Localization of waves in media with one-dimensional disorder

This chapter discusses the localization of waves in media with 1D disorder. 1D problems represent exactly solvable problems that enable the researcher to test sometimes uncontrollable approximations. In addition, the study of 1D models is important for understanding the physics of multiple scattering, as in the case of wave propagation in such media the interference effects are most pronounced. The strong localization in 1D systems and its natural applications to the problem of wave propagation in randomly layered media are considered. The chapter reviews the statistical properties of the various physical quantities in random media. The characteristics of the media—that is, the dielectric constant and the random potential, are spatially homogeneous random functions with decreasing correlations. The chapter focuses on 1D localization and also describes the waves in layered media.