Transverse limits on the uni-directional pulse propagation approximation

TL;DR

This paper investigates the limitations of the forward-only pulse propagation approximation by analyzing transverse effects like diffraction, providing a derivation that clarifies the conditions under which the uni-directional model remains valid.

Contribution

It offers a direct derivation of transverse limits on the uni-directional approximation based on the ratio of transverse to total wave vectors, extending previous nonlinearity-based analyses.

Findings

Limits on diffraction strength for uni-directional approximation

Derivation based on wave vector ratios

Comparison with nonlinearity constrained limits

Abstract

I calculate the limitations on the widely-used forward-only (uni-directional) propagation assumption by considering the effects of transverse effects (e.g. diffraction). The starting point is the scalar second order wave equation, and simple predictions are made which aim to clarify the forward-backward coupling limits on diffraction strength. The result is unsurprising, being based on the ratio of transverse and total wave vectors, but the intent is to present a derivation directly comparable to a recently published \emph{nonlinearity} constrained limits on the uni-directional approximation [Kinsler, J. Opt. Soc. Am. B (2007)].