TAILS AND DECAY OF A RAMAN-DRIVEN PULSE IN A NONLINEAR-OPTICAL FIBER

We consider the analytically asymptotic evolution of a pulse governed by the nonlinear Schrodinger equation with an additional term that acc ounts for the Raman intrapulse scattering. This term is taken in the s implest quasi-instantaneous approximation. First we find an asymptotic analytical solution describing a tail generated by action of the Rama n term. An important result is that this solution always remains essen tially nonlinear, which drastically changes its structure compared wit h the known linear approximations based on the Airy functions. It is s hown that a minimum temporal scale of the tail increases with the prop agation distance, so that the quasi-instantaneous approximation for th e Raman term remains valid. Our solution may directly apply to the des cription of the tails discovered in recent numerical and laboratory ex periments. Next, we consider a late asymptotic stage of evolution of a Raman-driven localized pulse. We demonstrate that, beyond the well-kn own approximation in which the pulse (soliton) is regarded as a mechan ical particle driven by a constant force, the pulse propagating in a l ong lossless fiber will slowly decay into the oscillating tail generat ed behind it. Using the analytical solution for the tail, the conserva tion of energy, and some natural assumptions, we predict that, asympto tically, the peak power of the soliton will vanish inversely proportio nally to the traveled distance. A real optical fiber should allow for the predicted process if it is much longer than several soliton period s, which may be realistic for the ultrashort solitons. Finally we demo nstrate that, in the model incorporating gain and losses, the tail can trigger a long-term instability of the solitary pulse, which has been observed in numerical simulations.