Scattering and Localization of Classical Waves Along a Wave Guide with Disorder and Dissipation

Abstract

The problem of localization of classical waves has recently attracted consider-able attention.^1,2 Classical waves have, of course, been the subject of extensive research already in the last century, as emphasized by Landauer in his historical sketch.³ A variety of interesting phenomena is associated with classical waves like seismic waves, tidal waves, acoustic as well as optical waves. A major topic is the transport of energy or information by these waves. The current interest in classical waves is stimulated by the development of microelectronics with its very small structures, in particular very thin wires (as connections between the components of integrated circuits) which may (or may not, depending on the situation) be considered as wave guides for the electrons. Similarly, optical wave guides like optical fibers for telephone connections are of technological interest. The interesting analogies between microelectronics and optics have been comprehensively discussed in a recent book.⁴ There are, of course, important differences between quantum mechanical waves describing electrons and classical waves like optical or acoustic waves, as discussed by Landauer,³ e.g., the conservation of electrons on the one hand or non-linear optics on the other hand. Nevertheless, it is promising to apply approaches, which have been successful in one area, to the other field.