Hexagonal dielectric resonators and microcrystal lasers

We study long-lived resonances (lowest-loss modes) in hexagonally shaped dielectric resonators in order to gain insight into the physics of a class of microcrystal lasers. Numerical results on resonance positions and lifetimes, near-field intensity patterns, far-field emission patterns, and effects of rounding of corners are presented. Most features are explained by a semiclassical approximation based on pseudointegrable ray dynamics and boundary waves. The semiclassical model is also relevant for other microlasers of polygonal geometry.Comment: 12 pages, 17 figures (3 with reduced quality

Spectral properties of quantized barrier billiards

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions, number variances, spectral form factors, and the level dynamics is carried out. For a special member of the billiard family, the form factor is calculated analytically for small arguments in the diagonal approximation. All results together are consistent with the so-called semi-Poisson statistics.Comment: 8 pages, 9 figure

Evanescent wave approach to diffractive phenomena in convex billiards with corners

What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper we use the well-known scaling quantization procedure to study them. We show how the scaling method can be applied to convex billiards with corners, taking into account the strong diffraction at them and the techniques needed to solve their Helmholtz equation. As an example we study a classically pseudointegrable billiard, the truncated triangle. Then we focus our attention on the spectral behavior. A numerical study of the statistical properties of high-lying energy levels is carried out. It is found that all computed statistical quantities are roughly described by the so-called semi-Poisson statistics, but it is not clear whether the semi-Poisson statistics is the correct one in the semiclassical limit.Comment: 7 pages, 8 figure

Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.Comment: 8 pages, 12 figure

The Quantum-Classical Correspondence in Polygonal Billiards

We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly related to the classical invariant surfaces in the semiclassical limit. This is illustrated for the barrier billiard. We expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines.Comment: 8 pages, 9 figures (in reduced quality), to appear in PR

Singular continuous spectra in a pseudo-integrable billiard

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is generalized. It is proven that the flow on invariant surfaces of genus two exhibits a singular continuous spectral component.Comment: 4 pages, 2 figure

Systematic study of carrier correlations in the electron-hole recombination dynamics of quantum dots

The ground state carrier dynamics in self-assembled (In,Ga)As/GaAs quantum dots has been studied using time-resolved photoluminescence and transmission. By varying the dot design with respect to confinement and doping, the dynamics is shown to follow in general a non-exponential decay. Only for specific conditions in regard to optical excitation and carrier population, for example, the decay can be well described by a mono-exponential form. For resonant excitation of the ground state transition a strong shortening of the luminescence decay time is observed as compared to the non-resonant case. The results are consistent with a microscopic theory that accounts for deviations from a simple two-level picture.Comment: 8 pages, 7 figure

Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity

We have investigated quasi-eigenmodes of a quadrupolar deformed microcavity by extensive numerical calculations. The spectral structure is found to be quite regular, which can be explained on the basis of the fact that the microcavity is an open system. The far-field emission directions of the modes show unexpected similarity irrespective of their distinct shapes in phase space. This universal directionality is ascribed to the influence from the geometry of the unstable manifolds in the corresponding ray dynamics.Comment: 10 pages 11 figure

Devil's Staircase in Magnetoresistance of a Periodic Array of Scatterers

The nonlinear response to an external electric field is studied for classical non-interacting charged particles under the influence of a uniform magnetic field, a periodic potential, and an effective friction force. We find numerical and analytical evidence that the ratio of transversal to longitudinal resistance forms a Devil's staircase. The staircase is attributed to the dynamical phenomenon of mode-locking.Comment: two-column 4 pages, 5 figure