Interplay of Goos-Hänchen shift and boundary curvature in deformed microdisks

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.

Extremely high Q and unidirectional laser emission due to combination of the Kolmogorov-Arnold-Moser barrier and the chaotic sea in a dielectric microdisk

Emission characteristics of an oval-shaped microcavity laser are studied. In experiments, modes localized on periodic orbits emit unidirectionally with a narrow in-plane divergence angle of about 12 deg. The origin of high directionality is elucidated by means of classical ray dynamics. Wave calculations show that the Q-factors of the resonances are higher than 10⁸. We explain this extraordinary high Q-factor in relation with a dynamical barrier region where Kolmogorov-Arnold-Moser curves significantly obstruct leakages of resonances.

Pair of Exceptional Points in a Microdisk Cavity under an Extremely Weak Deformation

One of the interesting features of open quantum and wave systems is the non-Hermitian degeneracy called an exceptional point, where not only energy levels but also the corresponding eigenstates coalesce. We demonstrate that such a degeneracy can appear in optical microdisk cavities by deforming the boundary extremely weakly. This surprising finding is explained by a semiclassical theory of dynamical tunneling. It is shown that the exceptional points come in nearly degenerated pairs, originating from the different symmetry classes of modes. A spatially local chirality of modes at the exceptional point is related to vortex structures of the Poynting vector.

Separatrix modes in weakly deformed microdisk cavities

Optical modes in deformed dielectric microdisk cavities often show an unexpected localization along unstable periodic ray orbits. We reveal a new mechanism for this kind of localization in weakly deformed cavities. In such systems the ray dynamics is nearly integrable and its phase space contains small island chains. When increasing the deformation the enlarging islands incorporate more and more modes. Each time a mode comes close to the border of an island chain (separatrix) the mode exhibits a strong localization near the corresponding unstable periodic orbit. Using an EBK quantization scheme taking into account the Fresnel coefficients we derive a frequency condition for the localization. Observing far field intensity patterns and tunneling distances, reveals small differences in the emission properties.

Q spoiling in deformed optical microdisks due to resonance-assisted tunneling

A recent experiment by Kwak et al. [Sci. Rep. 5, 9010 (2015)10.1038/srep09010] demonstrated the relevance of resonance-assisted tunneling for optical microcavities where resonance chains emerge in phase space due to boundary deformations. In this paper we adapt the perturbative description of resonance-assisted tunneling to calculate optical modes and the imaginary part of their complex wavenumber which determines the lifetime of the mode. We demonstrate our method at three example cavity shapes and compare our results to numerical data and perturbation theory for weakly deformed microdisk cavities.

Local chirality of optical resonances in ultrasmall resonators

In wavelength-scale cavities with chiral-symmetric geometry, wave optical effects can introduce local chirality, that is, a spatial separation of the clockwise and counterclockwise propagating resonant modes. We show that this local chirality results in unidirectional lasing emission in the far field. In the presence of a waveguide, the local chirality also allows for directional evanescent coupling of the lasing modes, and the output direction can be varied by selecting the coupling position along the cavity boundary. Our results demonstrate that the local chirality of optical resonances can be utilized to control the output directionality and enhance the collection efficiency of emission from ultrasmall resonators.

Trace formula for chaotic dielectric resonators tested with microwave experiments

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length spectrum showed good qualitative and reasonable quantitative agreement with the trace formula. It demonstrated, however, the need for higher-order corrections of the trace formula. The application of a curvature correction to the Fresnel reflection coefficients entering the trace formula yielded better agreement, but deviations remained, indicating the necessity of further investigations.

Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.

Fresnel filtering of Gaussian beams in microcavities

We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory.