Spectral properties of cylindrical quasioptical cavity resonator with random inhomogeneous side boundary.

A rigorous solution for the spectrum of a quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained. To accomplish this task, we have developed a method for the separation of variables in a wave equation, which enables one, in principle, to rigorously examine any limiting case-from negligibly weak to arbitrarily strong disorder at the resonator boundary. It is shown that the effect of disorder-induced scattering can be properly described in terms of two geometric potentials, specifically, the "amplitude" and the "gradient" potentials, which appear in wave equations in the course of conformal smoothing of the resonator boundaries. The scattering resulting from the gradient potential appears to be dominant, and its impact on the whole spectrum is governed by the unique sharpness parameter Ξ, the mean tangent of the asperity slope. As opposed to the resonator with bulk disorder, the distribution of nearest-neighbor spacings (NNS) in the rough-resonator spectrum acquires Wigner-like features only when the governing wave operator loses its unitarity, i.e., with the availability in the system of either openness or dissipation channels. It is shown that the reason for this is that the spectral line broadening related to the oscillatory mode scattering due to random inhomogeneities is proportional to the dissipation rate. Our numeric experiments suggest that in the absence of dissipation loss the randomly rough resonator spectrum is always regular, whatever the degree of roughness. Yet, the spectrum structure is quite different in the domains of small and large values of the parameter Ξ. For the dissipation-free resonator, the NNS distribution changes its form with growing the asperity sharpness from poissonian-like distribution in the limit of Ξ≪1 to the bell-shaped distribution in the domain where Ξ≫1.

Effect of random surface inhomogeneities on spectral properties of dielectric-disk microresonators: theory and modeling at millimeter wave range.

The influence of random axially homogeneous surface roughness on spectral properties of dielectric resonators of circular disk form is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields, the method of eigenmode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering that is highly responsible for nondissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object, we use a dielectric disk resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigenfrequencies and the Q factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.

Influence of random bulk inhomogeneities on quasioptical cavity resonator spectrum.

The statistical spectral theory of oscillations in a quasioptical cavity resonator filled with random inhomogeneities is suggested. It is shown that inhomogeneities in the resonator lead to intermode scattering which results in the shift and broadening of spectral lines. The shift and the broadening of each spectral line is strongly depended upon the frequency distance between the nearest-neighbor spectral lines. As this distance increases, the influence of inhomogeneities is sharply reduced. Solitary spectral lines that have quite a large distance to the nearest neighbors are slightly changed due to small inhomogeneities. Owing to such a selective influence of inhomogeneities on spectral lines the effective spectrum rarefaction arises. Both the shift and the broadening of spectral lines as well as spectrum rarefaction in the quasioptical cavity millimeter wave resonator were detected experimentally. We have found out that inhomogeneities result in the resonator spectrum stochastization. As a result, the spectrum becomes composite, i.e., it consists of both regular and random parts. The active self-excited system based on the inhomogeneous quasioptical cavity millimeter wave resonator with a Gunn diode was examined as well. The inhomogeneous quasioptical cavity millimeter wave resonator (passive and active) can serve as a model of a semiconductor quantum billiard. Based on our results we propose that such a billiard with the spectrum rarefied by random inhomogeneities be used as an active semiconductor laser system.