Light amplification and localization in randomly layered media with gain

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 ${\xi }_0$ and ${\mathit{l}}_{\mathit{g}}$ are the only two relevant parameters in such systems, where ${\xi }_0$ is the localization length in the absence of gain and ${\mathit{l}}_{\mathit{g}}$ is the gain length. The interplay of ${\xi }_0$ and ${\mathit{l}}_{\mathit{g}}$ gives rise to two new lengths ${\mathit{L}}_{\mathrm{sr}}$ and ξ. ${\mathit{L}}_{\mathrm{sr}}$, which behaves like (${\mathit{l}}_{\mathit{g}}$ ${\xi }_0$ ${)}^{0.5}$, is a manifestation of the threshold length for the super radiation, which is strongly suppressed in one dimension. ξ is the localization length in the presence of gain, which can be described by 1/ξ=1/${\xi }_0$+1/${\mathit{l}}_{\mathit{g}}$. Results for dissipative media are also presented.