Related papers: Trace formula for chaotic dielectric resonators te…
Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently…
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…
Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE, vol. 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts…
Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the…
The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction…
Open dielectric resonators of different shapes are widely used for the manufacture of microlasers. A precise determination of their resonance frequencies and widths is crucial for their design. Most microlasers have a flat cylindrical…
We derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results that were obtained either for systems with…
We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have…
Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial…
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schr\"odinger (or Gross-Pitaevski) equation. Our formula applies…
We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the…
We discuss the statistical properties of lifetimes of electromagnetic eigenmodes in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed…
The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties…
We present an experimental and numerical study of missing-level statistics of chaotic three-dimensional microwave cavities. The nearest-neighbor spacing distribution, the spectral rigidity, and the power spectrum of level fluctuations were…
We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices $n=2$ and 3, exhibit strong localization of simple geometric shape, and we…
We evaluate the Gutzwiller trace formula for the level density of classically chaotic systems by considering the level density in a bounded energy range and truncating its Fourier integral. This results in a limiting procedure which…
We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit…
Methods on reducing resonant frequencies and electrical sizes of resonators are reported in this paper. Theoreti-cal and numerical analysis has been used and the results for the broadside-coupled resonators from both studies exhibit good…