Three - University of Arkansas Physics Department

Experimental observation of chirped continuous
pulse-tr ain soliton solutions to the Maxwell-
Bloch equations
Shihadeh M. Saadeh, John L. Shultz, and Gregory J. Salamo
Department of Physics, University of Arkansas, Fayetteville, Arkansas, USA
Abstract: A frequency chirped continuous wave laser beam incident upon a
resonant, two-level atomic absorber is seen to evolve into a Jacobi ellipticpulsetrain
solution to the Maxwell-Bloch equations. Experimental pulse-train
envelopes are found in good agreement with numerical and analytical
predictions.
02000 Optical Society of America
OCIS codes: (190.5530) Pulse propagation and solitons, (190.5940) Self-action effects
References and links
I. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183,457-485 (1969).
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(1969).
3. M. D. Crisp, "Distortionless propagation of light through an optical medium," Phys. Rev. Lett. 22, 820-823
(1969).
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(1970).
5. L. Matulic and J. H. Eberly, "Analytic study of pulse chirping in self-induced transparency," Phys. Rev. A 6,
822-836 (1972).
6. M. A. Newbold and G. J. Salamo, "Effects of relaxation on coherent continuous-pulse-train propagation," Phys.
Rev. Lett. 42, 887-890 (1979).
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).
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Coherent propagation of trains of optical pulses through atwo-level absorber has beeninvestigated,
from a theoretical viewpoint, by many researchers. These investigations have been based on the
self-induced transparency (SIT) equations [I], both with [2-51, and without [6], the assumption of
zero relaxation. Recently, theoretical predictions have been supported by experimental
observations of the Jacobi elliptic dn solution [7]. In particular, experiments demonstrated the
evolution of an arbitrarily shaped input optical pulse train into the analytic shape-preserving Jacobi
elliptic pulse train solution to the Maxwell-Bloch equations [8]. A special feature of the observed
solution was that the chirp in the optical frequency of the pulse train was zero. In this paper we
report the experimental and numerical demonstration of the evolution of a continuous wave laser
beam into an analytic shape-preserving pulse train solution. In this case, the analytic solution to
the Maxwell-Bloch equations is a Jacobi elliptic function with a nonzero frequency chirp.
The interaction of a plane-wave optical field with an inhomogeneously broadened two-level
absorber can be described by two sets of equations. The Bloch equations describe the effect of the
optical field on the atom while the reduced Maxwell equations describe the effect of the atom on
the optical field. For significant absorption, self-consistent solutions to both equations describe the
propagation of the optical field through the two-level absorber. Together, the two sets of equations
are known as the reduced Maxwell-Bloch equations.
For circularly polarized light traveling in the z-direction, the electric field at the position of the
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(C) 200 1 OSA
Received November 22,2000; Revised January 10,2001
15 January 2001 1 Vol. 8, No. 2 1 OPTICS EXPRESS 153