Random lasing in a nanocomposite medium

The characteristics of a random laser based on a nanocomposite medium consisting of a transparent dielectric and scattering doped nanocrystals are calculated. It is proposed to use ytterbium laser media with a high concentration of active ions as nanocrystals and to use gases, liquids, or solid dielectrics with a refractive index lower than that of nanocrystals as dielectric matrices for nanocrystals. Based on the concept of nonresonant distributed feedback due to the Rayleigh scattering, an expression is obtained for the minimum length of a nanocomposite laser medium at which the random lasing threshold is overcome. Expressions are found for the critical (maximum) and the optimal size of nanocrystals, as well as for the optimal relative refractive index of nanocomposites that corresponds not only to the maximum gain but also to the minimum of the medium threshold length at the optimal size of nanocrystals. It is shown that the optimal relative refractive index of a nanocomposite increases with increasing pump level, but is independent of the other nanocomposite parameters.