Distortionless propagation of optical pulses in a resonant medium

R. C. Harney

Joseph Hayden Higginbotham, Robert T. Deck, D. G. Ellis

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 $D$ 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.

Md. Aminul Islam Talukder

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

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.

Yury V. Kistenev, Alexander V. Shapovalov

Michael D. Crisp

A combined analytical and numerical analysis of the propagation of a step-function light pulse in a resonant medium is presented. It is found that the light pulse evolves into a steady-state amplitude-modulated wave train very closely approximated by the Jacobian elliptic function $\mathcal{E}=1.25 {\mathcal{E}}_{0}dn[(\frac{1}{\ensuremath{\tau}})(t\ensuremath{-}\frac{z}{V}); \ensuremath{\lambda}]$, where the modulus of the elliptic function $\ensuremath{\lambda}$ is equal to $\frac{4}{5}$ and ${\mathcal{E}}_{0}$ is the amplitude of the input pulse. This result is consistent with an earlier analysis which showed that the elliptic $\mathrm{dn}$ function represented one of two classes of functions which satisfy the equations of resonant-pulse propagation and correspond to the distortionless propagation of an amplitude-modulated wave train through an inhomogeneously broadened medium. Expressions for the period, velocity, and parameter $\ensuremath{\tau}$ of the elliptic function are found as functions of the intensity of the input pulse. The form of the steady-state wave train is found to be the same in either an attenuating or amplifying medium. It is found that the velocity of the pulse train becomes significantly less than the speed of light when the density of energy that can be stored in the resonant atoms becomes an appreciable fraction of the energy density of the electromagnetic field. The conditions necessary for observing the amplitude-modulated pulse train in gaseous S${\mathrm{F}}_{6}$ and Na vapor are discussed.