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

Abstract

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.

Properties of cylindrical quasi-optical cavity resonator with randomly rough lateral boundary

“…Considering the dissipation and, consequently, the resonance line finite width leads to partial "Wignerization" of the NNS distribution, specifically, to the appearance of a significant dip of the function ( ) p s in the region of 0 s  . With the asperities being strongly sharpened, in the range of 1   , the resonance frequencies are to a reasonable accuracy represented by formula (4). The line widening related to the scattering-induced dephasing goes to zero in the limit of    .…”

Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

“…The set of equations (7) can be solved with respect to Green function mode components through the operator procedure applicable for potentials V n (z) andÛ nm (z) of quite arbitrary form [35]. Although this method was originally developed for open waveguide-like systems with potentials of volume nature, it was also expanded to closed systems in subsequent works, with the disorder available both in the bulk [45] and on the surface [29].…”

The sharpness-induced mode stopping and spectrum rarefication in waveguides with periodically corrugated walls

“…The technique was first elaborated in Ref. [24] for the open systems of waveguide configuration and then expanded to open-ended and closed resonator-type systems disordered in the bulk [25] as well as on the surface [13,26]. With regard to the waveguidetype systems, the method reduces (schematically) to the following action sequence.…”

“…Two embracing projectors in Eq. (13) have appeared due to the restriction of summation in Eqs. (9) and (5) by mode indices k = n. The operators standing between the projectors act in the subspace M n ∈ M which includes the coordinate axis z and the set of all mode indices other than the separate index n. The role of the projectors in operator potential Eq.…”

“…For this reason the studies on structures with sub-wavelength periodic variations of their parameters have for long remained beyond the main line of research until the previous decade, when anomalous wave transmission through sub-wavelength hole arrays in optically thick films was detected [11,12]. In our recent paper [13] it was also discovered that the small-scale distortion of wave resonator boundaries dramatically affects their spectra. Specifically, it was found that modal content of rough-side resonators was mainly controlled by the sharpness of boundary asperities rather than by their height.…”