Transmission statistics in nonconservative disordered optical medium

Abstract

We determine the cumulants of electromagnetic energy transmitted through one-dimensional disordered medium with absorption or amplification. For this purpose we derive the Keldysh nonlinear sigma-model action with a source term that generates the energy current fluctuations. The fluctuations over the ensemble of disorder realizations are found to decrease (increase) with increasing absorption (amplification). In the conservative medium the fluctuations can be related to the Dorokhov's distribution of transmission coefficients.