EXACT ANALYTIC SOLUTIONS TO THE NONLINEAR-WAVE EQUATION FOR A SATURABLE KERR-LIKE MEDIUM - MODES OF NONLINEAR-OPTICAL WAVE-GUIDES AND COUPLERS

Exact analytic solutions to the nonlinear wave equation for a lossless saturable Kerr-like medium are found. The nonlinearity is an intensit y-dependent refractive index which saturates according to the model n( 2) = n(0)(2) +/- a\E\(2)/(1+b\E\(2)). The solutions to the wave equati on are used to determine the TE power-dependent dispersion relations, and therefore the guided modes, of a single waveguide structure and of a directional coupler whose coupling medium is the nonlinear saturabl e material. Although the interaction between the sinh- and cosh-like m odes of the coupler, and therefore the coupling length, is not treated in this work, it is shown that the critical power, defined in the lit erature to be the level of input power above which 100% of the power c annot be switched between the guides of a coupler, is a mathematical m isinterpretation in both saturable media as well as in nonsaturable Ke rr media. The absence of a critical power in single waveguide structur es is also demonstrated. Parameters of GaAs-based waveguides and of a GaAs-GaAlAs MQW coupling medium [1] are used in the numerical analysis .