We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed-form analytical solutions. Starting with the assumption that the dielectric permittivity of the medium has delta-correlated spatial fluctuations, and using Ito’s lemma, we derive a linear stochastic differential equation for a one-dimensional random medium. The equation leads to localized wave solutions. The localized wave solutions have a localization length that scales as $L\sim {\omega }^{-2}$ for low frequencies whereas in the high-frequency regime this length behaves as $L\sim {\omega }^{-2/3}$.

• Received 22 July 2008

DOI:https://doi.org/10.1103/PhysRevE.79.036606