Recovery of the soliton self-frequency shift by optical phase conjugation

The recovery of the self-frequency shift effect on a soliton by optical phase conjugation is investigated. It is proved that, without third-order dispersion and fiber loss, the soliton self-frequency shift can be completely recovered. The recoveries for a fundamental soliton and a second-order soliton in the presence of third-order dispersion and of fiber loss, which is compensated by the distributed erbium-doped fiber amplifiers, are numerically studied. Recently optical phase conjugation (OPC) was used for the compensation for chromatic dispersion in a single-mode fiber. 1,2 The compensation of chromatic dispersion by OPC was been proposed by Yariv et al. in 1979.3 In fact, in addition to chromatic disper-sion, the effect of delayed nonlinear response on an optical pulse can also be completely recovered by OPC in the lossless case.4 In Refs. 5 and 6 soliton interac-tion resulting from the nonlinear Kerr effect is shown to be undone by OPC with the fiber loss compen-sated by the optical amplifiers. Because the Raman-effect-induced soliton self-frequency shift7 (SFS) is an effect of delayed nonlinear response, the shifts can also be recovered by OPC in the lossless case. In this Letter we numerically show recoveries of the ef-fect of the SFS on the fundamental soliton and the second-order soliton when the effects of third-order dispersion and fiber loss are considered, where the fiber loss is compensated by distributed erbium-doped fiber amplifiers (DEDFA's) to reduce the soliton pow-er perturbation. The soliton propagating in the fiber follows the modified nonlinear Schrbdinger equation8 (MNSE