at A == 0.5321 urn [3.627]; Point group: 2; Assignment of dielectric and crystallographic axes: Y II b, the axes a and c lie in XZ plane, the angle between them is f3 == 94.4°, the angle between the axes X and c is l1 == 50.6° (Fig. 3.9) [3.628, 629]; Transparency range at "0" transmittance level: 0.485-2.27 urn [3.629]; Linear absorption coefficient l1
A [J.lm]
l1 [em-I]
Ref
0.5-2.0 1.0
Vz
Interacting wavelengths [urn]
(Jexp
[deg]
(Jtheor
[deg] PI [deg]
[3.629]
SHG, e+e ~ 0 1.0642 ~ 0.5321 1.3188 ~ 0.6594
57.3 [3.629] 58.58 49.4 [3.629] 49.62
10.498 10.623
Experimental values of the internal angular bandwidth: == 0°, (J > Vz
XZ plane, ¢
Interacting wavelengths [urn]
(Jpm
SHG, e+e ~ 0 1.0642 ~ 0.5321
57.3
[deg]
~(Jint
[deg]
0.007 [3.629] 0.011 [3.628]
Effective nonlinearity expressions in the phase-matching direction [3.35]: XYplane d ooe
== d 23 cos ¢ ,
d eoe == d oee == d25 sin 2¢ ;
YZ plane d eeo
== d 25 sin 2(J
d oeo ==
deoo ==
,
d2I cos () ;
274
3 Properties of Nonlinear Optical Crystals
XZ plane, 8 < Vz
== d oee == d21 cos 2 8 + d 23 sin28 XZ plane, 8 > Vz d eoe
d eeo
== d 21 cos 2 8 + d 23 sin28 -
d25 sin 28 ;
d 25 sin 28 .
Nonlinear coefficients [3.629, 323, 37]: d21(I.0642 Jim) == 1.1 ± I.5pm/V , d22(1.0642Jlm)
== 3.9 ± 0.8pm/V ,
d23(1.0642Jlm)
== 37.5 ± 11.3pm/V ,
d 25(1.0642J.1m)
== 1.1 ± 1.5pm/V .
Laser-induced damage threshold [3.629]: A [Jim] Tp[ns]
Ithr X
1.064 15 0.1
0.8 50
IO-12[W1m2]
Note 30 Hz
3.. 4.18 Methyl-(2,4-dinitrophenyl)-aminopropanoate (MAP) Positive biaxial crystal: 2Vz == 79.9° at A == 0.5321 urn [3.630]; Point group: 2; Assignment of dielectric and crystallographic axes: Y " b, the axes a and c lie in XZ plane, the angle between them is f3 == 95.6°, the angle between the axes Z and a is l/., == 37° (Fig. 3.10) [3.630]; Transparency range at "0" transmittance level: 0.5 - 2.2 urn [3.630];
z a
c d.
x Fig. 3.10. Dielectric (X, Y, Z) and crystallographic (a, b, c) axes of MAP crystal. The Y axis is parallel to the b axis and normal to the plane of the figure
3.4 Other Organic Nonlinear Optical Crystals
Linear absorption coefficient ~
275
~:
== 3.7 cm " at A == 0.5321 Jim [3.630] ;
Experimental values of refractive indices:
A [Jim] nx
nz
ny
0.5321 1.5568 1.7100 2.0353 1.0642 1.5078 1.5991 1.8439 Sellmeier equations (A in urn, T
== 20°C)
[3.630]:
n2 =2.1713+ 0.10305A.2 -0.01667A,2 x A? - 0.16951 n 2 = 2.3100 + y
n2
0.22580 A,2 _ 0.01886 A,2 A2 - 0.17988
= 2.7523 + 0.60790 A,2 _ 0.05361 A,2 .
A? -
z
0.16060
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: YZ plane, 4J == 90° In teracting wavelengths [urn]
(Jexp
0 + e=>o 1.0642 => 0.5321
[deg]
(Jtheor [deg] P2 [deg] [3.630]
SHG,
XZ plane, 4J
11 [3.630]
10.40
2.541
== 0°, (J > Vz
In teracting wavelengths [urn]
(Jexp
[deg]
(Jtheor [deg] PI [deg] [3.630]
SHG, e + e=>o 56 [3.630]
1.0642 => 0.5321
55.03
11.316
Effective nonlinearity expressions in the phase-matching direction [3.35]: XYplane d ooe
== d 23 cos 4J ,
d eoe
== d oee == d25 sin 24J ;
YZ plane d eeo
== d 25 sin 2(J
d oeo
== d eoo == d 21 cos (J
, ;
276
3 Properties of Nonlinear Optical Crystals
XZ plane, 8 < Vz
d eoe = d oee = d21 cos 2 8 + d 23 sin28 - d25 sin 28 ; XZ plane, 8 > Vz
d eeo
= d 21 cos2 8 + d 23 sin28 -
d 25 sin 28 .
Nonlinear coefficients (in crystallographic reference frame a, b, c) [3.630]: d21(1.0642J.1m) = ±(23.9±3.0)pmjV , d 22( 1.0642 Jim) = ±(26.3 ± 3.0) pm/V,
d23(1.0642 J.1m) = ±(5.3 ± 1.2) pm/V, d 25(1.0642 J.1m) = =r(0.8 ± 0.6) pm/V .
The transformation of d-tensor coefficients to dielectric reference frame (X, Y, Z) is performed in [3.630]
Laser-induced damage threshold [3.630]: A [Jlm]
T: p
0.5321 7 1.0642 10
[ns]
Ithr X
10- 12 [W/m 2]
> 1.5 30
3.4.19 m-Nitroaniline (MNA) Negative biaxial crystal: 2Vz == 104 at A == 0.5321 urn [3.631]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y,Z ==? c,b,a; Transparency range at "0" transmittance level: 0.5 - 2 urn [3.632]; Linear absorption coefficient lJ, [3.632]: 0
0.5315 4 6
along b, Ell c along b, E II a
Experimental values of refractive indices [3.631]: A [J.1m] nx
ny
nz
0.5321 1.6982 1.7533 1.7887 1.0642 1.6283 1.6815 1.7168
3.4 Other Organic Nonlinear Optical Crystals
277
Experimental values of phase-matching angle: XY plane, fJ == 90°
Interacting wavelengths [flm]
Vz
d eoe == d oee == d21 cos 2 f) + d 23 sin 2 f) - d 25 sin 2f) .
Nonlinear coefficients [3.636]: d 21(1.34 J.1m)
== 56.5 ± 5 pm/V ,
d 22{1.34)lm)
== 18.7±2pmjV.
Laser-induced damage threshold [3.619]: A [)lm]
7:p
0.62
0.0001
[ns]
Ithr X
10- 12 [Wjm 2 ]
100
3.4.22 3-Methyl-4-methoxy-4'-nitrostilbene (MMONS) Positive biaxial crystal: 2Vz == 70.2° at A == 0.543 J.1m [3.639]; Point group: mm2; Assignment of dielectric and crystallographic axes: X, Y, Z ~ a, b, C [3.639] ; Calculated mass density: 1.282 g/crrr' [3.639]; Transparency range: 0.51 - 2.1 J.1m [3.639];
282
3 Properties of Nonlinear Optical Crystals
Experimental values of refractive indices [3.639]: A (Jlm]
nx
ny
nz
0.543 0.6328 1.0642 1.3188
1.597 1.569 1.530 1.525
1.756 1.693 1.630 1.622
2.312 2.129 1.961 1.940
Sellmeier equations (A in 11m, T n 2 = 1.987
+
0.314,1.2 (0.363)2 '
;? _
x n2 =
2.184 +
0.405,1.2 (0.403)2 '
;? -
Y
2
nz
== 20°C) [3.639]:
== 2.507 + 2
1.130;?
A - (0.421)
2 .
Experimental and theoretical values of phase-matching angle and calculated values of "walk-off" angle: XZ plane, ¢ == 0°,0 > Vz Interacting wavelengths [urn] SHG, e+o =} 0 1.047 =} 0.5325 1.0642 ~ 0.5321
Oexp
[deg]
Otheor [degJ [3.639]
77.6 [3.639] 77.57 73.2 [3.639] 73.18
PI [deg]
7.50 9.58
Experimental values of internal angular and temperature bandwidths [3.639]: == 0°
XZ plane, ¢
Interacting wavelengths [urn]
SHG,e+o ~ 0 1.047 => 0.5325 1.0642 ~ 0.5321
(}pm
[deg]
77.6 73.2
t14Jint
[deg] t1T rOC]
0.047 0.035
0.17
Effective nonlinearity expressions in the phase-matching direction for threewave interactions in the principal planes of MMONS crystal [3.35], [3.36]: XY plane deoe
== doee
2
== d31 sin lj>
+ d32 cos 2 ljJ ;
3.5 Properties of Crystalline Quartz (a-Si0 2 )
283
YZ plane
== d eoo == d 31 sin (); XZ plane, () < Vz d ooe == d 32 sin (); XZ plane, () > Vz d oeo == d eoo == d32 sin (). d oeo
Effective nonlinearity expression for three-waves interactions in the arbitrary direction of MMONS crystal are given in [3.36] Nonlinear coefficients [3.639, 37]: d 32(1.0642flm)
== 25 ± 5 pm/V ,
d 33(1.0642flm)
== 111 ±22pm/V.
3.5 Properties of Crystalline Quartz «(X-Si0 2) Positive uniaxial crystal: ne >no ; Point group: 32; Mass denisty: 2.649 g/cm' [3.59]; Mohs hardness: 7 [3.64]; Transparency range at 0.5 transmittance level for the 10 mm long crystal (along c axis): 0.193 - 3.6 urn [3.640, 641]; Linear absorption coefficient lJ, (along c axis) [3.59]: A [flm]
a [cm"]
2.9 3.0 3.3 3.5 3.8
1 0.5 0.06 0.2 0.87
Two-photon absorption coefficient
A [urn]
f3 x 1013 [m/W]
Ref.
0.216 0.266 0.270
40±7 4.5 < 1.5
3.399 3.71 3.399
f3 (along c axis):
284
3 Properties of Nonlinear Optical Crystals
Experimental values of refractive indices (T = 291 K) [3.642]: A [urn]
no
ne
A [um]
no
ne
0.185467 0.193583 0.20006 0.20255 0.204448 0.21107 0.214439 0.219462 0.226503 0.231288 0.242796 0.250329 0.257304 0.263155 0.274867 0.291358 0.303412 0.312279 0.325253 0.340365 0.35868 0.396848 0.404656 0.410174 0.434047 0.435834 0.467815 0.479991 0.486133
1.67578 1.65999 1.64927 1.64557 1.64288 1.63432 1.63039 1.62497 1.61818 1.61401 1.60525 1.60032 1.59622 1.59309 1.58752 1.58098 1.576955 1.57433 1.570915 1.56747 1.563915 1.55813 1.557156 1.556502 1.553963 1.553790 1.551027 1.550118 1.549683
1.68997 1.67343 1.66227 1.65842 1.65562 1.64671 1.64262 1.63698 1.62992 1.62559 1.61650 1.61139 1.6071"4 1.60389 1.59813 1.59136 1.58720 1.584485 1.58095 1.577385 1.573705 1.56772 1.56671 1.566031 1.563405 1.563225 1.560368 1.559428 1.558979
0.508582 0.518362 0.53385 0.546072 0.579066 0.587563 0.58929 0.62782 0.643847 0.656278 0.667815 0.670786 0.706520 0.728135 0.766494 0.794763 0.84467 1.00000 1.01406 1.08303 1.20000 1.30000 1.40000 1.52961 1.60000 1.80000 2.05820 2.50000 3.00000
1.548229 1.547651 1.546799 1.546174 1.544667 1.544316 1.544246 1.542819 1.542288 1.541899 1.541553 1.541466 1.540488 1.539948 1.539071 1.538478 1.537525 1.53503 1.53483 1.53387 1.53232 1.53102 1.52972 1.52800 1.52703 1.52413 1.51998 1.51156 1.49962
1.557475 1.556887 1.555996 1.555350 1.553791 1.553428 1.553355 1.551880 1.551332 1.550929 1.550573 1.550483 1.549472 1.548913 1.548005 1.547392 1.54640 1.54381 1.54360 1.54260 1.54098 1.53962 1.53826 1.53646 1.53545 1.53242 1.52814 1.51950 1.50700
Optical activity at T = 300 K [3.194]: A [urn]
p [deg/rnm] A [Jlm]
p [deg/rnm] A [urn]
0.1800 0.1825 0.1850 0.185398 0.185735 0.186209 0.1875 0.1900
410.5 391.5 374.0 370.9 368.6 365.6 357.5 342.5
328.5 325.31 322.76 315.5 295.65 226.91 216.50 202.27
0.1925 0.19303 0.193518 0.1950 0.198979 0.214702 0.221003 0.226334
0.226909 0.232749 0.235923 0.241331 0.247482 0.26283 0.273955 0.281329
p [deg/rnm] 200.90 187.25 180.43 169.98 158.66 135.66 122.12 114.29
3.5 Properties of Crystalline Quartz (ae-Si0 2 )
A [urn]
p [deg/rnm] A [Jlm]
0.291216 0.307573 0.322579 0.327100 0.338399 0.340365 0.349058 0.3694 0.372762 0.386553 0.390648 0.393582 0.397775 0.402187 0.407664 0.411855 0.413469 0.414768
104.97 91.97 82.13 79.49 73.43 72.46 68.36 60.06 58.84 54.21 52.95 52.07 50.85 49.62 48.14 47.07 46.66 46.34
p [deg/rnm] A [Jlm]
0.419144 0.423362 0.428241 0.431509 0.435274 0.435834 0.467816 0.468014 0.472216 0.479991 0.481054 0.508582 0.510554 0.515325 0.520908 0.535065 0.546074 0.546549
0.547155 0.570025 0.57696 0.578216 0.579066 0.588997 0.589593 0.636235 0.643847 0.670785 0.761 0.940 1.1 1.342 1.6 2.1 2.6 3.1
45.28 44.29 43.19 42.47 41.66 41.55 35.61 35.57 34.89 33.68 33.52 29.73 29.49 28.90 28.25 26.67 25.54 25.49
Temperature derivative of refractive indices [3.643]: A [urn]
dno/dT x 105 [K- 1]
(dne/dT) x 105 [K- 1]
0.441 0.467 0.480 0.508 0.589 0.643
-0.475 -0.485 -0.499 -0.514 -0.529 -0.549
-0.593 -0.681 -0.600 -0.616 -0.642 -0.653
Nonlinear coefficient [3.37]: d ll(I.064 urn]
== 0.30 pm/V
Laser-induced breakdown threshold (along c axis) [3.644]: A [urn]
'Tp
1.06
31
[ns]
Ithr X
10- 12 [W /m 2 ]
4000-6000
Thermal conductivity coefficient:
[W/rnK], II c
T[K]
K
273 293
11.42 11.7
K
[W/rnK], -.l c
6.82 6.5
Ref. 3.645 3.58
p
[deg/rnm]
25.43 23.31 22.72 22.62 22.55 21.75 21.70 18.48 18.02 16.54 12.59 8.14 5.836 3.89 2.656 1.46 0.922 0.584
285
286
3 Properties of Nonlinear Optical Crystals
3.6 New Developments During the time taken to publish this book a number of new works devoted to the properities of nonlinear crystals has appeared. In order to update the material presented in this chapter the most important achievements are briefly discussed below.
