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Quantum Electronics

Cooperative self-diffraction in an optical cavity

Anatolii V Andreev, Mikhail V. Fedotov

Published Jan 31, 1993• 6 citations
Publisher

Abstract

The dynamics of the cooperative decay of an excited system of two-level radiators is analyzed for the case of self-diffraction of counterpropagating waves by a light-induced population grating.
DOI
10.1070/qe1993v023n01abeh002940

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We discuss from first principles the cooperative decay of a system of two-level atoms, initially prepared in an uncorrelated excited state with population inversion NNN, and we give the conditions under which the superfluorescence effect occurs. Describing the atomic system in terms of collective variables, we derive a master equation for the reduced atomic density operator, which gives rise both to a damping and to a time-dependent frequency shift in the dynamics of collective modes. The coupled equations of motion are solved with a self-consistent approach. It is found that the system goes through a nonexponential decay if the maximum length of the active volume is smaller than a "cooperation range" and larger than a "threshold length," in agreement with the one-mode theory. The radiation burst has a time width proportional to ${N}^{\ensuremath{-}1}$, and its intensity is proportional to N2{N}^{2}N2. Specializing to a pencil-shaped volume, we find that only two atomic modes need to be considered; in this case, the average emitted radiation is all condensed in the two diffraction patterns of the opposite axial modes.
We present a nonperturbative theory of self-diffraction in thick, pseudostationary population gratings induced by the interference of two nearly collinear incident laser beams of arbitrary relative and absolute intensities. At large saturation parameters, the grating becomes nonsinusoidal, and high-order diffraction occurs efficiently. We obtain an exact expression for the Fourier coefficients of the grating that significantly simplifies the interpretation of the various coherent coupling mechanisms and permits efficient computer simulations. In the case of small depletion of the pump waves, we obtain simple analytic expressions for the scattered intensity into any order of self-diffraction. We present our results in a manner that should aid an experimenter in choosing the optical thickness of the unsaturated medium and the sum and ratio of the pump intensities to obtain optimum diffraction intensity in a given order.