Light Transport in Random Media with $\mathcal{P}\mathcal{T}$-Symmetry

The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size, with an enhanced 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 random medium and ${\xi }_{\gamma }(0)$ is the attenuation/amplification length of the corresponding perfect system with a $\mathcal{P}\mathcal{T}$-symmetric refraction index profile. While transmitance processes are reciprocal to left and right incident waves, the reflectance is enhanced from one side and is inversely suppressed from the other, thus allowing such $\mathcal{P}\mathcal{T}$-symmetric random media to act as unidirectional coherent absorbers.