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Physical Review Letters

Effects of Degeneracy on Self-Induced Transparency

G. J. Salamo, H. M. Gibbs, G. G. Churchill

Published Jul 29, 1974• 38 citations
Publisher

Abstract

The effects of degeneracy on self-induced transparency (SIT) have been studied using optical pulses gated from a cw dye laser and four different degenerate systems in Na. Delays, nonlinear transmission, peaking, and breakup were altered only slightly by degeneracy. This unexpected insensitivity to degeneracy of SIT features is in agreement with the McCall-Hahn pulse-area, pulse-energy description, computer simulations, and a simple physical explanation of general applicability.

DOI
10.1103/physrevlett.33.273

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The effects of degeneracy on self-induced transparency (SIT) have been studied using optical pulses gated from a cw dye laser and four different degenerate systems in Na. Delays, nonlinear transmission, peaking, and breakup were altered only slightly by degeneracy. This unexpected insensitivity to degeneracy of SIT features is in agreement with the McCall-Hahn pulse-area, pulse-energy description, computer simulations, and a simple physical explanation of general applicability.
A review is given of the current status of the self-induced transparency effect. The McCall–Hahn theory (2π pulses) is considered and its generalization to the case of phase modulation of radiation pulses, degeneracy of transitions, and two-photon resonance is discussed. The relationship with the theory of nonlinear waves, obeying the Korteweg–de Vries equation, is pointed out. The possibility of similar coherent effects in direct interband transitions in semiconductors is discussed. A summary is given of the experimental results demonstrating a strong fall in the absorption and a considerable slowing down of light pulses, typical of the self-induced transparency. Possible physical applications of the effect, based on these properties, are discussed.
Self-induced transparency (SIT) has been observed under the conditions of sharp-line absorption, i.e., with an inhomogeneous absorption width only one-fourth the spectral width of the pulse. A 5-nsec pulse from a 202Hg^{202}\mathrm{Hg}202Hg ii laser intersected perpendicularly an atomic beam of natural rubidium. The beam slits reduced the Doppler absorption width to about 30 MHz. A particular resolved MI{M}_{\mathrm{I}}MI​ transition of 85Rb^{85}\mathrm{Rb}85Rb was scanned into coincidence with the laser pulse by a 75-KOe magnetic field. With peak absorption depths of 3-6, nonlinear transmission, pulse delays, pulse breakup, and peak amplification were seen and found to be in excellent agreement with sharp-line computer solutions of the Maxwell-Bloch equations. The experimental realization of the sharp-line SIT is of interest because analytical formulas for pulse evolutions are more plentiful and because sharp-line SIT might permit compression of picosecond pulses.
Self-induced transparency has been studied in detail experimentally for a simple two-level atomic absorption. A Hg II laser pulse is used at resonance with the D1{D}_{1}D1​ line of Rb. This system eliminates many previous experimental problems such as nonuniform wave fronts and degenerate off-resonant absorbers. Nonlinear transmission, pulse delays, pulse breakup, peak amplification, incoherent-decay effects, off-resonance effects, and focusing effects have been observed. Quantitative comparison with theory is obtained by computer solutions which include the incoherent decay and optical-pulse shapes of the Hg-Rb system. Good agreement is obtained with the theory of McCall and Hahn. Pulse compression by an order of magnitude is obtained by focusing in the resonant absorber. The theory predicting preferred pulse widths and velocities proposed by Davidovich and Eberly is discussed and found inappropriate for the Hg-Rb and other similar systems.
The influence of degeneracy on coherent pulse propagation in an inhomogeneously broadened attenuator is examined by computer calculations, and the connection with self-induced transparency in a nondegenerate system is described. Specific modifications that arise in a degenerate system are the development of pulse shapes characteristic of the degeneracy, the association of a finite loss with propagation, a reduction of pulse delay times, and the suppression of pulse separation of multi-$2\ensuremath{\pi}$ pulses. Additionally, results of calculations pertaining to experiments on pulse propagation in SF6{\mathrm{F}}_{6}F6​ are presented which indicate two basically different phenomena. One corresponds to delay phenomena qualitatively similar to nondegenerate self-induced transparency, while the other is a coherent saturation effect generally characteristic of degenerate media. The computed results fully substantiate our earlier experimental findings.
Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the $^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}$, $F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ and $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area---pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.
Two types of nonlinear transmission of light pulses associated with phase modulation are observed in experiments connected with self-induced transparency (SIT) in ruby. Anomalous pulse-power transmission is observed to be an order of magnitude greater than linear transmission during the condition of zero-area pulse propagation, where the inhomogeneous line spectral width is greater than the applied pulse spectral width. For application of a pulse off-resonance by the order of a linewidth, nonlinear transmission occurs in which a type of "precursor" phase-modulated signal appears ahead of a developing SIT pulse. The precursor pulse velocity is greater than the SIT pulse velocity, but less than the background velocity of light in the medium.