CLBO First, the new nonlinear crystal from the borate family, namely cesium lithium borate (CsLiB 60 I 0 or CLBO) should be mentioned [3.646, 647]. It is a negative uniaxial crystal of point group 42m, and is transparent from 0.18 to 2.75 urn, The Sellmeier equations for CLBO at room temperature are as follows (A in um) [3.646]:
= 2.208964 +
0.010493 - 0.OI1306A,2 A,2 - 0.012865 '
n 2 = 2.058791 +
0.008711 - 0.006069 A,2 . A,2 _ 0.011393
n2 o
e
The CLBO nonlinear coefficient, measured in [3.646], is equal to: d36(1.064 urn) = 2.2 x d 36(KDP) = 0.86pmjV. The laser-induced damage threshold at A, = 1.064 urn is 25 GW/cm2 for 1.1 ns pulses [3.647].
BBO The "improved" set of dispersion relations recently proposed in [3.650]is much worse than the set presented above [3.145].
LBO The improved set of LBO dispersion relations have been reported by Kato (l in urn, T == 293 K) [3.648]: n2 = 2.4542 +
x
n2 y
0.01125 - 0.01388 l2 l2 - 0.01135 '
== 2.5390 +
0.01277 - 0.01849 l2 l2 - 0.01189 + 4.3025 x 10- 5 l4 - 2.9131 X 10- 5 l6 ,
n2 == 2.5865 + Z
0.01310 - 0.01862A,2 A2 - 0.01223 + 4.5778 x 10- 5 l4 - 3.2526 X 10- 5 l6 .
New information concerning the temperature derivative of LBO refractive indices is now available, e.g., for the spectral range 0.4 - 1.0 urn and temperature range 293 - 383 K (l in urn) [3.648]:
3.6 New Developments
dnx/ dT
= -(3.76A-2.3)
X
10-6K- 1
dny/dT == -(19.40J - 6.01 J) dnz/dT == -(9.70 - 1.50A)
X
X
287
,
10-6 K - 1
10- 6 K- 1
,
,
and for A == 0.6328 urn and a temperature range of 293 - 473 K (A in urn, T in K) [3.649]: dnx/dT == [0.20342 - (1.9697 x 10- 2)(T - 273) - (1.4415 x 10- 5 )(T - 273)2]
dny/dT == -[10.748
+ (7.1034 x
+ (5.7387 x
X
10-6 K- 1
,
10- 2)(T - 273)
10- 5)(T - 273)2] x 10- 6 K- 1
,
dnz/dT == -[0.85998 + (1.5476 x 10- 1)(T - 273) - (9.4675 x 10- 4)(T - 273)2
+ (2.2375
x 10- 6)(T - 273)3] x 10- 6 K- 1
.
CBO
Improved dispersion relations for eBO have been published by Kato (A in urn, T = 293 K) [3.651]:
+
0.01378 - 0.00612 A2 J2 - 0.01498 '
== 2.3704 +
0.01528 - 0.00939 A2 J2 - 0.01581 '
n2 == 2.3035 x
n2 y
n2 == 2.4753 z
+
0.01806 - 0.01654A 2 0.01752
A? -
•
KTP New data on the temperature derivative of refractive indices of flux-grown KTP have been reported for T = 288 - 313 K [3.652]:
1.0642
6.1
8.3
14.5
KTA The "infrared-corrected" Sellmeier equations proposed in [3.653] (A in urn, T = 293 K) are: 2 2 1.23552 A nx == 1.90713 + 2 2 A - (0.19692)
2
-
0.01025 A ,
288
3 Properties of Nonlinear Optical Crystals
n2 = 2.15912 + Y
2
nz
2
A?
== 2.14786 + 2
1.000991l. - (0.21844)2
1.29559 A?
A - (0.22719)
-
O.010961l.2
'
2
2 - 0.01436 A .
These indeed show better agreement with experiment in the specific case of 1.0642 urn pumped OPO in the XZ and YZ plane, but for SHG and SFG processes with shorter wavelength participation (A3 == 0.4 - 0.6 urn) the set from Kato [3.434] is preferrable. RTA Another KTP isomorph, rubidium titanyl arsenate (RbTiOAs04 or RTA), has been extensively developed in the last three years. RTA is a positive biaxial crystal of mm2 point group symmetry, and is transparent from 0.35 to 5.8 urn [3.654, 655]. The dispersion relations for RTA are as follows (A. in urn, T = 293 K) [3.656]: n2
= 2.22681 +
X
2
O.996161l. (0.21423)2
A2 _
ny
== 1.97756 + 2
1.25726 ,1.2
n2
= 2.28779 +
1.206291l. (0.23484)2
2
A - (0.20448)
Z
-
O.013691l.2
' 2
2 - 0.00865 A ,
2
A2 _
-
O.015831l. 2
.
The reported RTA nonlinear coefficients are: d31(1.0642J.lm)
== 1.4pmjV [3.654,37] ,
d32(1.0642 um)
== 4.6pmjV [3.654,37] ,
d33(1.0642J.lm)
== 12.1pmjV [3.654,37].
AgGaSe2 An improved set of Sellmeier equations, which gives much better agreement with experiment in the case of type I NCPM OPO, has been proposed by Kato [3.657] (A in urn, T = 293 K): n2
== 6.85070 +
o
n2 e
== 6.67920 +
A2
0.42970 _ 0.00125 A2 - 0.15840 '
A2
0.45980 _ 0.00126 A2 - 0.21220
.
4 Applications of Nonlinear Crystals
This chapter is devoted to applications of nonlinear crystals in nonlinear optical devices. It describes the generation of second and higher (up to sixth) optical harmonics of neodymium laser radiation, generation of optical harmonics of powerful wide-aperture neodymium glass laser radiation, generation of optical harmonics of other lasers (ruby, gas, semiconductor, and so on), sum-frequency generation, (including up-conversion of IR radiation to the visible range), difference-frequency generation, parametric light oscillation as a tool for generating tunable radiation, stimulated Raman scattering, and picosecond continuum generation. The chapter contains abundant tabular material on the parameters of converted laser radiation and many references.
4.1 Generation of Neodymium Laser Harmonics 4.1.1 Second-Harmonic Generation of Neodymium Laser Radiation in Inorganic Crystals Neodymium lasers are typical representatives of the solid-state laser family. Trivalent neodymium ions implanted into various crystals or glass matrices are the active medium of such lasers. Most neodymium lasers generate in the 1.051.08 urn, the neodymium phosphate glass laser emits at A == 1.054 urn, the neodymium silicate glass laser at A. = 1.060-1.064 urn (depending on the glass type), the neodymium-doped yttrium aluminate laser (Nd3+:YAI0 3 or Nd:YAP) at A == 1.0796 11m, the Nd 3+:LiYF4 (Nd:YLF) laser at A == 1.053 11m, and the Nd 3+ : CaW04 laser at A == 1.0584 urn. Most often the neodymiumdoped yttrium-aluminium garnet (Nd 3+ : Y3Als012 or Nd:YAG) laser is used, which emits at A == 1.06415 urn (see Appendix). Table 4.1 illustrates the results of studying SHG of Nd:YAG laser radiation in different inorganic crystals; for each crystal the type and the angle of phase matching, the intensity 10 of radiation of the fundamental frequency, second-harmonic pulse duration, crystal length, and energy- or power- conversion efficiency are given. For SHG of picosecond (or subnanosecond, 7:p = 1-500 ps) Nd: YAG laser radiation use is mainly made of KDP crystals or sometimes DKDP [4.5] or
tv
\0 0
~
Table 4.1. Second-harmonic generation of Nd:YAG laser radiation (1.064 Crystal
Type of interaction
8pm[deg]
10 [Wcm"]
tp [ns]
L[mm]
--+
>
0.532 Jlm) Conversion efficiencyl'' ]
"l:'
~
Refs.
Notes
s:
s:~ =::s
00
KDP
DKDP
CDA DCDA
RDA RDP LiI03 LiNb03 LFM
ooe ooe ooe ooe ooe eoe eoe eoe ooe eoe ooe ooe ooe ooe ooe ooe ooe ooe ooe eoe ooe ooe ooe ooe ooe
41 41 41 41 41.35 53.5 53.5 53.5 36.6 53.7
90 90 90 90 90 90 90 50 50.8 83.1 30 30 90 55.1 55.1
9
10
8 x 109 7 x 109 108 3x 8x 3x 3x 2x 4x 8x 3x 2x 9x
9
10 107 108 108 108 109 107 108 108 107
2 x 108 2 x 108 7 x 107 3 x 109 2 x 107 3.7 x 107 6.2 x 103
0.15 0.05 0.03 0.03 0.1 ms 18 0.25 20 8 8 10 0.007 a
20 20 10 15 10 10 10 0.04 10
25 25 14 20 40 30 40 30 20 20 17.5 13 21 16 13.5 29 20 15.3 15.3 18 5 20 15 15
32 (energy) 60 82 (energy) 81 (energy) 0.38 (energy) 50 (power) 70 (power) 50 (energy) 40 (energy) 50 (energy) 57 (power) 25 (energy) 40 (energy) 40 (energy) 45 (power) 50 (power) 57 34 (power) 36 (power) 11 (power) 44 (power) 50 40 36 0.08
4.1 4.2 4.3 4.3 4.4 4.5 4.5 4.6 4.7 4.7 4.8 4.9 4.6 4.6 4.8 4.10 4.11 4.12 4.13 4.13 4.14 4.15 4.16 4.17 4.17
0
-,
Z
0
::s
:r (D
Nd:YAG laser cooled to 253 K, A = 946 nm
f:aj "'1
(1 "'1
'
4.5%) [4.39-41] or LiNb0 3 crystals grown from congruent melt [4.42] are used, which ensure a
4.1 Generation of Neodymium Laser Harmonics
293
conversion efficiency of up to 50%. Table 4.2 shows the data on SHG of Nd:YAG laser radiation (A== 1.064Jlm, E== 100m], 'r p == 140s, !==20Hz, 10 == 35 MWcm- 2 ) in these crystals and also in LiI0 3 , DCDA, DKDP, and KTP. The possibility of suppression of the photorefractive effect by heating the LiNb0 3 crystal over 170° should also be mentioned. Among the crystals that double the frequency of Nd: YAG laser radiation, potassium titanyl phosphate (KTiOP04 or KTP) is of special interest. Possessing a very large nonlinearity (d 31 == 6.5 X 10- 12 m/V, d 32 == 5 X 10- 12 m/V), this crystal has large angular (~(}L == 15-68 mrad em) and temperature (~TL ::::: 20-25 °C ern) bandwidths for SHG of 1.06 urn radiation. These exceed similar parameters for KDP, DKDP, and other crystals by almost an order of magnitude. Besides, it is nonhygroscopic and has a rather high surface-damage threshold. The direction with qJ == 23° and () == 90° has the highest deff value and is more advantageous than other directions since its angular bandwidth is maximum and the birefringence angle is minimum. Experimental values determined for a crystal 1 em in length are ~qJ == 32' ± 5' and ~T == 20°C [4.24]. Table 4.1 illustrates the results of experimental studies of SHG of Nd:YAG laser radiation in KTP. In all cases interaction of the eoe type in the XY plane was used. The experiments of Moody et a1. [4.23] were carried out with a Nd:YAG laser generating trains of pulses of 175±25 ps duration. A 3x 3x 5 mm KTP crystal was used, and radiation was focused into the crystal to a spot 390 urn in diameter. Efficiency of conversion to the second harmonic equal to 55% was attained. Driscoll et a1. [4.22] studied in detail SHG of Nd:YAG laser radiation operating in single and multimode regimes with KTP crystals of different lengths (4-9 mm). In the 9 mm crystal, due to back transformation of the second-harmonic radiation to the fundamental one, a lowered conversion efficiency was observed. Maximum energy-conversion efficiency attained in a two-pass scheme with relatively short crystals (L == 5.1 mm) amounted to 60%. For SHG of 1.064 urn radiation in a "banana" crystal the phase-matching angle was (}ooe == 73°45' for the interaction in YZ plane (cp == 90°, d 3 1) and (}eeo == 75°26' when the interaction occured in the XZ plane (cp == 0°, T == 25°C,
Table 4.2. Second-harmonic generation of Nd:Y AG laser radiation in various crystals Nonlinear crystal LiNb03 grown from congruent melt LilO3 DCDA DKDP KTP LiNb03:MgO LiNb03:MgO
L[mm]
9 30 19 37 50 5 4 9
Bpm[deg] 90 90 29 90 53 24 (q>pm) 90 90
E (0.53 urn) [ml]
P (0.53 urn)
53 52 29 48 19 9.6 23 31
1.07 1.04 0.58 0.96 0.39 0.19 0.46 0.63
1'/[%]
[W] 50.9 49.5 27.6 47.6 19.5 42.6 23.0 35.2
294
4 Applications of Nonlinear Crystals
d 32 ) ; at fJ = 90° and qJ = 90° the phase-matching temperature was T = 101°C; at fJ = 90° and qJ = 0°, T = 89°C [4.43]. Note that the values of fJ and T vary for different crystals in the ranges 73-75° and 75-77° for fJ and 90-110°C and 80-100 "C for T, respectively. This crystal is widely used in cw intracavity SHG schemes because of its large nonlinear coefficient. Crystals of BBO and LBO are very promising for harmonic generation of Nd:YAG lasers due to their large transparency range, high damage threshold, high nonlinearity. For LBO also: large acceptance angle, small walk-off angle, and the possibility of being used under noncritically phase-matched conditions [4.36, 44a,b]. Both crystals are nonhygroscopic and are mechanicaly hard. Conversion efficiencies up to 60-700/0 to the second harmonic of Q-switched and mode-locked Nd:YAG lasers were attained by use of these crystals (Table 4.1). Noncollinear SHG and THG of the Nd:YAG laser in BBO crystal was studied by Bhar et al. [4.45,46].
