Diffraction of a Whispering Gallery Mode at a Jumply Straightening of the Boundary

Abstract

Diffraction of a high-frequency small-number whispering gallery mode running along a concave boundary, which turns into a flat one so that its curvature experiences a jump, is studied. The cases of rigid (Neumann) and soft (Dirichlet) boundary conditions are considered. Within the framework of the parabolic equation method, a mathematically correct scattering problem is obtained which is solved explicitly and investigated asymptotically in detail. Analytic expressions are found for all emerging wavefields. In particular, an edge wave diverging from the point of non-smoothness of the boundary is described. For the rigid condition, its amplitude is proportional to the magnitude of curvature jump, but not for the soft condition.