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Soviet Journal of Quantum Electronics

Superradiance and photon echo effects in the interaction of coherent optical pulses with inhomogeneously broadened systems

Sergey M. Zakharov, Edward A. Manykin

Published Feb 28, 1973• 2 citations
Publisher

Abstract

A theoretical analysis is given of the phenomena of superradiance and photon echo in the interaction of coherent light pulses with a resonant medium emitting inhomogeneously broadened lines. A delay of the superradiance signal is predicted. The properties of the response function of a two-level system and of the photon echo are considered.

DOI
10.1070/qe1973v003n02abeh004776

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A theoretical analysis is given of the phenomena of superradiance and photon echo in the interaction of coherent light pulses with a resonant medium emitting inhomogeneously broadened lines. A delay of the superradiance signal is predicted. The properties of the response function of a two-level system and of the photon echo are considered.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
The effect of two-pulse photon echoes at the complicated action on a two-level medium with large inhomogeneous broadening of supremely short and quasiresonant pulses is investigated. Two versions of the action sequence of both pulses are considered. It is shown that the temporal properties of the echo signal are depended largely on the action order of indicated pulses. The effect of suppression of the optical echoes in the both cases at the action on a medium of the supremely short zeroth 'area' pulse is predicted. The qualitative procedure of definition of the complicated echoes spatial properties has been proposed and applied. It is shown that in indicated cases the diagrams of the echo signal intensity direction are not so peaked as in the case of common light echo.
Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the local field effect, and the substrate dispersion are involved into analysis. For a certain intensity of incident pulses a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple responses to a double or triple pulse excitation is discussed.
Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the near dipole-dipole interaction, and the substrate dispersion are involved in analysis. Under certain intensity of incident pulses, a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple echoes to a double or triple pulse excitation in the presence ofnear dipole-dipole interaction is discussed.
A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.