Unbounded and scattered field representations of the Dyadic Green'sfunctions for planar stratified bianisotropic media

This paper presents a rigorous formulation of the spectral-domain dyadic Green's functions for planar stratified bianisotropic media. The media may consist of any number of layers bounded by optional impedance/admittance walls. Both electric and magnetic dyadic Green's functions for arbitrary field and source locations are derived simultaneously. Based on the principle of scattering superposition, these dyadics are decomposed into unbounded and scattered parts. The scattered dyadic Green's functions are determined without cumbersome operations using the concepts of effective reflection and transmission of outward-bounded and inward-bounded waves. The scattering coefficient matrices are expressed in compact and convenient forms involving global reflection and transmission matrices. Corresponding to the impedance/admittance boundary walls, the global reflection matrices are related directly to the wall impedance/admittance dyadics. For illustration, the general expressions of dyadic Green's functions are applied to the configuration of a grounded bianisotropic slab embedded in isotropic halfspace     

Transmission of horizontally polarized waves and trapped waveguide modes in inhomogeneous media

A generalized Wentzel-Kramer-Brillouin (WKB) approach is used to obtain full wave solutions for horizontally polarized waves in inhomogeneous media when no closed form analytic solutions are known. This approach is suitable for complex permittivity profiles with critical coupling regions even when the permittivity gradient approaches zero. The transmission and reflection coefficients and the characteristic surface impedance for inhomogeneous layers of finite thickness are computed for several permittivity profiles. Excitation of propagating and evanescent waves is considered and the results are shown to satisfy the realizability and reciprocity relationships in electromagnetic theory. Sinusoidal permittivity profiles for which closed form analytical solutions are known are also considered to provide an additonal check on the generalized WKB solutions. For permittivity profiles with several spatial periods, transmission windows with very narrow beamwidths are found to exist. When conditions for total internal reflection in the inhomogeneous dielectric layer are satisfied, the reciprocal of the reflection coefficient vanishes and propagating waves are trapped in the layer. For these trapped waveguide modes the inhomogeneous dielectric is characterized by a surface reactance.     

Dyadic Green's function in bounded media

A new theory for the evaluation of the dyadic Green's functions in a homogeneous medium bounded by perfectly conducting walls is presented. The peculiarities of this theory are 1) the Green's functions are systematically and explicitly decomposed in a singular and an analytical part, and 2) these two parts are formulated in a general manner, i.e., independent on the boundaries. As an application, the Green's functions in a conical guide are evaluated.     

"Buried modes" in planar media with nonmonotonically varying index of refraction

When guiding is due to a continuously varying, rather than discontinuous, index of refraction,n(z), andn(z)peaks at some point inside the propagation medium, there may result "buried modes," i.e., modes whose exponential decay takes place inside the guiding medium rather than, as is usual, in an adjacent medium. The conditions for obtaining these modes are discussed in the Wentzel-Kramer-Brillouin (WKB) approximation and the mode equations given for both these modes and the usual ones for an illustrative case.     

Dyadic Green's function for a multilayered planar medium-a dyadic eigenfunction approach

A new formulation of the dyadic Green's function for a planarly layered medium is presented, based on dyadic eigenfunctions of the Green's function operator. The general development of the dyadic Green's function is shown, resulting in a three-dimensional purely spectral representation. The spectral form is converted to a Hankel-function form using standard techniques, analogous to the sum-of-residues plus branch-cut representation often obtained from the Sommerfeld Green's function. Advantages and disadvantages of both the eigenfunction and Hankel function forms are outlined, and compared to other Green's function representations. Examples of the Green's dyadic for free space and for a grounded dielectric slab environment are provided, and the role of the continuous and discrete spectrum is discussed.     

Calculation of characteristic impedance of planar structures using coupling and decoupling of hybrid modes in the spectral domain

A new techniue based on the spectral domain method for calculating the characteristic impedance of planar dispersive structures with multilayer dielectric substrates is presented. The coupling and decoupling of LSE and LSM modes are introduced so that the calculation of whole power in the considered structure bcomes very easy and fast. Numerical results are presented for some complex structures.     

Simplified coupled-wave equations for cylindrical waves in circulargrating planar waveguides

A simplified form of the coupled-wave equations for cylindrical waves in circular grating distributed feedback (DFB) planar waveguides is presented. The coupling coefficients can be expressed as the product of a cylindrical-wave factor and the corresponding coupling coefficient between planar waveguide modes. Under the large radius approximation (βr≫1), which covers most practical cases, the interpolarization coupling between TE and TM cylindrical waves approaches zero. The coupled-wave equations can then be reduced to two independent families, one for TE- and the other for TM-cylindrical waves     

求解渐变折射率分布平面光波导模式的数值方法

本文用多种数值方法（积分插值法、有限元法及幂法）对具有渐变折射率分布的平面光波导率征方程进行了理论计算。这些方法不仅适用于任意的折射率分布，而且能够达到较高的计算精度。作为一个例子，作者对高斯分布波导进行了具体计算。计算结果表明，Arun Kumar等人用的微扰法是较好的方法。此外，本文作者通过迭代求出了更精确边界条件下的本征模。     

Energy relations for waves in strongly dispersive media

Expressions for the averaged stored energy, energy flow, and energy velocity of quasi-monochromatic waves in temporally and spatially dispersive media have been extended to take into account broad-band signals in strongly dispersive media.     

