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 non-linear material, are solved, both approximately and exactly. The solutions are then used to generate possible applications. In this investigation, both the fundamental and the second-harmonic waves have two transverse field components. It is shown that, by controlling the ratio of the components of the fundamental wave, one component of the second-harmonic wave can be rigorously controlled, and even switched off. The ratio of the harmonic field components depends strongly upon the polarization angle of the fundamental wave, with the extinction angle depending strongly upon the phase mismatch parameter. In a second application, an aperture is placed at the output and it is shown that if approximate stationary states are used as an input to a quadratically nonlinear medium, then varying the angle of incidence of two input beams produces an excellent output control. A numerical demonstration is given in which a switch from 80 of the input energy arriving at the output port to less than 3 is readily achievable. References: 44
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