Bifurcation Geometry of Optical Bistability and Self-Pulsing

Abstract

In optical bistability, as in most nonlinear systems, the underlying differential equations (here the Maxwell-Bloch-Equations) are in general not analytically tractable. Usually only partial information about the behaviour of the system in some limiting cases is available (mean field limit in the pure absorptive or the dispersion-dominated case). Alternatively, one has to rely on numerical solutions. In either case, one would like to know whether the results so obtained are in some sense general or exceptional, i.e. whether they are structurally stable or not. Structural stability is a keyword: In order that experiments be reproducible, the underlying physics must be structurally stable. This notion can be made more rigorous on the level of equations which one uses to model nature: A structurally stable system preserves its quality when its equations are perturbed: it is insensitive, not only against small changes in the initial data, but also against small changes in its own specification.

Work supported by the Stiftung Volkswagenwerk, FRG.