A study of disordered systems with gain: Stochastic amplification

A study of statistics of transmission and reflection from a random medium w ith stochastic amplification as opposed to coherent amplification is presen ted. It is found that the transmission coefficient t, for sample length L l ess than the critical length L, grows exponentially with L. In the limit L --> infinity transmission decays exponentially as [1n t] = -L/xi where xi i s the localization length. In this limit reflection coefficient r saturates to a fixed value which shows a monotonic increase as a function of strengt h of amplification alpha. The stationary distribution of super-reflection c oefficient agrees well with the analytical results obtained within the rand om phase approximation (RPA). Our model also exhibits the well known dualit y between absorption and amplification. We emphasize the major differences between coherent amplification and stochastic amplification where-ever appr opriate.