OPERATOR METHOD IN THE SCALAR WAVE DIFFRACTION BY AXIALLY-SYMMETRIC DISCONTINUITIES IN THE SCREEN

Abstract

Purpose: The scalar wave diffraction by the annular slot in an infinitely thin screen is considered in case of Dirichlet and Neumann boundary conditions. Diffraction problem by a flat ring is also considered as a dual one. The purpose of this paper is the development of the operator method to the axially-symmetric structures with the fields with continuous spectrum. Design/methodology/approach: The incident and reflected fields are represented as Fourier series with respect to the azimuthal angle and as Fourier–Bessel integral with respect to the radius. The problem for every individual harmonic can be considered separately from other ones. The slot scattered field is represented as a superposition of fields scattered by the disc and slot. To solve the problem with the operator method one should use scattering operators of individual elements which make a whole structure. It is supposed that integral reflection operators of a circular slot and disc are known. Spectral function of the scattered field is sought as a sum of two spectral functions of fields scattered by the disc and by the slot in the screen. These functions are obtained from the connected operator equations. The operator equations are equivalent to the integral ones. For their discretization, the infinite interval of integration is exchanged by the bounded one, and Gaussian quadrature rule is used for the integrals with a unit weight-function. The integrands may have a root-type singularity. Findings: The operator equations are obtained with respect to the spectral functions of the field scattered by the annular slot in the screen in case of Dirichlet and Neumann conditions. The directional patterns of a scattered field and dependences of scattering coefficient vs. frequency are represented, too. Conclusions: The effective algorithm for studying the field scattered by the annular slot is proposed. The developed approach can be useful in solving of a number of problems of antennas and microwave electronics.

Keywords

• slot
• infinitely thin ring
• integral equation
• wave diffraction