Spatio-temporal and finite element method for analysis of the propagation of optical ultra-short pulses in non-linear media

A new and efficient spatio-temporal formulation based on the finite element method 2D is applied to simulate the propagation of optical ultra-short pulses in nonlinear media. The excellent performance of this technique in terms of the computational efficiency is demonstrated from its capacity to analyze simultaneously the propagation of the pulses in time domain and spatial domain. The new formulation is expressed in terms of the electrical field and includes perfect matched layers (PML) at the truncated boundaries and the wide angle Pade approach. The propagation occurs along the Z-direction and some key integrated planar structures in non-linear media are analyzed. In addition the time is used as a discretization variable and it makes possible the spectral analyzes of the propagated pulses.