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Published June 1, 2007 | public
Journal Article Open

Modulational instability in nonlinearity-managed optical media


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.

Additional Information

©2007 The American Physical Society (Received 15 February 2007; published 5 June 2007) We acknowledge support from the DARPA Center for Optofluidic Integration (D.P.), the Caltech Information Science and Technology initiative (M.C., M.A.P.), the Alexander von Humboldt Foundation (M.C.) and Grants No. NSF-DMS-0204585, No. NSF-DMS-0505663, No. NSFDMS-0619492, and No. NSF-CAREER (P.G.K).


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