Solitons in fibers with loss beyond small perturbation
AbstractWe consider the evolution of fiber-optic solitons in the presence of loss. Localized power reduction can be cast into a well-known form for which changes of all parameters are known explicitly. We proceed to a sequence of such perturbations with the same total loss, so that still all parameters are known, and eventually take the limit to infinitely many steps. This establishes the connection with distributed loss, and in the limit of vanishing loss reproduces the known results from perturbation theory. Outside this adiabatic limit the mechanism becomes clear that causes deviations: interference between solitons and radiation upsets the balance of dispersive and nonlinear effects characteristic of solitons; as one consequence the soliton continually sheds energy, which goes into radiation. We derive an expression for the radiation production rate in a lossy fiber, and predict quantitatively the distance until the soliton finally decays. Our approach provides quantitative results for fibers with loss small or strong, localized or distributed, and numerical results confirm predictions. It can be generalized to gain rather than loss.