Planar Stratified Media Research Articles

Beam summation algorithm for wave radiation and propagation in stratified media

An efficient Gaussian beams summation (GBS) algorithm for tracking source excited wavefields in plane stratified media is introduced. It has two important features: (a) it involves an efficient calculation of the GB propagators, and (b) it involves rather sparse lattice of beams. For (a) we approximate the medium using layers with constant wavespeed gradient, and derive an efficient recursive algorithm for tracking the GB through such medium. This model not only reduces the number of layers, and thereby the algorithm complexity, in comparison with the conventional uniform layers model, but it also eliminates the reflection artifacts at layers interfaces. Property (b) is achieved by determining the beam expansion parameters for an efficient discretization of the source-excited beam spectra using a sparse lattice of beams. The algorithm has been validated and calibrated via thorough numerical comparisons with closed form ray solutions for source-excited fields in layered media. Perfect agreement between these independent solutions has been obtained in regions where the ray solution is valid, but the beam formulation also provided smooth and physically meaningful solutions in caustic regions where the ray solution fails.

Linear s-polarized surface waves in a medium inhomogeneous in one dimension

Linear s-polarized surface waves can exist at the boundary between an isotropic homogeneous medium and a medium inhomogeneous in one dimension (1D-inhomogeneous medium). This is related to deformation of the spatial envelope of the electric and magnetic components of the surface wave propagating in the 1D-inhomogeneous medium (in particular, in a plane-stratified medium). Such linear s-polarized surface waves can appear only provided that the refractive index of the inhomogeneous medium increases with the distance from the interface.

On the generalization of Snell's law

By means of Noether's theorem, it is shown that there is a large class of complicated refractive media for which there exists a Snell like law. Furthermore, a ray path through such a medium is shown to be related to one through an appropriate plane stratified medium. As a consequence, it is possible to find analytic expressions for the ray trajectories through a large subclass of such media.

Reference Forms of the Complete Spectral Electric and Magnetic Dyadic Green's Functions (DGF's) for Planar Stratified Media

The classical problem of determining the complete spectral electric and magnetic Dyadic Green's Functions (DFG's) for 3D current sources imbedded within planar stratified background media is performed in a modern concise manner and notation. The expressions are then rearranged into "reference forms". This annotation is justified by examining the correspondence with the familiar free space expressions and clarifying some difficulties encountered in the formulation and numerical solution of Surface and Volume Integral Equations (S/V-IE's).

Full-wave analysis of antennas containing horizontal and vertical metallizations embedded in planar multilayered media

The paper presents an efficient way of evaluating Green's functions arising in planar stratified media. In the spectral domain, the components are split into a singular and a regular part. The latter is expressed in terms of exactly four boundary coefficients, whose computation is extracted from the numerical kernel of the method, and the former is evaluated analytically via the Sommerfeld identity. The spatial counterparts are then evaluated by a method which combines the advantages of the complex image method (CIM) and the direct numerical evaluation of the Sommerfeld integral, while trying to avoid their respective drawbacks. The result is an efficient technique to treat horizontal and vertical metallizations embedded in multilayered media. Results for a three-dimensional (3D) planar inverted F antenna are obtained with this technique and successfully compared to measurements.

Semantics of dyadic and mixed potential field representation for 3-D current distributions in planar stratified media

The full spectral electric dyadic Green's function for three dimensional current distributions in planar stratified media can be obtained straight from Maxwell's equations. By following a physical reasoning analogous with the free space case but using general derivative relations for multilayered Green's functions, we derive a "basic" mixed potential form with a simple vector potential kernel but multiple scalar potential kernels, and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel. Mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential, or choice of gauge condition. The nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and/or vector potentials are believed to be clarified by the proposed approach. A discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations.

Hybrid dyadic-mixed-potential and combined spectral-space domain integral-equation analysis of quasi-3-D structures in stratified media

Planar circuits and antennas in stratified media are efficiently analyzed using an integral-equation formulation with a spectral-domain approach to construct the required Green's functions. This efficiency is largely lost when arbitrary three-dimensional (3-D) structures have to be analyzed. We, therefore, focus attention on quasi structures, which, although not fully 3-D, are still seen to cover most practical problems. The formulation of the electric field is adapted to the geometry as a hybrid dyadic-mixed-potential form. Evaluation of all z, z/sup '/-dependent parts of the reaction integrals is done analytically in the spectral domain. The remaining evaluation is done in the space domain with a mixed-potential formalism. We obtain a combined spectral-space domain approach to solve the integral equation. Numerical results demonstrate the applicability of the method to (most) 3-D problems that occur in planar stratified media.

Factorization of Transmission Line Type Green's Functions

The general cascaded transmission line Green's functions are given in a special factorized form, in which the dependence on the observation z- and source z'-coordinate are explicitly separated in very simple and symmetric form. The new expressions greatly simplify analytical manipulation of the expressions, pave the way for an efficient numerical computation, and apart from already having been used in the integral equation analysis of 3D structures in planar stratified media may find wider application in related areas.

Symbolic derivation and numeric computation of dyadic Green's functions using Mathematica

This paper presents a mathematical-software functional package that is capable of performing symbolic derivation and numeric computation of dyadic Green's functions for certain multilayered structures: a planar stratified multilayered medium, a spherical multilayered medium, a cylindrical multilayered medium, and a conducting rectangular waveguide with a multilayered dielectric load. The algorithms of this software package are based on the eigenfunction-expansion method. Using Mathematica/sup TM/, two packages were written to fulfill the aforementioned objectives. Upon completion of the software development, dyadic Green's functions for three-layered media were generated. A comparison of these outputs with published results showed good agreement. This demonstrated the applicability of the symbolic package. For the numeric package, the Green's dyadics for a particular three-layered spherical isotropic multilayered medium were generated as an illustration. These packages have been successfully implemented, and future derivation of dyadic Green's functions for these media may be performed.

