Related papers: Experimental test of a trace formula for two-dimen…
We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good…
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…
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…
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…
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…
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…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
In a 2D rectangular microwave cavity dressed with one point-like scatterer, a semiclassical approach is used to analyze the spectrum in terms of periodic orbits and diffractive orbits. We show, both numerically and experimentally, how the…
In this paper, the authors propose a two-dimensional, wide dynamic range, linear displacement sensor using microwave methods. The microwave sensor circuit employs a cylindrical dielectric resonator proximity coupled to a pair of orthogonal…
The construction of the trace formula for open dielectric cavities is examined in detail. Using the Krein formula it is shown that the sum over cavity resonances can be written as a sum over classical periodic orbits for the motion inside…
We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio of the complex conductances of both phases. We propose an algorithm to determine the conductance of a finite network, in…
We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those…
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate the radial dependence of the Woods-Saxon potential and quantum spectra in a bound region, was derived…
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…
Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign…
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 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…
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…
The basic theory underlying the realization of simple multiple-band non-homogeneous dielectric resonators, whose spectral response is the overlap of single-resonator frequency bands, is developed exploiting a general approach discussed in…