Dispersion in time and space: what propagating optical pulses
    in time (& not space) forces us to confront 


P. Kinsler, 

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

    http://arxiv.org/abs/1501.05569


I derive a temporally propagated uni-directional optical pulse
equation valid in the few cycle limit. Temporal propagation is
advantageous because it naturally preserves causality, unlike
the competing spatially propagated models. The approach
generates exact coupled bi-directional equations, which can be
efficiently approximated down to a uni-directional form in
cases where an optical pulse changes little over one optical
cycle. It also also allows a direct term-to-term comparison of
an exact bi-directional theory with an approximate
uni-directional theory. Notably, temporal propagation handles
dispersion in a different way, and this difference serves to
highlight existing approximations inherent in spatially
propagated treatments of dispersion. Accordingly, I emphasise
the need for future work in clarifying the limitations of the
dispersion conversion required by these types of approaches;
since the only alternative in the few cycle limit may be to
resort to the much more computationally intensive full Maxwell
equation solvers.  


Email: Dr.Paul.Kinsler@physics.org