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Applied Physics Letters

Distortionless propagation of zero-degree pulses in degenerate resonant medium

Eugene Y. C. Lu, L. E. Wood

Published Apr 15, 1974• 4 citations
Publisher

Abstract

We give arguments to show that distortionless propagation of zero-degree pulses is possible in an arbitrary degenerate resonant medium in agreement with recent experimental observation. In the case of overlapping Q (2) degeneracy, the analytic closed-form solution with zero area is given. The predicted pulse shape depends in the relative occupation of the degenerate levels and should be observable experimentally.

DOI
10.1063/1.1655226

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Analytic description of distortionless propagation in a resonant absorbing medium with overlapping Q(j) transitions

Eugene Y. C. Lu, L. E. Wood

Optics Communications•Feb 1, 1974•3 citations
We give arguments to show that distortionless propagation of zero-degree pulses is possible in an arbitrary degenerate resonant medium in agreement with recent experimental observation. In the case of overlapping Q (2) degeneracy, the analytic closed-form solution with zero area is given. The predicted pulse shape depends in the relative occupation of the degenerate levels and should be observable experimentally.
Experiments are described in which low-intensity laser pulses of zero area [∫−∞∞E(z,t) dt=0] are propagated through a degenerate resonantly absorbing medium with greatly reduced absorption. These pulses are constructed either electro-optically or by allowing a non-zero-degree pulse to evolve toward zero area by means of a resonant absorption and reradiation process. We observe the transmission of as much as 65% of the energy of such pulses through a resonant absorber which attenuates the same cw laser by e−αL, with αL ≈ 20.
Self-induced transparency effects are examined in an absorbing medium having degenerate optical transitions. Undistorted propagating light pulses exist under restrictive conditions for $j\ensuremath{\rightleftharpoons}j$ transitions (j>0j>0j>0) and for 0 \ensuremath{\rightleftharpoons} 1 and $\frac{1}{2}\ensuremath{\rightleftharpoons}\frac{3}{2}$. Pulses which propagate without energy loss for any transition ${j\ensuremath{\rightleftharpoons}j}^{\ensuremath{'}}$ also include zero-degree pulses defined as $\ensuremath{\int}\mathcal{E}(z,t)dt=0$.
We report on computer-generated solutions to the coupled matter-field equations which provide the first evidence for distortionless optical pulse propagation in an absorbing medium of three-level atoms. The associated phenomenon represents the three-level equivalent of self-induced transparency in two-level atoms. Results have application to the propagation of short, coherent optical pulses in a medium in which the atoms have two distinct transition frequencies in near resonance with the pulse carrier frequency. We relate in particular to the case of pulse propagation in a magnetically perturbed sodium vapor where the pulse carrier frequency is tuned near the frequencies of the well-known sodium DDD lines. Here we obtain particular solutions corresponding to three and five peak pulses with "areas" of approximately $6\ensuremath{\pi}$ and $10\ensuremath{\pi}$, respectively. The solutions are strongly supported by a number of analytical results. In particular, simple algebraic relations are found which give the populations of the levels in terms of the field variables.
The evolution of an electromagnetic wave with slowly varying polarization, which interacts resonantly with the medium formed by degenerate two-level atoms, is studied using the wave function approach under the conditions of electromagnetically induced transparency. It is shown that the amplitude of the wave field propagates at the velocity of light in such a medium. The equation obtained for the polarization parameter has a solution in the form of a simple wave. The breaking length is determined. It is shown that the velocity of propagation of polarization waves may be much smaller than the velocity of light. The proposed approach is common for two-level systems with an arbitrary degeneracy. The case of a system with Zeeman degeneracy is analyzed in detail. The dependence of the velocity of propagation of the polarization structure on the amplitude and polarization is determined for an arbitrary level degeneracy. The evolution of the polarization structure in such a medium is discussed.