Correlations in transmission of light through a disordered amplifying medium

The angular- and frequency-correlation functions of the transmission coefficient for light propagation through a strongly scattering amplifying medium are considered. It is found that just as in the case of an elastic-scattering medium the correlation function consists of three terms. However, the structure of the terms is rather different. Angular correlation has a power-law decay and exhibits oscillations. There is no ''memory effect'' as in the case of an elastic medium. Interaction between diffusion modes is strongly enhanced near the lasing threshold. The frequency-correlation scale decreases close to the lasing threshold. We also consider time correlations of the transmission in the case of nonstationary inhomogeneities. We find short- and long-range time correlations. The scale of the short-range correlation decreases, while the long-range correlation scale becomes infinite near the threshold.