Abstract
The theory of a random laser with an interface in the form of random or scale-free networks whose nodes are occupied by microcavities with quantum two-level systems has been proposed for the first time. The microcavities are coupled to each other through light-guiding channels forming edges of the network. It has been shown that such a laser has a number of spectral features associated with the statistical properties of the network structure. Among them are the existence of a topologically protected Perron eigenvalue caused by the presence of a strong mean field at the node of maximum influence located in the central part of the network and the delocalization/localization of radiation modes depending on the probability of coupling between arbitrary microcavities. The results obtained in this work open prospects for the fabrication of new low-threshold laser sources.
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