Mode distribution in coherently amplifying random media

We investigate the statistics of lasing modes in a disordered one-dimension al active system. Dielectric scatters are randomly embedded in an amplifyin g medium to increase the optical length of photon. The lasing mode of each individual sample is obtained numerically by carefully locating the frequen cy and the threshold gain at which the reflection and the transmission coef ficient first become divergent, a characteristic of the oscillation pole. A s the density of scatters increases, the characteristic threshold gain for lasing decreases while the distribution of mode frequency broadens around t he spontaneous emission frequency of the gain medium. The averaged gain thr eshold is indeed found to be proportional to the localization length, signi fying the enhancement of light amplification due to multiple scattering. In terestingly. we find that the actual value of the gain threshold larger tha n previous theoretical predictions by a factor of 3-5, in agreement with a recent experiment. (C) 2001 Published by Elsevier Science B.V.