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 water, and is compared to a recent model of Brabec and Krausz.
We demonstrate how the latter model and the classical Nonlinear Schroedinger
envelope equation follow under appropriate limiting conditions.
The derivation provides clear physical interpretation of the various
approximations underlying the Nonlinear Schroedinger and other optical
pulse-propagation equations.
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