Relation between transmission and energy stored in random media with gain

In this work, we investigate a possibility of using the ratio between optical transmission, T, and energy stored inside the system, E, as a quantitative measure of the enhanced mesoscopic corrections to diffusive transport of light through a random medium with gain. We obtain an expression for T /E as a function of amplification strength in the diffusive approximation and show that it does not a have tendency to diverge when the threshold for random lasing is approached, as both T and E do. Furthermore, we find that a change in T /E signifies a change in the electric field distribution inside the random medium. In the localization regime, we also investigate the correlations between transmission and energy stored in the medium with and without amplification. Our results suggest that T /E is a promising parameter which can help characterize the nature of wave transport in random medium with gain.