E. Erdogan, THE DIFFRACTION OF A WHISPERING-GALLERY MODE BY A SPHERICAL SOFT-HARDCAP, International journal of engineering science, 34(11), 1996, pp. 1247-1258
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