The method of characteristics in the theory of resonant or nonresonant nonlinear optics

Abstract

The method of characteristics is used to analyse the system of five nonlinear partial differential equations describing ultrashort optical pulse propagation through a medium of two-level atoms. Contrary to previous suggestions it is shown rigorously that the system is causal: no physical speeds exceed c. The method is well adapted to numerical integration. It can take full account of both back scattering and the effect of a surface to the dielectric. A number of new physical results obtained this way are briefly reported.