Multiple scattering of arbitrarily incident Bessel beams
by random discrete particles
Zhiwei Cui,* Yiping Han, and Xia Ai
School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China
*Corresponding author: zwcui@mail.xidian.edu.cn
Received August 29, 2013; revised September 27, 2013; accepted September 27, 2013;
posted October 1, 2013 (Doc. ID 196605); published October 24, 2013
In this paper, we introduce an efficient numerical method to characterize the multiple scattering by random
discrete particles illuminated by Bessel beams with arbitrary incidence. Specifically, the vector expressions of
Bessel beams that perfectly satisfy Maxwell’s equations in combination with rotation Euler angles are used to
represent the arbitrarily incident Bessel beams. A hybrid vector finite element–boundary integral–characteristic-
basis function method is utilized to formulate the scattering problems involving multiple discrete particles with a
random distribution. Due to the flexibility of the finite element method, the adopted method can conveniently deal
with the problems of multiple scattering by randomly distributed homogeneous particles, inhomogeneous
particles, and anisotropic particles. Some numerical results are included to illustrate the validity and capability
of the proposed method and to show the scattering behaviors of random discrete particles when they are
illuminated by Bessel beams. © 2013 Optical Society of America
OCIS codes: (290.5850) Scattering, particles; (290.4210) Multiple scattering; (140.0140) Lasers and laser
optics; (050.1755) Computational electromagnetic methods.
http://dx.doi.org/10.1364/JOSAA.30.002320
1. INTRODUCTION
The problem of multiple scattering by random media com-
posed of many discrete particles is an important subject of
research owing to the wide range of possible applications in
academic research and industry. Over the past few decades,
the multiple scattering of plane waves by random discrete
particles has been extensively investigated. Also, many meth-
odologies have been developed to analyze this problem, for
instance, multiple scattering theory [
1–4], radiative transfer
theory [
5,6], the T-matrix method [7–10], the sparse-matrix
canonical-grid method [
11,12], the characteristic basis function
method (CBFM) [
13,14], and the hybrid finite element–
boundary integral–characteristic-basis function method (FE-
BI-CBFM) [
15].
In recent years, with the development of laser sources and
the expansion of their applications, there has been a growing
interest in the study of multiple scattering by random discrete
particles illuminated by laser beams. For the case of an inci-
dent focused Gaussian beam, an early study was carried out
by Mackowski and Mishchenko [
16]. In that paper, they ap-
plied the T-matrix method to simulate the multiple scattering
of a Gaussian beam by multiple discrete particles with a ran-
dom distribution. However, they focused their attention on
the restricted case of an on-axis normally incident Gaussian
beam. Later, we generalized the CBFM based on surface
integral equations to include the case of illumination by an
arbitrarily incident focused Gaussian beam and applied it to
examine the scattering behavior of random discrete particles
[
14]. In our work, the incident Gaussian beam was described
by utilizing the Davis beam model in combination with rota-
tion Euler angles. Nevertheless, the scattering of arbitrarily
incident Bessel beams by randomly distributed particles
has not been reported. In fact, Bessel beams, as another kind
of laser beams, have attracted widespread attention in various
fields ever since their first introduction by Durnin [
17], be-
cause of their special characteristics of nondiffraction and
self-reconstruction. That is, these beams can maintain the
same intensity profile and the intensively localized intensity
distribution. Therefore, they will not suffer diffraction during
the wave propagation process within the Rayleigh distance.
Moreover, they are able to wholly reform at some distance
beyond the obstruction as long as the whole beam is not
blocked if such beams encounter an obstruction. It is thus im-
portant to understand their behavior upon interaction with
random media composed of many discrete particles.
In this work, we introduce an efficient numerical method to
characterize the multiple scattering by random discrete par-
ticles illuminated by Bessel beams. Because the zeroth-order
Bessel beam has the typical characteristics of nondiffraction
and self-reconstruction, and can be easily obtained in the lab-
oratory, here we only consider the zeroth-order Bessel beam.
Specifically, the arbitrarily incident beams are described by
the vector expressions of the zeroth-order Bessel beam
[
18,19] in combination with the rotation Euler angles [20].
The scattering problems involving multiple particles with
a random distribution are analyzed by adopting the hybrid
FE-BI-CBFM presented in the authors’ previous paper [
15].
This method exploits the unique features of the hybrid
finite element–boundary integral (FE-BI) method [
21–24] and,
more importantly, the unique features of random discrete par-
ticles. It is designed in such a manner that it first decomposes
the original problem into many subregions, where each sep-
arate particle is regarded as a subregion, and then it employs
the finite element method (FEM) to deal with each subregion.
The subregions are coupled to each other through the boun-
dary integral equations based on Green’s function. To reduce
2320 J. Opt. Soc. Am. A / Vol. 30, No. 11 / November 2013 Cui et al.
1084-7529/13/112320-08$15.00/0 © 2013 Optical Society of America
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