Influence of random bulk inhomogeneities on quasioptical cavity resonator spectrum

Abstract

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.

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

“…[2]. In this technique, for each of the modes the "seed" (or trial) mode propagator ( ) V G  is introduced, which represents the mode Green function calculated with no regard for inter-mode scattering, viz.,…”

“…Then, using the operator technique developed in Ref. [2], strict separation of oscillatory modes is performed at arbitrary level of inhomogeneity.…”

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.…”

“…The region includes the extended states of only first stability band of solutions to equation (20), as well as the evanescent states with negative mode energies. In terms of physical parameters of the system at hand, the inequalities (25) suggest the relative smallness of the corrugation amplitude and the smallness of its period against the wave length, i. e., the fulfillment of inequalities…”

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

“…In our recent papers, Refs. [9][10][11], using the method developed previously in Ref. [12] we have shown that one can separate variables in a wave equation and thus perform a comprehensive spectral analysis, for any restricted wave system, however disordered, lossy, or lossless it may be.…”