Solution Of Diffraction Problem Research Articles

On the Numerical Solution of Diffraction Problem by Random Spheres Using Electric Field Integral Equation

The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various approximations are next numerically validated in the case of high-frequency.

Application of the Method of Extended Boundary Conditions to the Solution of the Problem of Wave Diffraction by Magnetodielectric Scatterers Having a Compound Geometry

A technique allowing to model scattering characteristics for bodies of arbitrary geometries is suggested on the basis of the method of extended boundary conditions. The scattering characteristics include those ones, which are averaged over orientation angles. The 2D problem of diffraction of a plane wave by dielectric bodies having a complicated geometry of the cut and, in particular, by bodies similar to fractals is considered. The numerical algorithms of the diffraction problem solution on the basis of the systems of integral equations of the first and second kinds are compared. The correctness of the method is confirmed with the help of the verification of the optical theorem fulfillment for various bodies and by comparing with the calculation results obtained by the modified method of discrete sources.

Solution of Mixed Half-Plane Diffraction Problems of Non-Stationary Plane and Cylindrical Waves and Blast Wave Protection by Barriers

Exact analytical solutions of diffraction problems are obtained for nonstationary plane and cylindrical waves on a half-plane at following mixed boundary conditions: the Neumann condition on one side of the half-plane and the Dirichlet condition on the other one. The numerical analysis of near-front asymptotic solutions shows that there is a considerably greater attenuation of blast waves behind the half-plane (barrier) with sides of different noise absorption properties, than in the case of complete reflection from both sides of the half-plane.

Method of Integral Equations for the Solution of Diffraction Problems about the Calculation of Twisted Guiding Structures

The method of integral equations is suggested for calculating irregular twisted guided structures. The method is based on the Lorentz integral relationship and makes it possible to solve internal diffraction problems for waveguides, whose screening surface is described by analytical functions.

Edge Catastrophes in Diffraction Problems

Abstract—The application of the wave theory of edge catastrophes to the asymptotic solution of diffraction problems on bodies with curvilinear edges is considered. As an example, the diffraction of a converging scalar wave on a curvilinear ideally conducting screen in a homogeneous medium is studied, leading to the formation of C4 and K4, 2 edge catastrophes.

The method of transition boundary for the solution of diffraction problems

A new method, which enables one to solve some diffraction problems, is put forth. The technique is based on a relation between the diffracted and scattered geometric optics waves at the transition boundaries. The concept of initial waves is also used instead of the incident field. The general algorithm of the method is outlined and applied to the diffraction problems of waves by perfect electric conductor half-screen, resistive half-plane and impedance sheet junction.

Physical Interpretation of Strict Solutions of Diffraction Problems by Heuristic Relations

We propose a new approach to construct heuristic relations describing solutions of diffraction problems. Those relations are based on physical principles and allow one to interpret mathematically strict solutions. Since the heuristic relations possess high performance and accuracy, they can also be used along with any strict approach or experimental results for a significant improvement of efficiency of solutions of practical problems related to applications of the diffraction theory.

Diffraction simulation from wedges to finite-sized plates based on the physical theory of diffraction

Efficient predictions of sound diffraction around objects are of critical significance in room-acoustic simulations. An advanced diffraction theory has recently been investigated for potential applications in room acoustics for some semi-infinite, canonical wedges and for finite-sized rectangular plates [Rozynova and Xiang, J. Acoust. Soc. Am. 144 (to be published)]. The physical theory of diffraction (PTD) still relies on both geometrical and physical principles, yet emphasizes the physical one. Important features of the PTD approach are its computational efficiency and the high degree of accuracy for the diffracted sound field. This paper reviews the fringe field predictions of canonical semi-infinite wedges and further discusses solutions of diffraction problems on finite, rigid rectangular plates. The PTD is applied to approximate the solutions of a finite-sized, rigid rectangular plate that achieves high numerical efficiency. The PTD simulation allows sound diffraction contributions to be determined independently from two pairs of edges of the rigid plate, while ignoring the edge waves around the corner in far-field. This paper uses numerical implementations of the PTD predictions to demonstrate the simulation efficiency of the PTD in finite-sized objects. The numerical simulations are also validated by some preliminary experimental results carried out using an acoustic goniometer.

Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides

This paper describes the algorithm for the numerical solution of the diffraction problem of waveguide modes at the joint of two open planar waveguides. For planar structures under consideration, we can formulate a scalar diffraction problem, which is a boundary value problem for the Helmholtz equation with a variable coefficient in two-dimensional space. The eigenmode problem for an open three-layer waveguide is the Sturm-Liouville problem for a second-order operator with piecewise constant potential on the axis, where the potential is proportional to the refractive index. The described problem is singular and has a mixed spectrum and therefore the Galerkin method can not be used in this definition. One way to adapt the Galerkin method for the problem solution is to artificially limit the area, which is equivalent to placing the open waveguide in question in a hollow closed waveguide whose boundaries are remote from the real boundaries of the waveguide layer of the open waveguide. Thus, we obtain a diffraction problem on a finite interval and with a discrete spectrum, which can be solved by the projection method, as done in this paper.

ELECTROMAGNETIC WAVE DIFFRACTION PROBLEM BY PERIODICAL GRATING IN PLANE WAVEGUIDE

The problem of an electromagnetic wave diffraction by a periodical grating made of thin conducting screens between two conducting planes is reduced to an infinite set of linear algebraic equations. Three-dimensional case was considered when a field depends on all three spatial coordinates. According to the theorem of unique diffraction problem solution if an original wave is Floquet wave, then the desired solution of the Maxwell equations set can also be only the Floquet wave. We used the expansion of the desired functions along the orthogonal system of functions depending on a transverse coordinate, and the representation in the form of a quasiperiodic function along a longitudinal coordinate. The case when a field does not depend on a transverse coordinate is considered separately. From the boundary conditions and the field conjugation conditions in a grating plane, a pair-wise summatory equation is obtained with respect to the coefficients of the electromagnetic field expansion over an eigenwave of a waveguide. This equation is reduced to an infinite set of linear algebraic equations by the method of integral-summatory identity. An infinite set of linear equations is represented in vector-matrix form: the desired values are two-dimensional vectors, and their coefficients are the square matrices of the second order. Its approximate solution can be obtained by truncation.

Numerical simulation of the physical properties of Gaussian mode using the angular spectrum technique

This research aims to study the analytical and numerical simulation of the Gaussian beams variables of the fundamental mode TEM00 during its propagation in free space between two parallel planes, using the angular spectrum technique. A dedicated computational program in Borland C++ Builder was developed to calculate the diffraction through the angular spectrum technique with the application of two fast 2D Fourier transforms. Some 2D and 3D cross-sections of results are presented. That helped to present the complex amplitude of the Gaussian beams with its real and imaginary parts, Gouy phase shift and full phase and intensity distribution. The Gaussian beam is one of the rare cases when the diffraction problem solution, defined within the frames of scalar and paraxial approximation, is given in the exact analytical form. A comparison between that form and the results of the angular spectrum algorithm brings information about the performance quality of that algorithm.

A note on uniform asymptotic wave diffraction by a wedge

Summary New expressions for asymptotically uniform Green’s functions for high-frequency wave diffraction when a plane, cylindrical or point wave field is incident on an ideal wedge are derived. They are useful for deriving a uniform asymptotic expression for the exact solution in terms of the high-frequency diffracted and geometrical optics far field. The present method is simple and consists of differentiating out the singularities of the integral representations and using new representations for trigonometrical sums that arise when the wedge angle is a rational multiple of �. The new results make explicit the continuity of the fields across shadow and reflection boundaries. The geometrical theory of diffraction (GTD) was introduced by Keller (1) as an asymptotic method for the solution of diffraction problems at high frequencies. Keller’s GTD has proved to be very powerful in a wide variety of applications to physical problems. The method uses the saddle point method to derive asymptotic approximations from the exact solution of canonical wedge problems to derive so called ”diffraction coefficients”. The method gives a useful physical representation of the total far-field in terms of the geometrical optics and a diffracted field term. One drawback of Keller’s method is that it breaks down at shadow and reflection boundaries where the diffracted term predicts infinite fields. To overcome this defect, two uniform asymptotic techniques have been developed recently, namely the uniform asymptotic theory (UAT) of edge diffraction and the uniform geometrical theory of diffraction (UTD). A comparison of both these methods is given in the work of Boersma (2) where it is shown that the two different methods of asymptotically approximating integrals by pole subtraction or pole factorisation are equivalent if the complete asymptotic expansions are used. These asymptotic expressions are derived from integrals representing the exact solution. The starting point for our analysis is a particular periodic Green’s function for the solution of of the ideal wedge problem Rawlins(3) . This representation is related to the work of Sommerfeld, Carslaw, Macdonald and others at the beginning of the last century, see Rawlins(4) for a detailed history. The Sommerfeld approach was extended non-trivially to absorbing/impedance wedges by Mayuhzinets and Williams in the 1950’s, see Babich et al (5) for a comprehensive up to date history of general wedge problems solved by the so called Sommerfeld-Malyuzhinets technique. In order to derive useful physical results from these exact solutions the disposition of singularities and saddle points of integrals is crucial for getting accurate uniform results. Oberhettinger (6), (7) used asymptotic methods to derive results for diffraction by ideal

Diffraction problem solution based on use of spherical-wave sources

We consider an external problem of diffraction by compact bodies, for which the region containing a set of singularities of the analytic continuation of the wave field is known. The approach to solution of this problem is based on representing the scattered field as series of spherical waves divergent from several centers with the amplitudes determined from the boundary condition by solving the inverse problem. The condition indicating the minimum number of radiation centers and their optimal location inside the scatterer is obtained. The results of numerical simulation are reported.

