Scattering of E polarized whispering-gallery mode from concave boundary

Abstract

In this work we present numerical results for the 2D problem of scattering E polarised whispering-gallery mode from concave convex perfectly conducting boundary. The results were obtained by applying the developed method of currants integral equations (CIE) [6,7] for high frequency domain when the size of the scatterer match is greater than the wave length. We have applied the described procedure in order to find numerical solutions of scattering whispering-gallery mode by concave finite convex boundary as a part of a circular cylinder or part of parabolic cylinder. As incident wave we have considered cylindrical waves from line source and Gauss beam [6] with different effective width. It is shown that we have a complicated process of focusing and oscillating of the beam's reflected field, both cylindrical and Gauss beam incident fields. The distortions of reflected field depend on shape of the boundary and parameters of the incident fields.Keywords: Scattering problem, E polarized whispering-gallery mode, concave boundary, integral equation of the first kind, numerical solution. ResumenEn este trabajo presentamos resultados numéricos para el problema 2D de modo de galería susurrante E polarizada, de una frontera perfectamente conducente cóncava y convexa. Los resultados fueron obtenidos aplicando el método desarrollado de ecuaciones integrales pasas [6,7] para dominios de alta frecuencia cuando el tamaño de la pareja dispersora es mayor que la longitud de onda. Hemos aplicado el procedimiento descrito con tal de encontrar soluciones numéricas de modo galería susurrante de dispersión por frontera convexa finita cóncava, como parte de un cilindro circular * Russian New University, Radio Street 22, 107005 Moscow, Russia. E-Mail: anioutine@mtu-net.ru. † Russian New University 60-2-94, Novocheremushkinskaya UI 117420 Moscow, Russia. E-Mail: walter@robis.ru. 122A.P. Anyutin -V.I. Stasevich Rev.Mate.Teor.Aplic. (2005) 12(1 & 2) o parte de un cilindro parabólico. Como onda de incidencia hemos considerado ondas cilíndricas de fuente de línea y rayo de Gauss [6] con diferentes anchos efectivos. Se muestra que tenemos un proceso complicado de enfoque y oscilación del campo reflajado del rayo, tanto en el campo de incidencia cilíndrico como con el rayo de Gauss. Las distorsiones del campo reflejado depende en la forma de la frontera y los parámetros de los campos de incidencia.Palabras clave: Problema de dispersión, modo de galería susurrante E polarizada, frontera cóncava, ecuación integral de primer tipo, solución numérica.Mathematics Subject Classification: 34L25, 74S15, 65R20.

Calculation of the near field for concave and convex-concave screens with a variable curvature in the presence of whispering-gallery modes

“…This method is referred to as the method of extended boundary conditions. Its high efficiency has been demonstrated for a series of prob lems [10][11][12][13][14][15]. Recall that the method of extended boundary conditions is based on two ideas.…”

“…Studies [12][13][14][15] are an exclusion, but, in these studies, only the field in the far zone of such screens (scattering pat tern) is investigated. Therefore, solution of such prob lems in a rigorous formulation and analysis of the near scattered field obtained on the basis of these solutions are of practical and theoretical interests.…”