4.1.2 Second-Harmonic Generation of 1.064 um Radiation in Organic Crystals Organic crystals have parameters competitive with widely used crystals of the KDP type, niobates, and formates. Their preparation is cheap, their nonlinear susceptibilities are high, and their birefringence is sufficient for use in frequency converters. Damage thresholds are fairly high; for instance, urea has a breakdown threshold of several GW cm ? at nanosecond pumping, which exceeds that of LiNb0 3 and LiI0 3 . However, organic single crystals have significant drawbacks that limit their application in nonlinear optics: they are hygroscopic and extremely soft so that their surfaces must be protected with coatings. The efficiency of SHG of 1.064 urn radiation has been studied in polycrystalline powdery samples [4.47-49]. Optically active amino acids (tryptophan, asparagine, and others) [4.49], sugars (saccharose, maltose, fructose, galactose, lactose) [4.48], and other organic compounds were investigated. Up to now SHG of Nd:YAG laser radiation has been realized in the following organic single crystals: saccharose (C12H22011), 3-methyl-4-nitropyridine-loxide (POM), methyl-(2,4-dinitrophenyl)-amino-2-propanoate (MAP), metanitroaniline (MNA), 2-methyl-4-nitroaniline (MNA*), meta-dinitrobenzene (MDNB), 2-cyclooctylamino-5-nitropyridine (COANP), deuterated L-arginine phosphate (DLAP), 2-(N,N-dimethylamino)-5-nitroacetanilide (DAN), N-(4nitrophenyl)-N-methylaminoacetonitile (NPAN), 4-nitrophenol sodium (:Na) salt dihydrate (NPNa), its deuterated analogue (DNPNa), L-N-(5-nitro-2pyridyl) leucinol (NPLO), and 3-methoxy-4-hydroxy-benzaldehyde (MHBA). In the L-PCA crystal (L-pyrrolidone-2-carboxylic acid) the fourth-harmonic of Nd:YAG laser was obtained by frequency doubling of the second harmonic (Table 4.3). High conversion efficiencies have been attained due to large nonlinearities of these crystals. For instance, a conversion efficiency of 30 % was attained for a MAP crystal only 1 mm long [4.53]. Conversion efficiencies for
Table 4.3. Second-harmonic generation of Nd:YAG laser radiation in organic crystals Crystal
Type of interaction
Saccharose
eoe ooe eoe eeo eoe eeo eeo eoe oeo ooe eeo ooe ooe
POM
MAP MNA
MNA* MDNB COANP DLAP DAN NPAN NPNa DNPNa NPLO MHBA L-PCA
ooe oeo ooe Type II eeo Type I eeo oee Type II
d eff/d36 (KDP) 8pm[deg]
0.2 0.2 0.2 21.8 9.9 13.6 13.1 38.3 37.7 37.7 24.1 11.5 6.8 65.7 3.6 30.9 0.95 Q
Q
Q
129 11.5 85 6.9 30 0.64
90 90 15.8 35.7 12.8 18.1 (1.32 urn) 17.4 (1.34~) 2.2 11 90 44 90 90 35.3 26.4 90 76 40 90 51.7 33.0 90
(fJpm [deg]
60.5 33.7 0 90 0 90 90 0 90 55 90 14.5 8.5 0 0 22 42 0 8.5
Conversion efficiency [O~]
50 30 40 15 10 85 0.1-0.5 3.6
20 9 5 50
0
42
59 0.6
Refs.
4.50 4.50 4.50 4.51 4.51 4.52 4.52 4.53 4.53 4.54 4.54 4.54 4.55 4.56 4.57 4.58 4.59 4.59 4.60 4.61 4.62 4.62 4.63 4.63 4.64 4.65
Notes
L=7 mm, rp = 160 ps L=lmm L=1.7mm L = 2.5 mm, A8 = 2.9 mrad
~ ~
0 ::s
NCSHG in the XY plane, L = 1 mm NCSHG in the XY plane, L = 3 mm
(J) (J)
""1
L=2-4 mm, 10 = 50 MW cm- 2 L=0.9 mm, 10 = 1.3 MW cm- 2 , rp = 250 ns
~ s:
::s
0
~
Z
(J)
0
c, '
' 1.5 GW cm". Therefore, to obtain the effective FOHG, the pump intensity was 1-1.2 GWcm- 2 • With the type I interaction (ooe) maximum conversion efficiencies to 266 nm radiation were 64% (E == 50 J) and 55% (E == 44 J) for crystals 1 ern and 1.5 em in length, respectively. For antireflection coated crystals, n rises to 70% and 60%, respectively. These results [4.131] were theoretically interpreted by Craxton [4.138]. Ibragimov et al. [4.134] have theoretically analyzed the frequency-doubling process under the conditions applicable to large noedymium glass laser systems to evaluate the limiting conversion efficiency. Experimental investigation of SHG was performed on a multicascade neodymium glass laser (A == 1.06 urn) with the 45 mm aperture of the end cascade. Maximum second-harmonic radiation energy attained 90 J at 25 ns pulse duration; the fundamental laser beam intensity distribution corresponded to a hypergaussian function with N == 5. For doubling, KDP crystals were used with an aperture of 20 and 50 mm, the interaction type being ooe. Maximum energy-conversion efficiency to the second harmonic was obtained for KDP crystals with dimensions 50 x 50 x 40 mm : n == 80% at an incident radiation energy of 70 J and divergence 6 x 10- 5 rad. Gulamov et al. [4.129] obtained maximum conversion efficiencies to second (90%) and third (81%) harmonics of high-power neodymium phosphate glass laser radiation. For doubling, KDP crystals 18, 30, and 40 mm in length were used with an aperture 50 x 50 mm. The conversion efficiency to 527 nm radiation amounted to 75%, 90%, and 80%, respectively. The beam diameter was 32 mm, the divergence 5.5 x 10- 5 rad, and the depolarized fraction of the radiation did not exceed 3%. The polarization mismatch scheme with the 35% rotation of the fundamental wave polarization vector with respect to the 0wave polarization vector was used for THG. In both cascades KDP crystals
310
4 Applications of Nonlinear Crystals
17.5 mm long and with an aperture of 50 x 50mm were used; the interaction type was eoe. The fourth-harmonic generation of radiation of a large-aperture neodymium laser consisting of a LiYF4:Nd3+ oscillator and neodymium-phosphate glass amplifiers (A. = 1.053 urn, E = 115 J) has been studied [4.135]. The conversion efficiency to A. = 0.26 urn was 46.5% at /0 == 1.5 GW cm-'. High efficiency FOHG with A. == 0.264 urn was realized by Begishev et al. [4.132] with conversion efficiency from 0.527 urn, 11 == 92%. Further mixing of obtained radiation (0.264 urn) with the fundamental radiation (1.054 urn) in an ADP crystal (Oooe = 90°, T == -67.5°C, L = 10 mm) allows us to generate the fifth harmonic (211 nm) with overall efficiency of 19% [4.132].
4.2.6 "Quadrature" Scheme An interesting scheme for frequency conversion, introduced by Eimerl [4.139], called the "quadrature" scheme, uses two (instead of one) crystals at each conversion step. We shall illustrate the application of this scheme to SHG (Fig. 4.1). The quadrature scheme of SHG comprises two crystals oriented for type
E"2m
Fig. 4.1. Quadrature scheme of SHG
II interaction (eoe) and positioned so that the principal planes of these crystals
(where the optic axes and beam propagation direction are arranged) are orthogonal. The scheme has two specific features. First, the fundamental radiation after the first conversion cascade has polarization suitable for the second cascade, so that both crystals participate effectively in the conversion. Second, the second harmonic generated in the first crystal has polarization unsuitable for the second conversion step, and therefore, is not converted in the second crystal. The total conversion efficiency for two crystals is (4.2)
where 111 and 112 are the conversion efficiencies in the first and second crystals, respectively. The quadrature scheme of conversion has an undoubted advantage over a scheme where only one crystal is used: the dynamic range for the pump intensity variation in the quadrature scheme (100-1000) greatly exceeds that in a one-crystal scheme (rv 10). The advantage of this scheme was illustrated ex-
4.3 Harmonic Generation for Other Laser Sources
311
perimentally for SHG of radiation of a Nd:YLF laser with three neodymium phosphate glass amplifiers (A == 1.053 urn, 'l' == 1.2 ns). Two DKDP crystals 12 and 44 mm in length were used, the absorption at the fundamental frequency was (X == 0.006cm- 1, and Fresnel reflection amounted to 15.5-18.50/0. With a change in the pump intensity from 0.2 to 9.6 GW cm- 2 (the dynamic range 45) the conversion efficiency remained unchanged at 800/0. When the crystals were antireflection coated, n increased to 95 %. At low intensities the conversion takes place basically in the second long crystal, and at high intensities, in the first crystal. The dependences of t1 on the pump intensity for SHG were calculated also for KTP, P- BaB204 (A == 1.06Ilm), CdGeAs2(10.6Ilm). Quadrature schemes were also described for THG, FOHG, and SFG [4.139].
4.3 Harmonic Generation for Other Laser Sources 4.3.1 Ruby Laser
For SHG of ruby laser radiation (A == 694.3 nm), KDP, DKDP, ADP, RDA, RDP, LiI0 3 , and KB5 crystals have been used (Table 4.11). Maximum conversion efficiencies were attained in RDA, RDP, and Lil0 3 crystals. In a 1.45 em long RDA crystal, power-conversion efficiency was 58% both at room temperature (T == 20°C, (}ooe == 80°) and at 90 ° phase matching (T == 90°C). The output power was 62 MW. The RDA crystal is suitable for this purpose because of a large angular bandwidth (Table 4.11). The third harmonic of ruby laser radiation (A3m == 231.4 nm) was obtained in a KB5 crystal by mixing its first (694.3 nm) and second (347.1 nm) harmonics [4.146]. Interacting waves propagated in the XY plane at an angle qJ == 57 ° ± 1° to the X axis. The eeo interaction was used. The conversion efficiency calculated relative to the fundamental radiation was 0.2%; the output power was 40 kW at 'l'p == 6 ns.
Table 4.11. Second-harmonic generation of ruby laser radiation (1 = 694.3 nm)
Io[Wcm- 2 ] L [mm]
Power Refs. conversion efficiency [0/0]
Crystal
Type of interaction
Opm[deg]
KDP DKDP ADP RDA
ooe ooe ooe ooe
50.5 52 52 80.3 (90)
1.5 x 108
1.45
58
4.140 4.141 4.140 4.142
RDP
ooe
67
1.8 x 108
1.0
37
4.143
LilO 3 KB5
ooe eeo
52 1.3 x 108 26.5 (q>pm) -
1.1 1.0
40 10- 3
4.144 4.145
Notes
LAO = 1.75 mrad em LAO = 1.46 mrad cm LAO = 1.63 mrad em T = 20°C (90°C), LAO = 4.37 mrad em T = 20°C, LAO = 2.4 mrad em LAO = 0.2 mrad em XY plane
312
4 Applications of Nonlinear Crystals
4.3.2 Ti:sapphire Laser Second harmonic of Ti:sapphire (Ti : A1 20 3) laser radiation with A = 700-900 nm has been realized in LiI03, BBO, LBO, and KNb03 crystals (Table 4.12); two organic crystals, 3-rnethoxy-4-hydroxy-benzaldehyde (MHBA) and 8-(4'acetylphenyl)-1,4-dioxa-8..azaspiro [4.5] decane (APDA) were also used for this purpose. for continuous wave and cw pumping regimes of operation of Ti:sapphire laser most suitable are the schemes with frequency doubling inside the laser cavity (ICSHG) or in an external ring resonator (ERR). Note that KNb0 3 can be used at noncritical phase-matching conditions (propagation direction along the a axis); by changing the temperature of the crystal between 20-180 °C the wavelength range of 860-940 nm can be frequency-doubled. By use of a 55 urn thickness BBO crystal ICSHG of Ti:sapphire laser radiation was realized with pulse-width as short as 54 fs [4.150]. Maximum second harmonic powers were achieved in continuous wave and mode-locked regimes with high repetition rate (r == 1.5 ps) : P2w == 0.7 W [4.147, 156]. Third harmonic (272 nm) of mode-locked Ti: sapphire laser radiation was generated in a BBO crystal of6.5-12 mm in length (0 == 50°) with output power P3w == 150mW and 1" == 1ps used [4.147, 158]. Conversion efficiency was 30%. For fourth-harmonic generation (210 nm) a BBO crystal (Oooe == 75°, L == 78 mm was also used, the scheme of mixing of the fundamental radiation with the third harmonic OJ + 30J == 4w was employed [4.147, 158]. Maximum average output power was about 10 roW (r = 1 ps).
