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I derive unidirectional wave equations for fields propagating in materialswith both electric and magnetic dispersion and nonlinearity. The derivationimposes no conditions on the pulse profile except that the material modulatesthe propagation slowly, that is, that loss, dispersion, and nonlinearity haveonly a small effect over the scale of a wavelength. It also allows a directterm-to-term comparison of the exact bidirectional theory with its approximateunidirectional counterpart.

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