Nonlinear optical pulse propagation: Expansion to all orders in diffraction and dispersion

A new equation for self-focusing of extremely focused intense pulses is derived. This method can be generalized to derive propagation equations for intense focused pulses to all orders of diffraction and dispersion with nonlinearity present, including the self-consistent derivation of nonlinear derivative coupling terms. This generalizes both the previously formulation of linear optical pulse propagation to the nonlinear propagation regime, and the cw nonlinear regime to the pulsed regime by including temporal characteristics of the pulse. Here we present the results for isotropic Kerr-type nonlinear media.