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

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.

Optical Microcavities as Quantum-Chaotic Model Systems: Openness Makes the Difference!

“…The origin is the openness of the billiard, effectively described by the adjusted reflection law. Note that dissipative as well as attractive dynamics with the formation of repellors and attractors, respectively, is possible [24]. We are optimistic that more signatures of non-Hamiltonian ray dynamics will be identified soonand that quantum chaos in open systems will remain a fascinating research topic in the future.…”

“…On the other hand, they also exhaust the number of possible corrections because there are no more independent directions in phase space. We shall see in the last Section that the different nature of Goos-Hänchen shift and Fresnel filtering manifests itself in strikingly different effects on the dynamics in optical billiards described with an adjusted ray model that takes the above-discussed non-specular reflection near critical incidence into account [24].…”

“…2 can be addressed based on Goos-Hänchen shift (that is important for all angles of incidence χ > χ c ) and Fresnel filtering (that is important especially for χ ≈ χ c ). The two remaining examples, the existence of regular orbits in spiral microcavities and the breaking of time reversal symmetry in the Husimi functions, can be explained by Fresnel filtering [24].…”

“…Therefore, regular orbits (similar to those in the disk) may exist again [24]. They are unstable and, consequently, host true scars.…”

“…Responsible is the filtering correction that causes deviations of the Jacobian matrix determinant from unity, see [24] for details. The origin is the openness of the billiard, effectively described by the adjusted reflection law.…”