4.3.3 Semiconductor Lasers A KNb03 crystal is most convenient for SHG of semiconductor laser radiation (Table 4.13). Along with a very high nonlinear coefficient [d 32 = 50d36 (KDP) = 2.1 x 10- 11 m/V], this crystal has 90° phase matching at room temperature at the wavelength of a diode laser (A == 860 nrn). The spectral bandwidth for a crystal length 9 mm is L\A == 0.056 nrn, which makes it possible to double the GaAIAs laser radiation with ~A == 0.02 nm. The angular bandwidth at 90° phase matching is 51 mrad, which exceeds the divergence of the fundamental radiation beam under focusing into the crystal (12 mrad) [4.159]. Second-harmonic generation of pulsed Gal-xAlxAs laser radiation (860 nm) was realized in a 6 mm KNb0 3 crystal when the fundamental radiation propagated along the a axis (T == 31°C) [4.160]. The fundamental radiation was polarized along the b axis and the second harmonic along the c axis. At a pump intensity of 6 kW cm ? the conversion efficiency attained 1.8 x 10- 3. The output power was 0.35 mW. Efficient frequency doubling of a 856 nm diode laser was realized by use of a monolithic ring resonator of KNb03; optical conversion efficiency was 39% and conversion from electrical power was ~ 10% [4.165]. Continuous wave radiation at 429 nm with P == 62 mW was generated by frequency doubling in the KNb0 3 crystal of the emission of a
Table 4.12. Second-harmonic generation of Ti:sapphire (Ti:Ah03) laser radiation Crystal
Aw [nm]
!w
8pm[deg]
L[mm]
Output power [mW]
11 [%]
Refs.
Notes
700 23 450
50 0.38a 27 2.1 75 (5.2a ) 7.4a 30 20 1.0a 21.6
4.147 4.148 4.147 4.149 4.150 4.151 4.152 4.147 4.148 4.153 4.154
f = 82 MHz
P2w
LilO 3 LilO 3 BBO BBO BBO BBO LBO LBO LBO LBO LBO
720-850 720-800 720-850 760-865 860 766-814 700-900 720-850 720-800 820 74(}-900
KNb03 KNb03 MHBA APDA
860-940 860 800-900 760-900
1.5 ps
43
1.5 ps 134 fs 54 fs
30 ooe 27.5 ooe 90 (0), 22-40 (cp) 90 (0), 32 (cp)
12-25 ns 1.5 ps cw
35 ns cw 10 ns cw
90 (8), 31.8 (cp) 90 (8), 37-23 (cp) along a axis
Type I
10 7 8 1 55 urn 5 5 8 10 10.7 6 7.9 6 5 3
230 170 25 mJ 350 10-60 410
7.8 kW (peak) 650 0.03 mJ 0.8 J.lW
45 (2a ) 48 6 0.0003
4.155 4.156 4.64 4.157
External ring resonator (ERR)
f = 82 MHz Dispersive frequency doubler ICSHG, f = 72 MHz ICSHG /0 = 0.9 GWcm- 2 f = 82 MHz ERR ERR ATL = 7.8-15.3°C em, AU = 0.6-1.25 nm cm ICSHG, T = 2-180°C ERR
+;:.
w ::t ~
3
0
e.
o
0 =' (l)
(l) ~
~
aTotal conversion efficiency from the pump source.
o' ='
~ ~
0
;. (l)
~
14 ~ ~
(l) ~
Cf)
0
s::
~
o
(l) ~
w w
w
Table 4.13. Second-harmonic generation of semiconductor laser radiation Crystal KNb03
KTP LilO 3 K3Li197Nbs.0301S.06
Aco [nm]
Phase-matching conditions
860 860 842 842 865 842 856 972
along a-axis along a-axis T = 31°C T = -23°C T = -23°C along a-axis along a-axis along a-axis T = 15°C along b-axis
862 858 1500 740 820
L[mm]
~ P2w
[mW)
'1 [%J
Refs.
~
5 5 5 7 5
0.00028 0.35 0.72 24 0.215 6.7 41 1.2
0.005 0.04 0.27 14 1.7 0.57 39 4.8
4.159 4.160 4.161 4.162 4.163 4.164 4.165 4.166
T = 34°C
14
400 (peak)
6.3
4.167
-
12.4 10 6 2.4
1.1
4.168 4.169 4.170 4.171
(J = 54 0, cp == 0 0, type II (Jooe =:: 45 °
90 °
Notes
8.97 5.74 5
62 0.001 0.018 0.36
0.18 3.1
>
~
r = 10 ns
~
n' ~
g.
Crystal in an external resonator External ring resonator (ERR) ERR, cw regime External resonator Distributed Bragg reflection semiconductor laser GaAIAs amplifier injected by 5 ~sTi:sapphire laser
::s C'-l 0
~
Z
0
::s ~ ::s0 ~
101
o
~ C'-l
[
C'-l
ERR ERR External resonator
4.3 Harmonic Generation for Other Laser Sources
315
GaAIAs amplifier seeded by a laser diode [4.168]. Sum-frequency generation in a KTP crystal by mixing outputs of two diode lasers operating at wavelengths of 1.5 and 0.78 - 0.82 urn, allows us to generate radiation at 0.52 - 0.54 urn with P == 0.2 - 0.3 f.!W [4.169, 172].
4.3.4 Dye Lasers Table 4.14 shows some characteristics of nonlinear crystals used for doubling dye laser radiation: nonlinear coefficient deff for minimum wavelength attained by SHG at room temperature, the d~ff/n3 ratio proportional to the conversion efficiency, the minimum wavelength attained by SHG, and the "walk-off" angle p at different wavelengths. For all crystals under consideration (except LFM) this wavelength corresponds to 90 ° phase matching when radiation propagates in the direction orthogonal to the optic axis (() == 90°) for uniaxial crystals, and along the Y axis (fJ == 90 0, qJ == 90°) for biaxial crystals. For lithium formate (LFM) the limiting wavelength 230 nm corresponds to the boundary of the absorption band, whereas the phase-matching conditions allow shorter wavelengths to be attained. Upon cooling the crystals, smaller wavelengths can be achieved with the aid of SHG; for instance, in ADP A2wmin == 250 nm at T == 200 K [4.173]. Since 90 ° phase matching has some advantages, nonlinear crystals which possess 90 ° phase matching at a given pump wavelength are generally used for SHG. For example, for SHG of 860
Table 4.14. Parameters of crystals doubling dye laser radiation frequency Crystal
BBO DKB5 KB5 LFM KDP ADP DKDP LilO3 ADA DADA DKDA RDP RDA K Nb0 3 DCDA CDA
defT
a
d~fT/n3 a
0.3 0.1 0.1 1.4 1 1.2 0.9 12.7
0.06 0.01 0.01 2.1 1 1.5 0.9 107
0.9 0.9 30.3 0.9 0.9
0.9 0.8 390 0.8 0.8
12 min [nm] (0
204.8 216.2 217.1 230 258.5 262 265.5 293.2 294 296 310 313.5 342 430 517 525
"Walk-off" angle p[deg] at different 1(0 500 nm
600 nm
700 nm
800 nm
900 nm
4.96
4.71
4.28
3.89
3.57
1.99
1.96 7.22 1.51 1.57 1.41 3.34 0.80
1.56 6.76 1.69 1.81 1.59 4.98 1.88
1.05 6.43 1.69 1.82 1.57 5.00 1.42
0.11 6.19 1.65 1.79 1.51 4.74 2.03
0.87 0.65
1.06 1.22
1.10 1.35 0.94
aValues of defT and d~fT/n3 are calculated relative to
defT
and d~fT/n3 for KDP.
316
4 Applications of Nonlinear Crystals
nm radiation, KNb0 3 is most suitable, and for 592 nm radiation, a DADA crystal is used. Minimum wavelengths by SHG process were obtained in crystals of f3 - BaB204 (205 nm), potassium pentaborate (KB5), and its deuterated analog (DKB5) (217 nm). A KB5 crystal has been used for SHG of dye laser radiation at 434-630 nm [4.174-176] (Table 4.15). The dye laser radiation propagated in the XY (ab) plane and was polarized in the same plane. The second harmonic was polarized along the Z axis (the eeo interaction). The above spectral range was covered by varying the phase-matching angle ({Jooe from 90 to 30 If a much smaller spectral interaction takes place in the YZ plane «({J == 90 range (217.1-240 nm) is covered as the phase-matching angle Booe varies from 90 to 0 [4.175]. In the YZ plane the effective nonlinearity is much less than in 0
0
•
0
) ,
0
0
Table 4.15. Second-harmonic generation of dye-laser radiation Parameters of output radiation (energy, power, pulse duration); conversion efficiency
Refs.
267.5-310 280-385 280-310 280-315
0.1 kW, '1 = 10/0
280-310
50 mJ, '7 = 8.4% up to 1 mW, '1 = 3
4.177 4.178,179 Booe = 66-45° 4.180 4.181-183 Booe = 70-58°, T = 20°C 4.180 4.184 4.173 Booe = 90°, T = 200-280 K 4.185 L=3 mm
Crystal
;'2w
KDP KDP KDP ADP ADP
[nm]
ADpa 290-315 ADpa 250-260 ADpa 293
50 mJ
X
10- 4
120JlW
0.13 mW, '1 = 0.080/0, r = 3 ps ADpa 295 '1 = 10- 4 , r = 3 - 4 ps RDP 313.8-318.5 3.6 MW, '1 = 52% In power, r = 8 ns RDP 3.2 MW, '1 = 36%, r = 10 ns 310-335 f= 10 Hz ADA 292-302 30mW ADAa 285-315 400 mW (single-mode regime), 50 mW (multimode regime) 0.8-3.2 MW, '7 = 9-36%, DKDA 310-355 L = 10 ns, f = 10 Hz tno,« 295 '7 = 10- 4 , r = 2.1 ps uro,: 293-312 0.37 mW, cw regime LilO3 293-330 15 mW, cw regime 3 kW, '7 = 30% LilO3 293 LilO3 293-310 4 mW, '7 = 0.4%, cw regime 21 mW, '1 = 2%, cw regime LilO3 293-310 100 kW, 4-17%, 8 ns BBO 204.8-215 50 kW, 1-36%, 9 - 22 ns BBO 205-310
4.186 4.187 4.188
Notes
L=I-3mm B = 90°, T = 20° - 98°C, 10 = 36 MWcm- 2 L = 25 mm B = 90°
4.189 4.190
B = 90° B = 90°, temperature tuning, L = 30 mm
4.188
B = 90°, L = 15 mm
4.186 4.191 4.192 4.177 4.193 4.193 4.121 4.194
L = 0.3 mm L = 10 mm L= 1 mm L=6mm L = 6 mm, L\A = 0.03 nm L = 6 mm, L\v = 30 MHz B = 70°-90° L = 6 and 8 mm
4.3 Harmonic Generation for Other Laser Sources
317
Table 4.15 (Contd.) Crystal
Parameters of output radiation (energy, power, pulse duration); conversion efficiency
Refs.
Notes
20 mW (average), 43 fs 0.02---0.18 ml, 17 ns 30 mW, cw regime
4.195 4.196 4.197
(Jooe = 40° - 60°, L = 7 mm (Jooe = 55°, L = 8 mm,
217.3-234.5 0.3 kW, 1%, 7 ns 217.1-240 5 - 6 flJ, 10%, 3 - 4 ns 217.1-315.0 5 - 6 u J, 10%, 5 ns
4.174 4.175 4.175
XY plane, eeo YZ plane, (Jooe = 90-0° XY plane, qJeeo = 90-31 0,
A2w
[nm]
315 230-303 243
(J = 38°, qJ = 90°, L = 55 urn
Av = 200 Hz KB5 KB5 KB5
L= 10mm KB5 217.0-250 DKB5 216.15 LFM 230-300
0.1-5 u.r, 0.2%-5% 2 }J1, 5%, 3 ns 2%
4.176 4.198 4.199
XY plane, qJeeo = 90-65° (J = 90°, qJ = 90° XZ plane, (Jooe = 35-45°,
LFMa LFMa LFM
n = 10- 4
4.184 4.200 4.177
XZ plane, (Jooe = 45° (590 nm)
4.201 4.193 4.202
(Jooe
L= 10mm 290-315 238-249 237.5-260
LFMa 243 LFM 285-310 KNb0 3 425-468
KNb0 3 419-475 KNb03 425-435 urea urea a
238-300 298-370
70 flW (244 nm), cw regime 20 W, nanosecond regime, n = 0.7% 1.4 mW, cw regime 4 JlW, cw regime 400 kW, 43%
12 flW, n = 6.5 x 10-4, cw regime 21 mW, n = 1.1%, cw regime
4.159 4.203 4.204 4.204
XZ plane, (Jooe = 39° (486 nm)
= 36.8°, L = 15 mm
Angular tuning in planes XY and YZ, temperature tuning (20 - 220°C) along the a axis Along the a axis, T from -36 to +180°C, L = 9 mm Along the a axis, T = 0-50°C, L=9mm (Jeeo = 90 - 45°, L = 2 mm ()eoo = 90 - 50°, L = 2 mm
Intracavity SHG.
the XY plane, since for KB5 d 31 r-v 10d32 ; therefore, in KB5 crystals the interactions in the XY plane are mainly used. Kato [4.121] used a f3 - BaB 2 0 4 crystal for SHG of dye laser radiation. The following parameters were obtained: P == 1 MW, 1" == 8 ns, A up to 204.8 nm (90 0 phase matching of the ooe type). The fundamental radiation was focused on the crystal by a lens with F == 50 em; the conversion efficiency to A == 204.8nm was 4% and to A == 205.8nm, 17%. Miyazaki et al. [4.194] attained n = 36% in a BBO crystal for SHG of dye laser radiation at 10 == 423 MWcm- 2 • The fundamental radiation was focused by a lens with F == 50 em. The conversion efficiency obtained in BBO was 4-6 times that in ADP. Due to ICSHG of femtosecond dye laser radiation, UV radiation at A == 315 nm with L == 43 fs was obtained in a BBO crystal 55 urn in length [4.195].
