Electromagnetic Waves In Inhomogeneous Media Research Articles

Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium?

Abstract It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single scalar second order PDE, which is derived from Maxwell’s equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single scalar second order PDE rather than with the complete Maxwell system, the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media.

3D-PSTD simulation and polarization analysis of a light pulse transmitted through a scattering medium

A tridimensional pseudo-spectral time domain (3D-PSTD) algorithm, that solves the full-wave Maxwell's equations by using Fourier transforms to calculate the spatial derivatives, has been applied to determine the time characteristics of the propagation of electromagnetic waves in inhomogeneous media. Since the 3D simulation gives access to the full-vector components of the electromagnetic fields, it allowed us to analyse the polarization state of the scattered light with respect to the characteristics of the scattering medium and the polarization state of the incident light. We show that, while the incident light is strongly depolarized on the whole, the light that reaches the output face of the scattering medium is much less depolarized. This fact is consistent with our recently reported experimental results, where a rotation of the polarization does not preclude the restoration of an image by phase conjugation.

The finite element method applied to the study of two-dimensional photonic crystals and resonant cavities

A critical assessment of the finite element (FE) method for studying two-dimensional dielectric photonic crystals is made. Photonic band structures, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals are calculated by using the FE (real-space) method and the plane wave expansion or the finite difference time domain (FDTD) methods and a comparison is established between those results. It is found that, contrarily to popular belief, the FE method (FEM) not only reproduces extremely well the results obtained with the standard plane wave method with regards to the eigenvalue analysis (photonic band structure and density of states calculations) but it also allows to study very easily the time-harmonic propagation of electromagnetic fields in finite clusters of arbitrary complexity and, thus, to calculate their transmission coefficients in a simple way. Moreover, the advantages of using this real space method in the context of point defect cluster quality factor calculations are also stressed by comparing the results obtained with this method with those obtained with the FDTD one. As a result of this study, FEM comes out as an stable, robust, rigorous, and reliable tool to study light propagation and confinement in both periodic and aperiodic dielectric photonic crystals and clusters.

Group Classification of Eikonal Equations for the Wave Equation in Inhomogeneous Media

We present a group classification of the family of equations of the form (∇ψ)2 = 1/v 2(x, y, z), called the eikonal equations, which are equations of characteristics for equations describing acoustic and electromagnetic waves in inhomogeneous media. For some cases of equations with linear and quadratic functions v(x, y, z), having the sense of the speed of waves in a medium, we present explicit solutions (eikonals of point sources) and completely describe the geometry of rays.

S-Polarized surface electromagnetic waves in inhomogeneous media: exactly solvable models

The spectral properties and the spatial structure of S-polarized surface electromagnetic waves propagating near the interface of an inhomogeneous solid plasma are examined by means of an exact analytical solution of Maxwell equations for a smooth density profile, characterized by two free parameters. The drastic differences between these waves and traditionally considered P-polarized surface plasmons are emphasized. The spectral parameters, the depth of localization, and the energy flux of such waves are shown to depend essentially upon the profile of carrier density in the plasma.

Asymptotic completeness in optical scattering

In this paper time-dependent methods are developed in order to prove the existence of the wave operators and asymptotic completeness in the scattering theory of electromagnetic waves in inhomogeneous media. The medium has a localized perturbation of the dielectric susceptibility. There are no regularity assumptions about the dielectric susceptibility. It is shown directly that the range of the wave operator is the complete continuous subspace, and not just the absolutely continuous subspace of the generator of the time evolution describing the perturbed wave propagation.

Computation of transient electromagnetic waves in inhomogeneous media

A brief summary of the methods of solving transient electromagnetic wave problems in inhomogeneous media will be given. The two distinct general techniques, which are the inverse Fourier transformation of time‐harmonic solutions and the direct time‐domain formulation, will be illustrated by way of two examples. In the first example, an efficient numerical mode‐matching method to obtain the response of an electromagnetic source in a two‐dimensional cylindrical inhomogeneity is described. Using this method, the solution is first obtained in the frequency domain. The time‐domain solution is then found by inverse Fourier transforming the frequency‐domain solution. In the second method, a finite‐difference scheme is used to find the transient response of a point source in a two‐dimensional inhomogeneity. Two different methods are proposed to treat the source region singularity. Transmitting boundary conditions are applied on the walls of the finite difference grid so that a finite‐sized box can be used to model an infinite region.

Exact solutions for electromagnetic waves in inhomogeneous media

Exact solutions of the wave equation for the propagation of electromagnetic waves in some inhomogeneous media are found. The first solution corresponds to the barometric model of the atmosphere, whose index of refraction can be expressed by the formulaN 2(z)=1+(N 0 2 -1) exp (−z/z 0). The other cases correspond toN 2(z)=1+(N 0 2 -1) ch−2(βz) andN 2(z)=a-b. [1+exp(z/L)]−1.

Variational principles and operator equations for electromagnetic waves in inhomogeneous media

A variational characterization of the polarizations generated by electromagnetic waves in an inhomogeneous medium is developed, starting from more conventional variational principles which imply, in the static limit, the classical energy principles. Associated operator equations are generated and the Green's function kernels that appear in them are given explicitly for an infinite body. The formulation proceeds along a route directly parallel to one previously established by the author for elastodynamics.

Propagation of Plane Electromagnetic Waves in Inhomogeneous Media

The laws of propagation of plane electromagnetic waves along z are derived from Maxwell’s equations for inhomogeneous media in which the dielectric constant and the electric conductivity are functions of z and in which the magnetic permeability is constant. The corresponding wave equation is reduced to a Ricatti differential equation. A simple method is evolved for treating this Riccati equation without approximation. As a result, it is shown that the laws of propagation depend primarily upon two physical parameters v(z) and u(z) which have the property v(z)=n and −u(z)=nK for homogeneous media, where n is refractive index. The increase in phase retardation of the wave is always governed by the integral of v(z)dz, and v(z) is always the ratio of the phase velocity in vacuum to the phase velocity in the medium. It is shown that sufficiently continuous, single, infinite, inhomogeneous media cannot exhibit reflectance. Fresnel’s coefficients of reflectance and transmittance are derived for normal incidence upon a plane boundary between two inhomogeneous media. The theory includes homogeneous media as special cases.