Complex modes in open and shielded lossless planar transmissionlines and their correspondence with leaky modes

The wavenumber of complex modes in lossless planar transmission lines inside a metallic box, with or without top cover, are computed using the transverse resonance method. Without the top cover, some leaky modes can be observed. When these open guiding structures are covered, it is shown that these previous modes generate either evanescent or complex modes, depending on the metallic enclosure position     

New results for the effective propagation constants of nonuniform plane waves at the planar interface of two lossy media

This paper presents a correction and a generalization of the solution presented previously (for original papers see R. D. Radcliff and C. A. Balams, "Modified propagation constants for nonuniform plane wave transmission through conducting media," IEEE Transactions in Geoscience Remote Sensing, vol. GE-20, no. 3, p. 408-411 (1982) and C. A. Balams, Advanced Engineering Electromagnetics, New York: Wiley (1989)) for the effective propagation constants of nonuniform plane waves at the planar interface of two isotropic homogeneous possibly lossy media of infinite transverse dimensions.     

Nonorthogonality relations between complex hybrid modes: an application for the leaky-wave analysis of laterally shielded top-open planar transmission lines

In this paper, the orthogonality relations between complex modes are investigated to demonstrate the coupling effect that exists along a transverse direction (z-axis) between TE/sup z/ and TM/sup z/ hybrid modes when power storage, loss, or leakage occur in the longitudinal direction (y-axis) of a transmission line. As an example, the parallel-plate waveguide modes are used to study a laterally shielded top-open microstrip line. The study of leaky waves is a very interesting application of the novel orthogonality relations derived in this paper. This study is carried out using the correct and incorrect orthogonality formulations, showing that physically valid results are obtained only when the orthogonality relations derived in this paper are properly introduced in the formulation. A physical explanation of this novel coupling effect between TE/sup z/ and TM/sup z/ hybrid modes with respect to the y-direction is given in terms of inhomogeneous plane waves. Comparisons with previous results for a laterally shielded slot-line antenna are presented to confirm the accuracy and usefulness of this novel proposed method.     

Accurate approximation of Green's functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves

A robust and computationally-expedient methodology is presented for accurate, closed-form approximation of the Green's functions used in the mixed-potential integral equation statement of the electromagnetic boundary value problem in planar stratified media. The proposed methodology is based on the fitting of the spectrum of the Green's function, after the extraction of the quasistatic part, making use of rational functions. The effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit. The resulting closed-form approximation is in terms of both spherical and cylindrical waves. Thus, high accuracy is obtained in the approximation of the Green's function irrespective of the distance of the observation point from the source. The methodology is validated through its application to the approximation of the Green's function for a multi-layered, planar dielectric stack.     

Angularly propagating waves in a radially inhomogeneous, lossy dielectric cylinder and their connection with the natural modes

A physical interpretation is proposed for the natural modes of a radially inhomogeneous, lossy dielectric circular cylinder embedded in a homogeneous, lossless dielectric. These modes are either of the creeping-wave or of the whispering-gallery type. With the aid of a generalized Wentzel-Kramer-Brillouin (WKB) asymptotics, an asymptotic characteristic equation is derived for each type, which can be explained physically. Numerical results obtained from the exact characteristic equation and both approximate equations are presented and discussed.     

Forbidden directions for TM waves in anisotropic conducting media

We investigate the wave propagation properties of nonuniform plane waves in an (unbounded homogeneous) anisotropic conducting material. Such waves (for which amplitudes vary across surfaces of constant phase) characterize the refracted field in an imperfect dielectric, like the earth when a uniform electromagnetic plane wave is incident from the air. The results, presented in terms of polar diagrams of the attenuation, slowness, energy velocity, and quality factor predict the existence of “stopbands” beyond a given degree of nonuniformity (i.e., combinations of propagation and attenuation directions where there is no wave propagation). This is a peculiar, effect due to the joint presence of anisotropy and conductivity that may have application in the design of synthetic materials acting as absorbers of electromagnetic radiation     

Self-consistent calculation of lasing modes in a planar microcavity

The self-consistent calculation of lasing modes in a microcavity with infinite plane mirrors is presented. The semiclassical theory is used, with rigorous boundary conditions included for Maxwell's equations to describe both the emitter distribution and the cavity reflectors. The concept of gain-guided versus index-guided modes in such structures can be removed within the semiclassical model, as rigorous boundary conditions for both the radiation source and passive cavity can be handled exactly. We present calculated curves showing the angular dependence of various lasing modes on mirror reflectivity and the threshold gain susceptibility dependence on mirror reflectivity and active diameter. The linewidth dependence on the transverse lasing mode is also considered. Limitations of the semiclassical approach as compared to a fully quantum mechanical approach is emphasized     

Variational method for planar transmission lines with anisotropicmagnetic media

Upper and lower bounds on the line inductances are presented for the first time for planar transmission lines with anisotropic magnetic media. Green's functions are derived for the general structure by using recurrent relations. Numerical examples involving striplines and coplanar waveguide are presented, and the calculated values of the quasi-static characteristics of stripline on an anisotropic magnetic substrate with the tensor permeability are in good agreement with measured values     

Nonlinear slab-guided waves in non-Kerr-like media

Guided waves with unique, power-dependent properties arise when one or more of the media bounding a guiding film exhibits an intensity-dependent refractive index. Previous theoretical work on this problem has been based formalism-limited to Kerr-type nonlinear media in which the change in refractive index is quadratic in the optical field. In this paper, a formalism recently reported by Langbein et al. is used to investigate nonlinear guided wave solutions in more realistic material systems. It is shown numerically that saturation of the optically induced change in the refractive index can dramatically alter, and in some cases eliminate, the more interesting power-dependent features of the solutions. Nonlinear wave solutions are also investigated for a larger class of media characterized by refractive indexes which depend on the optical field raised to some arbitrary power.