Control of Photon Dynamics in Non-Euclidean Polygonal Microcavities by Joint Geometric Curvatures

TL;DR

This paper explores how non-Euclidean geometries influence photon behavior in polygonal microcavities, revealing unique phenomena like hyperbolic fixed points and phase transitions driven by curvature, with implications for quantum chaos and photonic device design.

Contribution

It introduces a unified model for non-Euclidean polygonal microcavities with joint curvature parameters, uncovering new phenomena and phase behaviors absent in Euclidean geometries.

Findings

Discovery of dissipative states with hyperbolic fixed points unique to non-Euclidean spaces

Identification of phase transitions marked by abrupt quality factor changes

Cavities with geodesic sides avoid certain phase transitions due to symmetry

Abstract

Non-Euclidean geometry has recently emerged as a powerful tool, offering new insights and applications in optical microcavities supporting Whispering Gallery Modes (WGMs). In this study, we extend the concept of polygonal microcavities to non-Euclidean spaces by developing a unified model that incorporates a joint geometric parameter of curvatures. This system uncovers a range of unexplored phenomena, mechanisms, and concepts that are unique to curved spaces. Notably, we observe dissipative states characterized by hyperbolic fixed points (HFPs) that appear exclusively in non-Euclidean scenarios, leading to the formation of phase diagrams within the parametric space of curvatures. Our results reveal phase transitions across geometric boundaries, marked by abrupt changes in the cavity quality factor. These transitions are strongly influenced by the wavelike nature of photon trajectories, offering intriguing insights into quantum chaos within curved spaces. Additionally, we discover that cavities with geodesic side lines exhibit a remarkable symmetry-driven avoidance of such phase transitions, highlighting the profound connection between physical dynamics and spatial geometry. Our findings establish a promising platform for optical simulations of non-Euclidean quantum chaos and open up potential applications in on-chip photonic devices.