Abstract

Matter itself is discrete. Thus there is a basic interest in understanding the dynamics of excitations in discrete systems, in particular when nonlinearity comes into play. Intrinsic localization resulting in the formation of discrete solitons has been initially predicted in atomic chains (discrete lattices) with an on-site cubic nonlinearity but could be also observed in proton dynamics in hydrogen-bonded chains, in biophysical systems, molecular crystals and in electrical lattices. In particular, if a spatial excitation involves only a few constituents the very discreteness of the respective system matters. This discreteness has remarkable consequences for the dynamical behaviour even if the system remains purely linear. Since many years the formation of localized Wannier-Stark states and the related occurrence of Bloch oscillations is well-known in a periodic, linearly increasing potential. An array of evanesently coupled wave guides is a prominent example of a discrete optical system. But in contrast to their atomic counterparts it permits the observation of many effects on an accessible macroscopic scale Beyond their relevance for the study of fundamental physical issues nonlinear waveguide arrays may hold promise for future ultrafast all-optical switching and routing applications.

© 2000 IEEE