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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 cavity. In the present paper we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays, but also of diffractive rays that occur in Kellers geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.
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 of the re
In the Terahertz (THz) domain, we investigate both numerically and experimentally the directional emission of whispering gallery mode resonators that are perturbed by a small scatterer in the vicinity of the resonators rim. We determine quality facto
Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test functions. In t
A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schrodinger operator with bounded potential. In solid state physics there is another celebrated measure associated with such operators --- the density of s
We consider the Landau Hamiltonian perturbed by a long-range electric potential $V$. The spectrum of the perturbed operator consists of eigenvalue clusters which accumulate to the Landau levels. First, we obtain an estimate of the rate of the shrinki