Numerical methods for the bidimensional Maxwell-Bloch equations in nonlinear crystals

Two numerical schemes are developed for solutions of the bidimensional Maxwell-Bloch equations in nonlinear optical crystals. The Maxwell-Bloch model was recently extended [1] to treat anisotropic materials like nonlinear crystals. This semiclassical model seems to be adequate to describe the wave-matter interaction of ultrashort pulses in nonlinear crystals [2] as it is closer to the physics than most macroscopic models. A bidimensional finite-difference-time-domain (FDTD) scheme, adapted from Yee [3], was already developed in [4]. This schemes yields very expensive computations. In this paper, we present two numerical schemes much more efficient with their relative advantages and drawbacks.