Optical harmonic generation and mixing in multilayer media: extension of optical transfer matrix approach to include anisotropic materials

The optical transfer matrix technique for the analysis of optical harmonic generation and mixing in laminar structures is extended to include the case of anisotropic media. This approach is applicable in the limit of low conversion efficiencies, where attenuation and phase shifts of the pump beams due to nonlinear interactions can be neglected. In this approximation one first solves the linear problem for the pump waves in the structure, using optical transfer matrices to take all reflections and linear attenuation into account. Then the nonlinear polarizations driven by these waves are found, and finally expressions for the waves at the harmonic and combination frequencies generated by these polarizations are derived, again using transfer matrices to account exactly for all reflections and linear attenuation. In the anisotropic case 4 × 4 transfer and propagation matrices are required, and all polarization components are treated simultaneously. The results are given in a computationally convenient form.