High‐frequency analysis of radiation field excited by incident whispering‐gallery mode over concave‐to‐convex boundary

Abstract

AbstractAn asymptotic method of analysis is studied for the radiation field when the lowest‐order whispering gallery (WG) modes propagating from the concave side of the concave‐to‐convex boundary with a variable radius of curvature are radiated into the free‐space on the convex side. The modal ray congruences of the WG mode are radiated into the free space after being converted to geometrical rays. Both the caustics and the shadow boundaries are created in the space. As the expression of the radiated field near the caustic, the modal rays incident into the concave part are used for deriving the physical optics integral.By applying the high‐frequency asymptotic analysis in the case of two saddle points closely spaced to the evaluation of the integral, the uniform asymptotic solution was derived. Also, as the radiating field on the sufficiently shadow side of the caustic, the complex ray solution was derived. On the other hand, as the radiating field in the transition region near the shadow boundary caused by the convex region, an asymptotic solution was derived in the form of an extension of the conventional UTD (Uniform GTD) to the case where the geometrical ray converted from the modal ray is incident to the boundary. The numerical results obtained by various asymptotic expressions are compared with the reference solution and the geometrical optics figure drawn by the modal ray tracing. The effectiveness of the asymptotic solution and the propagation and radiation phenomena of the WG mode were derived.