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Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system

L. Deng1, M. G. Payne1, Guoxiang Huang1,2, and E. W. Hagley1

  • 1Electron and Optical Physics Division, NIST, Gaithersburg, Maryland 20899, USA
  • 2Department of Physics and Institute of Theoretical Physics, East China Normal University, Shanghai 200062, China

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Phys. Rev. E 72, 055601(R) – Published 17 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.055601

Abstract

We investigate the simultaneous formation and stable propagation of ultraslow optical soliton pairs in a lifetime broadened four-state atomic system under double- excitation with large one- and two-photon detunings. We show that detrimental probe field distortions due to strong dispersion effects under weak driving conditions can be well balanced by self- and cross-phase modulation effects, leading to a pair of temporal, group velocity, and amplitude matched ultraslow optical solitons of different frequencies.

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References (20)

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  10. Such as two members of the same hyperfine manifold.
  11. This requires that the two input pulses have the same phase and envelope [see Ref. [12]] at the entrance of the medium. It, however, preexcludes the possibilities of bright-dark or dark-bright soliton pairs. A more generalized theory will be published elsewhere.
  12. For maximum efficiency, the two input pulses should be in-phase. This can be produced using techniques such as a combination of a laser and AOMs, EIT-based FWM [9], and inelastic two- and four-wave mixings [20].
  13. For arbitrary initial pulse shapes Eqs. (4a4b) lead to two pair pulses that travel with separately matched group velocities. See Ref. [7].
  14. Higher order terms in d3 are important when ∣δ3τ∣⪢1. It leads to higher attenuation of the fields and a different set of coupled nonlinear equations that may support solitary wave solutions.
  15. In the conventional three-state single channel EIT where δj=0 (j=1, 2, 3), the SPM coefficient g11 is imaginary, thus stable propagation of ultraslow solitons is not supported.
  16. Further studies, using the multiple-scales theory and operator formalism, of the formation and propagation dynamics of other combinations of solitons of different gray levels using this and other schemes in various regimes and under various driving conditions, including radiation damping and diffraction effects will be published elsewhere.
  17. For more rigorous treatment of a three-level system, see G. Huang and L. Deng, Phys. Rev. E 72, 016617 (2005). See also B. Hu, G. Huang, and M. G. Verlarde, 62, 2827 (2000).
  18. The initial/boundary conditions used in numerical calculations at z=0 and t=0, Ωp1(0,t)τ=Ωp2(0,t)=7.84 sech(t∕τ), and Ωc1(0,t)τ=Ωc2(0,t)τ=40.
  19. It is not necessary to start with two exactly matched sech (t∕τ) functions. Numerical calculations using two matched Gaussian inputs have shown that the soliton pair formation is completed at z=0.02 cm and the shape preservation is well maintained at even z=1 cm. The fit of the pulse shape to a sech (t∕τ) function at z=1.0 cm is better than 95%.
  20. L. Deng, M. G. Payne, and W. R. Garrett, Opt. Commun. 242, 641 (2004).

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Phys. Rev. E 72, 055601(R)– Published 17 November, 2005
  • Received 10 November 2004

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