WAVE-PROPAGATION THROUGH A COHERENTLY AMPLIFYING RANDOM MEDIUM

We report a detailed and systematic numerical study of wave propagatio n through a coherently amplifying random one-dimensional medium. The c oherent amplification is modeled by introducing a uniform imaginary pa rt in the site energies of the disordered single-band tight binding Ha miltonian. Several distinct length scales (regimes), most of them new, are identified from the behavior of transmittance and reflectance as a function of the material parameters. We show that the transmittance is a non-self-averaging quantity with a well defined mean value. The s tationary distribution of the super reflection differs qualitatively f rom the analytical results obtained within the random phase approximat ion in strong disorder and amplification regime. The study of the stat ionary distribution of the phase of the reflected wave reveals the rea son for this discrepancy. The applicability of random phase approximat ion is discussed. We emphasize the dual role played by the lasing medi um, as an amplifier as well as a reflector.