SCATTERING BY A PARABOLOID OF REVOLUTION DUE TO AN INTERIOR AXIAL POINT SOURCE
Abstract
For the most part the solutions of scattering problems have been confined to convex surfaces; relatively little has been done in the case of concave surfaces. The latter usually give rise, in the short wavelength limit, to such effects as caustics, multiple reflections and whispering gallery waves (a form of traveling waves). In this paper we will consider the paraboloid of revolution (Dirichlet or Neumann boundary condition) with an interior point source on the axis, but not necessarily at the focal point. The scattering by a paraboloid of revolution differs from the circular cylinder and sphere mentioned above (both closed bodies). Although it is found that multiple reflections, caustics and whispering gallery waves occur when the point source is not at the focal point, the point source at the focal point gives a concave surface scattering problem which does not exhibit these effects. In the short wavelength limit it shows only a single reflection. The case of a dipole, with moment perpendicular to the axis, at the focal point of a perfectly conducting paraboloid of revolution has been investigated. Although there is a double reflection, it is natural to consider the plane wave problem in this category. The scattering of a high frequency plane wave by the interior of a parabolic cylinder (Dirichlet boundary condition) was studied by Lamb (1906), who indicated that the method could be extended to the paraboloid of revolution.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1965
- Accession Number
- AD0487834
Entities
People
- Stephen E. Stone
Organizations
- University of Michigan