Localization of light in linear and nonlinear random layered dielectric systems that are periodic on average

We compute the localization properties of light in a random system of linear dielectric slabs and a random system of Kerr-like nonlinear dielectric slabs. Particular attention is paid to systems that are periodic on average, and studies are made of the localization of light in these systems at frequencies both within and outside the band gaps of the average periodic system. It is found that the average periodic properties have the greatest effect on the exponential localization of light in the linear system, and exhibit only a small transient influence on the power-law localization observed in the nonlinear system. The average periodic properties of the nonlinear system are observed to affect localization only in systems of finite extent.