Solution of diffraction problems by means of the modified Galerkin method

Using the problem of matching of planar waveguides as an example, an approach to solution of diffraction problems with the help of the modified Galerkin method is considered.

Dirichlet-Neumann conditions and the orthogonality of three-dimensional guided waves in layered solids

Orthogonality relations for homogeneous waves in layered plates are obtained, and they are generalized to the case of a contact with fluid layers. For layers of infinite thickness, it is shown that the homogeneous waves of the discrete spectrum are orthogonal to each other and to the waves of the continuous spectrum. For finite-size sources, exact formulas are derived for the coefficients multiplying the modes. Based on the orthogonality relations, a nonlocal radiation principle is proposed such that the infinite domain in the numerical solution of diffraction problems for layered plates can be replaced by a virtual cylinder.

A numerical model of propagation of waves from complex-shape emitters in an inhomogeneous medium

At present physical optics still calls for effective numerical solutions of diffraction problems. The main difficulty is a large amount of computation needed to perform integral conversions with rapidly oscillating cores. There are studies [1, 2] that offer effective algorithms of solving this kind of problems, yet these algorithms aim at determining amplitude-phase distributions in the detector’s plane only. The approach like that is barely suitable for computing the field at all points of the propagation medium between the emitter and detector. The necessity of such computations arises when one tries to model scattering of short waves on intricate-shape objects [3] in an inhomogeneous medium. The paper considers the application of algorithm [1] when visible light experiences scattering on plane triangular polygons in propagation through an inhomogeneous medium. The consideration of plane triangular apertures is important because of wide use of polygonal models for approximating real intricately shaped objects with a various degree of accuracy.

Dependence of the magnetic field of eddy currents on the parameters of a crack in aluminum alloys

On the basis of rigorous solutions of diffraction problems, we calculate the dependences of the magnetic field strength of eddy currents on changes in the length of an extended undersurface crack, the depth of its occurrence, and inclination to the surface as well as on a local change in the specific conductance of the base material. We determine the structural features of the field induced by a defect of the type of an arbitrarily oriented crack for the solution of defectometry problems.

FRACTIONAL BOUNDARY CONDITIONS IN PLANE WAVES DIFFRACTION ON A STRIP

New fractional boundary conditions (FBC) on plane boundaries are introduced. FBC act as intermediate case between perfect electric conductor and perfect magnetic conductor. In certain sense FBC are analogue of commonly used impedance boundary conditions with pure imaginary impedance. The relation between fractional order and impedance is shown. Plane wave diffraction problem by a strip described by FBC is formulated and solved using new method which extends known methods. Numerical results for physical characteristics are presented. Analyzing the scattering properties of the fractional strip new features are observed. FBC has one important special case where the fractional order equals to 1/2. For this special case the solution of diffraction problem can be found in analytical form for any value of wavenumber. Also for small values of wavenumber monostatic radar cross section has new specific resonances which are absent for other values of fractional order.

Structure of boundary diffraction wave revisited

The physically appealing boundary diffraction wave theory which suggests that diffraction patterns arise due to interference of an undisturbed (geometrical) wave and the boundary diffraction wave generated by edge of the diffracting aperture, simplifies the solution of diffraction problems by reducing the Fresnel–Kirchhoff surface integral into a line integral over the illuminated boundary of the diffracting aperture. The present work reports experimental investigations carried out on the structure of the boundary diffraction wave. It has been shown that the boundary diffraction wave is continuous behind the diffracting aperture and apparently there does not exist any discontinuity at the geometrically light to shadow transition boundary, as is required by the theory.

Software for designing and modeling the diffraction Gratings within the rigorous electromagnetic theory

The Grating software for the design and simulation of diffraction gratings within the rigorous electromagnetic theory is presented. The software is compared with the well-known commercial software GSolver in terms of computation speed. The comparison is based on the examples of 1D and 2D diffraction problem solutions. The application of Grating to the solution of diffraction problem on lens array is also considered.