Problem Of Wave Diffraction Research Articles

Physical optics theory of resistive surfaces

The physical optics current is obtained from the exact solution of the scattering problem of plane waves by a resistive surface. The edge point method is used for the determination of the physical optics surface current. The derived physical optics integral by considering the new surface current enables one to evaluate the scattering problems by various resistive surfaces with edge discontinuities. The method is applied to the diffraction problem of plane waves by a concave cylindrical reflector. The scattered fields are examined numerically.

Null field method in wave diffraction problems

Diffraction by an impermeable scatterer in ℝ3 with a Dirichlet boundary condition is considered. It is shown that the null field equation is equivalent to the original diffraction problem. The general theoretical constructions are illustrated by analyzing the excitation of a sphere by a point source. The evolution of the residual of the null field equation as the scatterer surface is approached by an auxiliary surface is estimated.

Hydroelastic wave diffraction by a vertical cylinder

A linear three-dimensional problem of hydroelastic wave diffraction by a bottom-mounted circular cylinder is analysed. The fluid is of finite depth and is covered by an ice sheet, which is clamped to the cylinder surface. The ice stretches from the cylinder to infinity in all lateral directions. The hydroelastic behaviour of the ice sheet is described by linear elastic plate theory, and the fluid flow by a potential flow model. The two-dimensional incident wave is regular and has small amplitude. An analytical solution of the coupled problem of hydroelasticity is found by using a Weber transform. We determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave.

A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges

The solution of Maliuzhinets of the diffraction problem of waves by an impedance wedge is transformed into a physical optics integral. The resultant expression is suitable for the investigation of various diffraction problems having impedance wedges. The method is applied to the scattering of waves by an impedance spherical reflector with wedge structure at its discontinuity. The results are examined numerically.

Solution of problems of electromagnetic wave scattering by bodies with an anisotropic impedance with the help of the pattern equation method

The pattern equation method is generalized to solution of problems of electromagnetic wave diffraction by bodies with an anisotropic impedance. A numerical algorithm of the method is developed for bodies of revolution. Techniques of simulation of artificially hard and soft surfaces with the help of an anisotropic impedance are indicated. The method is applied to calculate the scattering characteristics of bodies having a complex structure of conductivity lines on their surfaces.

Physical optics theory for the diffraction of waves by impedance surfaces

The solution of the scattering problem of waves by a half-screen with equal face impedances, which was introduced by Malyughinetz, is transformed into a physical optics integral by using the inverse edge point method. The obtained integral is applied to the diffraction problem of plane waves by an impedance truncated circular cylinder and the scattered waves are derived asymptotically. The results are examined numerically.

Physical Optics Scattering of Waves by a Half-Plane With Different Face Impedances

The theory of physical optics is extended for the diffraction problem of waves by a half-plane with different face impedances. The kernel of the modified theory of physical optics integral is expressed in terms of the Maliuzhinets function. The resultant integral is evaluated asymptotically for large values of the wavenumber. The results are examined numerically.

On dual representation in classical electrodynamics

A discussion is given of the use of the dual representation in solving multipole radiation and electromagnetic wave diffraction problems in classical electrodynamics. In the method discussed, actual electric field sources are replaced by 'magnetic' ones. It is shown that despite the absence of Dirac magnetic monopoles, such formalism allows for a physical interpretation of some frequently used methods.

Boundary-value problems for the Helmholtz equation and their discrete mathematical models

We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically.

Shear wave scattering generated by the interaction of a circular half-cylinder with a wavefield originated by a line source.

The problem of shear wave diffraction caused by a circular half-cylinder was considered. In this case, the incident field was assumed to be generated by a line source, which was set to be parallel to the axis of the cylinder. The solution of this eigenvalue problem was obtained through the application of the superposition principle. In this case, the wavefield outside of the half-cylinder was expressed in terms of the free field and the diffracted field. On the other hand, the wavefield inside of the cylinder was defined in terms of refracted fields. Since the scatterer and the source possess cylindrical symmetry, all the wavefields could be expressed in terms of series of Bessel and Hankel functions. The unknown coefficients of these series were obtained by evaluating boundary conditions. With the solution of this problem, the seismic response of a semi-circular alluvial valley was studied.

Н10 WAVE DIFFRACTION IN A RECTANGULAR WAVEGUIDE BY NARROW WALLS IMPEDANCE BUMP

Rigorous solution of the principal H10 wave diffraction problem at the joint of regular and non-regular (narrow walls are formed by secondary waveguides) rectangular waveguides has been obtained using the method of projection matching. On the basis of numerical results the dependence of the system diffraction characteristics on its parameters is determined and analyzed.

