Seeing Anderson Localization

Abstract

Anderson localization was discovered 50 years ago to describe the propagation of electrons in the presence of disorder. The main prediction back then, was the existence of disorder induced localized states, which do not conduct electricity. Many years later it turns out, that the concept of Anderson localization is much more general and applies to almost any type of propagation in time or space, when more than one parameter is relevant (like phase and amplitude). Here we propose a new optical scheme to literally see Anderson localization by varying the optical wavelength or angle of incidence to tune between localized and delocalized states. The occurrence of Anderson localization in the propagation of light, in particular, has become the focus of tremendous interest due to the emergence of new optical technologies and media, such as low dimensional and disordered optical lattices. While several experiments have reported the measurement of Anderson localization of light, many of the observations remain controversial because the effects of absorption and localization have a similar signature, i.e., exponential decrease of the transmission with the system size. In this work, we discuss a system, where we can clearly differentiate between absorption and localization effects because this system is equivalent to a perfect filter, only in the absence of any absorption. Indeed, only one wavelength is perfectly transmitted and all others are fully localized. These results were obtained by developing a new theoretical framework for the average optical transmission through disordered media.