At present the electromagnetic oscillations in confined resonant systems with random inhomogeneities, in particular, quasioptical microwave resonators, are under study. Up to date, however, the satisfactory solution to this problem was not found both in theoretically and experimentally. On the one hand, the well-elaborated theories of wave propagation in disordered media use the statistical isotropy and the scattering potential homogeneity conditions [1, 2], which basically cannot be implemented for confined systems. On the other hand, the random matrix theory (RMT) that is commonly used to analyze the confined systems [3,4] also has significant limitations. For RMT application it is necessary to express the Hamiltonian of the system in terms of a matrix whose elements are random. Such a matrix can belong, for instance, to the ensemble of Gaussian orthogonal matrices (GOE). In this case matrix elements are real, symmetrical to the time inversion, and invariant to orthogonal transformations. The system with such a Hamiltonian is not integrable and the motion in it is completely chaotic. The examples of the completely chaotic systems are microwave resonators similar to the Sinai and Bunimovich billiards. Their chaotic spectra are well described by RMT [3]. The quasioptical cavity resonator even with small random inhomogeneities being considered in the present paper belongs to neither an integrable system nor a completely chaotic one. In this system we found that by inserting the inhomogeneities into the resonator its spectrum becomes mixed, i.e., it contains both regular and chaotic components simultaneously. Therefore, strictly speaking, to study the spectrum we cannot use the RMT approach [4] so we need a different one. Experimental study of electromagnetic oscillations spectrum in a quasi-optical cavity resonator filled with inhomogeneities also requires new techniques at wide frequency range, including millimeter waves. In the paper, the physical nature of the broadening and the shift of spectral lines of the quasi-optical cavity resonator filled with filled with randomly distributed bulk inhomogeneities has been studied both theoretically and experimentally. We have elaborated the original spectral theory based on the mode separation technique. The technique previously developed in [5,6] for open waveguide-type systems is extended here to closed systems, in particular, to a cylindrical cavity resonator. The proposed method applied directly to the master dynamic equation of the problem enables one to identify the principal physical mechanism of unexpectedly large spectral lines broadening with nondissipative intermode scattering. This type of scattering causes the width of nearest-neighboring spectral lines to increase more intensely than the width of solitary spectral lines. Owing to this fact the quality factor and, respectively, the intensity of the nearest-neighboring spectral lines tend to decrease sharply, but these parameters of solitary lines are only slightly changed. Below we will refer to such a selective change in the spectral lines as the "spectrum rarefaction." In order to verify theoretical predictions, systematic measurements of the quasi-optical cavity resonator spectrum were performed with different realizations of random infill. We detected the predicted "rarefaction" effect and proved its origin to be related to the intermode scattering on non-dissipative random inhomogeneities. The possible applications of spectral study of the resonator with random inhomogeneities to nanoelectron systems are considered in the report. Such a resonator can be a model of semiconductor quantum billiard. Based on our results we suggest the use of such billiards with spectrum rarefied by random inhomogeneities as an active system of semiconductor laser.
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