Coupled multiwave interactions in aperiodically poled nonlinear optical crystals

A new type of coupled nonlinear optical interactions that can be implemented in crystals with an aperiodic modulation of the nonlinear susceptibility is studied. The quasi-phase matching condition is satisfied simultaneously for several conventional three-frequency processes involved in the interaction due to the aperiodic variation of the nonlinearity in space. A simple method for designing aperiodically poled nonlinear optical crystals is proposed and analyzed. The method is based on the superposition of nonlinearity modulations produced by several periodic functions simultaneously so that each of these functions individually corresponds to its own quasi-phase-matched nonlinear process. The dynamics of energy exchange during interaction of five waves with different frequencies that involves three coupled three-frequency parametric interaction processes is investigated thoroughly. The ratio between the effective nonlinear wave coupling coefficients and the amplitudes of pump waves is determined for the case in which the initial stage of the interaction is characterized by the parametric instability. It is demonstrated that the secondary simplification of the coupled differential equations with spatially modulated nonlinear coefficients, which leads to the system of equations with constant nonlinear coefficients, correctly describes the dynamics of interaction of the waves at distances of the order of 50 characteristic nonlinear lengths.