We study the effect of dynamical tunneling on emission from ray-chaotic microcavities by introducing a suitably designed deformed disk cavity. We focus on its high quality factor modes strongly localized along a stable periodic ray orbit confined by total internal reflection. It is shown that dominant emission originates from the tunneling from the periodic ray orbit to chaotic ones; the latter eventually escape from the cavity refractively, resulting in directional emission that is unexpected from the geometry of the periodic orbit, but fully explained by unstable manifolds of chaotic ray dynamics. Experimentally performing selective excitation of those modes, we succeeded in observing the directional emission in good agreement with theoretical prediction. This provides decisive experimental evidence of dynamical tunneling in a ray-chaotic microcavity.

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.

Advances in processing technology, such as quantum-well structures and dry-etching techniques, have made it possible to create new types of two-dimensional (2D) microcavity lasers which have 2D emission patterns of output laser light although conventional one-dimensional (1D) edge-emitting-type lasers have 1D emission. Two-dimensional microcavity lasers have given nice experimental stages for fundamental researches on wave chaos closely related to quantum chaos. New types of 2D microcavity lasers also can offer the important lasing characteristics of directionality and high-power output light, and they may well find applications in optical communications, integrated optical circuits, and optical sensors. Fundamental physics of 2D microcavity lasers has been reviewed from the viewpoint of classical and quantum chaos, and recently developed theoretical approaches have been introduced. In addition, nonlinear dynamics due to the interaction among wave-chaotic modes through the active lasing medium is explained. Applications of 2D microcavity lasers for directional emission with strong light confinement are introduced, as well as high-precision rotation sensors designed by using wave-chaotic properties.A resonant mode of a stadium-shaped cavity showing wave chaos.

The limaçon-shaped semiconductor microcavity is a ray-chaotic cavity sustaining low-loss modes with mostly unidirectional emission patterns. Investigating these modes systematically, we show that the modes correspond to ray description collectively, rather than individually. In addition, we present experimental data on multimode lasing emission patterns that show high unidirectionality and closely agree with the ray description. The origin of this agreement is well explained by the collective correspondence mechanism.

Light emission from a dielectric cavity with a stadium shape is studied in both ray and wave models. For a passive cavity mode with low loss, a remarkable correspondence is found between the phase space representation of a quasibound wave function and its counterpart distribution in the ray model. This result provides additional and more direct evidence for good ray-wave correspondence in low-loss modes previously observed at the level of far-field emission pattern comparisons.

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We show that the solution of fully nonlinear lasing equations for stadium cavities exhibits a highly directional emission pattern. This directionality can be well explained by a ray-dynamical model, where the dominant ray-escape dynamics is governed by the unstable manifolds of the unstable short periodic orbits for the stadium cavity. Investigating the cold-cavity modes relevant for the lasing, we found that all of the high-Q modes have the emission directionality corresponding to that of the ray-dynamical model.Establishing a correspondence between the ray ͑or classi-cal͒ picture and the wave ͑or quantum͒ picture has been a fundamental problem in the field of wave ͑or quantum͒ chaos ͓1͔. One encounters this problem when trying to understand the emission properties from two-dimensional ͑2D͒ microcavity lasers. In such lasers, as a way to extract highly directional emission, it has been proposed to deform the cavity shape smoothly from perfect circularity ͓2-6͔. The result is that rays start to exhibit a variety of dynamics from integrable to strongly chaotic, which is tunable by the deformation.The ray picture has been providing a simple and intuitive method to explain experimental observations of emission directionality. For instance, emission directionality has been associated with the existence of a periodic orbit with a particular geometry ͓6,7͔, drastic shape dependence of emission directionality has been successfully explained by the difference of phase-space structure ͓8͔, and the far-field intensity patterns have been closely reproduced by ray-tracing simulations ͓8-10͔.Among various cavity shapes, the stadium is a simple geometry for which ray dynamics has been rigorously proven to become strongly chaotic ͓11͔. For almost all initial conditions, a ray trajectory explores the entire phase space uniformly. Even for such a strongly chaotic cavity, if one considers refractive emission of light due to the dielectric nature of the cavity, the emission pattern can become highly directional. Namely, strongly chaotic dynamics and highly directional emission are compatible, as was demonstrated by Schwefel et al. ͓8͔, who associated this property with escape dynamics dominated by flow in phase space along the unstable manifolds of the unstable short periodic orbits of a chaotic system.In this paper, we report further evidence for the ability of a ray-dynamical model to describe the lasing states of twodimensional microcavities. Earlier work has focused on establishing a relationship between the ray model and a few quasibound-state solutions of the linear wave equation, without pumping or gain. Which modes to choose for comparison in this case has an intrinsic arbitrariness, although plausibility arguments can be made based on their Q values. Here we show that the solution of the full nonlinear lasing equations for a stadium cavity, uniquely determined by the pumping conditions, has highly directional emission in good agreement with the ray model. This is one of the first pieces of evidence that the multimode solut...