Electromagnetic localization in dispersive stratified media with random loss and gain

A theory of localization of waves in stratified weakly disordered dispersive media with random loss and gain is developed. We consider a one-dimensional model of a random medium, consisting of a stack composed of an arbitrary number of layers of equal thickness having random refractive indices. The properties of the structure are analyzed using a method that takes into account multiple reflections within the stack. We develop an asymptotic analysis for the case of strong and weak layer effects and show that the localization length is always positive for sufficiently short wavelengths, irrespective of whether the layers exhibit gain or loss. We include the effects of dispersion in our theory and consider two refractive index models, one following from the Lorentz model and the other from a lower-law dependence on wavelength. The results are compared with numerical simulations.