Computing for second harmonic generation in one-dimensional nonlinear photonic crystals

A numerical study of second harmonic generation (SHG) in one-dimensional nonlinear photonic crystals based on 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, which partly overcomes the known shortcoming of some existing models relied on the undepleted-pump approximation. We derive a general solution of SHG in one-dimensional nonlinear photonic crystals structures. The convergence of our method is fast. Numerical simulations also show 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.