Adiabatic formation of high-Qmodes by suppression of chaotic diffusion in deformed microdiscs

Abstract

Resonant modes with high-Q factors in a two-dimensional deformed microdisc cavity are analyzed by using a dynamical and semiclassical approach. The analysis focuses particularly on the ultra-small cavity regime, where the scale of a resonant free-space wavelength is comparable with that of the microdisc size. Although the deformed microcavity has strongly chaotic internal ray dynamics, modes with high-Q factors in this regime show unexpectedly regular distributions in configuration space and adiabatic features in phase space. By tracing the evolution process of such high-Q modes through the deformation from a circular cavity, it is uncovered that the high-Q modes are formed adiabatically on cantori. Due to the openness of microcavities, such adiabatic formation of high-Q modes around cantori is enabled, in spite of strong chaos in ray dynamics. Since the cantori are in close contact with short periodic orbits, their influence on the modes, such as localization patterns in phase space, can be also clarified. In order to quantitatively analyze the spectral range where high-Q modes appear, the phase space section of the deformed microcavity is partitioned by partial barriers of short periodic orbits, and the semiclassical quantization scheme is applied to the partitioned areas and their action fluxes. The derived spectral ranges for the high-Q modes show a good agreement with a numerically observed spectrum. In the course of semiclassical quantization, it is shown that the chaotic diffusion in the system that we investigate can be resolved by the scale of a quarter effective Planck's constant, and the topological structure of the manifolds in phase space allows for this resolution higher than a Planck constant scale. By analyzing flux Farey trees, the role of short periodic orbits in chaotic diffusion and their connection to cantori are verified. Contents

Decomposed entropy and estimation of output power in deformed microcavity lasers

“…Directional emissions have been investigated in terms of directionality and divergence angle at given FFPs so far [21][22][23][24][25]. In this sub-section, we present a method to estimate the degree of output power at given FFPs by exploiting the decomposed Shannon entropy.…”

“…In these studies, directional emission was only addressed in terms of a single variable. That is, the directionality and divergence angle are defined in terms of the intensity of far-field profiles (FFPs) as a function of a single variable θ [15,[22][23][24]. However, these physical quantities cannot fully capture the properties of FFPs because the FFPs are defined in two-dimensional microcavity lasers, rather than in one-dimensional lasers.…”

Decomposed Entropy and Estimation of Output Power in Deformed Microcavity Lasers

“…In these studies, directional emission was only addressed in terms of a single variable. That is, the directionality and divergence angle were defined in terms of the intensity of far-field profiles (FFPs) as a function of a single variable [ 15 , 22 , 23 , 24 ]. However, these physical quantities cannot fully capture the properties of FFPs because FFPs are defined in two-dimensional microcavity lasers, rather than in one-dimensional lasers.…”

Entropic measure of directional emissions in microcavity lasers

“…2(a) are measures of the unidirectionality associated with the emission windows. More precisely, the unidirectionality U C marked by blue squares is defined as follow [21,22]:…”