Transverse limits to the uni-directional pulse propagation approximation

P. Kinsler,

    Blackett Laboratory, 
    Imperial College London,
    Prince Consort Road,
    London SW7 2AZ,
    United Kingdom.

    arXiv:0810.5701

I calculate the limitations on the widely-used forward-only
(uni-directional) propagation assumption by considering the effects of
transverse effects (e.g. diffraction).  The starting point is the
scalar second order wave equation, and simple predictions are made
which aim to clarify the forward-backward coupling limits on
diffraction strength.  The result is unsurprising, being based on the
ratio of transverse and total wave vectors, but the intent is to
present a derivation directly comparable to a recently published
\emph{nonlinearity} constrained limits on the uni-directional
approximation [Kinsler, J. Opt. Soc. Am. (2007)]