Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations

Spatial- and time-domain versions of the unidirectional pulse propagation equation (UPPE) are derived and compared from the point of view of their practical application in simulations of nonlinear optical pulse dynamics. A modification of the UPPE suitable for ultrathin optical waveguides, such as submicron silica wires, is also presented. We show in detail how various, previously published propagation equations follow from the UPPE in a unified way that clearly elucidates their underlying approximations and areas of applicability.