Continuation Finite Element Simulation of Second Harmonic Generation in Photonic Crystals (Communications in Computational Physics, 2011)
A computational study on the enhancement of the second harmonic generation(SHG) in one-dimensional (1D) photonic crystals is presented. The mathematicalmodel is derived from a nonlinear system of Maxwell's equations, which partly overcomesthe shortcoming of some existing models based on the undepleted pump approximation.We designed an iterative scheme coupled with the finite element methodwhich can be applied to simulate the SHG in one dimensional nonlinear photonic bandgap structures in our previous work. For the case that the nonlinearity is strong whichis desirable to enhance the conversion efficiency, a continuation method is introducedto ensure the convergence of the iterative procedure. The convergence of our methodis fast. Numerical experiments also indicate the conversion efficiency of SHG can besignificantly enhanced when the frequencies of the fundamental and the second harmonicwave are tuned at the photonic band edges. The maximum total conversionefficiency available reaches more than 50% in all the cases studied.