Propagation of electromagnetic waves in planar metamaterial waveguides and radiation of antennas based on such waveguides

Propagation of electromagnetic waves in planar waveguides made of metamaterials with negative values of the relative permittivity and relative permeability is analyzed. The specific features of radiation from antennas manufactured on the basis of planar metamaterial waveguides are studied. It is shown that radiation of such antennas is characterized by the backfire radiation effect, i.e., the maximum of the radiation pattern is formed at 180°. The causes of this effect and the conditions for its appearance are revealed. It is proved that this effect appears only in the antennas manufactured on the basis of metamaterial waveguides with negative values of the relative permittivity and relative permeability. A design version of a scanning two-mode antenna operating on the basis of this effect is proposed.     

Diffraction of high-frequency electromagnetic waves by curvedstrips

The authors describe the construction of a high-frequency solution in the geometrical theory of diffraction (GTD) format for the generation of edge-diffracted space rays and edge-excited surface waves by an electromagnetic wave normally incident on the edge of a curved impedance strip. The transformation coefficients necessary for the analysis of the diffraction on curved surfaces with equal vanishing face impedances are tabulated in a form appropriate for numerical applications. The procedure for evaluating the diffracted field excited by the edge of a cylindrically curved strip, which can be associated with a reflector antenna or an aperture on a curved surface, is presented for both perfectly and nonperfectly conducting cases     

Diffraction of an electromagnetic wave by a three-dimensional planar lattice

The 3D problem of scattering by a planar lattice of impedance bodies of revolution is solved with the help of the modified discrete source method. A system of integral equations is derived. Numerical results are obtained for the case of perfectly conducting elements of the lattice. The validity of the law of energy conservation is checked.     

Diffraction of an electromagnetic beam by infinite planar periodicmetal-strip grating

An hybrid angular spectrum method-Galerkin moment procedure has been developed to analyze the diffraction of an electromagnetic beam incident obliquely on an infinite planar periodic metal-strip grating. The integral expression obtained for the scattered field is expanded by means of an asymptotic method for determining the diffracted far-field. Some numerical examples show the decomposition of the incident beam in several beams corresponding to the propagating Floquet harmonics excited in the grating. The propagation directions of these beams show deviations with respect to the directions predicted by the Floquet theorem. The profile of the scattered far-field is analyzed as a function of the geometrical and electrical parameters     

Reflection of electromagnetic waves from rough waveguides

The reflection coefficient of a section of randomly rough waveguide is calculated using a coordinate transformation developed by A.K. Mallick and G.S. Sanyal (ibid., vol.26, no.4, p.243-9, 1978). A perturbed analysis which assumes that the amplitude of the roughness is small compared to the average width of the waveguide is performed. A drastic difference at long wavelengths between TEM on the one hand and TE and TM on the other has been found     

Diffraction of electromagnetic waves by the boundary of a semi-infinite metamaterial

Diffraction of plane waves at the interface of two semi-infinite regions is considered for the case when one of the regions is filled with a metamaterial in the form of a 3D periodic lattice of dipole-type particles. The diffraction problem is solved via the method of compensating sources, which is extended to the case of 3D structures. Different formulations of the diffraction problem that is reduced to either a system of Wiener-Hopf functional equations or a system of linear algebraic equations are presented. Representation of a semi-infinite structure by a sequence of layers characterized by wave transmission matrices is analyzed. It is shown that such matrices can be used to obtain the solution to the diffraction problem in an explicit form.     

Scattering of electromagnetic waves by a metal lattice placed at the interface of two media

Simple formulas for determination of components of the scattering matrix of a plane electromagnetic wave incident along the normal onto a thin infinite 2D metal lattice with square windows placed at the interface of two media are derived for the first time. Frequency responses (FRs) of this structure calculated with the use of these formulas agree well with responses obtained by the numerical electromagnetic analysis of a 3D model in the case when the lattice period is less than one-half of the wavelength. The capability of efficient control of the FR of the analyzed structure by means of variation in the width of conductors and the lattice period enables application of this lattice for fabrication of a reflector with prescribed reflectivity. Such reflectors at interfaces of dielectric layers are required, for example, in the design of multilayer sufaces radio transparent in a specified frequency band or optical bandpass filters.     

Coupling of surface waves by two crossed dielectric waveguides

The coupling of surface waves by two crossed dielectric slab sections with curved transition waveguides is investigated by the method of staircase approximation. the coupling problem of the nonuniform structure is analyzed in terms of the scattering of incident surface wave by the crossed structure as a whole. The scattering characteristics of the crossed waveguides are calculated with a particular attention directed to the effect of radiation due to bending of the curved transition waveguides on coupling properties of the structure. Some useful guidelines for the design of the coupling structures are thereby suggested.     

