Diffraction of electromagnetic waves by a half-plane

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.

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.

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.

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.

A 2D theoretical model of the diffraction of a plane electromagnetic wave by a slot in a perfectly conducting screen is constructed based on the partial domain method. The Tikhonov regularization is used to solve a system of algebraic equations for the slot-mode amplitudes. This makes it possible to extend the domain of applicability of the theory to conducting screens of arbitrary thickness and to significantly increase the accuracy of solution in the cases when the slot width and the screen thickness are comparable to the wavelength of the diffracted radiation. The absence of a continuous passage to the limit of an infinitesimal screen thickness from the case of an arbitrarily small finite thickness is demonstrated. The boundary conditions for the energy-flux vector are considered. A concept of the energy potential that is convenient for the computer calculations of the energy-flux lines of 2D diffraction fields is introduced.

A theoretical study is made of the diffraction of surface electromagnetic waves by the open end of a strip optical microwaveguide. An approximation equivalent to the Kirchhoff approach is used to obtain analytic dependences for the angular distribution of diffracted waves in the far-field zone in the Fraunhofer diffraction case and a study is made of the distribution of electric fields of the diffracted waves in the near-field zone in the Fresnel diffraction case. It is shown that the angular distribution of the diffracted waves depends on the mode index of a strip microwaveguide and it differs considerably for thin-film and graded-index strip microwaveguides in a plane perpendicular to the waveguide. It is shown that in solving of the problem of the end contact between strip microwaveguides and fiber waveguides it is possible to ignore the distortion of the distribution of the electric field of the fundamental mode at the open end of a strip microwaveguide.

In order to create models of extended surfaces in the long and short wavelength parts of the wave spectrum, it is necessary to know the dispersion characteristics of tape-like obstacles perfectly located both in free space and on an extended surface. Methods of remote studying of extended surfaces, based on an analysis of signals that are generated by reflection or radiation of electromagnetic waves passing neoplasms allows us to view the topography, characteristics, and type of the different locations, sizes of various objects. One of the effective methods of study is to solve the problem of diffraction of electromagnetic waves on an infinitely extended object in free space. The purpose of this study is characteristics of electromagnetic waves during diffraction of electromagnetic waves at objects that can be used as radar systems. The method of statistical processing of experimental data from field tests and mathematical description of electromagnetic radar situation, as well as its computer simulation were used. The result of this study can be formulated as the development of analytical and software methods for analyzing diffraction pattern of electromagnetic waves in multi-wave mode of reception on infinitely extended object in free space, as well as a software method for calculating diffraction characteristics at frequencies exceeding the basic frequency, taking into account the inhomogeneity of electromagnetic fields in these conditions. The practical significance is the research results used in the development of a universal technique for design and development of radar systems capable of working adequately in conditions of electromagnetic environment in question. The results of this research will allow a complete description of the electrodynamic picture of wave propagation and its diffraction, namely, taking into account the diffraction properties of radar systems will allow us to develop a direction for their wider production and distribution.

The diffraction of electromagnetic waves by a conducting circular disc is investigated according to a method developed by Y. Nomura, et al. in the particular case where the incident wave is coming from an electric dipole which is placed at a finite distance from the disc and polarized parallel to the disc surface. The solution for the diffraction by an aperture with a magnetic dipole as a source is easily obtained by the application of Babinet's principle. Various physical quantities are evaluated for several distances between the disc and the dipole which is placed on the central axis of the disc. When the dipole is apart from the disc about five times of the radius, curves of the physical quantities resemble very much those for the normal incidence of plane waves.

A solution of the two-dimensional integro-differential equation describing diffraction of electromagnetic waves on metallic nanovibrators and on nanocrystals coated by a metallic film was obtained. Copper and gold nanoantenna characteristics were studied theoretically in the optical range. It was noted that the dependence of the scattered field on frequency is of a resonant character and the resonant wavelengths of nanovibrators are larger than those of an ideally conducting vibrator of the same size.

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.

For a long time, numerous problems in various applied fields [1-3] have been investigated with the use of singular integral equations. For example, some problems of aerodynamics [1], diffraction of electromagnetic and acoustic waves [2], elasticity [3], etc. can be reduced to the solution of such equations. The theory of singular integral equations was developed long ago [3], but related applied problems required the solution of these equations in the class of absolutely integrable functions. It was mentioned in [4] that, under specific conditions imposed on the coefficients of a singular integral equation, one can find solutions in the class of fimctions with nonintegrable singularity of the form 1/x as x -* 0. But the absence of applied problems leading to such solutions, numerical methods for their construction, and a theory of distributions developed for singular integral equations hindered the investigation of such singular solutions. However, in the framework of aerodynamics [5, 6], the mechanics of wings has recently been analyzed with the use of ejection of an external flow. It was shown in [6] that, in the case of a thin profile, this problem can be reduced to solving a singular integral equation of the first kind on a closed interval in the class of fimctions that have a nonintegrable singularity of the above-mentioned type at the ejection point. By [7], the investigation of the diffraction of an electromagnetic wave on an ideal conductor with a current thread on the surface leads to a similar mathematical problem. Such problems were numerically solved in [1, 7, 8] in sorne special cases with the use of the discrete vortex and discrete current methods. However, the integral operators constructed in these papers are continuously invertible in related pairs of spaces but have the property that their squares map the entire subspace of singular solutions to zero. In the present paper, in view of [9, 10], we give another mathematical treatment of the same applied problems, which permits one to consider them in the framework of the theory of pseudodifferential operators on a closed curve. Then we describe the construction of Sobolev type weighted spaces and develop the theory of linear operators (similar to pseudodifferential ones) in these spaces for open curves. We present examples illustrating the difference between the notions of integral in the sense of the Cauchy principal value and pseudodifferential operators on distributions that are singular solutions. Similar linear operators are constructed for singular integral equations of the second kind with Hilbert kernel and constant coefficients on a closed interval. We indicate the possibility of the generalization of the suggested construction of linear operators to some spatial problems.

The problem of diffraction of a plane-polarized electromagnetic wave incident on a right-angle dielectric wedge is formulated as a singular integral equation in k space. A solution of the singular integral equation is constructed as a power series in the index of refraction. This series converges when the index of refraction is near unity. Using this solution, the electric-field amplitude at the tip of the wedge is examined. We also prove as incorrect a closed-form analytic expression claimed in the literature to be a global solution of the problem considered here.

An algorithm is suggested permitting us to consider the impact of magnetodielectric filling on the scatter-absorption properties of periodic diffraction lattices of the “shutter” type made with resistive materials. The paper gives dependencies of the power reflection factor on the wavelength for spatial modes at different values of permittivity of the dielectric filling.

Diffraction of electromagnetic waves from an arbitrary source by an anisotropic cylindrical structure or by a cylindrical structure in an anisotropic medium is very difficult to handle in general. But if the source is a line source parallel to (or a plane wave normally incident to) the axis of an infinitely long cylindrical structure, where the transverse anisotropy of the structure is not coupled to that of the axial, the problems simplify in many cases. In all of these cases, Maxwell's equations lead to a single differential equation with parameters and boundary conditions which depend on the individual problems. Examples given are perfectly conducting wedges and a perfectly conducting cylinder in anisotropic media. There are a few cases where the electromagnetic waves depend only on the axial property of the medium, i.e. the waves do not see the anisotropic nature of the medium.