Group velocity and dispersion in nonlinear-optical fibers

Many of the nonlinear effects being studied in optical fibers depend critically on the dispersion characteristics of the fiber. We generalize the scalar form of Brown's identity for group velocity in a linear waveguide to deal with arbitrary nonlinearity and use this generalization to show that the dispersion characteristics of a step-index fiber at the high powers required for many nonlinear processes may be significantly different from their linear values.