Quasiscarred Resonances in a Spiral-Shaped Microcavity

Abstract

We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices n=2 and 3, exhibit strong localization of simple geometric shape, and we call them quasiscarred resonances in the sense that there is, unlike conventional scarring, no underlying periodic orbits. It is shown that the formation of a quasiscarred pattern can be understood in terms of ray dynamical probability distributions and wave properties like uncertainty and interference.

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

“…The SPD of Lee et al (2004) and the computed asymptotic behavior of initially randomly chosen rays by Schwefel et al (2004) is equivalent to the unstable manifold of the chaotic saddle extended by the intensity-weighted ray dynamics (13) as first noted by . A systematic and clear discussion of this extended version of the chaotic saddle and its relation to the ergodic theory of transient chaos can be found in (Altmann, 2009;Altmann et al, 2013).…”

“…The numerical simulation of intensity-weighted ray dynamics (13) In the same year Lee et al (2004) introduced the survival probability distribution (SPD) of intensity of rays inside the microcavity to explain the spatial localization of optical modes inside spiral-shaped cavities (an example is shown in Fig. 11(a)).…”

Scarred resonances and steady probability distribution in a chaotic microcavity

“…In a recent study [6], it was reported that in a spiralshaped chaotic microcavity there are many resonances showing special localized patterns, so-called quasiscarred resonances which have, unlike typical scarred resonances, no underlying unstable periodic orbit. This finding indicates that the openness of the system plays a crucial role in the formation of localized pattern, and implies that the properties of openness should be imprinted in scarred resonances also.…”

“…The type-I scarred resonances have a clear correspondence of the emission pattern with the scarring pattern, e.g., the bouncing point of the scarring pattern matches well with the emitting point. However, in the type-II scarred resonances there is no correspondence between emission and scarring patterns, and the emission pattern is determined by the structure of steady probability distribution (SPD) [6] near the critical line (p c = sin θ c = 1/n, n being the refractive index) for total internal reflection. Moreover, the SPD provides a consistent explanation about a novel feature of the type-I scarred resonances, i.e., the spatial splitting phenomenon of different chiral components of the scarring pattern.…”

“…Moreover, the SPD provides a consistent explanation about a novel feature of the type-I scarred resonances, i.e., the spatial splitting phenomenon of different chiral components of the scarring pattern. It is known that long time ray dynamical properties of a chaotic microcavity can be described by the SPD, P s (s, p), which is the spatial part of the exponentially decaying survival probability distribution in phase space (s, p), where s is the boundary coordinate and p = sin θ, θ being incident angle [6]. In chaotic microcavities this SPD is a useful tool in identifying both the structure of openness and the escaping mechanism of ray trajectories.…”