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We study, theoretically and experimentally, disorder-induced resonances in randomly-layered samples,and develop an algorithm for the detection and characterization of the effective cavities that give rise to these resonances. This algorithm enables us to find the eigen-frequencies and pinpoint the locations of the resonant cavities that appear in individual realizations of random samples, for arbitrary distributions of the widths and refractive indices of the layers. Each cavity is formed in a region whose size is a few localization lengths. Its eigen-frequency is independent of the location inside the sample, and does not change if the total length of the sample is increased by, for example, adding more scatterers on the sides. We show that the total number of cavities, $N_{mathrm{cav}}$, and resonances, $N_{mathrm{res}}$, per unit frequency interval is uniquely determined by the size of the disordered system and is independent of the strength of the disorder. In an active, amplifying medium, part of the cavities may host lasing modes whose number is less than $N_{mathrm{res}}$. The ensemble of lasing cavities behaves as distributed feedback lasers, provided that the gain of the medium exceeds the lasing threshold, which is specific for each cavity. We present the results of experiments carried out with single-mode optical fibers with gain and randomly-located resonant Bragg reflectors (periodic gratings). When the fiber was illuminated by a pumping laser with an intensity high enough to overcome the lasing threshold, the resonances revealed themselves by peaks in the emission spectrum. Our experimental results are in a good agreement with the theory presented here.
We study the relation between quasi-normal modes (QNMs) and transmission resonances (TRs) in one-dimensional (1D) disordered systems. We show for the first time that while each maximum in the transmission coefficient is always related to a QNM, the r
Selective excitation of a diffusive systems transmission eigenchannels enables manipulation of its internal energy distribution. The fluctuations and correlations of the eigenchannels spatial profiles, however, remain unexplored so far. Here we show
We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been explored. In thi
We consider the two-dimensional randomly site diluted Ising model and the random-bond +-J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of therm
Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the study of