Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

TL;DR

This paper explores how wave-inspired corrections to geometric optics alter ray dynamics in optical microcavities, leading to non-Hamiltonian behavior and observable effects in experiments, with implications for various wave-based systems.

Contribution

It introduces a modified ray dynamics model that accounts for wave effects, revealing non-Hamiltonian phenomena in optical microcavities not captured by traditional geometric optics.

Findings

Small modifications in reflection laws cause dramatic phase space changes.

The adjusted dynamics explain previously observed wave phenomena.

Signatures of non-Hamiltonian behavior can be observed experimentally.

Abstract

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.