Highly efficient third harmonic generation in quadratic and cubic nonlinear media by cascaded second harmonic generation

We report on a new highly efficient method for frequency tripling of optical waves based on cascaded secondharmonic generation in a medium with quadratic susceptibility, taking into account the cubic response of the medium. The fundamental frequency, secondharmonic and thirdharmonic waves interact under a large phase mismatching between the fundamental frequency and secondharmonic waves. In a medium with only quadratic susceptibility, this leads to the emergence of a response of the medium similar to the response inherent in a medium with cubic nonlinearity, the sign of which is determined by the sign of the mentioned phase mismatching. The process of wave interaction is theoretically considered based on the multiscale method. Without using the pump non-depletion approximation, the modes of frequency conversion, evolution of intensities and phases of interacting waves are analyzed without taking into account their second-order dispersion and diffraction. A bistable mode of frequency tripling, a mode of complete suppression of wave generation at a triple frequency, and a mode of suppression of the Kerr effect are observed. Computer simulation shows a possibility of transferring 98.5% of the energy of the incident wave into the third harmonic. A simpler and physically illustrative (compared to the multiscale method) method for analyzing cascade processes with a large phase mismatching between a pair of interacting waves is also proposed.