Vector CW and solitary wave interactions with mixed Type 1-Type II second-harmonic generation

The four vector equations, appropriate to a mixed type I-type II second-harmonic generation in a thin planar waveguide made from a second-order nonlinear material are solved both approximately and exactly. The solutions offer a richer set of possibilities than just Type II and always involve for both the harmonic and the fundamental. A new kind of polarisation control is shown to be possible, through which CW shut down, of one component of the second harmonic is achieved. The extinction angle is shown to depend strongly upon the phase mismatch parameter. In a second application, for solitary waves, an aperture is placed at the output and it is shown that if approximate stationary states are used as an input then varying the angle of incidence of two input beams produces an excellent output control. It is shown that a switch from 80% of the input energy arriving at the output port to less than 3% is possible.