Two-dimensional diffraction in homogeneous anisotropic media

Analysis of electromagnetic scattering from anisotropic cylindrical structures using state space method

The problem on the diffraction of the electromagnetic plane wave on the impedance interface between two media is investigated. The impedance is assumed to be different from a constant on a segment of the interface, where the impedance is described by piecewise-linear, quadratic, or step functions. Bibliography: 4 titles.

The Diffraction of Electromagnetic Waves on the Periodic Heterogeneities and Its Use for Realization of Practical Technical and Electronic Devices of Millimeter and Submillimeter Wavelength Range

We consider the problem of diffraction of an arbitrary electromagnetic wave by a thin disk made from different materials and located in free space. Here we imply a zero- thickness perfectly electrically conducting (PEC) disk, and also thin electrically resistive (ER) and dielectric disks whose thickness is much smaller than the disk radius and the free space wavelength, and also much smaller than the skin-layer depth in the ER disk case. The method used for the modeling is based on the integral equation (IE) technique and analytical regularization. Starting with Maxwell's equations, boundary conditions and the radiation condition at infinity we obtain a set of coupled dual IEs (DIEs) for the unknowns and then reduce this set of equations to the coupled IEs of the Fredholm second kind. To verify our results we calculate the far field characteristics in the case of the PEC disk with the incident field being the field of horizontal electrical dipole located on the disk axis. (5 pages)

Purpose: studies of electrodynamics properties of Fabry–Perot resonator formed by two parallel perfectly conducting screens of finite thickness with rectangular holes while its exciting by a plane wave. Design: operator method of diffraction problems solving based on the method of partial areas and the method of generalized scattering matrixes. Findings: The numerical modeling showed that module of the coefficient of plane wave reflection from the resonator is equal to zero at a fixed wavelength being prohibitive for segments of rectangular waveguides made in both screens. Here, a strong localization of electromagnetic field in the resonator volume is observed. Studying the frequencyselective properties of each screen individually it has been determined that there are no resonances of electromagnetic wave total transmission below the cut-off frequency of rectangular waveguides. It is found that with replacing one of the Fabry–Perot resonator mirrors by a solid metal plane, the amplitude of a plane wave in the resonator can increase by almost an order of magnitude as against the exciting field amplitude. Conclusions: Unique electrodynamic properties of the considered structure can find application in devices for amplifying or generating electromagnetic waves in millimeter and submillimeter bands, as well as in measuring electrical properties of composite materials with large losses.

The basic problem of the diffraction of an optical plane wave by an acoustic plane wave in an anisotropic homogeneous medium is considered. The acousto-optical interaction is considered indifferently of the isotropic or of the birefringent type. Coupled-wave equations are obtained rigorously and cast into an eigenvalue value problem. A general solution is obtained for the diffraction efficiency of diffracted orders, for any interaction length and diffraction regime. The theory includes the Bragg regime, the Raman-Nath regime, and all intermediate situations in the same formulation. The method of solution is both exact and computationally efficient. It is similar in character to the rigorous coupled-wave analysis of Moharam and Gaylord but differs by the choice of basis functions adapted to propagating rather than static gratings. Examples are given for acousto-optical interaction in paratellurite, TeO2.

The electromagnetic fields around a cylindrical boundary of variable curvature and surface impedance are expressed in terms of a complete set of local cylindrical modes, and Maxwell's equations are converted into coupled differential equations for the forward and backward wave amplitudes. The local cylindrical modes are shown to merge with the Fourier type expansion of the fields over plane surfaces. As an illustrative example, the launching of a surface wave over an infinite wedge with a rounded corner is considered in detail.

Thin inclusions of large or small conductivity in an anisotropic homogeneous medium

This paper considers the problem of scattering of electromagnetic waves by a strip conductor when the source is a line current source or a line magnetic current source. the problem is analyzed as a two‐dimensional boundary value problem when the strip conductor thickness is negligibly thin and the distance from the center of the strip to the source is larger than one‐half its width. the expansion functions of the current are selected to satisfy the edge condition. By means of the spectral domain method, the simultaneous equations for the expansion coefficients and the specific expressions for the coefficients are derived. the current distributions and the scattered far field are computed numerically. In the analysis process, it is shown that the coefficients derived are identical to those of the simultaneous equations in the analysis for the plane wave incidence making use of the Weber‐Schafheitlin discontinuous integral.

