Spectrum of three-wave mixing for multimode fields

Analytic solutions are developed for the time-dependent intensity that results from the three-wave mixing of multimode fields. These differ dramatically from the solutions for single-mode (time-independent) fields. New frequencies in the output spectrum are created as input intensities increase. Under conditions of strong nonlinear coupling the output spectrum broadens, ultimately reaching the phase-match bandwidth limit, and the dynamics can become chaotic. A new technique for enhancing mixing efficiencies is presented.