An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Transverse electromagnetic electric (TE) and transverse magnetic (TM) creeping waves on a surface with an anisotropic impedance boundary condition are considered. An asymptotic theory is developed for creeping waves. The theory is valid near the line where the attenuation parameters of two different types of waves coincide and, therefore, standard asymptotics are inapplicable. Asymptotic formulas describing physical effects that occur when a creeping wave propagates across the degeneracy line are derived. It is found that, behind the degeneracy line, a propagating TE wave excites a TM wave with a small amplitude (of order O(k ^−1/6)) and a propagating TM wave excites a TE wave.     

The snell and fresnel relationships for electromagnetic waves with the constant linear polarization

General conditions for the existence of plane electromagnetic waves with a single nonzero electric-field component (TE waves) in an anisotropic medium are established. A transformation that makes it possible to derive similar formulas for TM waves (plane electromagnetic waves with a single nonzero magnetic-field component) from the formulas expressing the properties of TE waves is considered. A general numerical algorithm is developed for calculating the amplitudes (with allowance for phases) of the TE waves formed when an external TE wave propagates through a system of plane-parallel plates consisting of media supporting TE waves. Formulas are obtained for the solution of the particular problem on the transmission of a TE wave through a plane interface between two media supporting TE waves. A series of relationships that can be interpreted as generalizations of the Snell and Fresnel relationships for media of the considered type are derived. Formulas for the transmission, reflection, and refraction coefficients are obtained. The existence conditions for TE (TM) surface waves are derived. A numerical method is proposed for computing the spectra of such surface waves formed on the interface between two media. For isotropic media, analytic expressions for the spectra of surface waves are derived. It is shown that the obtained formulas are similar to the known formulas for surface TM waves in dielectrics but, in addition, make it possible to take into account both the permittivities and permeabilities of the media.     

Computation of the electromagnetic field inside the source region

Explicit expressions are derived for the electric and magnetic fields generated in free space by a given, or assumed, distribution of electric and magnetic currents confined within a finite volume (source region). The fields are expansions of TM and TE spherical modes with additional radial terms, proportional to the respective radial current densities. The obtained expressions do not contain singular terms, satisfy Maxwell's equations both inside and outside the source region, and are suitable for practical numerical calculations ; there is no need to exclude any volume around the observation point. The fields outside the source region are also expansions of TE and TM spherical waves, but without the additional radial terms.     

Fundamental and Higher Mode Inversion of Dispersed GPR Waves Propagating in an Ice Layer

Dispersion of ground-penetrating radar (GPR) waves can occur when they are trapped in a layer. In this paper, we analyze the modal propagation of GPR pulses through a layer of ice that is overlying water. Dispersed transverse electric (TE) waves that are trapped in the waveguide have larger amplitudes than the critically refracted waves that travel through air, whereas the transverse magnetic (TM) critically refracted waves traveling through air are more dominant than the trapped dispersed TM waves. This can be explained by the leaky waveguide behavior of the ice layer. The reflection coefficients for the waves incident on the ice-water interface show that the TM modes are more leaky than the TE modes. Still, clear dispersion is observed in both cases, which depends on the permittivity and thickness of the ice. Similar to inversion of dispersed Rayleigh waves, these parameters can be estimated by calculating phase-velocity spectra, picking dispersion curves, and inverting the dispersion curves using a combined local and global minimization procedure. Synthetic data show several higher order modes of which separate and combined inversions return the input modeling parameters accurately. Experimental data acquired on a frozen lake show strong dispersion for the TE and TM modes. The phase-velocity spectra of the field data show three TE and four TM modes of which separate and combined inversion of different modes return similar values for the ice thickness and known permittivity of ice. Due to the more leaky behavior of the TM modes, the TE inversion is better constrained and more suitable for inversion.     

