Modulational instability in nonlinearity-managed optical media

Authors

Martin Centurion, University of Nebraska-LincolnFollow
Mason A. Porter, California Institute of Technology
Ye Pu, California Institute of TechnologyFollow
P. G. Kevrekidis, University of Massachusetts, Amherst
D. J. Frantzeskakis, University of Athens (Greece)
Demetri Psaltis, California Institute of Technology

Document Type

Article

Date of this Version

2007

Comments

Published in PHYSICAL REVIEW A 75, 063804 (2007); DOI: 10.1103/PhysRevA.75.063804. © 2007 The American Physical Society. Used by permission.

Abstract

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 equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the 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.