Multidimensional coupling owing to optical nonlinearities. I. General formulation

A beam propagating in a nonlinear, dispersive medium can experience nonlinear coupling among its parameters in the x, y, and t dimensions. We derive two new computational techniques that account for this coupling. The first technique uses the beam-propagation method to solve three coupled differential equations, and the second uses six coupled second-moment equations. Nonlinear coupling is especially important for the operation of self-mode-locked (Kerr-lens mode-locked) lasers, an example of which is considered in detail in an accompanying paper [J. Opt. Soc. Am. 13, 560 (1996)]. The two techniques derived here can be adapted to handle most of the physical effects of importance to self-mode-locked lasers, but we concentrate on the effects of diffraction, secondand third-order dispersion, and Kerr nonlinearity.  1996 Optical Society of America