One Dimensional Discrete Linear And Kerr Nonlinear Optics

Discrete optical phenomena occur in one dimensional periodic arrays of parallel coupled waveguides. Coupling between adjacent waveguides leads to a novel form of discrete diffraction, periodic dispersion relations involving multiple bands, and contain regions of both normal, anomalous and zero diffraction. This in turn impacts many linear diffraction phenomena, for example the Talbot effect. It also results in a diversity of phenomena in nonlinear optics including novel types of spatial solitons, beam break-up also known as filamentation, and solitonic interactions. The fundamental concepts are reviewed here and interesting examples of discrete optical phenomena discussed