Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.     

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.     

The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone

The work deals with the far field asymptotics of the classical solution for the problem of diffraction by an impedance cone. The incident acoustic plane wave completely illuminates the semi-infinite conical surface. The scattered field contains different components in the asymptotics, namely, the spherical wave from the vertex of the cone, the reflected waves, and, under some conditions, also the surface waves of Rayleigh type. We give integral representations for the scattering diagram of the spherical wave. The uniform (with respect to the observation direction) asymptotic expression for the wave field is also addressed and described by the parabolic cylinder ansatz. Dedicated to the memory of Vladimir Borovikov     

Solution of wave diffraction problems by the method of continued boundary conditions

Numerical solution of three-dimensional diffraction problems by the method of continued boundary conditions, which is known to be effective in the case of two-dimensional problems, is discussed. The basic idea of the method is that the boundary condition is imposed at a certain sufficiently small distance from the impedance surface that produces the diffraction field. This procedure reduces the boundary-value problem to the Fredholm integral equation of the first or second kind with a smooth kernel. Results are reported that show how to apply the MCBC most efficiently, depending on particular requirements regarding the accuracy of the solution and number of calculations. Examples illustrating the high efficiency of the approach are presented.     

Effective-dielectric-constant method for the problem of wave diffraction by a close-spaced dielectric grating

A simple method for determination of effective dielectric constants is proposed that allows a close-spaced two-dimensionally periodic dielectric layer with rectangular elements to be replaced by a homogeneous and anisotropic layer of the same thickness. The method makes it unnecessary to solve the complicated problem of determination of the fields within the elements for calculation of the plane-wave reflection and transmission coefficients in a long-wave approximation, which considerably simplifies the calculations. Comparison with known solutions obtained by rigorous methods for one-dimensionally periodic gratings shows exact agreement of the results. The method is easily extended to magnetodielectric media as well as to multicomponent media, including those whose dielectric constants are functions of the coordinate perpendicular to the layer.Academician A. L. Mints Radio-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-4, pp. 286–294, March–April, 1993.     

Solution of problem of electromagnetic-wave diffraction by multiangle dielectric cylinder using regions-product method

A method is developed for solution of the problem of diffraction of E- and H-polarized waves by a dielectric body with a multiangle cross section. In each of the regions formed by the interfaces of the media, the field is sought as a sum of functions that pertain to individual elements of the contour and are represented by series in Mathieu functions. The results of solutions of model problems are discussed. The possibility of using a triangular dielectric prism as a decelerating lens is shown.Zaporozh'ye Mechanical-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 798–805, July, 1991.     

Solving the diffraction problem of electromagnetic waves on objects with a complex geometry by the pattern equations method

A new efficient method for solving the problems of waves diffraction on complex-shaped objects with the use of their replacement by a group of bodies with more simple form (fragments of complex objects) is offered. By the expansion of the scattering patterns of separate bodies in the series of vector spherical harmonics, the problem is reduced to solving the algebraic system of equations. It is shown that the method possesses a high convergence rate. Examples of modeling the scattering patterns of various complex objects are considered. Reliability of the results obtained is validated using the Optical theorem.     

Numerical analysis of electromagnetic wave diffraction on a three-dimensional magnetodielectric body

A variant of the method of discrete sources suitable for solving problems of electromagnetic wave scattering on three-dimensional magnetodielectric bodies having a smooth surface of arbitrary shape is suggested and realized. A computer program implementing the suggested variant is briefly described. Some results of numerical calculations that illustrate the opportunities of the method are presented. Special attention is given to a study of the influence of deviations of the body shape from axisymmetric one on the bistatic scattering cross sections. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 50–57, October, 2005.     

Solution of the Fokker-Planck equation for the shock wave problem

An eigenexpansion solution of the time-independent Brownian motion Fokker-Planck equation is given for a situation in which the external acceleration is a step function. The solution describes the heavy-species velocity distribution function in a binary mixture undergoing a shock wave, in the limit of high dilution of the heavy species and negligible width of the light-gas internal shock. The diffusion solution is part of the eigenexpansion. The coefficients of the series of eigenfunctions are obtained analytically with transcendentally small errors of order exp(–1/M), whereM 1 is the mass ratio. Comparison is made with results from a hypersonic approximation.     

High-frequency wave diffraction by an impedance segment at oblique incidence

The plane problem of high-frequency acoustic wave diffraction by a segment with impedance boundary conditions is considered. The angle of incidence of waves is assumed to be small (oblique). The paper generalizes the method previously developed by the authors for an ideal segment (with Dirichlet or Neumann boundary conditions). An expression for the directional pattern of the scattered field is derived. The optical theorem is proved for the case of the parabolic equation. The surface wave amplitude is calculated, and the results are numerically verified by the integral equation method.     

Watermarking of three-dimensional objects by digital holography

We present an optical method for information watermarking of three-dimensional (3D) objects by digital holography. A hidden image is embedded by double phase encoding in a phase-shift digital hologram of the 3D object. We decode the watermarked hologram to reconstruct the hidden image and the 3D object. We use either the entire hologram or a part of it to decode the hidden image. Experiments are presented to illustrate the ability to recover both the 3D object and the decoded hidden image. Digital holograms of the 3D object are obtained by optical experiments. The watermarking process, 3D object reconstruction, and hidden image recovery are performed digitally. To the best of our knowledge, this is the first report of 3D object watermarking by use of a phase encoding technique and digital holography.     

A theory of the diffraction of an electromagnetic wave by a plane screen

The problem of the diffraction of an arbitrarily polarized electromagnetic plane wave by a perfectly conducting plane screen of infinitesimal thickness is reduced to scalar problems by the method known from earlier papers. The wave field diffracted either by a screen of infinite extent which is perforated by an aperture of arbitrary size and shape or by a complementary screen is then described by means of the bra-vectors, ket-vectors and linear operators introduced by the present author in one of his preceding papers.     

Fresnel diffraction mirror for an atomic wave

We have experimentally demonstrated a material-independent mirror for atomic waves that uses the Fresnel diffraction at an array of parallel ridges. He* (2 (3)S(1)) and Ne* (1s(3)) atomic waves were reflected coherently on a silicon plate with a microfabricated grating structure, consisting of narrow wall-like ridges. We measured the reflectivity at grazing incidence as a function of the incident velocity and angle. Our data show that the reflectivity on this type of mirror depends only on the distance between the ridges, the wavelength, and the incident angle, but is insensitive to the material of the grating structure. The reflectivity is observed to increase by 2 orders of magnitude, compared to that of a flat polished silicon surface, where the reflection is caused by the attractive surface potential. For He* atoms, the measured reflectivity exceeds 10% for normal incident velocities below about 25 cm/s.