Theory of the soliton laser

An analytic theory is presented of a model of the soliton laser constructed by L. F. Mollenauer and R. H. Stolen. Use is made of the fact that the solitons are characterized completely by the pole locations and residues of the reflection coefficient obtained from the inverse scattering method. The effects of loss, gain, dispersion, and temporal shaping due to a time-dependent gain are described by the change of pole locations. The steady state is determined by the requirement that the pole locations return to their "starting" positions and residues to their "starting" values in one round trip around the laser. This requirement picks the pulse shape, energy, and soliton order. The analytic predictions are confirmed by numerical simulations of the non-linear Schroedinger equation. Several experimental observations are explained: a) The pulsewidth is determined by fiber length. b) The temporal shape of the pulse intensity at the output of the laser can approximate a squared secant hyperbolic, but may not in fact be equal to a squared secant hyperbolic. c) The soliton is excited preferentially over the soliton. Furthermore, theory shows that the fiber length is equal to, and not a multiple of, the envelope repetition period.