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We study the frequency behavior of coherent random lasers consisting monodisperse scatterers with single-particle resonances. A three-dimensional photon propagation model is employed to compute the wavelength-sensitive path length distribution of fluorescence photons in this system. We observe that a persistence interval of wavelengths exists for the coherent random lasing modes, corresponding to the Mie resonances of the individual resonant scatterer. Within the interval, characteristic pulse to pulse fluctuations continue to be observed from the system. The gain competition in the random laser suppresses likely coherent modes in other regions of the emission band, thereby reducing the wavelength fluctuations in the random laser. We further illustrate the tunability of this persistence interval by varying the size parameter of the resonant scatterers.

Persistent coherent random lasing using resonant scatterers