THE DIFFRACTION OF A WHISPERING-GALLERY MODE BY A SPHERICAL SOFT-HARDCAP

An asymptotic solution is obtained for the problem of the diffraction of a rotationally symmetric high-frequency scalar whispering-gallery m ode by a spherical cap. The convex side of the cap is assumed to have a soft (pressure release) boundary condition while the concave side is a rigid boundary. By considering the fact that the diffraction of a h igh frequency wave is a local phenomenon, the problem is formulated in an extended abstract space for which the polar angle theta varies in (-infinity, infinity). This extension permits one to reduce the proble m into a matrix Hilbert equation which is solved by using the Daniele- Khrapkov method of factorization. Various ray contributions are isolat ed and fairly simple non-uniform expressions for certain diffraction c oefficients are obtained. Copyright (C) 1996 Elsevier Science Ltd