Theory of Single Filamentation
The propagation of a femtosecond optical pulse is described by Maxwell’s equations. A number of linear and nonlinear effects such as self-focusing, dispersion, self-phase modulation, and ionization have to be taken into account. The overall dynamics of such pulses can be complicated where both transverse and temporal effects play equally important roles (Chin et al., 2005; Couairon and Mysyrowicz, 2007; Bergé et al., 2007 and references therein). Unfortunately, so far there is no analytical solution to the problem. Finding direct numerical solutions with a computer requires enormous computational efforts and in many cases does not provide an insight to the basic physical understanding of the various linear and nonlinear effects involved. Therefore, an approximate wave equation is used instead with a more reasonable mathematical solution. The interaction of intense optical pulses in a bulk medium is highly nonlinear and the material response must therefore couple self-consistently with the wave equation. The following is adapted from Chin et al. (2005).