doi:10.1016/S0167-2789(03)00245-8 
Copyright © 2003 Elsevier B.V. All rights reserved.
Polarization switching of light interacting with a degenerate two-level optical medium
a Mathematics Department, Siena College, 515 Loudon Road, Loudonville, NY 12211-1462, USA
b Mathematics Department, University of Arizona, 617 North Santa Rita, P.O. Box 210089, Tucson, AZ 85721, USA
c Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Received 12 December 2002;
revised 9 June 2003;
accepted 25 June 2003;
Communicated by C.K.R.T. Jones
Available online 26 August 2003.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
Polarization switching of light in a degenerate two-level medium, known as the Λ-configuration, is described. The polarization dynamics of light pulses is investigated by means of the inverse-scattering transform. The mathematical formalism of the inverse-scattering transform that takes into account the initial fluctuations of the medium polarization components corresponding to atomic transitions between the excited state and the two degenerate ground sub-levels in Λ-configuration atomic system is formulated. The characteristic switching length is evaluated via the physical parameters of the prepared medium and the optical pulse.
Author Keywords: Polarization switching; Degenerate two-level medium; Maxwell–Bloch equations; Solitons
Fig. 1. Quantum diagram for the Λ-configuration transition.
Fig. 2. The simplest one-soliton solution of the type given by
(34a) and
(34b) with parameters γ=0, μ=1/3,
=0, α
2=5/6, α
3=1/6,
d2=
d3=−i.
Fig. 3. A one-soliton solution of the type given by
(34a),
(34b),
(39a),
(39b) and
(39c) with parameters γ=0, μ=1/3,
=1/10,
L=15, α
2=5/6, α
3=1/6, β
2=1/5, β
3=4/5,
d2=
d3=−i.
Fig. 4. A two-soliton solution with parameters γ
1=γ
2=0, μ
1=1/3, μ
2=2/3,
=1/10, α
2=5/6, α
3=1/6,
dj2=
dj3=−i,
j=1,2.
Fig. 5. A two-soliton solution with step-like initial populations, as described by formulas (
(38a),
(38b) and
(38c)), and parameters γ
1=γ
2=0, μ
1=1/3, μ
2=2/3,
=1/10,
L=15, α
2=5/6, α
3=1/6, β
2=1/5, β
3=4/5,
dj2=
dj3=−i,
j=1,2.
Fig. 6. A soliton-breather solution with parameters γ
1=0, γ
2=1/3, γ
3=−1/3, μ
j=1/3,
=1/10, α
2=5/6, α
3=1/6,
dj2=
dj3=−i,
j=1,2,3.
Fig. 7. A soliton-breather solution with step-like initial populations, as described by formulas (
(38a),
(38b) and
(38c)), and parameters γ
1=0, γ
2=1/3, γ
3=−1/3, μ
j=1/3,
=1/10,
L=15, α
2=5/6, α
3=1/6, β
2=1/5, β
3=4/5,
dj2=
dj3=−i,
j=1,2,3.
Fig. 8. Polarization ellipse in the plane perpendicular to the propagation of light.
Fig. 9. The Poincaré sphere.
Fig. 10. The Poincaré sphere for the one soliton solution shown in
Fig. 3.
Fig. 11. The Poincaré sphere for the complex one-soliton solution with step-like initial populations, as described by formulas (
(38a),
(38b) and
(38c)), and with parameters γ=2, μ=1/3,
=1/10,
L=300, α
2=5/6, α
3=1/6, β
2=1/5, β
3=4/5,
d2=
d3=−i.
Fig. 12. The Poincaré sphere for the two-soliton solution with step-like initial populations, as described by formulas (
(38a),
(38b) and
(38c)), and parameters γ
1=0, γ
2=1/3, μ
j=1/3,
=1/10,
L=15, α
2=5/6, α
3=1/6, β
2=1/5, β
3=4/5,
dj2=
dj3=−i,
j=1,2.
Abstract
Purchase PDF (401 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (8)
Purchase PDF (65 K)