涂层圆柱爬行波传播常数和模式阻抗的分析与计算

本文分析了介质涂层圆柱爬行波的电磁特性。找到了一种求解爬行波传播常数和模式阻抗的有效方法－微扰－迭代法，这种方法简单、快速，便于工程应用。最后给出公式并计算了一些实例。     

An accurate and efficient analysis for transient plane wavesobliquely incident on a conductive half space (TM case)

We develop a method for the analytical evaluation of the inverse Laplace transform representations for transient transverse magnetic (TM) plane wave obliquely incident on a conductive half-space. We assume that the permittivity and conductivity of the dispersive half-space are independent of frequency. The time-domain expressions for the reflected and transmitted waves are first represented as inverse Laplace transforms. The transient fields are then shown to consist of two canonical integrals. The canonical integrals, in turn, are solved analytically, thereby yielding close-form solutions involving incomplete Lipschitz-Hankel integrals (ILHIs). The ILHIs are computed numerically using efficient convergent and asymptotic series expansions, thus enabling the efficient computation of the transient fields. The exact, closed-form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast Fourier transform (FFT) algorithms. An asymptotic series representation for the ILHIs is also employed to obtain a relatively simple late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the fields over a large portion of its time history     

Finite-element formalism for nonlinear slab-guided waves

A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined     

The theory of propagation of electromagnetic waves in a waveguide with a magnetoactive anisotropic modulated filling

Propagation of electromagnetic waves in a waveguide with an arbitrary cross section is considered. The waveguide is filled with a magnetoactive anisotropic medium periodically modulated in space and time. The wave equations for the potentials of transverse electric (TE) and transverse magnetic (TM) fields are derived. Expressions for the TE and TM waveguide fields observed in the region of weak interaction between the signal wave and the modulation wave are found in the first approximation for small modulation indexes of the filling. The frequency near which strong (resonance) interaction between the signal wave and the modulation wave develops is expressed in an analytic form. The propagation of TE and TM waves in the strong-interaction region is investigated.     

多层环状导电媒质中离轴偶极子辐射场的级数解

当偶极子源(电偶极子或磁偶极子)置于多层环状导电媒质中偏离轴线的任意一点时,所激发的电磁场既存在TE波又存在TM波。文中导出了各层媒质中电磁场的通解,用边界条件建立了系数传递矩阵,从而完全确定了电磁场表达式。计算实例中给出了一组离轴偶极子的响应曲线。     

Creeping wave propagation constants and modal impedance for a dielectric coated cylinder

The electromagnetic characteristics associated with the creeping waves supported by a dielectric coated cylinder are investigated. The propagation constants and wave impedances of the creeping waves are obtained numerically. Higher order modes which are significant for a thick coating are also investigated. The propagation constants and creeping wave modal impedance are compared with those obtained for a planar dielectric slab backed by a ground plane. It is found that, contrary to the planar configuration, no cutoff frequencies exist for the creeping waves associated with the coated cylinder. In fact, the coated cylinder supports an infinite number of modes. However, depending upon the thickness of the coating, only a few Elliott type creeping wave modes with low attenuation can exist. Furthermore, for each of the Elliott type creeping waves, there is a critical radius for the cylinder below which the Elliott type creeping wave cannot exist. The results are also compared with an impedance boundary cylinder, where the impedance is chosen to be purely imaginary.     

Two-Dimensional Scattering by a Conducting Elliptic Cylinder Coated With a Homogeneous Anisotropic Shell

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a confocal homogeneous anisotropic elliptical shell is obtained. The transmitted field of the anisotropic shell is expressed as an integral equation based on waves with different wave numbers and different directions of propagation. The waves in all directions are represented as the eigenfunction expansion in elliptic coordinates in terms of Mathieu functions. In order to solve the nonorthogonality properties of Mathieu functions, Galerkin's method is applied and a matrix is required for the computation of unknown expansion coefficients of the scattered and transmitted fields. Only the transverse magnetic (TM) polarization is presented, while the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented in graphical forms. The result is in agreement with that available as expected when a coated elliptic cylinder degenerates to the coated circular one.      

On the location of leaky wave poles for a grounded dielectric slab

A simple numerical procedure for finding the loci of TE and TM leaky wave poles as the frequency or the thickness of the slab varies is presented. These loci provide important information when the integration path of the Sommerfeld integral for the grounded dielectric slab problem is deformed into the improper sheet of the Riemann surface. The accuracy of the loci has been checked extensively against contour plots of separate expressions for the electric flux density for the TE and TM cases     

Scattering from and penetration into a dielectric-filled conductingcylinder with multiple apertures

The theory of characteristic modes for aperture problems is used in this paper to solve the equivalent magnetic current and aperture fields due to a conducting cylinder with multiple slots. It is assumed that these slots are illuminated by either a transverse electric (TE) or a transverse magnetic (TM) plane wave and the media inside and outside the cylinder exhibit different electromagnetic properties. The formulation is given for the general case and numerical results for a limited number of slots are presented     

