Fulfilling causality: two numerical techniques for accurately computing the propagation of independent laser beams through a nonlinear medium
Résumé
We identify the origin of some numerical difficulties related to causality which appear in the simulation of transport equations. Two numerical techniques are presented for the integration of models describing counter-propagating laser beams in interaction with a nonlinear medium. One, based on the characteristic method, rests on the transport properties of first-order derivatives and is able to propagate a signal in a linear non-dispersive medium without any deformation. The other, fully explicit, directly handles both first and second order derivatives. Both numerical schemes are applied to a physical example.