Near-field evanescent waves scattered from a
spatially deterministic and anisotropic medium
JIA LI,* LIPING CHANG, AND ZHEFU WU
Institute of Fiber Optic Communication & Information Engineering, College of Information Engineering, Zhejiang University of Technology,
Hangzhou 310023, China
*Corresponding author: leejia@zjut.edu.cn
Received 27 March 2015; accepted 11 May 2015; posted 14 May 2015 (Doc. ID 236982); published 2 June 2015
The scattering of light from an anisotrop ic medium, which
may present either spatially random or deterministic statis-
tics, has attracted substantial interest where the measure-
ment of structural properties of scatterers is concerned.
To date, however, no literature has studied near-zone evan-
escent waves scattered from a spatially deterministic and
anisotropic medium. In this Letter, integral expressions
are derived to represent electric fields of evanescent waves
in the near-zone scattered field. In addition, the dependen-
ces of spectral densities of scattered field on the propagation
distance of evanescent waves and effective radius of the
scattering potential (ERSP) are also shown by numerical
graphs, respectively. Potential applications of our study
include the near-field optical microscopy and biomedical
sensing.
© 2015 Optical Society of America
OCIS codes: (260.0260) Physical optics; (290.5825) Scattering
theory.
http://dx.doi.org/10.1364/OL.40.002680
The spatially anisotropic medium, of which the refractive in-
dices satisfy fluctuating distributions in different positions, has
showed substantial prospects in the measurement of biological
tissues [
1], determination of correlation statistics of unknown
scatterers [
2], and knowledge of properties of light scattered
from particles [
3]. In general, information extracted from scat-
tered fields can be used to reconstruct structural properties of
unknown scatterers. The representative work among these
studies was the introduction of scattering theories of light from
a quasi-homogeneous (QH) anisotropic medium. By suppos-
ing the correlation function of the scattering potential satisfies
the Gaussian profile, the far-zone spectral density and degree of
coherence were derived for light that scatters from a QH aniso-
tropic medium. [
4]. Later, these results were generalized to the
case where a coherent plane wave scatters from a collection of
anisotropic particles [
5]. Scattering theories of a polychromatic
light from rotational QH anisotropic medium and anisotropic
particles were addressed in the literature [
6–8], respectively,
which demonstrated that the spectral density and spectral
degree of coherence of a scattered field can be modulated by
rotating an anisotropic scatterer. Reciprocal relations were
obtained to connect statistics of scattered field with properties
of incident light [
9]. Coherence and polarization properties
of light, which is generated from the scattering of a linearly
polarized electromagnetic plane wave from a QH anisotropic
medium, were studied in [
10,11]. In addition, it was found
that spectral shifts and spectral switches will occur in light
waves scattered from a system containing two sorts of aniso-
tropic particles if the scattering potential of the medium
satisfies certain conditions [
12].
The aforementioned investigations are of importance to the
development of scattering theories. However, recent studies in
the super-resolution imaging (accomplished by using nano-
scale optical instruments) require knowing properties of evan-
escent surface waves scattered from an inhomogeneous medium
[
13–16]. These properties have shown substantial prospects in
the devise of near-field optical microscopy [
17]. According to
the literature [
18,19], both homogeneous and evanescent waves
exist in scattered field, provided that a plane wave, which can be
either homogeneous or evanescent, scatters from a random
medium. To the best of our knowledge, research on properties
of a scattered evanescent wave have not been fully addressed in
any of current literature. In this Letter, we propose the scatter-
ing theory of a plane wave from a spatially deterministic and
anisotropic medium in the near field. Integral expressions are
derived for the electric field of evanescent waves in the near-
zone region. Dependences of spectral densities of scattered field
on several factors, including the propagation distance of evan-
escent waves and effective radius of the scattering potential
(ERSP), are shown by numerical graphs.
We start our work by reviewing the scattering theory of a
light wave from a spatially deterministic and anisotropic
medium. The polarization effect will not be considered in our
study, thus scattering equations will be solved by using the
scalar wave theory. Let us suppose that the initial electric field
of a unit-amplitude monochromatic plane wave has the follow-
ing form:
U
i
r
⇀
; ω
0
expik
0
s
⇀
0
· r
⇀
; (1)
where k
0
ω
0
∕c is the wave number, c denotes the speed of
light propagating in vacuum, and s
⇀
0
represents the unit vector
2680
Vol. 40, No. 12 / June 15 2015 / Optics Letters
Letter
0146-9592/15/122680-04$15/0$15.00 © 2015 Optical Society of America