ABCD MATRIX ANALYSIS OF PROPAGATION OF GAUSSIAN BEAMS THROUGH KERR MEDIA

A new formalism and a nonlinear ABCD matrix, derived from the aberrationless theory of self-focusing, are introduced to treat the propagation of gaussian beams in materials with Kerr nonlinearity. The analysis of propagation of gaussian beams shows that the effect of the Kerr medium can be interpreted, to the first order in the beam power, as due to a lens and propagation over a negative distance. The latter effect has been named self-shortening. The formalism has been applied to find the optimal focusing condition for the maximum nonlinear effects and to the calculation of gaussian modes in resonators containing a Kerr medium.