EFFECTS OF INTRAPULSE STIMULATED RAMAN SCATTERING

The properties of dark solitons considered thus far are based on the simplified propagation equation ( $[*]$ ). When the pulse duration reaches the subpicosecond regime, it becomes necessary to include higher-order nonlinear and dispersive effects.[#!ZBF!#] These effects represent higher-order terms in the derivation of wave equation from the Maxwell's equations. Intrapulse stimulated Raman scattering (ISRS) is one of the dominating effects. It causes soliton self-frequency shift for both bright solitons[#!MG!#,#!GD!#] as well as for dark solitons.[#!WD!#] Since its discovery for bright solitons,[#!ZBF!#] considerable attention has been paid to such effects. ...

The effect of ISRS on bright solitons is to shift in both the temporal and spectral domains. It has been demonstrated that the frequency red shift of bright solitons is linear with propagation length, at a rate of -8t_d/15τ₀⁴ per unit propagation distance, where t_d is the delay time the nonlinear response of the medium (typically 6 fs) and τ₀ is the normalized soliton duration. The temporal shift is a direct consequence of the group velocity dispersion of the fiber. The temporal shift was found to be 4t_dz²/15τ₀⁴.[#!BB!#] Note that the shifting rate is proportional to | u|⁴ because τ₀ is the inverse of the normalized amplitude. ISRS is especially pronounced for high peak power pulses. Therefore, when a higher-order soliton is launched, the ISRS will cause soliton fission.[#!TA!#] Because of such effects, the initially bound state ceases to exist and solitons of different amplitudes are separated from one another. The energies of these separating solitons are distributed in such way to ensure conservation of momentum. ...

iu_z - 1/2u_tt + | u|²u

τ_d $\displaystyle {\partial \vert u\vert^2 \over \partial t}$ u,

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We introduce a simple model of the shift for fundamental dark solitons: $\begin{mathletters} \begin{eqnarray} {{\rm d}\omega \over {\rm d}z} &=& {4\tau_d... ..., \\ {{\rm d}\theta \over {\rm d}z} &=& \omega. \end{eqnarray}\end{mathletters}$ ...

We next study the behavior of dark solitons when both adiabatic amplification and ISRS are present. Figure 6(a) shows the pulse shape of a fundamental dark soliton in such a case. In this case the fundamental dark soliton loses its amplitude contrast, as it does in Fig. 4(a), and the ISRS temporal shift is enhanced by the effect of adiabatic gain. In the simple model described by Eqs. ( $[*]$ ) and ( $[*]$ ), the temporal shift by ISRS has the functional form

θ = $\displaystyle {\tau_d \over 60 \Gamma^2}$ (e^4Γz -1 - 4Γz).

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In summary, the ISRS causes a shift of dark solitons. A salient feature of dark solitons is that the rate of such shift is half the value for bright solitons, when the slow loss of contrast is neglected. This leads to a better stability of a fundamental dark soliton against such perturbations. However, the situation for higher-order dark solitons is more complicated because there are amplitude changes associated with each soliton. The symmetry of higher-order solitons is broken. Red secondary solitons gain energy at the expense of blue ones. The primary soliton ceases to be a fundamental dark soliton and suffers energy losses and frequency blue shift.