Spectral properties of cylindrical quasi-optical cavity resonator with random-inhomogeneous side boundary: correlation between dephasing and dissipation

Abstract

A rigorous solution for the spectrum of quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained for the first time. To accomplish this task, we have developed a novel method for variables separation in wave equation, which enables one, in principle, to rigorously examine any limiting case --- from negligibly weak to arbitrarily strong disorder. 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 equation 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 wave operator loses its unitarity, i.e., with the availability in the system of either openness or dissipation channels. Our numeric experiments suggest that in the absence of dissipation loss the random-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 $Ξ>>1$.