Optical pulse propagation with minimal approximations

Details Optical pulse propagation with minimal approximations Optical pulse propagation with minimal approximations

2008-10-31

arxiv.org/abs/0810.5689v6

Phys. Rev. A 81, 013819 (2010)

Physics

Optics

14 pages, v4 submitted to Phys. Rev. A, v5 include magnetic effects, v6 published in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.81.013819]

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.

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