Localized random lasing modes and a path for observing localization

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Abstract
We demonstrate that a knowledge of the density of states and the eigenstates of a random system without gain, in conjunction with the frequency profile of the gain, can accurately predict the mode that will lase first. Its critical pumping rate can also be obtained. It is found that the shape of the wave function of the random system remains unchanged as gain is introduced. These results were obtained by the time-independent transfer matrix method and finite-difference time-domain methods in a one-dimensional model. They can also be analytically understood by generalizing the semiclassical Lamb theory of lasing in random systems. These findings provide a path for observing the localization of light, such as looking for the mobility edge and studying the localized states.