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Title: Noise-induced perturbations of dispersion-managed solitons

Abstract

We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems.

Authors:
; ;  [1]
  1. Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260 (United States)
Publication Date:
OSTI Identifier:
20982594
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.053818; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; DENSITY; DISTURBANCES; LASER RADIATION; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; NOISE; NONLINEAR PROBLEMS; OPTICAL FIBERS; PERTURBATION THEORY; PROBABILITY; SCHROEDINGER EQUATION; SIMULATION; SOLITONS; TRANSMISSION; TRAVELLING WAVES

Citation Formats

Li, Jinglai, Spiller, Elaine, and Biondini, Gino. Noise-induced perturbations of dispersion-managed solitons. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.053818.
Li, Jinglai, Spiller, Elaine, & Biondini, Gino. Noise-induced perturbations of dispersion-managed solitons. United States. doi:10.1103/PHYSREVA.75.053818.
Li, Jinglai, Spiller, Elaine, and Biondini, Gino. Tue . "Noise-induced perturbations of dispersion-managed solitons". United States. doi:10.1103/PHYSREVA.75.053818.
@article{osti_20982594,
title = {Noise-induced perturbations of dispersion-managed solitons},
author = {Li, Jinglai and Spiller, Elaine and Biondini, Gino},
abstractNote = {We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems.},
doi = {10.1103/PHYSREVA.75.053818},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • We quantify noise-induced phase deviations of dispersion-managed solitons (DMS) in optical fiber communications and femtosecond lasers. We first develop a perturbation theory for the dispersion-managed nonlinear Schroedinger equation (DMNLSE) in order to compute the noise-induced mean and variance of the soliton parameters. We then use the analytical results to guide importance-sampled Monte Carlo simulations of the noise-driven DMNLSE. Comparison of these results with those from the original unaveraged governing equations confirms the validity of the DMNLSE as a model for many dispersion-managed systems and quantify the increased robustness of DMS with respect to noise-induced phase jitter.
  • We find that in a dispersion-managed fiber, in which the strength of the dispersion management is above some threshold, solitons can exist with normal average dispersion. When the normal average dispersion is below some limiting value there exist two soliton solutions with the same pulse duration and different pulse energies. When the normal average dispersion is above this limiting value, no soliton exists. Both higher-energy and lower-energy solitons are dynamically stable in the parameter range that we considered. {copyright} {ital 1998} {ital Optical Society of America}
  • The authors simulated dispersion-managed soliton propagation in optical fiber transmission systems with lumped amplifiers and loss. The energy enhancement of dispersion-managed solitons can be more or less than in the lossless case, depending delicately on the amplifiers arrangement. In all cases, there is a maximum enhancement factor beyond which the dispersion-managed soliton no longer exists and which also depends delicately on the arrangement.
  • We investigate both numerically and experimentally soliton propagation in a fiber loop with dispersion management, in-line filters, and frequency shifting. More than 90{percent} of the fiber in the loop is in the normal-dispersion regime, but the net dispersion is anomalous. Stable pulses in the loop have an enhanced power relative to solitons in a fiber with uniform dispersion equal to the loop{close_quote}s path-averaged dispersion. Because the loop{close_quote}s path-averaged dispersion is small, the in-line filtering and the frequency shifting play an important role in pulse shaping. Recirculating loop experiments that demonstrate stable pulse propagation over 28,000 km are consistent with resultsmore » from computer modeling. {copyright} {ital 1997} {ital Optical Society of America}« less
  • We present a class of solutions with a period multiple to that one of the standard dispersion-managed soliton in the nonlinear Schroedinger equation with periodic variations of dispersion.