Related papers: Trace formula for dielectric cavities II: Regular,…
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…
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…
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 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…
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…
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…
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…
This paper is concerned with the scattering resonances of open cavities. It is a follow-up of "Perturbation of the scattering resonances of an open cavity by small particles. Part I" where the transverse magnetic polarization was assumed.…
We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We…
We present a versatile numerical algorithm for computing resonances of open dielectric cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the…
The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in details. The obtained formulae are checked on the example of cut disks. A good agreement is found with direct numerical simulations and…
This paper aims at providing a small-volume expansion framework for the scattering resonances of an open cavity perturbed by small particles. The induced shift of the scattering frequencies by the small particles is derived without…
The resemblance between electrons and optical waves has strongly driven the advancement of mesoscopic physics. However, electron waves have yet to be understood in open cavity structures which have provided contemporary optics with rich…
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…
An overview is provided over the physics of dielectric microcavities with non-paraxial mode structure; examples are microdroplets and edge-emitting semiconductor microlasers. Particular attention is given to cavities in which two spatial…
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 semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over…
A new electromagnetic cavity structure, a lattice of 3D cavities consisting of an array of posts and gaps is presented. The individual cavity elements are based on the cylindrical re-entrant (or Klystron) cavity. We show that these cavities…
We present an analysis of electromagnetic oscillations in a spherical conducting cavity filled concentrically with either dielectric or vacuum layers. The fields are given analytically, and the resonant frequency is determined numerically.…
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…