A computational study on the enhancement of the second harmonic generation (SHG) in one-dimensional (1D) photonic crystals is presented. The mathematical model is derived from a nonlinear system of Maxwell’s equations, which partly overcomes the shortcoming of some existing models based on the undepleted pump approximation. We designed an iterative scheme coupled with the finite element method which can be applied to simulate the SHG in one dimensional nonlinear photonic band gap structures in our previous work. For the case that the nonlinearity is strong which is desirable to enhance the conversion efficiency, a continuation method is introduced to ensure the convergence of the iterative procedure. The convergence of our method is fast. Numerical experiments also indicate the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental and the second harmonic wave are tuned at the photonic band edges. The maximum total conversion efficiency available reaches more than 50% in all the cases studied.

In this paper, we model laser-gas interactions and propagation in some extreme regimes. After a mathematical study of a micro-macro Maxwell-Schrödinger model [1] for short, high-frequency and intense laser-gas interactions, we propose to improve this model by adding a plasma equation in order to precisely take into account free electron effects. We examine if such a model can predict and explain complex structures such as filaments, on a physical and numerical basis. In particular, we present in this paper a first numerical observation of nonlinear focusing effects using an ab-initio gas representation and linking our results with existing nonlinear models.