Existence and stability of multihumped femtosecond solitons

Abstract

The propagation of bound soliton pairs in nonlinear photonic crystal fibers has recently been experimentally observed. The system may be modeled by a generalized nonlinear Schrödinger equation (GNLSE) which includes higher intrapulse Raman Scattering, self-steepening and higher order dispersion. Here, we find multihumped pulses as result of an accelerating similarity reduction of a GNLSE containing the intrapulse Raman scattering. Numerical simulations of the suitable GNLSE using these solutions as input showed that they are not stable, however, they may be related with the experimentally observed bound pairs since they propagate steadily for distances compared to the ones observed. Keywords: intrapulse Raman scattering; bound solitons; photonic crystal fibers. INTRODUCTIONIn recent experiments, the propagation of bound pairs of short pulses was observed in highly nonlinear photonic crystal fibers (PCF) [1,2]. The propagation of such short pulses in nonlinear fibers is affected by the standard group velocity dispersion and the Kerr effect, which are well described by the nonlinear Schrödinger equation (NLS), and by higher order effects like third order dispersion, self-steepening and intrapulse Raman scattering (IRS) [3]. The occurrence of bound solitons in the NLS is possible and predicted by the inverse scattering method as N-soliton solutions for which the velocities are all equal [4].The NLS bound solitons propagate with periodic oscillations, with a period related to its beating frequencies, and are known to decay when they are in presence of higher order effects like the IRS [5]. Nevertheless, twohumped solutions that propagate without change of form were already associated with the model NLS plus IRS [6]. They accelerate along the fiber distance and their mean frequency linearly downshifts, in accordance to what is also observed in single hump propagation, which is known as soliton self-frequency shift [7].Here, we obtain multihumped solutions of the NLS plus IRS equation as solutions of the ordinary differential equation (ODE) that results from an accelerating similarity reduction. Their profiles have characteristics that suffer small changes with the IRS strength. The stability of these solutions is studied by numerical simulation of the full evolution equation and their relation with the observed bound soliton pairs in PCFs is studied.