The scattering properties of randomly layered optical media with $\mathcal{PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmittance decays exponentially as a function of the system size, with an enhanced rate ${\xi }_{\gamma }{\left(W\right)}^{-1}={\xi }_0{\left(W\right)}^{-1}+{\xi }_{\gamma }{\left(0\right)}^{-1}$, where ${\xi }_0\left(W\right)$ is the localization length of the equivalent passive random medium and ${\xi }_{\gamma }\left(0\right)$ is the attenuation and amplification length of the corresponding perfect system with a $\mathcal{PT}$-symmetric refraction index profile. While transmittance 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 $\mathcal{PT}$-symmetric random media to act as unidirectional coherent absorbers.

• Received 23 December 2011

DOI:https://doi.org/10.1103/PhysRevA.85.055802