Numerical solution of the three-dimensional stationary diffraction problem for elastic waves

Three-dimensional problems concerning the propagation of stationary elastic oscillations in media with three-dimensional inclusions are solved numerically. By applying potential theory methods, the original problem is stated as a system of two singular vector integral equations for the unknown internal and external densities of auxiliary sources of waves. An approximate solution of the original problem is obtained by approximating the integral equations by a system of linear algebraic equations, which is then solved numerically. The underlying algorithm has the property of self-regularization, due to which a numerical solution is found without using cumbersome regularizing algorithms. Results of test computations and numerical experiments are presented that characterize the capabilities of this approach as applied to the diffraction of elastic waves in three-dimensional settings.

Diffraction on the Two-Dimensional Square Lattice

We solve the thin-slit diffraction problem for two-dimensional lattice waves. More precisely, for the discrete Helmholtz equation on the semi-infinite square lattice with data prescribed on the left boundary (the aperture), we use lattice Green's functions and a discrete Sommerfeld outgoing radiation condition to derive the exact solution everywhere in the lattice. The solution is a discrete convolution that can be evaluated in closed form for the wave number $k=2$. For other wave numbers, we give a recursive algorithm for computing the convolution kernel.

Surface wave diffraction by a sloping ‘left-handed’ region

An exact analytical solution to the problem of surface wave diffraction by a penetrable `left-handed` medium (LHM) e = μ = -1 material slope of arbitrary angle (subject to valid physical constraints) is presented. Standard analysis involving discontinuous angular eigenfunctions resulted in a discrete spectrum leading to a series solution that exhibits the expected negative refraction phenomenology. Numerical results are presented, some of which seemed paradoxical, but are explainable by classical ray optics means. A new type of illusory edge radiation is observed and explained. Although the exact solution applies to the lossless case only, it compares very favourably with independent finite difference time-domain (FDTD) solutions involving causal Lorentzian materials with small but significant loss. Since exact solutions for penetrable materials are virtually non-existent, the author`s solution represents a significant addition to the theory of surface wave diffraction.

Solution of wave diffraction problems by the null-field method

Numerical realization of the null-field method for solving wave diffraction problems is investigated. It is shown that this method provides correct and stable algorithms only when the null-field surface encloses the set of singularities of the analytic continuation of the wave field inside the scatterer. Considering specific examples of diffraction problems, it is demonstrated that the null-field surface is best constructed by analytic deformation of the scatterer’s boundary.

Operator method in the analysis of electromagnetic wave diffraction by planar screens

Some problems of electromagnetic wave diffraction by a system of planar screens are considered. As a key problem, the problem of diffraction by a single screen is solved. The obtained solution is used to study the structures with semi-infinite and finite numbers of identical equidistantly placed screens. The solution is found using the operator method. The possibility of propagation of eigenwaves between screens is taken into account. Dependences of the reflection coefficient of the structure and excitation coefficient of planar waveguides on the distance between the screens are analyzed.

Electrodynamic calculation of plane waveguide phased array with penetrating area method

We consider a new method application for solution of a problem of electromagnetic wave diffraction at plane infinite phase array of rectangular waveguides with triangle grid of their position. Boundary problem is stated in form of the second genus Fredholm’s integral equation on a basis of penetrating area method (PAM). Convergence of numerical results was analyzed and comparison of obtained results with known data was carried out.

Time harmonic wave diffraction problems in materials with sign-shifting coefficients

Some electromagnetic materials present, in a given frequency range, an effective dielectric permittivity and/or magnetic permeability which are negative. We are interested in the reunion of such a “negative” material and a classical one. More precisely, we consider here a scalar model problem for the simulation of a wave transmission between two such materials. This model is governed by a Helmholtz equation with a weight function in the Δ principal part which takes positive and negative real values. Introducing additional unknowns, we have already proposed in Bonnet-Ben Dhia et al. (2006) [1] some new variational formulations of this problem, which are of Fredholm type provided the absolute value of the contrast of permittivities is large enough, and therefore suitable for a finite element discretization. We prove here that, under similar conditions on the contrast, the natural variational formulation of the problem, although not “coercive plus compact”, is nonetheless suitable for a finite element discretization. This leads to a numerical approach which is straightforward, less costly than the previous ones, and very accurate.

Spatial polarization structure of radiation formed by a retroreflector with nonmetallized faces

A polarization-wave analysis is performed for a retroreflector with nonmetallized faces, which forms a complex pattern of radiation intensity distribution due to different shifts between the strength vector components upon total internal reflection. Using the representation of the polarization-inhomogeneous field in the form of a set of Hermite-Gaussian modes, the problem of a plane wave diffraction on a retroreflector is solved and the spatial polarization structure is calculated in both the near- and far-field zones. It is shown that the considered type of retroreflectors is preferable for application in satellite ranging

The variational method and the method of moments in the problem of plane wave scattering by a rectangular cavity in an impedance screen

The problem of electromagnetic plane wave diffraction by a rectangular cavity in an impedance screen is solved. The problem is reduced to solution of a Fredholm integral equation for the field function in the aperture. The equation has a symmetric kernel. Expressions for the angular distribution of the scattered far-field are obtained by the method of moments and the variational method. Numerical results are analyzed and compared.