318
4 Applications of Nonlinear Crystals
ADA crystals have been used for SHG of rhodamine 6G laser radiation with n = 5 x 10- 3 [4.190]. Generation of cw UV radiation in the 299-330 nm range with P = 215mW was achieved in Lil0 3 because of ICSHG of dye laser radiation [4.192]. Argon laser radiation at A = 514.5nm and P = 2.5 W was used as a pump for a rhodamine 6G laser. The UV radiation bandwidth was 180-500 kHz. By SHG under 90° phase matching in LiI0 3 , Buesener et al. [4.191] obtained the wavelength A,2m = 293.15 nm. With the help of ICSHG of coumarin 102 laser radiation in a lithium formate crystal (LFM), UV radition at A = 243 nm was attained [4.201]. The fundamental radiation in the crystal propagated in the XZ plane at () == 36.8°. The ooe type interaction was used, and the length of the crystal was 15 mm. The cross-sectional diameter of the focused fundamental radiation beam in the crystal was 20 urn. The conversion efficiency was 1.5 x 10- 4 • Radiation with A = 243 nm was also generated in a ADP crystal [4.205, 206] due to ICSFG of argon and dye laser radiations. Although the nonlinear coefficient of LFM exceeds that of ADP, ICSFG in ADP is more effective than ICSHG in LFM, since ADP crystals can be used at 90° phase matching by proper choice of the interacting wavelengths. Third-harmonic generation has been obtained in potassium pentaborate (KB5) crystals [4.188]. Tunable UV radiation in the 207.3-217.4 run region was attained at a peak power of 25 kW and an average power of 15 mW. Interactions of the eeo type (in the XYplane) and of the ooe type (in the YZ plane) were used. Third-harmonic generation of dye laser radiation in urea has been obtained [4.118]: A3co = 231 nm, Beeo = 77°. ~[J.Ul1]
0.3
0.5
0.4
0.6
0.7
e [deg] 80
60
40
20 ""'---0.5 0.6
--"'_----a._--.J._--.J._.-.A.o_-..L._--L.._--I-_-.L-..I
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Al[J.Ul1] Fig. 4.2. Tuning curves for SHG in KDP, ADP, and RDP crystals (ooe interaction)
4.3 Harmonic Generation for Other Laser Sources
319
Figures 4.2-7 illustrate the tuning of the phase-matching angle versus the fundamental wavelength for SHG in crystals of KDP, ADP, RDP, LilOJ , LiNbO J , f3 - BaB204, KB5 (planes XY and YZ), LFM (XZ) , KTP (XY), KNbOJ (XY, YZ, XZ), and urea.
0..5
1.0
1.5
1
2
3
9O,.........,r----r------~-----,-----~--,-----,
e [deg] 70
50
30
4
Fig. 4.3. Tuning curves for SHG in Lil0 3 and LiNb03 crystals (ooe interaction)
0.4
0.5
0.6
0..7
0.8
Fig. 4.4. Tuning curves for SHG in LFM (XZ plane, ooe interaction) and BBO (ooe interaction)
320
4 Applications of Nonlinear Crystals
0.2 90 ,..--.__
0.3
~---,---...,...----r--~--T""'"'"1
Fig. 4.5. Tuning curves for SHG in crystals of KB5 (XY, eeo; YZ, ooe) and urea (eeo)
9,
0.507 urn conversion was 24%. Efficient upconversion of 10.6 urn radiation into the near IR in HgGa2S4 crystal with a Qswitched Nd:YAG laser a as pump source was realized with power conversion efficiency up to 60°A> [4.357]. Table 4.28 shows that proustite and silver thiogallate are the most promising nonlinear materials for up-conversion of CO 2 laser radiation to the visible range: quantum conversion efficiencies were 1Q-400/0 in the pulse regime and 4 x 10- 6 in the cw regime. Up-conversion of CO laser radiation to the visible region has also been reported. Researchers obtained a quantum conversion efficiency of 2.8 x 10- 8 in a proustite crystal 0.8 em long using He-Ne laser radiation (0.633 urn) as a pump source, Booe being 33 - 36° [4.370]. In other work [4.361], a GaSe crystal was used for this purpose with Nd: YAG laser radiation (1.064 urn) as a pump source, Booe == 18.8°.
4.5 Difference-Frequency Generation Difference-frequency generation or "down-conversion" is generally used for obtaining radiation in the middle and far IR regions as well as in the millimeter range of wavelengths. In some cases DFG is used for tuning high-power laser radiation in the visible region.
4.5.1 DFG in the Visible Region Lyutskanov et al. [4.276] have reported the effective conversion of high-power XeCI laser radiation (A == 308.0, 308.2, 308.5 nm; 'rp == 12ns) to the region with A == 434nm using Nd:YAG laser radiation (A == 1.064Jlm, 'rp == 0.7ns) as a pump. A KDP crystal 43 mm in length was used; the phase-matching angle was B == 53° and interaction was of the ooe type. High-efficiency conversion of
340
4 Applications of Nonlinear Crystals
rhodamine 6G laser radiation at 2 = 555-580 nm to 2 == 490-510 nm was obtained with a DKDP crystalS cm long [4.371] (Table 4.29).
4.5.2 DFG in the Mid IR Region To obtain IR radiation in the 1-6 urn region, Lil0 3 [4.281, 373-385] and LiNb0 3 [4.328, 386-391] crystals are mainly used. In this spectral region the mentioned crystals have high transparency, relatively high optical breakdown thresholds, and high nonlinear coefficients. Recently for a 1-3 urn region BBO crystals have also found application [4.392-395]. Crystals of proustite [4.396, 397], silver thiogallate [4.398-412], and GaSe [4.413, 410, 414-416] as well as AgGaSe2 [4.231,413,417,418], CdGeAs2 [4.240,419], CdSe [4.401,420], and Te [4.421] are most often used in the wavelength range from 4 to 23 urn. Table 4.30 lists the data on the crystals used for DFG in the mid IR range, corresponding sources of interacting radiation, and some output parameters of the generated IR radiation. Generation of cw IR radiation in the 2.3-4.6 urn region has been demonstrated [4.378]. With the aid of noncollinear DFG in Lil0 3 crystal the radiation from a rhodamine 6G laser (2 == 570-630 nm) and from an argon ion laser (2 == 514 or 488 nm) was mixed. A LiI0 3 crystal 10 mm in length was placed inside the dye laser cavity; the phase-matching angle was varied from 40° to 50°, and the angle a between the interacting beams amounted to 4 - 5°. The conversion efficiencywas 10- 6 ; IR radiation power reached 0.5 JlW in a single-mode regime and 4 JlW in a multimode, the bandwidth being 5 cm:'. Generation of cw radiation in the 11.4-16.8 urn range with 4JlW power has been attained in a CdGeAs 2 crystal with the use of DFG between CO 2 and CO laser radiations [4.240]. For the type II interaction the phase-matching angle was 46-47°. An effective generation of nanosecond IR radiation in the regions 2-4 urn, 4.4-5.7 urn, and 5-11 urn has been reported [4.384, 389, 399] in LiI0 3, LiNb0 3, and AgGaS2 crystals, respectively. In all three cases radiation from a dye laser and a Nd:YAG laser radiation was mixed. In a LiNb03 crystal f'..J
f'..J
Table 4.29. Difference frequency generation in the visible region Crystal
ADF[nrn]
Sources of interacting radiations
Conversion efficiency [%]
Refs.
KDP
434
25
4.276
DKDP
490-510
87
4.371
ADP
680-1100
ADP
490-510
Nd:YAG laser (r = 0.7ns) + XeCI laser (308 nm, 12 ns) Dye laser + 4mof Nd:YAG laser (266 nrn) Nitrogen laser (337 nrn) + dye laser Booe = 49-53° Dye laser + 4m of ND:YAG laser (266 nrn)
4.372 80
4.371
Table 4.30. Generation of IR radiation by DFG Crystal
A[urn]
Sources of interacting radiations, crystal parameters
Conversion efficiency, energy, power, 'tp
Refs.
Lil0 3
4.1-5.2 1.25-1.60; 3.40-5.65 2.8-3.4 1.1-5.6 2.3-4.6 4.3-5.3 0.7-2.2 3.8-6.0 3.5-5.4 1.2-1.6 4.4-5.7 f'Y5 3-4 2.2-4.2 2-4.5 2-4 2.04 1.7-4.0 2.5
Dye laser + ruby laser, ICDFG, L = 12 mm Dye laser + Q-switched Nd:YAG laser (1.064 and 0.532 Jlm,ICDFG, (Jooe = 21-28.5° Dye laser+Q-switched ND:YAG laser, L = 10 mm Dye laser + Nd:YAG laser (1.064 and 0.532 urn), (Jc = 23° Dye laser + argon laser (514 and 488 nm) Dye laser + 2w of Nd:YAG laser, (Jooe = 24.3° Dye laser + nitrogen laser, (Jooe = 51-31° Dye laser + copper vapor laser (511nm), (Jc = 21-24° Dye laser + 2ev of Nd:Y AG laser, (Jooe = 20° Two dye lasers, (Jooe = 29° Dye laser + Nd:YAG laser, (Jooe = 20-22° Two dye lasers, (Jooe = 20°, L = 3 mm Dye laser + ruby laser Dye laser + argon laser Dye laser(1.2 ps) + argon laser (100 ps), (J = 90°, T = 20Q-400°C Dye laser + Nd:Y AG laser, (Jooe = 46--57° Two dye lasers, (Jooe = 90° CPM dye laser + subpicosecond continuum, (Jc = 55°, L = lrnm Dye laser (620 nm) + picosecond continuum (825 nm), (Jooe = 20.3°, L = 5 mm Dye laser + Nd:YAG laser, (Jooe = 20.5-24.5°, L = 10 mm Two dye lasers, NCDFG, (Jooe = 12-17°, L = 6 mm Dye laser + Ti:sapphire laser Dye laser + Nd:YAG laser, (Jeoe = 76--78°, 1/1 = 0° Two dye lasers OPO (1.60-1.67 urn) + 2w of phosphate glass laser (527 nm) Two dye lasers, (J = 90° Dye laser + Nd:Y AG laser, (Jeoe = 38-52° Dye laser + Nd:Y AG laser
100 W (peak) 0.5-70 W (peak), L\v = 0.1 em:", 60 ns
4.373 4.374
80 mW (peak)
4.375 4.280 4.378 4.379 4.380 4.381 4.382 4.383 4.384 4.385 4.386 4.328 4.387, 388 4.389 4.390 4.391 4.392
LiNb0 3
LiNb03 BBO
KTP Ag3AsS3 AgGaS2
0.9-1.5 2.04-3.42 1.23-1.76 1.4-1.6 11-23 3.7-10.2 5.5-18.3 5-11 3.9-9.4
0.5-4 JlW,cw 3 ns 10-100 JlW,20 ns 0.8 mJ, 10 ns 1.5-5 ps 550 kW, 8 ns 100/0, 10 nJ, 400 fs 10/0,6 kW 1 JlW,CW 25 JlW(average), 1.2 ps, f = 138 MHz 60%, 1.6 MW 500/0, L\A = 0.03 nm 10 kW (peak), 0.2 ps, L\v = 100 cm" 5%, 4 ur, 0.5 ps
~
Vt
o
~
(iJ
= s ~
ri
230/0, 4.5 mJ, 8 ns 300-400 W (peak) 10 JlW(average), 150 fs, f= 80 MHz 8.4 kW, f= 76 MHz, 94 fs 3 W (peak), 30 ns 25-50 J.!l, 10 ps 4 W, 4 ns 180 kW, 12 ns 10/0, 8 ps
~
4.393 4.394 4.395 4.421 4.396 4.397 4.398 4.399 4.400
~ ::s o
"
~ (=). ~
o'
::s
("J'.l
0
~
Z 2.S'
0
('D
~
'"1
o
~
~
~ ("J'.l
4.5 Difference-Frequency Generation
343
25 mm long, maximum IR power at A == 2 - 4 urn amounted to 1.6 MW and the average power to 130 mW. The pulse duration at a difference frequency was 8 ns; the phase-matching angle varied from 46° to 57°. For the 4.4-5.7 urn region covered by DFG in the 19 mm long Lil0 3 crystal, the peak IR power was 550 kW at 'r == 8 ns; average power amounted to 45 mW at A == 4.9 urn. The phase-matching angle Booe was 20-22°. The IR radiation bandwidth at A==4.9 urn was evaluated as 0.1 cm- I . For the region 5-11 urn covered by DFG in a 10 mm AgGaS2 crystal, the peak power was 180 kW at 'r == 8 ns with an average power of rv 14 mW. The phase-matching angle Booe varied from 38° to 52° with a simultaneous tuning of the dye laser radiation wavelength from 1.35 to 1.17 urn. The IR radiation bandwidth was evaluated as 0.10.2cm- I . In a proustite crystal DFG between radiation from two dye lasers covered the wavelength range from 11 to 23 urn [4.396]. The peak IR power at A= 1620 urn amounted to 1-3 W (pulse duration: 3 ns). An Ag 3AsS3 crystal 4 mm long cut at the angle Bc == 20° to the optic axis was used. The above mentioned spectral range was covered when the crystal was rotated by 7°. The transmittance ofproustite at A up to 24 urn has also been measured [4.396]: a rv 70cm- I at A == 24 urn. The down-conversion process in LiNb0 3, AgGaS2' and CdSe crystals has been used to cover the 1.4-22 urn spectral range [4.401]. In the LiNb03 crystal the radiation from a Nd:YAG laser and a dye laser (610-710 nm) was mixed; as a result of DFG, tuning in the 1.4-2.13 urn region (IR 1) was possible. In another LiNb0 3 crystal, OPO in the 2.13-4 urn spectral region ( IR 2) was realized. In AgGaS2 and CdSe crystals DFG was realized upon mixing IR 1 and IR 2, which makes it possible to cover the 4-11 urn and 9-22 urn spectral regions, respectively. In the region 1.4-4 urn the output power was several MW, in the region 4-10 urn several kW, and in the region 9-22 urn, 10-100 W for 'r == 8 ns and f == 10Hz. Some papers have demonstrated generation of picosecond IR radiation at A= 1-9.4 urn by means of DFG. The mixing of radiation from two modelocked dye lasers in a Lil0 3 crystal 1 mm long produced radiation at A= 1.21.6 urn, with a peak power up to 10 Wand pulse duration 1.5-5 ps [4.383]. The pulse length was measured by the correlation method using SFG between IR and dye laser radiation in a Lil0 3 crystal 1 mm long (B ooe == 37°). Difference frequency generation in a 5 mm long LiNb0 3 crystal covered the IR spectral range 2-4.5 urn [4.388]. The radiation of an acousto-optically mode-locked argon laser (A == 514.4nm, 'r == lOps) was mixed with rhodamine 6G laser radiation (r == 1.2 ps) pumped by the same argon laser. The spectral bandwidth of IR pulses at A == 2.43 urn was 2.6 nm; other characteristics are given in Table 4.30. Elsaesser et al. [4.400] realized DFG of IR pulses in the 3.9-9.4 urn region with 'rp == 8 ps when Nd:YAG laser radiation (A == 1.064 urn, 'r == 21 ps) was mixed with dye laser radiation (A = 1.2-1.46 urn) in a 15 mm AgGaS2 crystal. The phase-matching angle varied from 36° to 48°. The IR radiation bandwidth
344
4 Applications of Nonlinear Crystals
was 6.5 cm" over the whole tuning range. The quantum efficiency of downconversion to IR radiation was several percent with respect to Nd:YAG laser pulse energy. The generation of IR radiation at A= 1.4-1.6 urn, f = 3.8 MHz, and rp = 94 fs has been reported [4.422]. Radiation of an acousto-optically mode-locked cw Nd:YAG laser (r == lOOps) was mixed in a KTP crystal (Bc == 76°, XZ plane, L == 3.4mm) with radiation of a cavity-dumped dye laser synchronously pumped by the second harmonic of Nd:YAG laser radiation. An average power of IR radiation was 3 mW. If a BBO crystal was used instead of KTP, an average power at A== 1.42Jlm was 50 JlW. Difference-frequency generation in AgGaS2 and GaSe 1 em in length by mixing the output of a mode-locked Nd:glass laser (1.053 urn, 2 ps) with the travelling wave dye laser radiation (1.1-1.4 urn) allows to obtain ultrashort (1 ps) IR pulses in the range of 4-18Jlm [4.410]. The limiting wavelength corresponds to the absorption edge of the respective crystal: 10 urn AgGaS2 and 18 urn for GaSe. IR pulses as short as 400 fs in the range of 4.5-11.5 urn were generated by mixing the Ti:sapphire laser and travelling wave dye laser outputs in AgGaS2 crystal [4.411]. The duration of the IR pulses was measured by means of the pump-probe technique in silicon plate. The radiation-induced generation of hot carriers in Si by Aex == 815 nm results in the increase of IR absorption, which was monitored at Aprobe == 8.0 urn, The two-cascade method of shortening the C02 laser pulse duration has been proposed and realized [4.423]. The C02 laser radiation (A == 10.6 urn, r == 150ns was mixed with Nd:YAG laser radiation (A == 1.064Jlm, r == 20ns), in the first proustite crystal. The difference-frequency radiation at A == 1.2 urn, was mixed once more with 1.064 urn, radiation in the second proustite crystal and became down-converted to 10.6 urn radiation (r == 20 ns). The powerconversion efficiency from A == 1.064 urn radiation was 0.05%, which made it possible to obtain IR radiation intensitites of about 10 kW cm- 2. In both cascades of nonlinear conversion 1 em proustite crystals were used with Beeo == 20°.
