Abstract

A frequency chirped continuous wave laser beam incident upon a resonant, two-level atomic absorber is seen to evolve into a Jacobi elliptic pulse-train solution to the Maxwell-Bloch equations. Experimental pulse-train envelopes are found in good agreement with numerical and analytical predictions.

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References

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  1. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
    [CrossRef]
  2. J. H. Eberly, "Optical pulse and pulse-train propagation in a resonant medium," Phys. Rev. Lett. 22, 760-762 (1969).
    [CrossRef]
  3. M. D. Crisp, "Distortionless propagation of light through an optical medium," Phys. Rev. Lett. 22, 820-823 (1969).
    [CrossRef]
  4. D. Dialetis, "Propagation of electromagnetic radiation through a resonant medium," Phys. Rev. A 2, 1065-1075 (1970).
    [CrossRef]
  5. L. Matulic and J. H. Eberly, "Analytic study of pulse chirping in self-induced transparency," Phys. Rev. A 6, 822-836 (1972).
    [CrossRef]
  6. M. A. Newbold and G. J. Salamo, "Effects of relaxation on coherent continuous-pulse-train propagation," Phys. Rev. Lett. 42, 887-890 (1979).
    [CrossRef]
  7. J. L. Shultz and G. J. Salamo, "Experimental observation of the continuous pulse-train soliton solution to the Maxwell-Bloch equations," Phys. Rev. Lett. 78, 855-858 (1997).
    [CrossRef]
  8. N. Akhmediev and J. M. Soto-Crespo, "Dynamics of solitonlike pulse propagation in birefringent optical fibers," Phys.Rev.E 49, 5742-5754 (1994).
    [CrossRef]

Other

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

J. H. Eberly, "Optical pulse and pulse-train propagation in a resonant medium," Phys. Rev. Lett. 22, 760-762 (1969).
[CrossRef]

M. D. Crisp, "Distortionless propagation of light through an optical medium," Phys. Rev. Lett. 22, 820-823 (1969).
[CrossRef]

D. Dialetis, "Propagation of electromagnetic radiation through a resonant medium," Phys. Rev. A 2, 1065-1075 (1970).
[CrossRef]

L. Matulic and J. H. Eberly, "Analytic study of pulse chirping in self-induced transparency," Phys. Rev. A 6, 822-836 (1972).
[CrossRef]

M. A. Newbold and G. J. Salamo, "Effects of relaxation on coherent continuous-pulse-train propagation," Phys. Rev. Lett. 42, 887-890 (1979).
[CrossRef]

J. L. Shultz and G. J. Salamo, "Experimental observation of the continuous pulse-train soliton solution to the Maxwell-Bloch equations," Phys. Rev. Lett. 78, 855-858 (1997).
[CrossRef]

N. Akhmediev and J. M. Soto-Crespo, "Dynamics of solitonlike pulse propagation in birefringent optical fibers," Phys.Rev.E 49, 5742-5754 (1994).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Geometrical representation of the Bloch vector, P, under the influence of a driving, “torque” vector, Ω

Fig. 2.
Fig. 2.

Schematic of experimental apparatus

Fig. 3.
Fig. 3.

Experimental input (solid horizontal line) and output (dashed line) field envelope for a phase modulation amplitude of 20 MHz, compared with the numerical simulation (solid line).

Fig. 4.
Fig. 4.

Experimentally observed output field envelope (dots) for a phase modulation amplitude of 30 MHz, compared with the analytic Jacobi sn solution of Equation 5 (solid line). Here, k=.776 and l=.760.

Fig. 5.
Fig. 5.

Experimental input (solid horizontal line) and output (dashed line) field envelope for a phase modulation amplitude of 50 MHz, compared with the numerical simulation (solid line).

Equations (11)

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E ( t , z ) = E 0 ( t , z ) [ e i { ω t K z + ϕ ( t ) } + c. c . ]
ω ( t ) = ω + d ϕ d t
u t = ( Δ ω ϕ ˙ ) v E 2 w u T 2
v t = ( Δ ω ϕ ˙ ) u + E 1 w v T 2
w t = E 1 v + E 2 u ( w + 1 ) T 1
E 1 z = α 2 π g ( 0 ) v ( t , z , Δ ω ) g ( Δ ω ) d Δ ω
E 2 z = α 2 π g ( 0 ) u ( t , z , Δ ω ) g ( Δ ω ) d Δ ω
E 0 = 2 k τ l [ 1 l 2 sn 2 ( t τ ; k ) ] 1 2
d φ d t = ( 1 l 2 ) 1 2 ( l 2 k 2 ) 1 2 l τ [ 1 l 2 sn 2 ( t τ ; k ) ]
d P d t = Ω × P
d ϕ ( t ) d t = ϕ 0 sin δ t , or ϕ ( t ) = ϕ 0 δ cos δ t ,

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