Statistical studies of random lasing modes and amplified spontaneous emission spikes in weakly scattering systems

We measured the ensemble-averaged spectral correlation functions and statistical distributions of spectral spacing and intensity for lasing modes in weakly scattering systems, and compared them to those of the amplified spontaneous emission spikes. Their dramatic differences illustrated the distinct physical mechanisms. Our numerical simulation revealed that even without reabsorption the number of potential lasing modes might be greatly reduced by local excitation of a weakly scattering system. The lasing modes could be drastically different from the quasimodes of the passive system due to selective amplification of the feedback from the scatterers within the local gain region.Comment: 25 pages, 8 figure

A congruence involving products of qq-binomial coefficients

In this paper we establish a $q$-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.Comment: 9 page