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Nonlinear dynamics of optical waveguide arrays

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Abstract

We have studied the nonlinear dynamical properties of 2,3, and 5 element optical waveguide arrays in both short and long propagation range limits. At least in principle, these arrays have the potential for demonstrating chaotic behavior in an environment that can be well controlled, i.e., the number of interacting modes can be selected. As such the arrays represent possible testing grounds for the evolution of nonlinear dynamics from few oscillator motions to the continuum limit. The dynamics are characterized by spectra-power diagrams, Lyapunov curves, and Poincare maps. Nearest neighbor couplings between elements are assumed. In the short range limit these waveguide arrays yield sharp all-optical switching features and large differential gain. In the long propagation range limit, the arrays exhibit a rich variety of nonlinear dynamic features ranging from spatio–temporal solitons to chaos. In some conditions chaos can manifest itself at arbitrarily low power. Regular stochastic transitions are ubiquitous in the system.

© 1991 Optical Society of America

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