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

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Concept of the equiphase sphere for light scattering by nonspherical dielectric particles
Zhigang Chen and Allen Taflove
Department of Electrical and Computer Engineering,Northwestern University,Evanston,Illinois 60208
Vadim Backman
Department of Biomedical Engineering,Northwestern University,Evanston,Illinois 60208
Received June 6,2003;revised manuscript received August 20,2003;accepted August 20,2003
We introduce the concept of the equiphase sphere for light scattering by nonspherical dielectric particles.
This concept facilitates the derivation of a simple analytical expression for the total scattering cross section of
such particles.We tested this concept for spheroidal particles and obtained a bound on the minor-to-major
axis ratio for the valid application of this technique.We show that this technique yields results that agree
well with the rigorous numerical solution of Maxwell’s equations obtained with the finite-difference time-
domain method.The new technique has the potential to be extended to the study of light scattering by arbi-
trarily shaped convex dielectric particles.?2004 Optical Society of America
OCIS codes:290.5850,290.0290.

1.INTRODUCTION
The physical basis and phenomenology of light scattering
by small particles is of interest in a variety of science and
engineering disciplines.1
,2It is well known that light
scattering by homogeneous or layered spheres comprised
of isotropic dielectric materials can be analyzed with the
Mie theory and its extensions.2
,3However,because most
particles of interest are neither spherical nor homoge-
neous,their scattering properties cannot be obtained ana-
lytically.Numerical methods for solving Maxwell’s equa-
tions or approximate techniques are needed in such
circumstances.
In previous work4we have shown numerically and ana-
lytically that the spectral dependence of the total scatter-
ing cross section of randomly inhomogeneous dielectric
spheres of size in the resonant range can closely resemble
that of their homogeneous counterparts with volume-
averaged refractive index.The next step is to under-
stand how departing from a spherical shape affects the to-
tal scattering cross section.For scattering by
nonspherical particles,there exists no universal analogy
to the Mie theory.It is not practical to develop a theory
for each conceivable particle shape.But it is possible to
construct a method that will include the effect of particle
shape in a simplified way.
A prototypical nonspherical particle is the spheroid.
Spheroids are attractive for modeling light scattering by
nonspherical particles because the spheroidal shape can
be changed from mildly aspherical to needle-like(prolate)
or disk-like(oblate)by varying just the ratio of the major
to the minor axis,i.e.,the aspect ratio.Therefore the
spheroidal particle becomes a natural choice when one
wants to extend studies of scattering from spherical par-
ticles to nonspherical particles.The exact analytical so-
lution for a single homogeneous,isotropic spheroid by use
of the separation-of-variables method was pioneered by
Asano and Yamamotoand then was significantly im-
proved by Voschinnikov and Farafonov.6This complex
procedure involves an infinite set of linear algebraic equa-
tions for the unknown expansion coefficients that has to
be truncated and solved numerically.For spheroids sig-
nificantly larger than a wavelength and/or for large re-
fractive indices,the system of linear equations becomes
large and ill-conditioned.Moreover,the computation of
vector spheroidal wave functions is a difficult mathemati-
cal and numerical problem.Results obtained with this
approach indicate that small-diameter,highly elongated
spheroids have a scattering behavior comparable to that
of infinite circular cylinders with properly defined cross-
section diameter.7
In this paper we introduce the concept of the equiphase
sphere for light scattering by nonspherical dielectric par-
ticles.The equiphase sphere is defined as the sphere
that gives rise to the same maximum phase shift of the
penetrating light as the nonspherical particle of interest.
This concept facilitates the derivation of a simple analyti-
cal expression for the total scattering cross section of non-
spherical particles when(n 1)kd 1 and(n 1)
1,where k is the incident wave number,d is the char-
acteristic size of the particle,and n is the refractive index
of the particle.
To demonstrate the application of our equiphase sphere
concept,we report studies of the effects of ecc ..

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