Parabolic optical pulses under the action of the third-order dispersion

Research output: Contribution to conferenceAbstract

Abstract

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.
Original languageEnglish
Pages4
Number of pages1
Publication statusPublished - Jan 2009
EventSolitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference - Nice , France
Duration: 6 Jan 20099 Jan 2009
http://www-n.oca.eu/cpnlw09/

Conference

ConferenceSolitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference
Abbreviated titleCPNLW 2009
CountryFrance
CityNice
Period6/01/099/01/09
Internet address

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pulses
nonlinear equations
fibers
chirp
solitary waves
perturbation
nonlinear optics
group velocity
asymmetry
scaling
profiles
simulation
energy

Bibliographical note

Published in Book of Abstracts of Solitons in Their Roaring Forties,
Coherence and Persistence in Nonlinear Waves Conference (CPNLW 2009), p. 4,
Nice, France, January 2009.

Cite this

Boscolo, S., Bale, B., & Turitsyn, S. (2009). Parabolic optical pulses under the action of the third-order dispersion. 4. Abstract from Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference, Nice , France.
Boscolo, Sonia ; Bale, Brandon ; Turitsyn, Sergei. / Parabolic optical pulses under the action of the third-order dispersion. Abstract from Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference, Nice , France.1 p.
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abstract = "Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.",
author = "Sonia Boscolo and Brandon Bale and Sergei Turitsyn",
note = "Published in Book of Abstracts of Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference (CPNLW 2009), p. 4, Nice, France, January 2009.; Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference, CPNLW 2009 ; Conference date: 06-01-2009 Through 09-01-2009",
year = "2009",
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Boscolo, S, Bale, B & Turitsyn, S 2009, 'Parabolic optical pulses under the action of the third-order dispersion' Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference, Nice , France, 6/01/09 - 9/01/09, pp. 4.

Parabolic optical pulses under the action of the third-order dispersion. / Boscolo, Sonia; Bale, Brandon; Turitsyn, Sergei.

2009. 4 Abstract from Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference, Nice , France.

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - Parabolic optical pulses under the action of the third-order dispersion

AU - Boscolo, Sonia

AU - Bale, Brandon

AU - Turitsyn, Sergei

N1 - Published in Book of Abstracts of Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference (CPNLW 2009), p. 4, Nice, France, January 2009.

PY - 2009/1

Y1 - 2009/1

N2 - Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

AB - Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

M3 - Abstract

SP - 4

ER -

Boscolo S, Bale B, Turitsyn S. Parabolic optical pulses under the action of the third-order dispersion. 2009. Abstract from Solitons in Their Roaring Forties, Coherence and Persistence in Nonlinear Waves Conference, Nice , France.