Averaged Lagrangian method applied to resonant nonlinear optics. The self-steepening of light pulses

The averaged Lagrangian method of Whitham for treating nonlinear, dispersive wave propagation is used to formulate the problem of optical pulse propagation in a resonant medium. For the particular case of self-steepening, it is shown that this formulation takes the same mathematical form as Light-hill's treatment of the propagation of wave trains on deep water. Certain aspects of the solution are discussed and compared with alternative treatments of self-steepening. Some comments are given concerning the applicability of the averaged Lagrangian method to other problems of coherent, nonlinear optics. © 1975 The American Physical Society.