Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium.

The exact analytical solutions for the interacting waves in the quadratic nonlinear medium with the periodic structure are detailedly derived and obtained, and the properties of solutions are analyzed. Three applicable examples employing the exact solutions in the all-optical processing are given and analyzed. The optimized results show that the phase of signal can obviously be increased by proper choosing k, and that the intensity of pump can greatly be decreased in the all-optical switching by means of optimizing k, increasing medium length, and choosing sum-frequency generation.