Diffraction of Electromagnetic Waves on an Impedance Interface between Two Media with Different Perturbations in Impedance

This paper is a contribution to the study of the diffraction of an electromagnetic plane wave by a cylindrical rod of arbitrary cross-section and optical index. The incident wave vector is not necessarily perpendicular to the rod. This vectorial diffraction problem is solved using the method of fictitious sources which has proven to be effective for scalar problems. Theoretical and numerical aspects are both studied.

A finite width screen with perfect conductivity and double periodicity slots was considered. Let such the system be placed in an isotropic medium and be excited at an arbitrary angle by a plane electromagnetic (EM) wave. We solved the problem of finding the field distribution in space and calculated its electromagnetic parameters. The problem was solved by means of the method of subsections. Resulting from the calculation, the dependence of the field transmission coefficient on the different parameters and the field distribution inside the waveguide were obtained. An analysis of the structure was also conducted.

The 3D problem of reflection of a plane electromagnetic wave by an irregular boundary containing a locally inhomogeneous well conducting section is considered. The boundary value problem for the system of Maxwell equations in an infinite section with an irregular boundary is reduced to the solution of systems of singular equations. A numerical algorithm for their solution is developed. Results of calculation of the currents induced on the irregularity and reflected field patterns are presented for the case of the E polarization.

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.

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.

A matrix Wiener–Hopf equation connected with a new canonical diffraction problem is solved explicitly. We consider the diffraction of a plane electromagnetic wave by an impedance loaded parallel plate waveguide formed by a two-part impedance plane and a parallel perfectly conducting half-plane. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to a matrix Wiener–Hopf equation. The exact solution is obtained in terms of two infinite sets of unknown coefficients satisfying two infinite systems of linear algebraic equations. These systems are solved numerically and the influence of the parameters such as the waveguide spacing and the surface impedances of the two-part plane on the diffraction phenomenon is shown graphically. Copyright © 2005 John Wiley & Sons, Ltd.

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.

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.

In the present paper the problem of plane electromagnetic wave diffraction by a thin metal plate is considered. A numerical algorithm is developed using method of moments with NVIDIA CUDA technology implementation. The results of numerical modeling of a plane wave diffraction by the square thin metallic plate is shown. Comparative analysis of the performance for CPU and GPU is carried out. It is shown that the method of moments implementation by graphical processor provides a sufficient gain in the performance.

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.

Summary form only given. Interference and diffraction of electromagnetic waves on periodic structures is a fundamental topic which has proven to be relevant and applicable to many areas of physics. Periodic structures (also known as Bragg, or photonic band gap structures) have been considered as distributed elements of the interaction space of high power sources of coherent radiation. In this role they are extremely important for a number of applications in optics and microwave electronics. Periodic lattices are considered as an alternative material for constructing wave-guiding systems, highly selective filters and pulse compressors. These are usually achieved by machining structures with specific defects, which modify the properties of the band-gap. The localised defect inside periodic structure creates a special state, or pass band which allows of specific energy and momentum to pass freely through the band gap. The measurements of the phase of the wave passed through such a structure allow one to analyse the dispersion characteristics of the lattice, which determine its suitability for a number of applications. We present the results of experimental studies of a system based on a waveguide periodic structure driven by a frequency-chirped electromagnetic wave. A comparative study of one-dimensional (1D) periodic lattices with and without localized defects is presented. The influence of the step change of the period, on the structurespsila dispersion characteristics and photonic band gap are studied. Results of the measurements and analysis of the properties of periodic structures are demonstrated and discussed. The parameters of the band gap and pass band associated with the defect are studied via measurement of the relative phase of the system photons - periodic lattice and the amplitude of the transmitted signal.