The cancellation of nonlinear and dispersive phase components on the fundamental optical fiber soliton: a pedagogical note

We consider the separate effects of nonlinear and dispersive propagation on a hyperbolic secant pulse propagating in an optical fiber. In particular, for small propagation distances, we present a straightforward derivation of the time-varying phase components developed across the pulse due to self-phase modulation (SPM) and group velocity dispersion (GVD). In this limit, we show that GVD is associated with a nonparabolic temporal phase which can exactly cancel the nonlinear phase component due to SPM across the entire pulse profile. The cancellation condition gives the launch condition for a fundamental optical fiber soliton.