Quantifying the limits of unidirectional ultrashort optical pulse propagation

In this paper we explore the limits of the unidirectional pulse propagation equation (UPPE) in general nonlinear media. Our main aim is to investigate under which physical conditions two-way propagation becomes significant, and leads to a breakdown of the unidirectional approximation. Using a spectral constraint appearing in the derivation of UPPE we derive a first correction which renormalizes the forward-propagating amplitude. This correction is the main result of our paper and we investigate its effects through numerical simulations.