Unidirectional optical pulse propagation equation

A unidirectional optical pulse propagation equation, derived directly from Maxwell's equations, provides a seamless transition between various nonlinear envelope equations in the literature and the full vector Maxwell's equations. The equation is illustrated in the context of supercontinuum generation in air and is compared to a recent scalar model of Brabec and Krausz. Fully vectorial aspects of the model are illustrated in the context of extreme focusing of a femtosecond pulse.