Electromagnetic localization in one-dimensional stacks with random loss and gain

We study both analytically and numerically the properties of a one-dimensional stack consisting of layers with the same thickness, but random complex refractive indices. Thus the stack as a whole may exhibit loss or gain. We present a simple expression for the localization length in the domain of intermediate and long wavelengths. For short wavelengths we show that, in contrast to the case of a stack with layers having real refractive indices, the localization length tends to zero as a linear function of the wavelength, rather than approaching a nonzero constant. Numerical calculations confirm the analysis.