Ray dynamics of whispering-gallery modes in curved space

TL;DR

This paper introduces a new mathematical model for ray dynamics in whispering-gallery mode microcavities on curved surfaces, revealing significant differences from flat space and enabling better analysis of 3D curved photonic circuits.

Contribution

The paper develops a novel geodesic-based ray dynamics model for WGMs on curved surfaces, expanding analysis beyond traditional flat-space approaches.

Findings

Ray trajectories follow geodesic lines on curved surfaces.

Ray dynamics differ significantly from flat microcavities.

Provides a universal tool for 3D curved photonic circuit analysis.

Abstract

Microcavities supporting Whispering-gallery modes (WGMs) are of great significance for on-chip optical information processing, which is frequently analyzed using ray dynamics that conventionally involves straight light trajectories in flat space. We develop a novel mathematical model of ray dynamics that allows investigating photon movement in WGM-microcavities defined on curved surfaces, which consists of curved or twisted light trajectories following the geodesic lines of the space. We show that the resulting ray dynamics differs dramatically from those in flat microcavities, and in various manners depending on whether the curved surface can be unfolded to flat. Our methods suggest a redefinition of the WGM symmetry in curved space and provides a universal tool for analyzing three-dimensional (3D) photonic circuits containing curved structures with boundaries.