Full vectorial, ultrashort unidirectional pulse propagators

Rapid progress in recent years in the development of high power ultrashort pulse laser systems has opened up a whole new vista of applications and computational challenges. Amongst those applications that are most challenging from a computational point of view are those involving explosive critical self-focusing with concomitant explosive growth in the generated light spectrum. Moreover, new experimental developments in the field of extreme nonlinear optics will require more rigorous propagation models beyond those existing in the current literature. Specific applications areas chosen for illustration in this paper include atmospheric light string propagation and nonlinear self-trapping in condensed media. These examples exhibit rather different aspects of intense femtosecond pulse propagation and demonstrate the robustness and flexibility of the unidirectional Maxwell propagator. A novel aspect of our approach is that the pulse propagator is designed to faithfully capture the light-material interaction over the broad spectral landscape of relevance to the interaction. Moreover the model provides a seamless and physically self-consistent means of deriving the many ultrashort pulse propagation equations presented in the literature.