Derivation of a generalized double-sine-Gordon equation describing ultrashort-soliton propagation in optical media composed of multilevel atoms

Hervé Leblond, Houria Triki, and Dumitru Mihalache
Phys. Rev. A 86, 063825 – Published 20 December 2012

Abstract

We consider the propagation of ultrashort optical solitons in media described by a general Hamiltonian of multilevel atoms. Assuming that all transition frequencies of the medium are well below the typical wave frequency, i.e., only the contribution of infrared transitions is taken into account, we use a short-wave approximation and a rigorous application of the reductive perturbation formalism to derive a cumbersome coupled system of nonlinear partial differential equations describing ultrashort soliton evolution in such systems. The rather complicated set of coupled equations can be simplified to a generic double-sine-Gordon equation for a special case of identical three-level atoms, whereas for a special case of identical four-level atoms the system of coupled equations can be reduced to a generalized double-sine-Gordon equation. Numerical simulations showing the formation of robust breather-type solutions of both the standard double-sine-Gordon and of the generalized double-sine-Gordon equations from sinusoidal inputs with Gaussian envelopes are also presented.

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  • Received 7 October 2012

DOI:https://doi.org/10.1103/PhysRevA.86.063825

©2012 American Physical Society

Authors & Affiliations

Hervé Leblond1, Houria Triki2, and Dumitru Mihalache1,3,4

  • 1LUNAM Université, Université d'Angers, Laboratoire de Photonique d'Angers, EA 4464, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France
  • 2Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P. O. Box 12, 23000 Annaba, Algeria
  • 3Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
  • 4Horia Hulubei National Institute for Physics and Nuclear Engineering, 30 Reactorului, Magurele-Bucharest 077125, Romania

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Issue

Vol. 86, Iss. 6 — December 2012

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