Journal of Applied Mathematics and Physics, 2014, 2, 47-50
Published Online January 2014 (http://www.scirp.org/journal/jamp)
http://dx.doi.org/10.4236/jamp.2014.21008
OPEN ACCESS JAMP
Propagation of Electromagnetic Wave through Anisotropic
Graded Refractive Index Profile
Arnold Abramov, Lin Luan
Kuang-Chi Institute of Advanced Technology, Shenzhen, China
Email: qul aser@gmail.com
Received November 2013
ABSTRACT
Propagation of electromagnetic wave (EW) through multilayer structure consisting anisotropic layers with gra-
dient refractive index material is studied theoretically. Analytical solution for linear dependence of refractive
index profile is examined. The structure consist the forbidden gaps, which are sensitive to parameters of refrac-
tive index profile.
KEYWORDS
Electromagnetic; Refractive Index; Gradient; Layer
1. Introduction
Propagation of EM waves in gradient index medium has been extensively studied in the past century. Materials
with refractive indices gradually varying in space are important type of inhomogeneous medium. They can be
used in radar devices in the centimeter wavelength range, mobile satellite communications, transformation op-
tics, medical applications, as an optics component to optoelectronic system, etc. In particular in 1944 Luneburg
analyzed [1] a more common type of spherical inhomogeneous medium with central symmetry where the focus
is situated outside the lens. But the use of Luneburg lenses in practical application hampered by technical com-
plexity of manufacturing the lens with variable index of refraction, which determines their high cost. New op-
portunities to create graded refractive index (GRIN) medium emerged with the discovery of a new class of arti-
ficially structured materials [2-4] called metamaterials which make it possible to achieve both negative effective
dielectric permittivity ε and magnetic permeability μ parameters in a certain frequency bandwidth. This means
the ability to have materials in which refractive index changes from negative (left-handed metamaterials (LHM))
to positive (conventional, right-handed metamaterials (RHM)) values (and vice versa). Propagation of EW in
GRIN media studied in [5,6]. The choosing of hyperbolic tangent dependence for permittivity and permeability
allowed analytical results presented in [5]. Resonant enhancement of EW propagating at oblique incidence in
metamaterials, with dielectric permittivity and magnetic permeability linearly changing from positive to nega-
tive values, has been predicted and theoretically studied in [6]. In [7] optical properties of one dimensional pho-
tonic crystals containing graded materials investigated theoretically. Affect of gradation profiles on photonic
band gap engineering was shown.
Anisotropic media is additional tool to manipulate EM wave propagation. The term “anisotropic media” is
applied to a medium where refractive index is different in measurement along different axes (is directionally
dependent). As a result the induced polarization is not parallel to the electric field, and this factor leads to many
optical phenomena such as birefringence effect, conical refraction, optical rotation etc. These and other effects
have found wide application, and anisotropic structures are an important and fundamental part of many modern
semiconductor and optical devices.
In the present work we study theoretically propagation EM wave through anisotropic layers with linear gra-
dient refractive index. The linear dependence is examined as functions of refractive index profile. We studied
influence of graded region and angle of incidence on propagation of EM wave in the structure.
2. Theoretical Formalism
We consider propagation of EM waves in a nonmagnetic (we put everywhere for dielectric permeability μ = 1)