The attenuation vector plays an important role in investigating waves propagating in dissipative, isotropic or anisotropic media. It is defined as the imaginary part of the complex-valued traveltime gradient. The real part of the complex-valued traveltime gradient is referred to as the propagation vector. In this paper, simple expressions for the attenuation vector are derived for seismic body waves propagating in heterogeneous, weakly dissipative, anisotropic media. The ray-theory perturbation method is used, in which the dissipative medium is considered to be a small perturbation of a perfectly elastic medium. The general perturbation procedure proposed by Klimeš (2002) is very suitable for this purpose, as it does not require ray tracing in dissipative media; the computation of rays in the reference perfectly elastic medium, followed by quadratures along them, is quite sufficient. It is shown that the waves propagating in a heterogeneous, weakly dissipative, anisotropic or isotropic medium are, in general, inhomogeneous. This means that their attenuation vector is not parallel to the propagation vector. This holds even for waves generated by a point-source in a homogeneous anisotropic weakly dissipative medium. An exception is a wave generated by a point-source in a homogeneous isotropic dissipative medium, where the generated wave is homogeneous. Thus, the commonly used concept of homogeneous waves can be applied neither to heterogeneous nor to anisotropic dissipative media. The situation is different for plane waves propagating in homogeneous dissipative isotropic or anisotropic media. In this case, the homogeneity or inhomogeneity of the plane wave may be chosen freely. Besides the attenuation vector, we also study the complex-valued ray-velocity vector. In heterogeneous media, the complex-valued ray-velocity vector is generally inhomogeneous, that is, its real and imaginary parts are not parallel. It is also shown that twice the scalar product of the attenuation vector with the ray-velocity vector in the reference medium yields 1/Q, where Q is the position- and direction-dependent quality factor. Quality factor Q does not depend on the inhomogeneity of the wave under consideration and offers a convenient measure of intrinsic material dissipation.

Formulation of the problem in general. During radio relay communication, electromagnetic waves propagate along the earth's surface, and due to refraction, the polarization of signals can change, which leads to loss of signal power. This problematic situation can be solved by polarization adaptation of antenna systems built on the basis of lattice structures that convert signals with any polarization into a circle. Such antenna arrays are polarization-holographic antennas.Analysis of recent researches and publications. In the theory of antenna synthesis, closed translucent surfaces, methods of synthesis of directional properties of reflective antenna arrays, which take into account the presence of mutual communication between irradiators of any type, as well as models of electrodynamic structures for arrays of different shapes are considered. This approach has a generalized nature and requires the adaptation of mathematical methods and models to antenna systems of a specific design. The polarization-holographic antenna can be considered as a non-homogeneous translucent structure, the problem of diffraction of electromagnetic waves in which it is expedient to solve the Fredholm integral equations of the first kind.Presenting the main material. The mathematical formalization of the electrodynamic model of a non-homogeneous translucent body, which in its properties corresponds to the polarization-adaptive antenna array, is considered as the formulation and solution of the inverse electrodynamic problem connecting the primary electromagnetic field, surface current, and surface impedance. This surface impedance is the holographic kernel of the integral equation, which makes it possible to synthesize the impedance surface for circularly polarized waves. Diffraction of electromagnetic waves on a multilayer impedance body is described by a system of Fredholm integral equations of the first kind for different resonant wavelengths.Conclusion. The method of Fredholm integral equations of the first kind makes it possible to determine the parameters of the antenna array through the transformation of the primary electromagnetic field into a secondary one based on the principles of holography. The result of solving the integral equation is its holographic core, which corresponds to the transparent (reflector) of the antenna. A system of integral equations was obtained, which mathematically formalizes the electrodynamic model of a planar antenna array with several layers, taking into account the mutual influence of these layers.The perspectives of future researches. Further studies should be considered the description of the propagation process of electromagnetic waves, taking into account their multiple reflections, in a planar impedance body and the improvement of the matrix method for determining the transmission and reflection coefficients in such bodies.

Problem of diffraction of monochromatic electromagnetic waves as well as electromagnetic impulses on metal nanodipoles and dielectric nanocrystal coated with a metal film is solved. Obtained theoretical results are confirmed by experiment.

Deals with the problem of diffraction of a plane electromagnetic E-polarized simple harmonic wave falling on a compound boundary structure at an angle /spl alpha/. Maxwell equations that describe the model can be reduced to the Helmholtz equation.

It is shown that there exists a category of two-dimensional diffraction problems, which can be put into a ‘standard form‘ of dual integral equations. These diffraction problems include: diffraction of electromagnetic waves by a finite strip, a finite slit, the diffraction of scalar or vector elastic waves by a rigid strip or crack, etc. A general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions. The sufficient conditions for a given dual integral equations to be solvable in this manner are also determined. Hence, the method forms a complement to the Weiner-Hopf method. To illustrate the method solutions are obtained for a bench-mark problem : the diffraction of light by a finite perfectly conducting strip (or equivalently the diffraction of SH waves by a crack). Comparison with results obtained by others for low, intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies. Both the near field and the far field are obtained, the latter is shown to correspond to the Fraunhoffer diffraction pattern for high frequency. It is also shown that for the equivalent crack problem the stress intensity factor (SIF) fluctuates rapidly with changes in the angle of incidence for high frequencies, thus making the SIF especially sensitive to angle of incidence at high frequencies.

A method is developed for simulation of nonlinear propagation and diffraction of electromagnetic waves in guiding structures containing highly nonlinear distributed semiconductor inclusions. A planar Gunn effect diode located in a strip-slot guiding structure is considered, and the nonlinear effect of frequency multiplication in such a diode is simulated. The simulation is performed with the use of a computational algorithm based on universal autonomous blocks with Floquet channels.