Abstract

The numerical modeling of the self-focusing of intense optical beams has been the subject of keen interest for more than two decades. We shall review our own attempts to model this phenomenon as it occurs in a variety of situations. Among the applications reviewed are time-dependent self-focusing in Kerr-active organic liquids, time-dependent self-focusing in laser-heated plasmas, and time-independent self-focusing in Kerr-active extended media and in glass laser systems. We shall also describe self-focusing effects in nonlinear optical waveguide devices, which tend to be rather subtle. Our modeling of time-dependent phenomena has been based on the representation of the transverse behavior of the beam in terms of cubic splines, whereas our modeling of steady-state self-focusing has been based on a representation of the transverse dependence in terms of finite Fourier series. One of the unsatisfactory features of the paraxial theory is the catastrophic behavior of the beam at a self-focus. Our efforts to remove this singular behavior by introducing nonparaxiality as well as the consequences of the noncatastrophic propagation of self-focusing beams will also be described.

© 1989 Optical Society of America