Soliton self-frequency shift: Self-similar solutions and their stability

M. Facao, M. I. Carvalho, D. F. Parker

Research output: Contribution to journalArticlepeer-review

Abstract

Ultrashort pulse propagation in fibers is affected by intrapulse Raman scattering (IRS) which causes both a linear frequency downshift and a quadratic displacement of the peak pulse, as functions of the propagation distance. This effect has been known and treated by perturbation methods applied to the nonlinear Schroumldinger equation since the period of intense research on soliton propagation. Here, we find solutions of the model equation using an accelerating self-similarity variable and study their stability. These solutions have Airy function asymptotics which give them infinite energy. For small IRS, the algebraically decaying tail is negligible and these solutions are a very good approximation of the profiles observed in the full equation simulations. For strong IRS (but beyond the regime in which the evolution equation is valid for silica fibers), the self-similar pulses have noticeable left tails exhibiting Airy oscillations. Whenever their truncated forms are used as initial conditions of the full equation, they experience amplitude decay and show left tails that are consistent with radiation escaping from the central pulse. These observations are interpreted as being the effects of a continuum constitution of the infinite left tail.

Original languageEnglish
Article number046604
Pages (from-to)-
Number of pages6
JournalPhysical Review E - Statistical, Nonlinear and Soft Matter Physics
Volume81
Issue number4
DOIs
Publication statusPublished - Apr 2010

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