Numerical Modeling of Laser Pulse Behavior in Nonlinear Crystal and Application to the Second Harmonic Generation

We propose an efficient numerical strategy for the full wave integration of the nonlinear Maxwell equations by a finite difference approach (finite-difference time-domain). We compare it to the asymptotic limit described by an extended nonlinear Schrodinger equation. This is achieved by considering the nonlinear behavior of high intensity ($\geq 5GW/cm^2$) ultrashort ($ \leq 100 fs$ FWMH) laser beams in a KDP crystal (type I). We assume that this crystal can be characterized by two linear dispersion Lorentz resonances, as well as instantaneous quadratic and cubic nonlinearities. Investigations are performed, for different optical regimes, in the context of the second harmonic generation for one-dimensional and two-dimensional models.