Pulse propagation methods in nonlinear optics

P. Kinsler,

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

    arXiv:0707.0982

I present an overview of pulse propagation methods used in
nonlinear optics, covering both full-field and
envelope-and-carrier methods. Both wideband and narrowband
cases are discussed. Three basic forms are considered -- those
based on (a) Maxwell's equations, (b) directional fields, and
(c) the second order wave equation. While Maxwell's equations
simulators are the most general, directional field methods can
give significant computational and conceptual advantages.
Factorizations of the second order wave equation complete the
set by being the simplest to understand. One important
conclusion is that that envelope methods based on forward-only
directional field propagation has made the traditional
envelope methods (such as the SVEA, and extensions) based on
the second order wave equation utterly redundant.