Light Transport in Disordered Media with PT-symmetry

The localization properties of randomly layered optical media with ${\cal PT}$-symmetric refraction index are studied both theoretically and numerically using the transfer-matrix method. The transmission coefficient decays exponentially as a function of the system size, with a rate $\xi_{\gamma}(W)^{-1}=\xi_0(W)^{-1}+\xi_{\gamma}(0)^{-1}$, where $\xi_0(W)$ is the localization length of the equivalent passive disordered system and $\xi_{\gamma}(0)$ is the attenuation/amplification length of the corresponding perfect system with combined gain/loss refraction index profile. While transmission processes are reciprocal to left and right incident waves, one-sided reflection is found.