The Ring Laser Configuration Studied by Collective Coordinates

J.G. Caputo, N. Flytzanis, and M.P. Sørensen

Journal of the Optical Society of America B, 12(1), 1995, pp.139-145.

A perturbed nonlinear Schr\"{o}dinger equation is used to model an optical laser fiber ring for generation of femto second optical pulses. The ring is built from a nonlinear laser fiber joint together with a passive nonlinear fiber. We assume that the optical pulses are solitons perturbed by loss and gain. Starting from the single soliton solution of the nonlinear Schr\"{o}dinger equation, we use a collective coordinate approach to derive a Lagrangian as function of the collective coordinates. The evolution equations for the collective coordinates emerge from the Lagrange equations including the associated generalized forces resulting from the perturbations. Remarkably good agreement is obtained between the collective coordinate approach and the full numerical simulations of the fiber ring laser.