Abstract

By extending the electromagnetic field representation on a cylindrical concave boundary with a constant radius of curvature, two types of representations are proposed for analysis of high-frequency electromagnetic field on a concave boundary in which the radius of curvature depends on the location. They are: (1) a combination of the ray-tracing method and the adiabatic whispering gallery (WG) mode; and (2) a combination of the ray-tracing and the modified integral-type interference waves. The limitations of the application of these field representations also are presented. Especially, the adiabatic WG mode is obtained by an approximate analysis of a parabolic equation in a curvilinear coordinate system under the condition that the radius of curvature changes slowly. A transformation equation is obtained from the lower-order WG modal solution on a cylindrical concave boundary to the adiabatic WG mode. The foregoing transformation which is similar to the one proposed in the problem of diffraction of a creeping wave on a convex boundary is applied to an integral-type interference wave and subsequently a modified integral-type interference wave is derived which can be applied to the case where the radius of curvature changes as an adiabatic approximation. Further, a ray-tracing algorithm is proposed for determination of the geometrical rays arriving at an arbitrary observation point within a concave surface and its usefulness is clarified.

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