4.5.3 DFG in the Far IR Region Difference-frequency generation between the radiations of two lasers generating at close frequencies is one of the methods of producing far IR radiation (A == 50 um-Ztl mm). For instance, the mixing of frequencies of two temperature-tunable ruby lasers in LiNb0 3 and quartz gave rise to far IR radiation with the frequency 1.2-8.1 cm- l [4.424]. One laser with a wide spectrum of radiation can also be used as a pump source. Then frequency components inside the generation spectrum interact and, as a result, the bandwidth-determined difference frequency is generated. This method was used for generating IR radiation at a fixed frequency of 100 cm" in LiNb0 3 pumped by neodymium silicate glass laser radiation [4.425].
4.6 Optical Parametric Oscillation
345
Table 4.31. Difference frequency generation in the far IR region Pump sources
Crystal
vjcm"]
A[urn]
Nd:glass laser (1.06 um) Ruby laser(0.694 urn) Two ruby lasers(0.694 um), 1 MW, 30 ns Nd:glass laser (1.06 urn), 50 mJ, 10 ps Nd:glass laser (1.06 JlID) 10 ps Dye laser (0.73-0.93 urn), 11-15 ns, 4-13 MW Nd:glass laser (1.064 urn), 10 ps Two ruby lasers(0.694 urn) 20 ns Ruby laser(0.694 urn) Two dye lasers: '["1 = 1-2 ps, Al = 589 nm, E I = 0.2 mJ; '["2 = 20 ns, A2 = 590-596 nm, E2 = 20 mJ CO 2 laser at two frequencies Two C02 lasers
LiNb03 LiNb03 LiNb03 quartz ZnTe, LiNb03 LilO 3 ZnTe, ZnSe, LiNb03 LiNb03 LiNb03
100 29 1.2-8.0
Power, energy
Refs.
100 330 1250-8330
20mW
4.425 4.426 4.424
8-30
330-1250
20 mWjcm- I
4.427
5-30
330-2000
lW (ZnTe)
4.428 4.429
0.4-2.5 1-3.3
4000-25000 3000-10000
60W 0.5W
4.430 4.431
LiNb03 LiNb03
1.67-3.3 20-200
3000-6000 50-500
3 nJ
4.432 4.433
GaAs ZnGeP2
2-100 70-110
100-5000 90-140
1.7 JlW
4.434 4.435
LiNb0 3 is mainly used as the nonlinear material for the IR region, since it is fairly transparent in this region. Some isotropic crystals (GaAs, ZnTe, and ZnSe) possessing high nonlinearities are also used (Table 4.31). Down-conversion to v = 20-200 em -1 with quantum efficiency 0.1-0.3 % was attained [4.433]. Two dye lasers were used with nanosecond and picosecond pulse durations. The amplifiers of two lasers were pumped with the second harmonic of Nd:YAG laser radiation, which ensured synchronization between the interacting pulses. The two interacting beams were focused into a 4 mm LiNb0 3 crystal at a small angle a. Tuning of the far IR radiation frequency was attained by simultaneously varying the angle rx from 5 to 50 mrad and changing the frequency of the nanosecond dye laser. The generated energy was 3 nJ at a pulse duration of 10 ps.
4.6 Optical Parametric Oscillation 4.6.1 OPO in the UV, Visible, and Near IR Spectral Regions Optical parametric oscillation (OPO) in nonlinear crystals makes it possible to obtain radiation with a tunable frequency. The methods of angular and temperature phase-matching tuning are used for a smooth change of the wavelength in parametric light oscillators. Along with the advantages, both methods have certain drawbacks. Angular tuning is rather simple and more rapid than
346
4 Applications of Nonlinear Crystals
temperature tuning. Temperature tuning is generally used in the case of 90° phase matching, i.e., when the birefringence angle is zero. This method is mainly used in crystals with a strong temperature dependence of phase matching: ADP (Apump == 266 nm), LiNb03 (Apump =: 530 nm), LBO (A pump == 266, 355 and 530 nm), Ba2NaNbsOlS (Apump == 530 nm), KNb03 (Apump == 532 nm), and DKDP (Apump == 266 nm). At present, optical parametric oscillation makes it possible to obtain continuously tunable radiation from the UV (300 nm) to middle IR range (18 urn). Minimum pulse durations in the near IR region are -as short as 57-65 fs ( in visible, less than 100 fs), and the OPO radiation bandwidths are down to 0.02 cm": Maximum efficiencies of OPO operation up to 50%, corresponding to 70-80% pump depletions (see below), were observed in femtosecond, picosecond, nanosecond, and continuous wave regimes by use of KTP, LBO, BBO, and LiNb03:MgO crystals, respectively. Since the excitation of parametric oscillation requires high intensities of radiation (107-10 10 W cm"), nanosecond and picosecond pump sources are usually used for OPO. All OPO schemes can be reduced to two schemes: the travelling-wave OPO (without a cavity) and the resonant OPO. The travelling-wave OPO scheme (TWOPO) usually consists of one or two nonlinear crystals. TWOPO is simple and can be realized within the whole transparency range of the crystal; however, it has certain disadvantages. For instance, to attain high conversion efficiencies, high pump intensities are required (up to 30 GW cm") close to the damage threshold of the crystal. Maximum conversion efficiencies in TWOPO schemes, were attained with crystals of KDP (67-74%) and ADP (60%) at total OPO pulse energies up to 2.3 J. Singly-resonant OPO, or SROPO, uses resonant feedback at only the signal or idler frequency. Doubly-resonant OPO, or DROPO, uses resonant feedback of both signal and idler frequencies. Exotic triply-resonant OPO, with resonant feedback also at pump frequency, and intracavity OPO, with the crystal placed inside the laser cavity, e.g., CPM dye laser, are used very seldomly. Quadruply-resonant OPO, with SHG inside the OPO cavity and resonant feedback also at the second harmonic, can be mentioned as well. Picosecond and femtosecond OPO with synchronous pumping is the most promising type of resonant OPO. A nonlinear crystal is placed in the cavity (or in two cavities), which ensures a positive feedback at one or two frequencies, and is pumped by a train of ultrashort pulses. The time period between pulses is equal to the double passing time of the cavity (axial period). The cavity generally consists of two broadband mirrors with reflection R 1 == 99% and R2 == 4-80% at the OPO wavelengths. Synchronously pumped OPO is advantageous in that the generation threshold here is low (I < 100MW cm- 2) and space and time pulse coherences are close to limiting. That is, in the synchronously pumped OPO scheme the shortest femtosecond pulses (60 fs) are attained. The drawback of this scheme is the necessity for special dielectric mirrors and its complexity as compared with the traveling-wave OPO scheme.
4.6 Optical Parametric Oscillation
347
Injection seeding from an external source of radiation, mainly from other OPO, or from of the narrow-bandwidth laser radiation source, e.g., a singlefrequency dye laser, significantly enhances the reproducibility and efficiency of parametric generators. Operating in this way, optical parametric amplifiers (OPA) ensure narrow-band output without using wavelength-selective elements. In the case of the seed at a fixed frequency, the tunability of the OPOOPA system is achieved by changing the pump wavelength (dye-laser or Ti:sapphire laser radiation). Mode-locked or Q-switched Nd:YAG (A = 1.064 urn), Nd 3+ phosphate glass (A == 1.054 um), and Nd:YLF (A == 1.047 um] lasers, as well as their second, third, and fourth harmonics, are generally used as an OPO pump source. A Nd:YAG laser operates with high reliability in the mode-locked regime at a high repetition rate. Pulse durations of passively mode-locked Nd:YAG lasers are about 25-45 ps. Currently, Nd:YAG laser systems can deliver 1 GW powers in a single picosecond pulse at a pulse repetition rate of more than 10 Hz. Nd 3+: phosphate glass lasers can deliver shorter pulses (1-2 ps); however, their operation is much less stable, and pulse repetition is low because of the low heat conductivity of the active elements. As a pump source for OPO, the XeCI lasers (A = 308 nm) are also often used. Recently, very promising Ti:sapphire lasers (A == 700 - 900 nm) have found wide application in OPO devices. Compact schemes of OPO are realized with the aid of diode-laser-pumped Nd:YAG lasers as pump sources. Crystals with high nonlinearity, i.e., LiNb0 3 and KTP, are used in these devices. Different OPO schemes and their energetic, temporal, spectral, and spatial characteristics are considered in detail in [4.38, 436-438]. A large variety of useful information on the OPO and their applications can be found in two special issues of the Journal of the Optical Society of America, B (vol. 10, No 9 and 11, 1994) devoted to optical parametric oscillators. In this handbook we list only the main output OPO parameters realized in practice. The inorganic crystals KDP, DKDP, ADP, CDA, LiI0 3, LiNb0 3, BBO, LBO, KTP, KTA, "banana", rx - HI0 3 , and KNb0 3 and the organic crystals of urea, NPP, and DLAP have been used as nonlinear materials for OPO in the 0.3-5 urn spectral range. Table 4.32 lists pump wavelengths, phase-matching angles, pump thresholds (peak intenstity and/or average power), tuning ranges, OPO pulse durations, and conversion efficiencies for OPO experiments in the UV, visible, and near IR spectral ranges. The column headed "notes" gives data on the OPO type, pump intensities, crystal lengths, phase-matching temperatures, and output characteristics of OPO radiation (energy, power, bandwidth). Note, that for the KTP crystal in the XY plane (0 = 90°) eoe interaction occurs, and in the XZ plane (qJ == 0°), it is oeo interaction. For the LBO crystal in the XY plane (0 == 90°), kz plane (qJ == 0°), and YZ plane (qJ == 90°), respectively, ooe, oee, and eoo interactions take place. Picosecond optial parametric oscillators are most thoroughly described in [4.439, 444, 483], Travelling-wave OPO in KDP, LiI0 3, LiNb0 3, and a - HI03, crystals has been realized [4.439]. High-efficiency (10-12%) con-
w
Table 4.32. OPO in the UV, visible, and IR regions
~
00
Crystal
KDP
Phase-matching angle, type of interaction
Apump
[urn]
Pump thre- AOPO [urn] shold, Ithr [MW cm- 2 ]
eoe
0.532
0.8-1.7
eoe eoe
0.532 0.532
0.8-1.67 0.9-1.3
eoe
0.82-1.3
0.527
tp
35 ps 40 ps 30 ps 0.3-0.5 ps
Conver- Refs. sion efficiency [0/0] 6-8
4.439
25 51
4.440 4.441, 442
2
4.443, 444
Notes ~
>
"t:S
TWOPO, 10 = 15GW cm", L. = 2.5 em, L2 = 4cm TWOPO, E = 1mJ, L. = L2 = 4cm TWOPO, AvA't' = 0.7, L. = 4cm, L2 = 6 em, 10 = 15-20 GW cm- 2 Synchronously pumped OPO, E=20~
eoe
0.532
eoe
0.355
eoe
0.35
eoe
0.35
KDP + BBO eoe (KDP) ooe (BBO) DKDP Oooe = 90° Oooe = 90° ADP Oooe = 51-45° ooe ooe Oooe = 90° CDA Oooe = 90° Oooe = 90°
1000--2000
-
1000
0.45-0.64 0.79-1.69 0.45-0.6
45 ps
67-74a
4.445
15
4.446
70
4.447
0.5 ns
67a
4.448
0.6 ns
13
4.449,450 4.451 4.452 4.453 4.454 4.455 4.456 4.457 4.458 4.459
0.75-1.77
0.266 0.266 0.527 0.352 0.266 0.266 0.266 0.532
0.47-0.61 0.37-D.6 0.93-1.21 0.44-1.75 0.42-D.73
5 ps 2 ns
0.44-0.68 0.854-1.41
10 ps
60a 0.1-1.0 25 30 10 30-60
0.8-1.3
10 ps
12.5
0.53
1000
(;. ~
g. ::s
CI:l
0
~
Z 0
e.
