Theory of directional pulse propagation

P. Kinsler, S.B.P. Radnor, G.H.C. New

    Department of Physics, 
    Imperial College London,
    Prince Consort Road,
    London SW7 2BW, 
    United Kingdom.

    Phys. Rev. A 72, 063807 (2005) 

We construct combined electric and magnetic field variables
which independently represent energy flows in the forward and
backward directions, respectively, and use these to
reformulate Maxwell's equations. These variables enable us to
not only judge the effect and significance of
backward-traveling field components, but also to discard them
when appropriate. They thereby have the potential to simplify
numerical simulations, leading to potential speed gains of up
to 100% over standard finite difference time-domain (FDTD) or
pseudospectral spatial-domain (PSSD) simulations. We present
results for various illustrative situations, including an
example application to second harmonic generation in
periodically poled lithium niobate. These field variables are
also used to derive both envelope equations useful for
narrow-band pulse propagation, and a second order wave
equation. Alternative definitions are also presented.