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Physical Review A

Amplified-spontaneous-emission intensity fluctuations

N. B. Abraham, John C. Huang, David A. Kranz, Edward B. Rockower

Published Nov 1, 1981• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.24.2556

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Statistical moments of laser intensity passing through an amplifier with stochastic gain are evaluated. This situation happens when turbulent flows exist in the gain medium, which is assumed to be a two-level atomic system. Also, it is assumed that the turbulence structure is fully characterized by a stochastic process. This gain medium is assumed to be partially homogeneously broadened and slightly saturated. In the derivations, the paraxial approximation is combined with the perturbation method to solve for the random laser field inside the amplifier. For mathematical simplicity, a plane wave is propagated through the gain medium which contains only weak turbulence fluctuations. Dependences of the average laser intensity and contrast on turbulence fluctuation strength, characteristic length of the turbulence, and gain saturation and numerically demonstrated. It is found that the turbulence fluctuations make both average intensity and contrast stronger. Also, the gain saturation reduces both average intensity and contrast. In addition, it is shown that the contrast increases as the characteristic length of turbulence is increased.>

IEEE Journal of Quantum Electronics•Jan 1, 1989•1 citation
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 an optical amplifier, when the gain is non-linear due to gain saturation, the intensity fluctuation statistics are significantly altered from the statistics of the negative-exponential intensity probability distribution function (IPDF) for spontaneous emission and unsaturated amplifiers. We have systematically computed bivariate moments, trivariate moments and central moments, tetravariate moments, as well as bivariate and trivariate cumulants of intensity fluctuations for non-linear coupled-mode optical systems starting from a k -variable multivariate IPDF of a system of n ( k < n ) coupled modes. The multivariate IPDF is a negative polynomial that rests on the assumption that the variation of intensity has a maximum-intensity distribution with the constraint that the total intensity is constant. The assumption holds for multimode optical systems including a thin, long, mirrorless, gas laser where under heavy gain saturation the output tends to become constant although the intensity of any mode displays rapid fluctuations about the average intensity. The multivariate IPDF reduces to the negative-exponential IPDF of spontaneous emission when n is infinite, as expected. The new results for the multivariate characteristics of the intensity fluctuations have shown characteristic signatures that depend on the number of interacting modes, n . The results are also useful for testing the multivariate IPDFs and identifying n for heavily saturated coupled-mode optical systems.
The intensity fluctuations in the output of a saturable optical amplifier are studied as the amplifier length is increased. Characteristics are determined by calculation of the diagonal elements of the density matrix of the optical field. Saturation affecting both upper-state and lower-state atomic populations is considered. Spontaneous emission distributed along the amplifier causes the "photon-number" distribution to approach a Bose-Einstein distribution during linear amplification if the input field is not Bose-Einstein. The onset of saturation reduces the relative fluctuations of the optical field both by introducing nonlinear gain and by reducing the spontaneous emission. Limiting solutions show that strong saturation leads to a major reduction in the fluctuations causing the photon-number distribution to approach a Poisson distribution.
Spontaneous emission from incoherently excited atoms has a negative exponential intensity probability distribution function (IPDF) In an optical amplifier when the gam is non-lincar (due to gam saturation), the intensity lluctuation statistics is sigmllcanlly altered from that of spontaneous emission as is evidenced by experimental results We have derived the expressions for (i) univariate cumulants of intensity lluctuations up to tenth order from a single mode IPDF and (ii) bi\ariate moments of intensity fluctuations up to fifth order starting from a bivariate IPDF 3'he IPDFs arc negative polynomials (whose powers depend on the number of interactive modes), which rest on the assumption that the variation of intensity has a maximum entropy distribution with the constraint that the total intensity is constant This approximation holds for a heavily saturated source of amplified spontaneous emission (ASI-) and some other coupled-mode optical systems Both the normalized cumulants and bivariate moments have shown unique features that depend only on the number of interacting modes m the system The theoretical results have been compared with the experimental ones for ASH The comparison is useful to lest the model and to identify the number of interacting modes m coupled-mode optical systems Keywords Amplified spontaneous emission, coupled-mode optical systems, univariate cumulants and bivariate moments PAC^S Nos.42 50 Ar, 02 70 --c
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
Statistical moments of laser intensity passing through an amplifier with stochastic gain are evaluated. This situation happens when turbulent flows exist in the gain medium, which is assumed to be a two-level atomic system. Also, it is assumed that the turbulence structure is fully characterized by a stochastic process. This gain medium is assumed to be partially homogeneously broadened and slightly saturated. In the derivations, the paraxial approximation is combined with the perturbation method to solve for the random laser field inside the amplifier. For mathematical simplicity, a plane wave is propagated through the gain medium which contains only weak turbulence fluctuations. Dependences of the average laser intensity and contrast on turbulence fluctuation strength, characteristic length of the turbulence, and gain saturation and numerically demonstrated. It is found that the turbulence fluctuations make both average intensity and contrast stronger. Also, the gain saturation reduces both average intensity and contrast. In addition, it is shown that the contrast increases as the characteristic length of turbulence is increased.>