Second harmonic generation in generalized ferroelectric superlattices

The goal of the work presented in this investigation is to achieve the efficient parametric interaction of narrow beams (in particular second harmonic generation) using a nonlinear (ferroelectric-LiTaO3) photonic crystal tuned to self-collimation (nondiffractive) regimes. A numerical study of second harmonic generation (SHG) in one-dimensional nonlinear photonic crystals based on a full nonlinear system of equations, implemented by a combination of the method of finite elements and fixed-point iterations, is reported. This model is derived from a nonlinear system of Maxwell’s equations that partly overcomes the known shortcoming of some existing models that rely on the undepleted pump approximation. We derive a general solution of SHG in one-dimensional nonlinear photonic crystals structures. Numerical simulations also show that the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental wave are located at the photonic band edges or are assigned to the designed defect states.