iv : n lin / 0 61 10 28 v 1 [ nl in . P S ] 1 4 N ov 2 00 6 Modulational Instability in Nonlinearity - Managed Optical Media

The modulational instability, a destabilization mechanism for plane waves, occurs ubiquitously in spatially extended dynamical systems arising in fluid dynamics, nonlinear optics, atomic physics, and other disciplines. In this paper, we investigate analytically, numerically, and experimentally the modulational instability in a layered cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney ordinary differential equation, numerical simulations of the NLS partial differential equation, and the diagnostics of our optical experiment for the modulational instability. Because of the structural periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.