Abstract

Nonlinear coherent coupling between guided modes may become extremely sensitive to small changes in the input conditions.^1,2 This effect has potential use in ultrafast all-optical signal processing and switching in two-mode couplers, such as fiber polarization switches1 or integrated waveguide nonlinear directional couplers. The unavoidable presence of mode-coupling imperfections, however, may lead to chaotic mode conversion that dramatically spoils the power-dependent transmission characteristics.² Analogous stochasticity may arise whenever two intense light beams counterpropagate in an optical fiber or copropagate in two parallel linearly coupled fiber cores. Numerical integration of chaotic solutions suffers by exponential amplification of errors. However, a statistical description of the properties of a chaotic trajectory turns out to be unaffected by error propagation. Such a characterization has been obtained for the above waveguiding structures by means of different statistical estimators: among others, the maximal Lyapunov exponents (yielding the local rate of divergence of nearby trajectories) and the Grassberger-Procaccia correlation exponent (related to the fractal dimension of the chaotic domain in phase-space). We estimated stochasticity thresholds in terms of key physical parameters (e.g., critical input optical power, perturbation strength, and spatial frequency and maximal useful lengths of nonlinear switching devices.

© 1987 Optical Society of America