Spatial Hysteresis and Optical Patterns

This book addresses a subject at the crossing point of two lines of investi- gation - synergetics and modern nonlinear optics. First, the book is devoted to optical patterns that previously were mainly attributed to the display of instabilities of homogeneous field distributions. Second, we deal with optical bistability and hysteresis, which historically were studied predominantly for point (lumped, spatially nondistributed) systems. In the book, which seems to be the first monograph devoted to opti- cal patterns, I attempt to demonstrate that the variety of optical patterns and other synergetical phenomena is especially rich in spatially distributed bistable systems, and that instabilities of homogeneous states are not neces- sary for the formation of the patterns. Of special interest are patterns such as dissipative optical solitons, which individually have particle-like features and when combined resemble molecules, crystals, biological objects, and even social groups. Another essential point is the key role of inhomogeneities of bistable sys- tems. As for hysteresis, it has been studied mostly in point systems, in which, with fixed characteristics of the input signal, one of several sets of steady- state output signal characteristics can form, depending on the prehistory. In spatially distributed optical systems, the kinetics of hysteresis acquires the form of "spatial hysteresis", or hysteresis of spatial distributions of field char- acteristics. This problem of "stereoscopic vision" of such hysteresis was solved in optical bistability some 20 years ago, and the concepts proposed were later confirmed and expanded.