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Proceedings Paper

Propagating arbitrarily shaped pulses in a nonlinear normally dispersive fiber using moments
Author(s): Bryan Burgoyne; Nicolas Godbout; Suzanne Lacroix
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Paper Abstract

We use the method of moments to calculate the propagation of an arbitrarily shaped pulse in a nonlinear dispersive fiber. By assuming that the pulse is linearly chirped, we are able to determine analytically the evolution of the second order moments (representing the duration, bandwidth and chirp of the pulse) along propagation regardless of the initial pulse shape. The evolution of the moments is given by an implicit equation and several invariants. These invariants allow an easy estimation of the different pulse parameters. The linear chirp approximation implies that the arbitrary pulse shape remains invariant along propagation but allows to calculate the propagation in both dispersion regimes from the same solution. The solution show an oscillatory behavior in the anomalous dispersion regime and a monotonic behavior in the normal dispersion regime. In both regimes the calculations are compared to numerical split-step simulations and are shown to agree for propagation over many dispersion and nonlinear lengths. While this method describes well the evolution of the pulse duration, bandwidth and chirp, we need to proceed differently to find the evolution of the pulse shape. From these propagation equations for the moments, we derive an approximate implicit solution describing the propagation of a Gaussian pulse in the normal dispersion regime. This approximate solution describes the pulse shaping toward a parabola that the pulse undergoes along propagation. A good agreement is found between the pulse obtained from numerically solving the implicit equation and the split-step propagation of the same pulse. Numerically solving the implicit analytical function describing the pulse is much faster than using purely numerical simulations, which becomes time consuming for highly chirped pulses with large bandwidths over long propagation distances. These and other results suggest that pulse shaping along propagation is only adequately modeled by implicit functions.

Paper Details

Date Published: 12 August 2008
PDF: 6 pages
Proc. SPIE 7099, Photonics North 2008, 70991V (12 August 2008); doi: 10.1117/12.807213
Show Author Affiliations
Bryan Burgoyne, École Polytechnique de Montréal (Canada)
Nicolas Godbout, École Polytechnique de Montréal (Canada)
Suzanne Lacroix, École Polytechnique de Montréal (Canada)

Published in SPIE Proceedings Vol. 7099:
Photonics North 2008
Réal Vallée; Michel Piché; Peter Mascher; Pavel Cheben; Daniel Côté; Sophie LaRochelle; Henry P. Schriemer; Jacques Albert; Tsuneyuki Ozaki, Editor(s)

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