Optical pulse propagation with minimal approximations
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.
Cite
@article{arxiv.0810.5689,
title = {Optical pulse propagation with minimal approximations},
author = {Paul Kinsler},
journal= {arXiv preprint arXiv:0810.5689},
year = {2014}
}
Comments
14 pages, v4 submitted to Phys. Rev. A, v5 include magnetic effects, v6 published in Phys. Rev. A, v7 minor corrections