Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems

Instability of Optical Solitons in the Boundary Value Problem for a Medium of Finite Extension

“…The key steps of this evolution are illustrated in Figure 2. After an initial stage, at T = 1000 the evolution results in the formation of the soliton, whose shape perfectly matches the analytic result given by Equations (4)- (6). For some time this soliton stands still in the center of the medium, but then it starts to slowly move (17)-(19).…”

“…On the left panel of Figure 1 we show the soliton solution which is constructed according to the formulas (4)- (6). In parallel, we performed numerical simulations based on the method developed in Ref.…”

“…The initial shapes which are shown in Figure 2 are chosen in such a way that the center of the forward (backward) beam is shifted towards the left (right). Note that the choice of z shift = 0 in the above equations corresponds to the soliton solution given by Equations (4)- (6). The input shapes of Equations (17)- (19) evolve with time inside the medium.…”

“…It may also apply to the case of a randomly birefringent optical fiber, as discussed in [6,13], but in this case the coefficient matrix J has a different form, namely J = diag(−β, β, −β).…”

“…If the powers of the beams are different, then soliton solutions are also possible, now in the form of moving structures, whose speed linearly depends on the difference of the powers [6,[12][13][14]. These moving solitons are not of interest to us here.…”