TRIDS I. FDTIADIS • CHRISTDS V. MASSALAS EDITORS
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TRIDS I. FDTIADIS • CHRISTDS V. MASSALAS EDITORS
I : iop
AA
- # < ^"v' /// 2 1
\N^^_C^^^ / ^ ' \^^~^£^^^^^ ~'-" \
^ \ i 240 ^
^ •
I ~ ~ "T " -
~
^
/ ' ">/
^
"
/
330
/ v/
^
^
300
270
Figure 3. Distribution of the radial scattering amplitude \gr\ for f-incidence with ki„c=it/9
In Figs. 4-6, the magnitude of the tangential scattering amplitude | g > W l f° r transverse S-incidence at several angles is examined. In this case, kinc = 0 has almost no effect on the computed quantity for any value of the anisotropy factor. In contrast, a n 14 incidence is shown to be the one that reveals the anisotropy and up to a point its measure. Our previous remarks relatively to the symmetry of the distributions w.r.t. the angle of
13
incidence are also valid here as one may observe from the case of 7t 19 incidence.
Figure 4. Distribution of the tangential scattering amplitude \gr\ for S-incidence with fe„=0.
\
,./\>2a ^ a ^ f
~~---^ 60
\
150
— ,4=1.0 — ,4=1.5 ^=1.25 —• .4=0.75 — ,4-0.5
30
X. | J 1
X/^Vlt X ;
J
0
210^
2*0^-
j____--^300 270
Figure 5. Distribution of the tangential scattering amplitude |g,| for S-incidence with ki„c=7t/4.
14
90
150 f
120 ^~^~~~
' /P*^~^
/
b (see Fig. 1). A number of N AS's, in the form of elementary electric currents, are located on each one of S" or S"", radiating elementary electric fields, proportional to the two-dimensional Green's function. The AS's on S" radiate outside the scatterer, whereas AS's on 5°"' radiate inside it. Matching the boundary condition (equality of the electric
18 and magnetic tangential fields) at M= N collocation points (CP's) on the z-plane projection of the scatterer surface, and using the addition theorem for cylindrical functions [6,7], yields the MAS square linear system. This system can finally be written, in a compact, block matrix form as
p] Ml [w] [r\
Mi
(i)
where [u\ \y\ \fV\\Y\ are NxN square matrices with elements given by CO
(2) /=-00
* °°
v
«- = i X J> (k°a'» K ( 2 ) (^i>xp{- jifym - „)}
(3)
/=-oo
w
=-
4
V j , (kb)H\2\kaoul >xp{- jlfam - fa )} L*
(4)
/=-00
7
™
m
i^Ji(k0aM2)(k0bhp{-Jl^m-*„)}
(5)
/=-00
In (2)-(5), oo, verifying the convergence properties of MAS, just like in the PEC [4] and the SIBC [5] cylinders. In the general case, (19) can be evaluated explicitly after a considerable amount of tedious algebra. The final result for the normalized error can be written as
e{ain,a0Ul,b,N) =
m=\
•NEi where
(20)
21 JV 1
• ^ S i
JV_
" i Z «=i
whereas 0p = p-IK/N
7o i)
N
Sexpl-Xm-^fc'k
1 2
^)-^
i e x p { - X — K ) ( / i 2 l ) 4 +/
?
_ ¥rv
= TT/N corresponds to the midpoints (MP's) between the CP's (see Fig. 1). Following a procedure similar to [5], the error e, defined in the mean square sense over the scatterer surface, is finally given by i
e(a,b,N,