Expansion of a zero-order Bessel beam in spheroidal
coordinates by generalized Lorenz–Mie theory
L. Han
n
, Y.P. Han, Z.W. Cui, J.J. Wang
School of Physics and Optoelectronic Engineering, Xidian University, Xi’an, Shannxi 710071, China
article info
Article history:
Received 17 March 2014
Received in revised form
16 June 2014
Accepted 18 June 2014
Available online 25 June 2014
Keywords:
Zero-order Bessel beam
Generalized Lorenz–Mie theory
Spheroidal particle
Spheroidal beam shape coefficients
abstract
An analytic solution to the scattering of the zero-order Bessel beam by a spheroidal
particle is constructed on the basis of the generalized Lorenz–Mie theory (GLMT).
The spheroidal beam shape coefficients (BSCs) of the zero-order Bessel beam are directly
expressed in spheroidal coordinates and computed conveniently using an intrinsic
method. Utilizing the tangential continuity of the electromagnetic fields, the expression
coefficients of scattered and internal fields are determined. Numerical results concerning
scattered field in the far zone are displayed for various parameters of the incident
electromagnetic beam and of the scatter. These results are expected to provide useful
insights into the scattering of a Bessel beam by spheroidal particles and particle
manipulation applications using Bessel beams.
& 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Bessel beam, as an exact solution to the free-space
Helmholtz equation, has special characteristics of nondif-
fraction and self-reconstruction [1–3]. That is, the beam
can maintain the same intensity profile and the intensively
localized intensity distribution at any vertical plane to the
propagation direction. Thus, it will not suffer diffraction
during the wave propagation process within the Rayleigh
distance. Moreover, Bessel beam is able to wholly reform
at some distance beyond the obstruction as long as the
whole beam is not blocked if such beam encounters an
obstruction. The common interest to Bessel beam is mostly
caused by the promises of its practical application in
optical levitation and manipulation [4–6], non-linear
optics [2], optical acceleration [7], optical guiding and
alignment [8,9], and so on. Recently, several scholars have
been devoted to calculation of the scattering of Bessel
beam by dielectric objects. Čižmár et al. [10] presented the
first theoretical and experimental study of dielectric
sphere behavior in an optical field generated by interfer-
ence of co-propagating Bessel beams, where the spherical
beam shape coefficients (BSCs) are given in terms of a
numeric integral. Taylor and Love [11] improved the
expressions for calculating the spherical BSCs for Bessel
beam, for use in Mie scattering calculations. Subsequently,
Chen et al. [12] derived the explicit analytical expression of
the spherical BSCs for Bessel beams of arbitrary order and
polarization using angular spectrum representation. Based
on the expansion of Bessel beam in terms of spherical
vector wave functions, Ma and Li [13] investigated the
scattering of an unpolarized Bessel beam by a homoge-
neous sphere, and Qu et al. [14] discussed the scattering of
a zero-order Bessel beam by an anisotropic spherical
particle in the off-axis configuration. Later, Mitri analyzed
the arbitrary scattering of a zero-order Bessel beam [15]
and a high-order Bessel vortex (helicoidal) beam [16] by a
homogeneous water sphere in air, and expressed the radial
components of the electric and magnetic scattering
fields using partial wave series involving the BSCs and
Contents lists available at ScienceDirect
journal ho mepage: www.elsevier.com/locate/jqsrt
Journal of Quantitative Spectroscopy &
Radiative Transfer
http://dx.doi.org/10.1016/j.jqsrt.2014.06.010
0022-4073/& 2014 Elsevier Ltd. All rights reserved.
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Corresponding author.
E-mail address: luhan@stu.xidian.edu.cn (L. Han).
Journal of Quantitative Spectroscopy & Radiative Transfer 147 (2014) 279–287