Light amplification and localization in randomly layered media with gain

Abstract

Light amplification and localization behaviors in randomly layered media with gain are studied using the transfer-matrix method. It is found that localization is enhanced due to the amplification of coherent backscattering effect. It is also found that ${\ensuremath{\xi}}_{0}$ and ${\mathit{l}}_{\mathit{g}}$ are the only two relevant parameters in such systems, where ${\ensuremath{\xi}}_{0}$ is the localization length in the absence of gain and ${\mathit{l}}_{\mathit{g}}$ is the gain length. The interplay of ${\ensuremath{\xi}}_{0}$ and ${\mathit{l}}_{\mathit{g}}$ gives rise to two new lengths ${\mathit{L}}_{\mathrm{sr}}$ and \ensuremath{\xi}. ${\mathit{L}}_{\mathrm{sr}}$, which behaves like (${\mathit{l}}_{\mathit{g}}$${\ensuremath{\xi}}_{0}$${)}^{0.5}$, is a manifestation of the threshold length for the super radiation, which is strongly suppressed in one dimension. \ensuremath{\xi} is the localization length in the presence of gain, which can be described by 1/\ensuremath{\xi}=1/${\ensuremath{\xi}}_{0}$+1/${\mathit{l}}_{\mathit{g}}$. Results for dissipative media are also presented.