Transmission, Reflection and Localization of Waves in One-dimensional Amplifying Media with Nonlinear Gain

Transmission, Reflection and Localization of Waves in One-dimensional Amplifying Media with Nonlinear Gain

We study theoretically the influence of nonlinear gain effects on the transmission and the Andersonlocalization of waves in both uniform and random one-dimensional amplifying media by using thediscrete nonlinear Schr¨odinger equation. In uniform amplifying media with nonlinear gain, wefind that the strong oscillatory behavior of the transmittance and the reflectance for odd andeven values of the sample length disappears for large nonlinearities. The exponential decay rateof the transmittance in the asymptotic limit is found to be independent of nonlinear gain. Inrandom amplifying media, we find that the maximum values of the disorder-averaged logarithmictransmittance and reflectance depend nonmonotonically on the strength of nonlinear gain. We alsofind that the localization length is independent of nonlinear gain. In other words, the Andersonlocalization is neither enhanced nor weakened due to nonlinear gain. In both the uniform and therandom cases, the crossover length, which is the critical length for the amplification to be efficient,is strongly reduced by the nonlinear nature of the gain.

We study theoretically the influence of nonlinear gain effects on the transmission and the Andersonlocalization of waves in both uniform and random one-dimensional amplifying media by using thediscrete nonlinear Schr¨odinger equation. In uniform amplifying media with nonlinear gain, wefind that the strong oscillatory behavior of the transmittance and the reflectance for odd andeven values of the sample length disappears for large nonlinearities. The exponential decay rateof the transmittance in the asymptotic limit is found to be independent of nonlinear gain. Inrandom amplifying media, we find that the maximum values of the disorder-averaged logarithmictransmittance and reflectance depend nonmonotonically on the strength of nonlinear gain. We alsofind that the localization length is independent of nonlinear gain. In other words, the Andersonlocalization is neither enhanced nor weakened due to nonlinear gain. In both the uniform and therandom cases, the crossover length, which is the critical length for the amplification to be efficient,is strongly reduced by the nonlinear nature of the gain.