Axial slot antenna on dielectric-coated elliptic cylinder

The radiation properties of an axial slot antenna on a conducting elliptic cylinder with a homogeneous dielectric coating are investigated. In the dielectric coating and in the exterior free-space region the field is expanded in elliptic waves using the Mathieu functions. The Mathieu angular functions are employed as basis and testing functions to enforce the boundary conditions at the interface between the dielectric and the free-space regions. The equations of continuity at the boundary are solved by Galerkin's method. Numerical results are presented in graphical form for the transverse electric (TE) and transverse magnetic (TM) polarizations to illustrate the far-field radiation patterns, the gain versus coating thickness, and the aperture conductance versus coating thickness     

Scattering at Circular-to-Rectangular Waveguide Junctions

A formally exact solution is given for the problem of scattering at a circular-to-rectangular waveguide junction and at a thick diaphragm, with a centered circular aperture, in a rectangular waveguide. The method uses normal TE and TM mode expansions of the waveguide fields and traditional mode matching of the transverse electric and magnetic fields at the junction boundary. Exact closed-form expressions are obtained for the electric field mode-matching coefficients which couple the TE(TM) modes in the rectangular guide to the TE(TM) and TM(TE) modes in the circular guide. Numerical results are presented for the case of TE/sub 10/ mode propagation in the larger rectangular guide with all other modes cutoff. Convergent numerical results for the equivalent shunt susceptances of such junctions are obtained when about 12 modes (eight TE and four TM) are retained in the circular waveguide or in the circular aperture of the diaphragm. The results are graphically compared with formulas and curves due to the quasi-static theory of Bethe and the variational theory given in the Waveguide Handbook [2].     

Electromagnetic scattering from a coaxial dielectric circularcylinder loading a semicircular gap in a ground plane

An exact dual series solution of a plane wave incident on a coaxial dielectric circular cylinder imbedded in a semicircular gap of a ground plane is presented. Both TM and TE cases are considered here. The scattered field is represented in terms of an infinite series of cylindrical waves with unknown coefficients. By applying the boundary conditions and employing the partial orthogonality of the trigonometric functions the scattering coefficients are obtained. The resulting infinite series is then truncated to a finite number of terms to produce numerical results. For the sake of comparison with the published data some special cases are introduced first. The comparisons showed excellent agreement in all cases     

Reflection by a Sinusoidally Modulated Surface Reactance at Oblique Incidence

The reflection characteristics of the TM and the TE surface waves by a weak sinusoidal modulation of the surface reactance are investigated for the oblique incidence in which the wavevectors are not aligned with the grating vector. A superposition of TM and TE wave fields is needed for the fulfillment of the required boundary conditions. For both the TM and the TE surface waves, the Brewster phenomenon of total transmission occurs at the angle of incidence theta=theta/sub B/ = 45°. A modulation in the surface reactance, in general, causes the TE surface waves to be more efficiently reflected than the TM surface waves.     

Hybrid UTD-MM analysis of the scattering by a perfectly conducting semicircular cylinder

A hybrid UTD-MM technique which combines the uniform geometrical theory of diffraction (UTD) and the method of moments (MM) is employed to analyze efficiently the problem of electromagnetic diffraction of transverse electric (TE) and transverse magnetic (TM) waves by a perfectly conducting semicircular cylinder. An analysis of this problem is useful for understanding the coupling between the mechanisms of edge and convex surface diffraction. The accuracy of the numerical results for the far-zone fields based on this solution is established by comparison with an independent formally exact MM solution.     

The Dyadic Green's Functions for Cylindrical Waveguides and Cavities

Four dyadics are derived to find the electric and magnetic fields generated by a given distribution of electric and magnetic (including aperture) currents in cylindrical waveguides and cavities of arbitrary cross sections. Two sets of vectors are used to form the dyadics: oneset is an expansion of "electric field" vectors, and the other is an expansion of "magnetic field" vectors. Explicit expressions in terms of TE and TM modes are obtained for the resulting electric and magnetic fields. Inside the source regions there are additional components proportional either to the axial components of the current demities (waveguides), or to the current densities vectors (cavities).