Abstract
Finite difference equations are given for second-harmonic generation in two-dimensional planar structures for coupling between TE polarizations at two frequencies as well as for TM polarizations at two frequencies, including the effect of birefringence in the latter case. Attention is given to obtaining accurate expressions for the finite difference operators for points close to interfaces, and it is shown how the equations for nonlinear coupling can be incorporated into the beam-propagation method and the coupled-mode theory. Computational results of second-harmonic generation incorporating both the coupled mode theory and the beam-propagation method are given and discussed.
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