Propagation of electromagnetic waves in two-dimensionally periodic thin-film waveguides

A simplified mathematical model of two-dimensionally(2D) periodic thin-film wavegmide is proposed and the characteristics of wave propagation are shown to be governed by a five-term recurrence relation with dyadic admittance coefficients. The generalized transverse resonance method can be used to analyze any complicated 2D periodic thin-film waveguide. The dispersion characteristics are described by both approximation analysis and numerical calculation. The theoretical explanation and physical understanding of the effecis of 2D periodic modulation provided by our analysis and resulis can give sound support to the engineering applications.     

Analysis and calculation of planar waveguides with two-dimensionally periodic interface

General two-demensionally periodic interface (2DPI) model are proposed to describe a class of two-dimensionally periodic structure. Rigorous mode matching techniques show that the existence of 2DPI introduces only one scalar set of Fourier coefficients in terms of which the general formulation of mode voltages and currents on the both side of 2DPI can be established. Any planar waveguide with arbitrary number of periodic and flat interfaces can then be analyzed. The dispersion curves are presented and compared with those from other models.     

A Planar transversal junction of two planar waveguides

A rigorous analytic method is used to solve the wave-propagation problem for a planar transversal junction of two planar waveguides. The problem is reduced to an iteratively solved system of integral equations of the second kind. Dependences of the transmission and reflection coefficients of guided waves, radiation patterns, and the power of the radiation field on the ratios of the waveguide thicknesses and the waveguide permittivities are obtained.     

Axisymmetric spherical traveling electromagnetic waves in an isotropic medium

The problem of propagation of spherical electromagnetic waves traveling in an isotropic space in the absence of sources is solved in the axisymmetric case for the first two modes varying along the latitude. The solution is obtained from the homogeneous Maxwell equations represented in spherical coordinates in a real form. Analytic expressions for the components of the fields of these E and H waves are used to derive the equations of the corresponding field lines. Field-line patterns are displayed that illustrate the dynamics of propagation of converging and diverging spherical electromagnetic waves in the case when the former are transformed into the latter.     

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     

A transverse displacement at the junction of two planar dielectric waveguides

The guided-wave transmission and reflection coefficients, the pattern, and the energy of the radiated field are calculated as functions of the value of the displacement at the junction of two single-mode waveguides for various values of the permittivity of waveguiding layers. It is shown that the correction to the wave transmission coefficient calculated at the first and second iteration steps increases while the permittivity grows, and the way this correction increases is demonstrated.     

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.     

Coupling and decoupling of electromagnetic waves in parallel 2Dphotonic crystal waveguides

The behavior of two nearby straight photonic crystal waveguides is analyzed. It is shown that the two guides, considered as a single system, may realize a very efficient wavelength selective directional coupler, that may be used as a channel interleaver in a WDM communications system. In addition, we also show that, by properly designing the geometry of the dielectric region between the guide cores, waveguide decoupling can be obtained. Necessary conditions for this feature to be obtained are analytically derived, and an electromagnetic explanation of the decoupling process is given     

Diffraction of plane waves by a resistive strip residing between two impedance half-planes

A uniform asymptotic solution is presented for the diffraction of E_z polarized plane waves by a resistive strip residing between two impedance half-planes. The analysis proceeds from triple integral equations approach which leads to a system of uncoupled modified Wiener-Hopf equations (MWHE). This system is then reduced to two pairs of Fredholm integral equations of the second kind which are solved by successive approximations. Diffracted field expressions are derived up to the third order terms which include the surface wave field effects in a uniform manner.     

Analysis of planar waveguides formed by nonuniform nonlinearity

A planar waveguide containing a nonlinear film whose thickness varies in the transverse direction can be used to simulate propagation in a one (transverse)-dimensional medium with constant refractive index but a spatially varying nonlinearity. This idea is illustrated by finding the steady-state solutions for several examples.<>     

Diffraction of electromagnetic waves by spherical bodies formed from a material with a negative refractive index

Scattering and absorption characteristics of linearly and circularly polarized electromagnetic waves that are diffracted by spherical bodies formed from a material with a negative refractive index are studied. Unique properties of scattered fields are discussed. Numerical results are presented.     

On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface

A method for the scattering of electromagnetic waves from cylindrical bodies of arbitrary materials and cross sections buried beneath a rough interface is presented. The problem is first reduced to the solution of a Fredholm integral equation of the second kind through the Green's function of the background medium. The integral equation is treated here by an application of the method of moments (MoM). The Green's function of the two-part space with rough interface is obtained by a novel approach which is based on the assumption that the perturbations of the rough surface from a planar one are objects located at both sides of the planar boundary. Such an approach allows one to formulate the problem as a scattering of cylindrical waves from buried cylindrical bodies which is solved by means of MoM. The method is effective for surfaces having a localized and arbitrary roughness. Numerical simulations are carried out to validate the results and to show the effects of some parameters on the total field. The present formulation permits one to get the near and far field expression of the scattered wave.