Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes which agrees well with the predictions from an effective non-Hermitian Hamiltonian. A comparison to ray-tracing simulations is given.

We investigate lasing and output directionality of limaçon-shaped microdisk lasers of dimensions comparable to the emission wavelength. The far-field patterns are shown to differ between lasing modes, unlike in large cavities where lasing modes exhibit universal emission directionality determined by chaotic ray dynamics. Unidirectional emission is obtained for certain modes in the wavelength-scale cavities. It results from weak coupling of nearly isotropic high-quality resonances to anisotropic low-quality resonances, combined with chiral symmetry breaking of clockwise and counterclockwise propagating waves. The latter is described by an extended ray dynamics which includes the Goos-Hänchen shift and the Fresnel filtering. Mode hybridization and wave effects in open cavities make it possible to control the output properties of individual lasing modes in wavelength-scale lasers.

We experimentally demonstrate directional far field emission from whispering gallery modes (WGMs) in electrically driven quantum dot micropillar lasers. In-plane directionality of whispering gallery mode emission is obtained by patterning micropillars with Limaçon-shaped cross-section and an upper air-bridge contact for current injection. The micropillar lasers with radii R0 down to 4.5 μm show Q-factors of 40 000 and threshold currents of 40 μA at low temperature. We achieved a far field divergence of about 30° and a directionality of 1.67 ± 0.15 for an optimal Limaçon deformation factor ɛ ≈ 0.5. Parameter dependent studies of the directional emission as a function of ɛ reveal good qualitative agreement with theoretical predictions.

The fractal Weyl law connects the asymptotic level number with the fractal dimension of the chaotic repeller. We provide the first test for the fractal Weyl law for a three-dimensional open scattering system. For the four-sphere billiard, we investigate the chaotic repeller and discuss the semiclassical quantization of the system by the method of cycle expansion with symmetry decomposition. We test the fractal Weyl law for various symmetry subspaces and sphere-to-sphere separations.

We show that coupling among multiple resonances can be conveniently introduced and controlled by boundary wave scattering. We demonstrate this principle in optical microcavities of quasicircular shape, where the couplings of multiple modes are determined by the scattering from different harmonic boundary deformations. We analyze these couplings using a perturbation theory, which gives an intuitive understanding of the first-order and higher-order scattering processes. Different scattering paths between two boundary waves can either enhance or reduce their coupling strength. The effect of controlled multimode coupling is most pronounced in the direction of output from an open cavity, which can cause a dramatic change of the external cavity field distribution.

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

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