Hybrid Ray-Fdtd Moving Coordinate Frame Approach for Long Range Tracking of Collimated Wavepackets

Modeling of long range propagation of collimated wavepackets poses some major difficulties with the conventional FDTD scheme. The difficulties arise from the vast computer resources needed to discretize the entire region of interest and the accumulation of numerical dispersion error. As a means for circumventing these difficulties, the moving frame FDTD approach is in this work. In this approach, the computational grid size is limited to the order of the pulse length, and it and moves along with the pulse. The issues discussed in conjunction with this method are those of numerical dispersion, which is shown to be reduced substantially compared with the stationary formulation, numerical stability, and absorbing boundary conditions at the leading, trailing and side boundaries, Numerical results of pulsed beam propagation in both homogeneous and plane stratified media are shown, and the capability of the method is demonstrated with propagation distances exceeding the order of 10 4 pulse lengths.

Observation of irregularities of the scattering coefficient in plane-stratified media using the method of reflecting confocal microscopy

Based on the vision theory for turbid media, we develop a model for detection and visualization of plane-stratified irregularities of the scattering coefficient in biological tissues using the method of reflecting confocal microscopy. General formulas for calculating the backscattering signal are presented for the continuous and impulse illumination. The influence of the observation-system parameters on the maximum vision depth of irregularities is analyzed for several stratification types of optical characteristics of biological tissues.

Explicit Stokes reciprocity relations for plane stratified media

Some results previously published are used to obtain an explicit form of the Stokes reciprocity relations valid whatever the number of plane interfaces may be.

Hybrid Ray-Fdtd Moving Coordinate Frame Approach for Long Range Tracking of Collimated Wavepackets - Abstract

Modeling of long range propagation of collimated wavepackets poses some major difficulties with the conventional FDTD scheme. The difficulties arise from the vast computer resources needed to discretize the entire region of interest and the accumulation of numerical dispersion error. As a means for circumventing these difficulties, the moving frame FDTD approach is in this work. In this approach, the computational grid size is limited to the order of the pulse length, and it and moves along with the pulse. The issues discussed in conjunction with this method are those of numerical dispersion, which is shown to be reduced substantially compared with the stationary formulation, numerical stability, and absorbing boundary conditions at the leading, trailing and side boundaries, Numerical results of pulsed beam propagation in both homogeneous and plane stratified media are shown, and the capability of the method is demonstrated with propagation distances exceeding the order of 104 pulse lengths.

Ray travel time and distance for the planar polytrope

Ray travel time and distance are determined for the planar polytrope using analytic techniques that are specialized to plane stratified media. It is found that an adiabatically stratified polytrope yields non-dispersed wave fields for a full circuit of a ray through a trapping region. Non-adiabacity, however, leads to dispersion, and a consequent loss of correlation with successive circuits of the trapping region. An acoustic waveguide with fixed boundaries and a similar waveguide containing an isothermal stratified medium are also examined to illustrate the approach and to highlight various aspects of the ray behavior.

Correction to "Scattering of arbitrarily polarized plane waves obliquely incident on infinite slots or strips in a planar-stratified medium"

Correction to "Scattering of arbitrarily polarized plane waves obliquely incident on infinite slots or strips in a planar-stratified medium"

Equation for the envelope of the field in a linear array of semiconductor lasers and an analysis of nonlinear effects

An equation is derived for the smooth envelope of a wave field propagating in a plane stratified medium possessing the resonance small-scattering effect on one period of the structure. Rectilinear propagation of the envelope of the field is detected in the xz plane, where x is normal to the layers. The conditions under which this equation can be used are indicated. For a linear array of semiconductor diodes with a stepwise dependence of the permittivity on the coordinates, the conditions for stable propagation of the radiation are analyzed and an explicit solution of the isolated-soliton type is found.

A general method of construction for dyadic Green functions of plane-stratified media in uniform open or closed waveguides with separable cross sections

A general method of construction for dyadic Green functions of plane-stratified media in uniform open or closed waveguides with separable cross sections

Elastic waves in a transitional solid with arbitrarily small rigidity

Summary The system of ODE that governs elastic-wave propagation in plane stratified media becomes singular as the elastic rigidity approaches zero. Two approximate methods are presented to address the problem. First, for P–SV waves, one can impose the condition that the displacement is curl-free in the transitional solid. This condition suppresses shear waves. Second, one can represent a thin transitional solid as a massive elastic interface (MEI). The MEI boundary conditions do not become singular as the MEI rigidity approaches zero.

Scattering of arbitrarily polarized plane waves obliquely incident on infinite slots or strips in a planar-stratified medium

An exact analysis of three-dimensional scattering by a slot or by a strip right on an interface between two adjacent layers of a planar stratified isotropic medium is presented. The most general case of arbitrarily polarized obliquely incident plane waves is considered. The formulation is based on systems of singular integral-integrodifferential equations (SIE-SIDE). These systems are discretized with the help of two independent algorithms developed by Tsalamengas (see ibid. vol.46, p.1560-70, 1998). Filling up the matrix elements involves rapidly convergent spectral integrals. The expression of the far-radiated field is derived and numerical results are presented for several cases.

Frequency domain wave-splitting techniques for plane stratified bianisotropic media

A plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered. A covariant wave-splitting approach, based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept, is presented. It encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions, including the physical and vacuum wave splittings treated earlier in the literature, and provides a convenient means for both analytical investigation and numerical calculation of evolution operators (Green’s functions) and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media. The potentialities of the approach are illustrated by its application to the problems of reflection, transmission, and guided propagation, and by generalizing the method of multiple reflections to the case of stratified bianisotropic media.