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Physical Review A

Comparison of statistical properties of two models for saturated laser-light amplifier

C. Bendjaballah, Guy Oliver

Published Dec 1, 1980• 8 citations
Publisher

Abstract

Two models of saturated coherent light amplifier are studied and compared from the statistical point of view. For one of the models the absorption process is not saturated. The first- and second-order moments of the photon distribution exhibit very different behaviors according to the considered model. The reduced second-order moment measuring the fluctuations becomes more important when the absorption process is not saturated.

DOI
10.1103/physreva.22.2726

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Two models of saturated coherent light amplifier are studied and compared from the statistical point of view. For one of the models the absorption process is not saturated. The first- and second-order moments of the photon distribution exhibit very different behaviors according to the considered model. The reduced second-order moment measuring the fluctuations becomes more important when the absorption process is not saturated.
A theory of a quantum amplifier based on two-photon transitions is presented. The model consists of an assemblage of atoms interacting with a single mode of the light field via two-photon absorption and emission. The treatment is quantum mechanical, and the emphasis is on the photon-statistical aspects of the problem. Difference-differential equations for the density matrix of the field mode are derived. The equations are solved for a special case. Differential equations for the expectation vaues of the number of photons and of the field amplitudes, and for their higher statistical moments, are also obtained. Approximate solutions for the average number of photons are found, and the effect of the amplification process on the statistical fluctuations of the number of photons and the field amplitudes is discussed. The results of this study suggest that such an amplifier does not have the coherence properties of a laser amplifier because it tends to increase the statistical fluctuations of the field.
Intensity fluctuation characteristics of amplified-spontaneous emission are found using intensity rate equations and the noise-amplifier approximation for saturation coupling between two and four competing modes. The existence of more than one mode leads to the retention of relatively large fluctuations in each mode even as the amplifier gain is saturated, an operating regime which by contrast has been shown to reduce significantly the fluctuations when only a single beam is present. The noise-amplifier approximation is found to be an adequate approximation of the effects of the spontaneous emission distributed along the length of a laser amplifier. The intensity fluctuations in all cases approach limiting distributions functions as the amplifier becomes heavily saturated. Characteristics of these limiting distributions are found for one, two, and four beams; for combinations of beams copropagating and counterpropagating; in the presence and absence of loss; for differences in gain; and for saturation of the sources due to high intensities.
In the work, analytic expressions describing the behaviour of a strongly saturated nonlinear optical amplifier are deduced. These expressions make possible the calculation of the mean and variance of the amplified light photon number. Results are compared with those obtained by the numerical resolution of the photon density matrix equation, and good accordance is observed in the strong saturation regime. The results numerically obtained enable us to make conclusions about the statistical fluctuations of the optical power at the nonlinear optical amplifer output.
The effects of two-photon absorption from a single beam of light on the statistical properties of the beam are considered. Simple expressions are obtained for the initial rates of change and limiting steady-state values of the mean photon number and degree of second-order coherence of the beam. The general time dependences of these properties of the light and of the complete photon probability distribution are evaluated for several initial types of beam. The physical significance of the results is described, and their relationship to calculations which use a classical representation of the light is discussed.
The light statistical dependence of stationary saturated two-photon transitions is discussed. While at low intensities, in comparison with light having a stable amplitude, Gaussian amplitude fluctuations of the exciting radiation are more effective in populating the excited resonant state, light with amplitude fluctuations is less effective in saturating a two-photon transition. The amplitude fluctuations are shown to wash out the resonance curves. While at low intensities the effective Stark shift (i.e. the maximum of the dispersion curve) is larger by a factor of three in light with Gaussian amplitude fluctuations compared with radiation of constant amplitude, this enhancement factor becomes intensity dependent with increasing intensity.