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We have developed a numerical method for calculating the second harmonicgeneration (SHG) generated by an anisotropic material whose optical propertiespresent an arbitrary modulation in one dimension. The method is based on theBerreman 4x4 matrix formalism, which is generalized to include nonlinearoptical phenomena. It can be used under oblique incidences of the input beam,and is valid even when the SHG frequency is close to photonic bands, where theusual slowly-varying-amplitude approximation breaks down. As an example ofapplication, we have studied the SHG performance of ferroelectric andhelielectric nematic liquid crystals. The latter present a helicoidal structurethat can be distorted under electric field. In the different tests of themethod we have analyzed the conditions for the most efficient SHG, and comparedwith previous results in the case there were any. The obtained results indicatethat the present procedure may contribute to improve the structural design andenlarge the variety of nonlinear optical materials for their application inoptical devices.

Second harmonic generation in anisotropic stratified media: A generalization of the Berreman method and its application to photonic materials