Optical pulse propagation with minimal approximations

TL;DR

This paper derives a minimal-approximation, first-order optical pulse propagation equation that accurately models complex media, enabling precise comparison between bi-directional and uni-directional theories.

Contribution

It introduces a straightforward factorization method to derive exact bi-directional equations and reduces them to a simple uni-directional form under a slow evolution approximation.

Findings

Exact coupled bi-directional equations derived

Reduction to a single uni-directional wave equation demonstrated

Facilitates comparison between bi-directional and uni-directional models

Abstract

Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward "factorization" mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a single uni-directional first order wave equation by means of a simple "slow evolution" approximation, where the optical pulse changes little over the distance of one wavelength. It also also allows a direct term-to-term comparison of an exact bi-directional theory with the approximate uni-directional theory.