Er ~
= 4cm, L2 = 6cm, = L2 = 4cm
~ l""I
o
l""I ~ CI:l
S"
v;"
0.5 ps
a
0.5275
1500
TWOPO, L, E= 2J TWOPO, L.
~
TWOPO, L. = 2cm, L2 = 6cm, E = 0.35J, 10 = 6 - 8GW cm- 2 TWOPO, L = 5 em, injection-seeding, 10 = 0.3 GW cm- 2 TWOPO, L(KDP) = 4cm, L(BBO) = 1em, 10 = 60GW cm- 2 TWOPO, T = 40-100°C TWOPO, E = 2.3J, 10 = 10GW cm- 2 TWOPO, L. = 2.5 cm, L2 = 3 em TWOPO, T = 50-105°C L = 6em, 10 = 1GW cm- 2 TWOPO, T = 50-110°C, L = 5cm L = 3cm, T = 50-70°C, 10 = O.3GW cm- 2 synchronously pumped OPO, L = 4 cm, 10 = 3GW cm- 2
LilO 3
Oooe = 21°
1.06
80
Oooe = 24° Oooe = 23.1-22.4° Oooe = 21.8-19.3°
1.06 1.06 0.694 0.694
50 50 5
10 10
ooe
0.53 0.53 0.53 0.532 0.532 0.532
Oooe == 25-30°
0.53
3000
0.68-2.4
0.53 0.532 0.347 1.06 1.06 1.06 1.06
10
Oooe = Oooe == Oooe = Oooe = Oooe =
0.74-1.85 4.1 0.41-2.1 2.13 1.43-4.0 1.1-4.45 1.4-4.0
Oooe = Oooe = Oooe = Oooe = Oooe =
LiNb0 3
ooe ooe
25-30° 29.5° 22-34° 26° 23-30°
22.5° 53-37° 90° 90° 90°
45-51 ° 47°
1.06 1.064 1.064 1.054
47°
1.064
10
100
10 ns 1.4-2.7 2.5-3.2 1.15-1.9 0.95---0.84, 2.5-4.0 0.68-2.4 0.61-2.7 1.4-3.8 0.63-3.4 0.63-3.35 0.61-4.25
2
4.460
15 50b
4.461 4.462 4.319,463 4.464
0.01-1 ns 20 ns
15 ns 0.01-1 ns 6 ps
8
30 ns 6 ps
20 4
4.465 4.461 4.466 4.467 4.468 4.439,469
5
4.470
10 ns 50 ps
0.4
100 ns 6 ps 20 ns 3.5 ns
8 3 15 10
1.55-3.5 1.37-4.83 1.35-2.11
0.5 ns 20 ns 40 ps 0.5 ps
2.5-4.0
10 ns
5-20 17 15
4.471 4.472 4.473 4.474 4.475 4.476 4.477 4.478 4.420 4.479 4.480 4.481
SROPO, 10 =: 250MW cm- 2 , vector phase matching SROPO, P = 30-50 MW SROPO, L = 6cm, E = 0.1 J DROPO, L =: 0.85cm, P = 10kW
SROPO, L = 1.6cm SROPO, P = 12MW Synchronously pumped OPO SROPO, P == 100kW, ~v = 0.1 cm" SROPO TWOPO, L I == 1em, L2 = 2.5 em, 10 = 2GW cm- 2 TWOPO, LI = L2 = 4cm, 10 = 6 GW cm- 2 E = 0.5J Injection seeding, L = 3 em, E = 3 ~ ~
DROPO, L =: 3mm TWOPO, L =:: 2cm, 10 == 8GW cm- 2 SROPO, 10 =: 10MW cm- 2 TWOPO, ~v = 6.5cm- I 10 = 1 GW cm- 2 TWOPO SROPO, L == 5cm TWOPO Synch. pumped OPO, L = 18mm, 10 = 0.14GW cm- 2 Injection seeding, L = 5cm, E = 4mJ, ~v == 0.2cm- 1
0'\
0 a. o
~
E. ~
~
'"1
~
3
~
a. o 0C"I'.l
~
[
o'
= w
~
'0
w
VI
0
Table 4.32 (Contd.) Crystal
LiNb03
Phase-matching angle, type of interaction
Apump [urn] Pump thre- AOPO [urn] shold, Ith!2 [MWcm- ]
47°
1.064
90°
0.53
50-90° 84° 90° 90° 90° 90° 90° 90°
0.53 0.53 0.532 0.532 0.532 0.532 8 0.532 < 30 0.473---0.659 -
1.50-1.58, 3.27-3.65 0.75-0.64 1.8-3.1 0.59-3.7 0.66-2.7 0.68-0.76 0.93-1.3 0.63-3.6 0.85-1.4 0.65-3.0 0.55-3.65
90°
1.06 0.532 0.532
O.4mW 35mW 12mW
1-1.14 1.01-1.13 1.007-1.129
90°
0.532
13mW
MgO : LiNb0 3(Jooe
(Jooe
BBO
== 90°
== 60-84°
0.532
90° ooe
0.532 0.62
ooe,ooe ooe, eoe eoe,ooe
0.6 0.6 0.6
tp
Conver- Refs. sion efficiency [%] 4.482
Notes
~
(5'
Injection seeding, L == 5 em, E == 20 mJ,
~
o' ::s
t"'}
4.215
T = 180-400°C
17.5 7.2 46(67b )
4.483 4.479 4.484 4.444 4.485 4.486 4.459 4.487
cw cw cw
40(60b ) 34(78b )
4.488 4.489 4.490
0.966--1.185 cw
38(73b )
4.491
0.7-2.2
30 ps
5.4
4.492
0.75-2.8
cw 200 fs
15
4.493 4.494
0.75-3.1 0.75-3.1 0.75-3.1
180-250 fs 200-250 fs
20-25 23 20-25
4.450 4.450 4.450
TWOPO, L} == L2 == 15mm TWOPO, T == 46-360°C Synch. pumped OPO Synch. pumped OPO L == 5cm, T == 5D-450 °C SROPO, P == 30kW, f == 10kHz Synch. pumped OPO, L == 25mm SROPO, T == 110 - 430°C, Pay == 105mW Quadruply resonant OPO DROPO, T == 107-110 °C DROPO, T == 107 -111°C, P== 8.15mW DROPO, L== 15mm, T== 113-126°C, P== 100mW TWOPO, Al == 0.3 nm(0.7 urn) and l.4nm(2Jlm) DROPO, L == 12.5 mm, T == 107°C, TWOPO, L} == 5mm, L2 == 7mm, E==20J.LT TWOPO-OPA, L} == L2 == 8 mm, 10 == 70GW cm- 2
20mW
~
>
1j
5 ps 40 ps 20 ps 20 ps 30 ps 15 ps 10 ps 130-700 ns
17 9 2-3
0
~
Z 0
a
5' ~
~
'"1
(1
~ t"'}
S"
~
BBO
(Jooe (Jooe
= 21.7-21.9° = 20.7-22.8°
0.532 0.532
278
0.94-1.22 0.67-2.58
12 ns 18 ps
10 13
4.496 4.497
0.7-1.8 1.04-1.07 0.63-3.2 0.406-3.17
65-260 fs 70 fs 1.3 ps 20 ps
3 25 30
4.498-500 4.501 4.450 4.502
ooe ooe ooe ooe
0.527 0.527 0.53 0.36
ooe
0.355 0.355 0.355
130
0.45-1.68 0.43-2.0 0.41-2.6
8 ns
9.4
4.503 4.504 4.504
= 24-33°
0.355 0.355
20 27
0.412-2.55 0.42-2.3
2.5 ns 8 ns
24 32
4.505 4.506
= 33.7-44.4°
0.355
38
8 ns
12
4.507
0.355
39
0.48--0.63; 0.81-1.36 0.59-0.89
20-30 ps
2
4.508
0.4-2.0
15 ps
30
4.509
= 26-33° Booe = 25-55°
(Jooe
(Jooe
ooe (Jooe
ooe (Jooe
= 26-33°
ooe
ooe ooe ooe ooe
0.355
0.355
(Jooe = 27-33° (Jooe = 23-33°
(Jooe
500
= 35.5-37°
0.355 0.355 0.355 0.355 0.308 0.308 0.308
0.4-2.86
20-40 300 150 18
0.45-1.768 0.402-3.036 0.407-2.78 0.43-2.1 0.422~.477
24 ps
7 ns 9 ps 15 ps 8 ns
6.5 2 40-61 30 10
0.354-2.37
64b
0.~.56
15
4.510 4.511 4.512,513 4.514 4.515 4.516 4.517 4.518
SROPO, L = 9mm, E = 1mJ TWOPO, L, = L2 = 9mm, 10 = 2.5-3.8GW cm- 2 , E = 0.1~.5mJ Synch. pumped SROPO, L = 5.8 mm OPA with gain ratio 2 x 104 TWOPO-OPA, L, =L2 = 8mm Synch. pumped OPO, L = 12mm, 10 = 2 GWcm- 2 , E = 3mJ, A). = 0.24nm SROPO, L = 11.5mm, E = 15mJ L = 7.6mm L = 6.5mm, SHG of OPO radiation to 205 nm in BBO SROPO, L = 12mm, Pay = 140mW SROPO, L, = 11.5mm, L2 = 9.5mm A). = 0.03mm SROPO, L, = 17mm, L2 = 10mm A). = 0.05~.3 nm Synch. pumped OPO, L = 11.8mm, P = 15kW OPO-OPA, L, = 12mm, L2 = 6 mm, L 3 = 15mm, 10 = 3GW cm-2 , A). = O.3nm TWOPO, L, = L2 = L 3 = 8mm, 10 = 5GW cm- 2 , Av == 10cm- 1 SROPO, L = 10mm, E = 0.2mJ SROPO, L = 15mm, E = 0.1~.2J DROPO, L = 7mm Injection seeding, L = 15mm SROPO, L = 7 mm, E = 0.26 mJ SROPO, L = 20mm, E = 20mJ SROPO, L = 20mm, Av = 0.07cm- 1 (with intracavity etalon)
~
~
0
~
(5'
e. ~ ~ '"1 ~
8 ~
a.o
0
~
o
a ~
o'
=
w
Ul
w
V'l
N
Table 4.32 (Contd.) Crystal
Phase-matching angle, type of interaction
Apump [um] Pump threshold,/thr [MW cm- 2]
AOPO [urn]
tp
Conversion efficiency [%]
Refs.
~
Notes
> s g.
