Ray-Wave Correspondence in Microstar Cavities.

In a previous work by the authors (Phys. Rev. Research 2, 012072(R) (2020)) a novel concept of light confinement in a microcavity was introduced which is based on successive perfect transmissions at Brewster's angle. Hence, a new class of open billiards was designed with star-shaped microcavities where rays propagate on orbits that leave and re-enter the cavity. In this article, we investigate the ray-wave correspondence in microstar cavities. An unintuitive difference between clockwise and counterclockwise propagation is revealed which is traced back to nonlinear resonance chains in phase space.

Regulated Photon Transport in Chaotic Microcavities by Tailoring Phase Space.

Manipulating light dynamics in optical microcavities has been made mainly either in real or momentum space. Here we report a phase-space tailoring scheme, simultaneously incorporating spatial and momentum dimensions, to enable deterministic and in situ regulation of photon transport in a chaotic microcavity. In the time domain, the chaotic photon transport to the leaky region can be suppressed, and the cavity resonant modes show stronger temporal confinement with quality factors being improved by more than 1 order of magnitude. In the spatial domain, the emission direction of the cavity field is controlled on demand through rerouting chaotic photons to a desired channel, which is verified experimentally by the far-field pattern of a quantum-dot microlaser. This work paves a way to in situ study of chaotic physics and promoting advanced applications such as arbitrary light routing, ultrafast random bit generation, and multifunctional on-chip lasers.

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.

Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems.

For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling in a nonperturbative way. This provides the foundation for future semiclassical complex-path evaluations of resonance-assisted regular-to-chaotic tunneling. Our approach is based on a new class of integrable approximations which mimic the regular phase-space region and its dominant nonlinear resonance chain in a mixed regular-chaotic system. We illustrate the method for the standard map.

Integrable approximation of regular regions with a nonlinear resonance chain.

Generic Hamiltonian systems have a mixed phase space where regions of regular and chaotic motion coexist. We present a method for constructing an integrable approximation to such regular phase-space regions including a nonlinear resonance chain. This approach generalizes the recently introduced iterative canonical transformation method. In the first step of the method a normal-form Hamiltonian with a resonance chain is adapted such that actions and frequencies match with those of the nonintegrable system. In the second step a sequence of canonical transformations is applied to the integrable approximation to match the shape of regular tori. We demonstrate the method for the generic standard map at various parameters.