[数值]1[FDTD][Taflove-2004]Concept of the equiphase sphere for light scattering .....

Concept of the equiphase sphere for light scattering by nonspherical dielectric particles LgA>,.  
Zhigang Chen and Allen Taflove D?r% Y  
Department of Electrical and Computer Engineering,Northwestern University,Evanston,Illinois 60208 !&Us^Q^  
Vadim Backman !tuK.?q|l  
Department of Biomedical Engineering,Northwestern University,Evanston,Illinois 60208 sW!MVv  
Received June 6,2003;revised manuscript received August 20,2003;accepted August 20,2003 Hu$JCB-%  
We introduce the concept of the equiphase sphere for light scattering by nonspherical dielectric particles. 0ZtH  
This concept facilitates the derivation of a simple analytical expression for the total scattering cross section of  A}n7A   
such particles.We tested this concept for spheroidal particles and obtained a bound on the minor-to-major ]V
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axis ratio for the valid application of this technique.We show that this technique yields results that agree -A1:S'aN-  
well with the rigorous numerical solution of Maxwell’s equations obtained with the finite-difference time- 5S&^mj-9  
domain method.The new technique has the potential to be extended to the study of light scattering by arbi- uN(N2m  
trarily shaped convex dielectric particles.?2004 Optical Society of America BHZSc(-o  
OCIS codes:290.5850,290.0290. :6}cczQE|O  
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1.INTRODUCTION /P/::$  
The physical basis and phenomenology of light scattering _H$Z}2g<z  
by small particles is of interest in a variety of science and .jRv8x b
 
engineering disciplines.1 bE2{^5iG  
,2It is well known that light HG[gJ7  
scattering by homogeneous or layered spheres comprised GlaZZ,   
of isotropic dielectric materials can be analyzed with the F1&7m )f$l  
Mie theory and its extensions.2 ufS0UD8%H  
,3However,because most u&$1XZ!es  
particles of interest are neither spherical nor homoge- ]d,#PF  
neous,their scattering properties cannot be obtained ana- G>W:3y  
lytically.Numerical methods for solving Maxwell’s equa- %)j^>W5  
tions or approximate techniques are needed in such ??XtN.]7  
circumstances. S{qn^\0  
In previous work4we have shown numerically and ana- x DX_s:A  
lytically that the spectral dependence of the total scatter- 1xMD )V:  
ing cross section of randomly inhomogeneous dielectric k1M?6TW&  
spheres of size in the resonant range can closely resemble lK #~lC  
that of their homogeneous counterparts with volume- 2%t!3F:  
averaged refractive index.The next step is to under- *mfPq"/  
stand how departing from a spherical shape affects the to- /n#t.XJY*  
tal scattering cross section.For scattering by 4mF=A$Q_/  
nonspherical particles,there exists no universal analogy a8r+G]Z  
to the Mie theory.It is not practical to develop a theory W[.UM
 
for each conceivable particle shape.But it is possible to dF0:'y  
construct a method that will include the effect of particle }t5pz[z
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shape in a simplified way. }#9 |au`  
A prototypical nonspherical particle is the spheroid. 5c3&4,,eR  
Spheroids are attractive for modeling light scattering by ;q" ,Bs  
nonspherical particles because the spheroidal shape can b;t b&o  
be changed from mildly aspherical to needle-like(prolate) v
X"jL  
or disk-like(oblate)by varying just the ratio of the major N;XJMk_ H  
to the minor axis,i.e.,the aspect ratio.Therefore the aKkY)  
spheroidal particle becomes a natural choice when one '2c4 4F)i  
wants to extend studies of scattering from spherical par- KS(Ms*k;'  
ticles to nonspherical particles.The exact analytical so- =!PUKa3f<  
lution for a single homogeneous,isotropic spheroid by use _D."KU|  
of the separation-of-variables method was pioneered by Xc7Qu?}  
Asano and Yamamotoand then was significantly im- p|R]/C0f  
proved by Voschinnikov and Farafonov.6This complex 3|.KEJC"
 
procedure involves an infinite set of linear algebraic equa- =s[P =dU  
tions for the unknown expansion coefficients that has to yy$7{9!  
be truncated and solved numerically.For spheroids sig- -vBk,;^>  
nificantly larger than a wavelength and/or for large re- wq`\p['Q,  
fractive indices,the system of linear equations becomes ,v*<yz/  
large and ill-conditioned.Moreover,the computation of -Hu]2J)  
vector spheroidal wave functions is a difficult mathemati- B<?fD  
cal and numerical problem.Results obtained with this 5 }F6s  
approach indicate that small-diameter,highly elongated /S)&dN`  
spheroids have a scattering behavior comparable to that aW#_"Y}v'  
of infinite circular cylinders with properly defined cross- ?kM53zbT#  
section diameter.7 d
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In this paper we introduce the concept of the equiphase #ui7YUR=2  
sphere for light scattering by nonspherical dielectric par- +G>
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ticles.The equiphase sphere is defined as the sphere Q5qQ%cu  
that gives rise to the same maximum phase shift of the ShRkL<  
penetrating light as the nonspherical particle of interest. n{r
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This concept facilitates the derivation of a simple analyti- XW9 [VUW~  
cal expression for the total scattering cross section of non- ppo\cy;  
spherical particles when(n 1)kd 1 and(n 1) @ei:/~y3  
1,where k is the incident wave number,d is the char- 0qMf6  
acteristic size of the particle,and n is the refractive index D1<$]r,  
of the particle. *`.4M)Ym~  
To demonstrate the application of our equiphase sphere @X*r5hjc  
concept,we report studies of the effects of ecc .. .6#Y-iJqc  
?$FvE4!n  

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