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.     

Scattering of waves by an aperture in an impedance screen

The transmission and diffraction of waves by an aperture in an impedance screen is investigated. The Senior's solution of the scattering problem of waves by an impedance half-plane is transformed into a physical optics type integral. The obtained method is applied to the transmission problem of waves by a slit in an impedance screen. The results are compared with the aperture problem in black and conducting screens numerically.     

Fringe waves on an impedance cylinder

Surface diffraction of the plane waves from an impedance cylinder was investigated by the method of physical theory of diffraction (PTD). Physical optics (PO) method was used to gain the uniform scattered fields which are produced by the induced surface currents. Nonuniform currents and scattered fields were obtained by the method of PTD with the assistance of the exact solutions.     

The MTPO/Malyughinetz hybrid method for the scattering analysis of parabolic impedance reflectors

The scattering process of cylindrical waves, radiated by a line source, from a parabolic reflector is investigated with the MTPO/Malyughinetz hybrid method. The geometrical optics and diffracted waves are evaluated asymptotically from the radiation integral. The scattered, diffracted and geometrical optics waves are plotted numerically for different impedance values.     

阻抗劈绕射对破碎波后向散射特性的影响

海浪的破碎区会导致海面电磁散射特性发生很大改变,导致海尖峰现象的产生.本文结合阻抗劈结构模型分析了劈绕射对破碎波后向散射特性的影响.首先利用基尔霍夫近似求解破碎波的物理光学场;基于Maliuzhinets方法,从波动方程及精确阻抗边界条件出发,由谱函数的积分形式得到阻抗劈的一致性绕射系数,结合物理光学绕射系数导出阻抗劈等效边缘电磁流;利用边缘绕射场修正物理光学场,得到考虑劈绕射效应的破碎波散射总场.数值结果表明,阻抗劈的绕射场在Keller锥内出现HH极化大于VV极化的现象,因此计入绕射场的影响会使得破碎波生长到临近坍塌阶段时,小擦地角逆风观测出现总场的后向散射截面HH极化大于VV极化的现象,说明劈绕射是造成海尖峰现象产生的原因之一.     

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.     

The effect of impedance boundary conditions on the potential function of the boundary diffraction wave theory

A novel potential function of the boundary diffraction wave theory is obtained for the impedance surfaces by the asymptotic reduction of the modified theory of physical integrals. The function is expressed in terms of the direction vectors of the incident and scattered rays. The application of the method is performed on the problem of diffraction of plane waves by an impedance half plane for oblique incidence.     

MTPO based potential function of the boundary diffraction wave theory

A novel potential function is introduced by using the modified theory of physical optics integrals for a perfectly conducting half-plane. The function is valid for arbitrary aspects of observation. The line integration of these functions gives the total scattered fields. The method is applied to the problem of diffraction of plane waves by an opaque half-plane for oblique incidence.     

Scattering of plane-waves by an impedance half-plane at the interface between isorefractive media

The scattering of plane waves by an impedance half-plane located at the interface of two isorefractive media is investigated. The scattered field, in addition to the diffracted and geometrical optics fields, is analyzed numerically and compared to the scattered field of perfectly conducting half-plane. The effect of the isorefractive media on the scattered field is also examined.     

The physical optics integral on the scatterer's unlit surface

The scattering integrals of the modified theory of physical optics are redefined according to the illuminated and unlit surfaces of the scattering object. With this aim the canonical problem of wedge diffraction is taken into account. It is shown that the new scattering integral contain two geometrical optics and diffracted fields. One of the geometrical optics waves is the reflected field component that propagates in the real space. The other one transmits to an imaginary space through the scattering surface and does not have any influence in the real space. The diffracted waves exist in the real space and satisfy the related boundary condition on the scattering surfaces. The resultant field expressions are compared with the exact series solution of the problem numerically.     

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.     

The physical optics of phase-conjugate mirrors: Scalar theory

A scalar theory of physical optics is developed for the scattered waves by finite or infinite phase-conjugate mirrors. The method is applied to the scattering problem of waves by a semi-infinite phase-conjugate mirror. The results are examined numerically and compared with the scattered waves by a conducting half-plane. The effect of the phase-conjugation to the location of the transition region is outlined.     

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.     

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.     

Boundary diffraction wave theory of junctions between two surfaces with different face impedances

The line integral of the boundary diffraction wave theory is derived for the diffraction process of waves by a junction between two surfaces with different face impedances. The exact solution of Maliuzhinets is used with this aim. The resultant integral is applied to the diffraction of waves by a circular junction between two impedance surfaces. The results are examined numerically.     

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     

Diffraction of entangled photon pairs by ultrasonic waves

In this paper, we have presented and established a new theoretical formulation of photon optics based on photon path and Feynman path integral idea. We have used Feynman path integral approach to discuss Fraunhofer, Fresnel diffraction of single photon and entangled photon pairs by ultrasonic wave and obtained the following results: i) quantum state and probability distribution of single photon and entangled photon pairs by Fraunhofer and Fresnel ultrasonic diffraction, ii) oblique incidence Raman-Nath and Bragg diffraction conditions, iii) total correlation state and its probability distribution. Our calculation results are in agreement with the experiment results. Comparing one-photon and two-photon diffraction effects by ultrasonic waves, we have found that two-photon diffraction by ultrasonic waves is also a sub-wavelength diffraction.     

General formulation of the edge-diffracted paraxial waves

A general formula for edge-diffracted paraxial waves is derived in terms of the Fourier integral transform. It is observed that the scattered paraxial wave can be divided into components of the geometrical optics and diffracted fields in the spectral domain. An edge-diffracted Gaussian beam is examined numerically as an application of the formula.     

Diffraction of electromagnetic plane wave by an infinitely long conducting strip on dielectric slab

Diffraction of electromagnetic plane wave by an infinitely long conducting strip which is placed on a dielectric slab of finite thickness is formulated rigorously. Both the principal polarizations have been considered. The method of analysis is Kobayashi potential. Imposition of boundary conditions result in dual integral equations. These dual integral equations are reduced to matrix equations with infinite number of unknowns. The elements of the matrix equations are given in terms of infinite integrals. These integrals are hard to solve analytically, so computed numerically. Diffracted far field patterns for different angle of incidence have been computed. Current distributions on the strip are also presented. We have compared our field patterns with those of obtained through physical optics. The agreement is good.     

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.