~
~ ~
o = 81°, qJ = 5° o= 85°, qJ = 9°
0.57-0.63 0.57-D.63
0= 0°, qJ = 0°
0.532
o = 90°, qJ = 0°
0.532
1.13-1.21 0.75-1.8
20
4.33
0= 90°, ooe
0.53
0.65-2.5
24
4.526
o = 90°, qJ = 0°
0.532
1500
0.77-1.7
100 ps
30
4.527
o = 90°, qJ = 0°
0.5235
0.652-2.65
12 ps
13
4.528-530
o = 90°, qJ = 0°
0.5235
0.909-1.235
33 ps
50
4.530, 531
DROPO, T
= 167-180 °C
o= 90°, qJ = 0° o = 90°, qJ = 0°
0.5235 0.5235
2500 (10 mW) 1100 (4.5 mW) 15 (30 mw) 700
SROPO, L = 20.5 mm, 10 = 23 MW cm- 2 SROPO DROPO, L = 2cm, T = 13{}-185 °C, p= 30mW TWOPO, L, = 8 mm, L2 = 17mm, 10 = 0.8GW cm- 2 , E = 10~ TWOPO, Ll =L2 =L3 = 15mm, T = 3{}-85 °C, 10 = 25 GW cm- 2 Injection seeding by 1.08 urn Injection seeding by 1.08 urn (40 ps, L = 9mm, 10 = 1TW cm- 2 ) SROPO, T = 2{}-120 °C, 10 = 250 MW cm- 2 ~A = O.4nm Injection seeding from OPO (0.72-2 urn), T = 106.5-148.5 °C, 10 = 3.1 GW cm- 2 OPA, angle (qJ = 8.7-15.9°) and temperature (T = 103-210 °C) tuning, E = 0.45mJ Synch. pumped SROPO, L = 15mm T = 105-137 °C, ~A = 0.14nm SROPO, L = 12mm, T = 125-190 °C
0.65-2.65 0.924-1.208
1.7 ps 12 ns
50 45
4.530 4.532
DROPO, L DROPO, L
= 12mm, P = 0.21 W = 12mm, T = 156-166 °C
BBO
Oooe = 36.5-47.5° 0.266 0.266 Oooe = 30-48°
23
LBO
o = 90°, qJ = 0°
0.78-D.81
(360 mW)
o = 86°, qJ = 0°
0.6515
o = 90°, qJ = 0°
0.605
220
0.33-1.37 0.302-2.248 1.49-1.70
9 ns 7 ns cw
6.3 40b
4.519 4.512 4.520
1.2-1.4
20 ps
0.8
4.521
200 fs
1{}-15
4.450, 522
0.85-D.97; 1.6-2.1 1.2-1.5 1.2-1.5
580 fs 400 fs
10 25
4.523 4.524
0.95-1.006;
10 ns
0.5
4.525
=
CI:l
0
~
Z 0 ::s
S' ~
~
"'1
(1 "'1
~ CI:l
S
v;-
LBO
() == 90°, qJ == 0°
0.523
100
o== 90°, qJ == 0° o== 90°, qJ == 0°
0.523 0.5145
80 (70 mW) 0.8-1.5 (50 mW) 0.966-1.105
o== 0°, qJ == 90°
0.364
(115 mW)
0== 0°,
0.355
qJ =::
0°
0=::90°, qJ
0.72-1.91
34
4.533
1.2-1.5 ps cw
27(75b )
10
4.534 4.535
0.494-D.502; cw 1.32-1.38 0.47--{).487 10 ns
9.4
4.536, 537
9
4.538
0.435-1.922
10 ns
22
4.539
0.46-1.6
15 ps
30
4.540
Injection seeding from OPO,
27
4.541
L = 16mm,10 =:: 2.8 GWcm- 2 , E SROPO, T =:: 20-200 °C
35b
4.542
SROPO, L == 16mm
12 ps
28
4.543
30 ps
37.6
4.544,545
9 ps
26
4.514
TWOPO, L, == L2 == 15mm, 10 == 5GW cm- 2,E=0.1-1mJ TWOPO, L =:: 10mm, T == 21°-450°C, 10 == 18 GW cm", 6). = 0.15nm DROPO, L = 10.5mm, E == 0.15mJ
P==90mW
0.355
14
0.355
== 27-43° 0== 0°, qJ == 0°
0.355
15
0==90°,
0.355
60
qJ
0.48---0.457; 12 ns 1.355-1.59 0.455-D.655; 10 ns 0.76-1.62 0.403-2.58
0.355
== 18-42° o== 0°, qJ == 0°
0.355
2300
0==90°,
0.355
1000
qJ
0.41590.4826 0.452-1.65
== 30-42°
0==90°, qJ
== O.3mJ
== 27-42°
0== 90°,
qJ
SROPO and DROPO, L == 20mm, T== 18-86°C, P== 103mW SROPO, L =:: 12mm, T == -35° + 100°C, E =:: 4.5mJ DROPO, 10 =:: 40MW cm- 2 , E =:: 2.7mJ
== 24-42°
0==90°,
qJ
Synch. pumped SROPO, L == 13mm T == 125-175 °C, Pay == 89mW SROPO, L =:: 12mm, Pay == 78mW TROPO, L = 20mm, T == 183° ± 3 ° C,
1 ps
0
~
s
E~
~
'"1
0.308
26
== 26-52°
type II in XZ and 0.3078 YZ planes,
30
~
8
0.355---0.497; 0.809-2.34 0.381---0.387; 5 ns 1.5-1.6
28-40 b
35
4.547
L
0.314-1.74,
10
4.548
SROPO, L == 16mm, T == 20°C
4.517, 546
SROPO, L == 15mm
== 16mm, 10 == 0.1 GW cm-
2
~ ::!. o
0CI:l §;
[
0==0-9°
o== 0°, qJ == 0°
~
~
0.266
10
10 ns
o' l:S w w
Ul
w
VI
~
Table 4.32 (Contd.) Crystal
KTP
~
Phase-matching angle, type of interaction
Apump [urn] Pump threshold, Ithr [MW cm- 2]
= 50-58°, qJ = 0° 1.064 1.064 f} = 90°, qJ = 53° f} = 82-90°, qJ = 0° 1.064 f}
= 90°,
f}
f}
qJ
= 0°
= 81-90°,
qJ
= 90°,
qJ
= 0°
f}
= 90°,
qJ ==
f}
= 54°, = 67°,
qJ
f} f}
= 45°,
qJ ==
qJ
= 0° = 53°, qJ = 0°
f}
qJ
qJ
= 0°
0°
= 0° = 0°
= 40-70°, = 90° f} = 40-80°,
1.06 1.064
= 0° 1.053
f}
0°
0.7-0.95 0.7650.815 0.720.853
(5.8 W) 70
150
0.73-0.80 0.765 0.68
40000; (180 mW)
0.645 0.61
(110 mW)
0.526
f}
80 (0.8 W)
AOPO[J.lm]
1.8-2.4 3.2 1.57-1.59; 3.21-3.30 1.61 2.128 1.55-1.56; 3.22-3.28 1.04-1.38; 2.15-3.09 1.22-1.37; 1.82-2.15 1.052-1.214; 2.286--2.871 1.38-1.67 1.2-1.34; 1.78-2.1 1.16-2.2; 0.58-0.657 1.2-1.34 0.755-1.04; 1.5-3.2 0.6-2.0
'tp
10 ns 10 ns 2-3 ps 15 ns
12 ps
Conversion efficiency [%]
Refs.
10 5 15
4.549 4.550 4.551
47(66 25 21
b
)
Notes
= 0° 0.526
0.6-4.3
~
n·
s:~
4.552 4.553 4.554
10 ns
20
4.555
57-135 fs
55b
4.556
1.2 ps
42
4.557
cw 62 fs
0.001
4.558 4.559
57 fs
60b
4.560
DROPO, E = 0.1-{).5 mJ SROPO, L = 15mm, P = 0.2W SROPO, L = 10mm, f = 75 MHz, 61 = 1.5nm Diode-pumped Nd:YAG laser Synch. pumped OPO with 6 KTP (total length 58 mm), P = 14W Synch. pumped OPO, L = 6 mm, P=2W SROPO, L = 15mm
220 fs 13 105-120 fs -
4.561 4.562, 563
30 ps
10
4.564
L = 1.15mm, f == 90MHz, P = 340mW (135 fs) and 115mW (57 fs) Synch. pumped OPO, L = 6mm, P=0.7W L= 10mm,P=2J.lW Synch. pumped OPO, L = 1.5mm, f = 76 MHz, P = 175mW L = 1.5mm, P = 0.68W, ICSHG in BBO (L == 47 urn) Synch. pumped OPO, P = 30mW Synch. pumped OPO in CPM dye laser cavity, L == 1.4mm L = 20mm
30 ps
10
4.564
L = 20mm
qJ
qJ
>
"'l:j
::s
Cf.l
0
~
Z
0
e.
5"
(ll
~
1-1
o
~ Cf.l
[
Cf.l
KTP
() = 90°,
q>
= 0°
(} = 90°, q> = 10-35° q> = 0° 0=90°, q> = 25.3°
0.532
80
0.531
(40 mW)
0.5235
cw
4.493, 565
SROPO and DROPO, L P = 1.07W
1.002-1.096 2.2 ps
16(79b )
4.566
0.7-0.9; 1.3-2.2 1.0617
3.5 ns
12
4.418, 567
Synch. pumped OPO, L = 5mm, P == 42mW L = 15mm, E = 3mJ, 6v
cw
30
4.568
DROPO, L = 8 mm
10(56b )
4.530, 569
16
4.570
44
4.554
0.523
0= 90°, q> = 0 - 33° 0= 53 -72°
0.526
(0.5 W)
q>
69°, q> = 0°
= 0°, oeo
Type II
"Banana" Oooe = 90° Booe = 90° Oooe = 90°
0.5235 0.5235 0.532
0.7730.792 0.77 0.532 0.532 0.53
= 0.02 cm"
1.29-1.44; 1.83-1.91 1.45; 1.7
85-150 fs
10-15
4.572
Synch. pumped SROPO, L=5mm,P=2mW SROPO, L = 5mm, f = 125 MHz, P=40mW Synch. pumped OPO, L = 6 mm, P = 0.58 W Synch. pumped OPO, L = 9 mm, Av = 10 cm- 1 cw mode-locked DROPO L = 15 mm, ICSHG in BBO with t1 = 40% (380-520 nm) L = 1.47 mm, P = 75 mW
300 ns
0.3
4.573
DROPO, L = 7 mm
1.435;1.662
-
4.560
L = 1.5 mm
1.01-1.1
14 ps
1.2-1.9
1.5 ps
4 (150 mW) 1.02; 1.075 0.76-1.04 7
0.78
= 10mm,
35
() = 90°
() = 53°,
57 10-12 10
16-20
qJ
~
Synch. pumped SROPO, L = 10 mm, f = 139 MHz, T = 75-350°C L = 23 mm, /0 = 20 MWcm- 2 TWOPO, L]=L2=2 em, /0=4-5 GWcm- 2 Synch. pumped OPO, AvA'! = 0.7 L = 9mm DROPO, L = 19 mm, T = 184-220 °C DROPO, T = 180-200°C, P = 12 MW SROPO, L = 12.7 mm, 10 = 90 MWcm- 2
0.308 0.266 0.62
o= 9.5-13°,
Notes
4.576,577
Ooeo =64-90°
NPP
Refs.
8.1
0.355
eeo
Conversion efficiency [%]
15-45ps
= 50-90°
Ooeo
DLAP
'!p
"'l:j
"Banana" Oooe = 90°
eoe eoe type II
AOPO [JIm]
aConversion efficiency was determined from Eq. 4.4. bPump depletion.
L = 1.5 mm
~ (5. ~
g.
::s ~
0
~
Z
0
~
s
(ll
~ '"1
o '"1
"< ~
[
~
4.6 Optical Parametric Oscillation
357
version to parametric radiation was attained in an a - HI03 crystal at pump intensity 3--4 GW cm ? without focussing. For KDP and LiNb0 3 crystals, cylindrical telescoping was used with optimum conditions found experimentally. For LiNb03 a one-crystal scheme and 2:1 spherical telescoping were used. In Cl-HI03 an effective SRS was observed, which competed with OPO and consumed up to 30 % of the pump energy. The SRS threshold was very low and amounted to 0.3 GW crrr'. In Lil0 3 SRS was less effective: up to 5% of the pump energy was consumed for stimulated scattering. Study of the parametric pulse shape has shown that in KDP the parametric pulse duration decreases to 17 ps, and in Lil0 3 to 6 ps in comparison with pump pulse duration 45 ps. Danelyus et al. [4.444] realized OPO with synchronous pumping by a train of picosecond pulses of the second harmonic of Nd:phosphate glass laser radiation (2 == 527 nm). A KDP crystal (L == 4 em, eoe interaction) was placed in a resonator with an optical length of 130 em, equal to the axial period of the pumping laser. The shortest OPO pulses were 0.3-0.5 ps at an energy of 20 JlJ (the tuning range was from 0.8 to 1.5 urn). Then, the OPO pulses were amplified to 1 mJ in F! :LiF crystals (L = 2 em) pumped with the second harmonic of electro-optically mode-locked Nd:YAG laser radiation. The pulses of parametric radiation can be considerably shortened in a two-cascade TWOPO by introducing the corresponding time delay between the pump and signal (or idler) waves. For this purpose, for instance, a CaC03 crystal several millimeters in length can be placed between the TWOPO crystals, which ensures the temporal delay between the signal and pump waves with different polarizations and, hence, different refractive indices in a CaC03 crystal [4.478, 592]. This method shortened the OPO pulses to 4 ps when the pump pulse duration (r pump ) was 21 ps [4.592], and to 0.5 ps when Lpump = 8 ps [4.478]. In the latter case the temporal delay amounted to 8.5 ps. Maximum OPO efficiency in traveling-wave OPO schemes 11eff == 60-70% has been attained with two KDP or ADP crystals spaced at a great distance from each other (up to 1 m) [4.445, 447, 453]. The efficiency 11eff was calculated by the equation 'Jeff == Eopo/(Eopo
+ E une )
(4.4)
where EoPO is the total OPO radiation energy (signal + idler) and E une is the energy of unconverted pump radiation measured after second crystal. The value 11eff is greater than the ordinary 'J value calculated from the equation 'J == Eopo/E pump , since (Eopo
+ Eune)/Epump == 50-80%.
(4.5)
This is because the pump and OPO radiations are always partially lost due to scattering and absorption in the crystals [4.453]. Conversion efficiency can also be determined in terms of pump depletion: 1'/
== 1 -
Eune/Epump.
(4.6)
Pump depletions are usually much greater than the ordinary 11 values.
358
4 Applications of Nonlinear Crystals
Generation of ultrashort OPO pulses (r < 1OOfs) was reported in a number of articles [4.498-501, 556, 559, 560, 572]. Synchronously pumped OPO schemes are mainly used in these devices. Laenen et al. [4.499] pumped BBO (L = 5.8 mm, Bc = 23°) based SROPO by the train of 300 pulses with 0.8 ps duration from a frequency-doubled Nd:glass laser. Near the degeneracy point (A= 1.0796 mm) OPO pulse durations were 65 fs (FWHM). With a KTP crystal (L = 1.5 mm, Be = 67°, ip = 0°) and additional external pulse compression, 175 mW IR radiation near 1.3 J.1m was generated with r = 62 fs andf=76 MHz [4.559]. As a pump source a Ti:sapphire laser (765 nm, 800 mW, 110 fs) was used. The measurements of pulse duration were carried out by the autocorrelation method with 1 mm thick Lil0 3 [4.499] or 0.3 mm thick KDP [4.559]. Minimum OPO pulse durations obtained up to now are as short as 57 fs [4.556, 560]. Here the Ti:sapphire laser (2.5 W, 125 fs) was also employed for synchronous pumping ofKTP (1.15 mm) based OPO. The use of an intracavity dispersion compensation allows generation of 57 fs unchirped pulses with a high repetition rate (90 MHz): average power was 115 mW. Output OPO powers up to 1 W were attained at r= 135 fs. When a BBO crystal (L=47 J.1m) was placed inside the ring OPO cavity the tuning range ofOPO was shifted into the visible by ICSHG: A = 580-657 nm, r