A uni-directional optical pulse propagation equation for materials with both electric and magnetic responses

TL;DR

This paper derives a unidirectional wave equation for optical pulses in materials with electric and magnetic responses, enabling simplified modeling while maintaining accuracy under slow modulation conditions.

Contribution

It introduces a new derivation method for unidirectional equations that applies to complex materials with both electric and magnetic dispersion and nonlinearity.

Findings

The derived equations accurately approximate bidirectional theory under slow modulation.

The method allows direct comparison between exact and approximate models.

It broadens the applicability of unidirectional wave equations to more complex materials.

Abstract

I derive unidirectional wave equations for fields propagating in materials with both electric and magnetic dispersion and nonlinearity. The derivation imposes no conditions on the pulse profile except that the material modulates the propagation slowly, that is, that loss, dispersion, and nonlinearity have only a small effect over the scale of a wavelength. It also allows a direct term-to-term comparison of the exact bidirectional theory with its approximate unidirectional counterpart.