Mode distribution in coherently amplifying random media

Abstract We investigate the statistics of lasing modes in a disordered one-dimensional active system. Dielectric scatters are randomly embedded in an amplifying medium to increase the optical length of photon. The lasing mode of each individual sample is obtained numerically by carefully locating the frequency and the threshold gain at which the reflection and the transmission coefficient first become divergent, a characteristic of the oscillation pole. As the density of scatters increases, the characteristic threshold gain for lasing decreases while the distribution of mode frequency broadens around the spontaneous emission frequency of the gain medium. The averaged gain threshold is indeed found to be proportional to the localization length, signifying the enhancement of light amplification due to multiple scattering. Interestingly, we find that the actual value of the gain threshold larger than previous theoretical predictions by a factor of 3–5, in agreement with a recent experiment.