Directional pulse propagation in beam, rod, pipe, and disk geometries

P. Kinsler, 

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

    http://arxiv.org/abs/1210.6794

I derive directional wave equations useful for pulses propagating in
beam, rod, pipe, and disk geometries by using a cylindrical coordinate
system; the scheme works equally well for either long multi-cycle or
single-cycle ultrashort pulses. This is achieved by means of a
factorization procedure that conveniently generates exact
bi-directional and first order wave equations after the selection of
propagation direction - either axial, radial, or even angular. I then
discuss how to reduce these to a uni-directional form, and discuss the
necessary approximation, which is essentially a paraxial approximation
as appropriately generalized to the specific geometry.