Is a Layered Medium One Dimensional?

In the study of wave transport, a randomly layered medium is generally considered one dimensional due to its localizing character in the layering direction. However, we show that when the system is perturbed by the addition of a small amount of isotropic randomness, wave propagation in the direction parallel to the layers can exhibit significant leakage out of the localizing layers. Numerical study of this phenomenon in 2D anisotropic models reveals the existence of wave-energy tunneling via evanescent waves in the layering direction, which gives rise to finite-size scaling behavior intermediate between 1D and 2D.