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IEEE Journal of Quantum Electronics

Statistics of laser intensity after passing through an amplifier with stochastic gain distributions

Jenn‐Hwan Tarng, Chuan Choong Yang

Published Jan 1, 1989• 1 citation
Publisher

Abstract

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.>

DOI
10.1109/3.42060

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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.>
We evaluate the average intensity and contrast of the output of a laser amplifier in which stochastic gain distributions exist. This situation occurs when turbulence flows are developed in a gas- or liquid-laser amplifier. The gain medium is assumed to be partially homogeneously broadened and slightly saturated and to consist of two-level atoms. In our computations, a plane wave is propagated through the gain medium with weak turbulences, under the assumption that the size of the first Fresnel zone is much smaller than the characteristic length of turbulences.
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.
We present calculations of the intensity smoothing of stochastic light by a semiconductor optical amplifier (SOA). We predict spectral changes of the light that are due to amplitude-to-phase coupling in the gain medium. The intensity smoothing of noisy optical signals with an SOA carries a penalty of spectral broadening (increased phase noise) that increases with increasing alpha parameter (linewidth enhancement factor). The spectral broadening also increases with increasing strength of the intensity fluctuations being smoothed.
It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δ ν = 1 + I ν 1 / I s Δ ν H for condition 2). Here, I v 1 and Is are the intensity of the large signal and the saturation intensity at the center frequency Vo, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.
It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δν = √1+Iν1 / IsΔνH for condition 2). Here, Iν1 and Is are the intensity of the large signal and the saturation intensity at the center frequency ν0, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.
The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The fundamental concern of this investigation is the spectral behavior of the radiation in the nonlinear regime; hence, the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. These expressions should be easily susceptible to detailed experimental observations. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed with some detail. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is extensively explored in several numerical examples. The connections of this study with the time-domain work of Risken and Nummedal, on self-pulsing in a ring-laser configuration, are clearly established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ("Raman-type terms"), and saturation phenomena. The predicted narrowing-rebroadening rate is compared with expressions found in previous literature.