The Influence Of Continuous Waves On Optical Solitons In The Optical Soliton Storage Ring

The scheme using a folded optical soliton storage ring to detect gravitation wave is the project proposed by our group. In the scheme, the solitons will propagate in fiber for a long time. Solitons propagating stably by balancing nonlinearity and dispersion is proposed as information carriers in the communication, and it has been studied theoretically and experimentally. Solitons running in the fiber are perturbed inevitably by various noises. These noises can excite the time jitter and bit error in the communication, and may induce error in measurement results too. These perturbations are studied comprehensively and many methods suppressing noises are proposed and are carried out. However, in the long-time propagation of soliton, the effect of continuous wave (cw) is regarded as an important factor affecting the soliton run, and the effect is not studied deeply because of the difficulties in mathematics. So, present methods suppressing the effectively the cw effect is no universally effective. Because of periodic condition, the main form of cw in the fiber is the cnoidal wave. It will influence the propagation of soliton in the storage ring. This paper will make an analytic computation of the effect of cnoidal wave using the soliton perturbation theory. Here, we can use the adiabatic perturbation when the amplitude of cnoidal wave is small enough. Cnoidal waves only perturb the amplitude and velocity of soliton that change the unperturbed amplitudeηo and velocityκ_o of soliton toη_o→η( Z ) =η_o+Δη( Z),κ_o→κ( Z ) =κ_o+Δκ( Z). The computation shows that bothΔη( Z) andΔκ( Z) are periodic. It means that the amplitude and velocity of solitonη( Z) andκ( Z) will restore initial value when the soliton propagates one or several periods. This result builds the foundation for the next investigation of effect of continuous wave on soliton in storage ring under more complex conditions.