Collective coordinate theory for light pulses in fibers: The reduced projection operators

E. Tchomgo Felenou, P. Tchofo Dinda, C. M. Ngabireng, K. Nakkeeran*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider optical waveguides in which light pulses may execute complex dynamical behaviors including translational motions accompanied with strong internal vibrations. Such systems necessarily generate various types of collective motion, in which each collective mode is describable by a collective coordinate. We present a novel projection operator formalism for deriving the equations of motion of the collective coordinates and coupled fields. This formalism is built up by treating separately the dynamics of the pulse phase and that of its amplitude, that is, by using two distinct projection operators (one for the amplitude, and the other one for the phase). This new pair of operators, which we call reduced projection operators, has as main virtue of having dimension reduced by half as compared to that of the conventional operators that includes both pulse amplitude and phase together. The main interest of the reduced projection operators lies in the ease with which the equations of motion are derived when compared with the amount of algebra needed to obtain the same equations from the conventional projection operators. We provide examples of concrete situations that illustrate the effectiveness of the collective-coordinate approach based on the reduced projection operators. (C) 2013 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)770-777
Number of pages8
JournalPhysics Letters A
Volume377
Issue number10-11
Early online date21 Jan 2013
DOIs
Publication statusPublished - 1 Apr 2013

Keywords

  • OPTICAL COMMUNICATION-SYSTEMS
  • DISPERSION MANAGEMENT
  • VARIATIONAL APPROACH
  • RING LASER
  • TRANSMISSION-SYSTEMS
  • SOLITON
  • PROPAGATION
  • EQUATIONS
  • DESIGN

Cite this

Collective coordinate theory for light pulses in fibers : The reduced projection operators. / Felenou, E. Tchomgo; Dinda, P. Tchofo; Ngabireng, C. M.; Nakkeeran, K.

In: Physics Letters A, Vol. 377, No. 10-11, 01.04.2013, p. 770-777.

Research output: Contribution to journalArticle

Felenou, E. Tchomgo ; Dinda, P. Tchofo ; Ngabireng, C. M. ; Nakkeeran, K. / Collective coordinate theory for light pulses in fibers : The reduced projection operators. In: Physics Letters A. 2013 ; Vol. 377, No. 10-11. pp. 770-777.
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AU - Dinda, P. Tchofo

AU - Ngabireng, C. M.

AU - Nakkeeran, K.

N1 - Acknowledgements E. Tchomgo Felenou acknowledges the Service de Coopérarion et dʼAction Culturelle (SCAC) de la France au Cameroun, for his financial support.

PY - 2013/4/1

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N2 - We consider optical waveguides in which light pulses may execute complex dynamical behaviors including translational motions accompanied with strong internal vibrations. Such systems necessarily generate various types of collective motion, in which each collective mode is describable by a collective coordinate. We present a novel projection operator formalism for deriving the equations of motion of the collective coordinates and coupled fields. This formalism is built up by treating separately the dynamics of the pulse phase and that of its amplitude, that is, by using two distinct projection operators (one for the amplitude, and the other one for the phase). This new pair of operators, which we call reduced projection operators, has as main virtue of having dimension reduced by half as compared to that of the conventional operators that includes both pulse amplitude and phase together. The main interest of the reduced projection operators lies in the ease with which the equations of motion are derived when compared with the amount of algebra needed to obtain the same equations from the conventional projection operators. We provide examples of concrete situations that illustrate the effectiveness of the collective-coordinate approach based on the reduced projection operators. (C) 2013 Elsevier B.V. All rights reserved.

AB - We consider optical waveguides in which light pulses may execute complex dynamical behaviors including translational motions accompanied with strong internal vibrations. Such systems necessarily generate various types of collective motion, in which each collective mode is describable by a collective coordinate. We present a novel projection operator formalism for deriving the equations of motion of the collective coordinates and coupled fields. This formalism is built up by treating separately the dynamics of the pulse phase and that of its amplitude, that is, by using two distinct projection operators (one for the amplitude, and the other one for the phase). This new pair of operators, which we call reduced projection operators, has as main virtue of having dimension reduced by half as compared to that of the conventional operators that includes both pulse amplitude and phase together. The main interest of the reduced projection operators lies in the ease with which the equations of motion are derived when compared with the amount of algebra needed to obtain the same equations from the conventional projection operators. We provide examples of concrete situations that illustrate the effectiveness of the collective-coordinate approach based on the reduced projection operators. (C) 2013 Elsevier B.V. All rights reserved.

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KW - RING LASER

KW - TRANSMISSION-SYSTEMS

KW - SOLITON

KW - PROPAGATION

KW - EQUATIONS

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