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Analytical solution for problem of generation of summary frequency wave in medium with quadratic and cubic nonlinearities

The paper is devoted to an analytical solution of SFW generation for femtosecond pulses taking into account the quadratic and cubic nonlinear response of medium. Using analytical solution, which obtained in the framework of long pulses approximation, the generation regimes are analyzed. It was shown that there are generation regimes with high and low efficiency and they exist simultaneously for given set of laser pulses interaction parameters. It means that there is a bistable process of generation. Optimal input intensities of two waves for achievement of region of generation of summary frequency wave with high efficiency were found. This property of frequency conversion can be used for creation of all optical switching. The switching between two stable states can be realized due to introducing of phase mismatching in definite section of nonlinear medium. It should be noticed that computer simulation results that are made with taking into account second order dispersion and without it confirm the analytical results.