Diffraction of large-number whispering gallery mode by boundary straightening with jump of curvature

TL;DR

This paper investigates how high-frequency whispering gallery modes diffract when encountering a boundary with a sudden change in curvature, using asymptotic analysis and the parabolic equation method.

Contribution

It develops a parabolic equation approach and derives asymptotic formulas for wave behavior near boundary curvature discontinuities in whispering gallery modes.

Findings

Asymptotic formulas for wave diffraction at curvature jumps

Detailed analysis of the wavefield's ray skeleton

Insights into wave behavior near boundary non-smoothness

Abstract

Diffraction of a high-frequency large-number whispering gallery mode is studied, which runs along a concave curve turning to a straight line. At the point of straitening, the curvature of the boundary suffers a jump. The parabolic equation method is developed in the problem, and asymptotic formulas are presented for all waves arising in the vicinity of the non-smoothness point of the boundary. The ``ray skeleton'' of the wavefield is investigated in detail.