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IEEE Journal of Quantum Electronics

Noise properties of pulsed ruby laser amplifiers

I. J. D’Haenens, Concetto R. Giuliano

Published Dec 1, 1965• 5 citations
Publisher

Abstract

The spontaneous emission noise properties of a pair of pulsed ruby laser amplifiers have been studied. Absorption and scattering loss measurements coupled with gain measurements as a function of pump time gave a measure of the inversion attained in the amplifiers. The high inversions reached enabled the authors to overcome the inherent noisiness of a 3-level system by having N2considerably larger than(m_{2}/m_{1}) N_{1}. Total spontaneous emission power was measured at gain saturation for each amplifier. Comparison of the observed with the theoretically expected spontaneous noise power gave good agreement.

DOI
10.1109/jqe.1965.1072257

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The spontaneous emission noise properties of a pair of pulsed ruby laser amplifiers have been studied. Absorption and scattering loss measurements coupled with gain measurements as a function of pump time gave a measure of the inversion attained in the amplifiers. The high inversions reached enabled the authors to overcome the inherent noisiness of a 3-level system by having N2considerably larger than(m_{2}/m_{1}) N_{1}. Total spontaneous emission power was measured at gain saturation for each amplifier. Comparison of the observed with the theoretically expected spontaneous noise power gave good agreement.
We present a theoretical analysis and an experimental study of the statistical properties of the noise accompanying an optical pulse propagating in a nonlinear semiconductor optical amplifier. Several degrees of gain saturation corresponding to different levels of optical signal-to-noise ratios (OSNRs) are examined. We employ the Heun numerical procedure to ensure proper convergence to the Stratonovich solution of the multiplicative propagation equation. This algorithm takes also into account the effect of gain saturation due to the amplified spontaneous emission noise. Moreover, the multicanonical Monte Carlo algorithm is used to efficiently calculate the probability density functions (pdfs), including the tails, of the peak of a pulse which emerges at the output of a saturated semiconductor optical amplifier. The results are compared to the corresponding pdfs obtained in a linear amplification system (where the optical noise is additive and Gaussian) having the same gain and under identical OSNR levels. We demonstrate that the pdf of the saturated amplifier is shifted toward lower power levels and is narrower, or equivalently, the mean and variance for the saturated amplifier case are smaller. Also, the difference between the two configurations increases with the degree of gain saturation. The theoretical predictions are confirmed by a series of experiments in which the pdfs at the output of the linear amplification scheme and saturated semiconductor optical amplifier are measured for an optical pulse of /spl sim/ 70-ps duration.
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.
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A classical approach for treating the noise properties of spatially inhomogeneous laser amplifiers is presented. Based on the Green’s function method, the amplifier output is related to the input and the amplified spontaneous emission noise. By using the correlation properties of spatially distributed spontaneous emission, the amplifier noise variance is obtained in a rigorous way. Compared with the density operator method, this approach can easily take into account the influence of spatially inhomogeneous amplifier structures, such as in the case of erbium-doped fiber amplifiers and distributed-feedback semiconductor amplifiers. The results show that the canonical expression of noise variance is valid for any type of amplifier if one defines an effective gain and noise power density, which can be accurately calculated by this approach.
A theoretical study is presented of the gain and the noise spectra of laser amplifiers at pumping rates both above and below the oscillation threshold. The theory is valid for both class-A and class-B laser systems, where the decay rate of the collective atomic dipole moment greatly exceeds the decay rates of the atomic population inversion and the laser cavity. The gain and the noise properties are shown to be strongly influenced by a four-wave mixing of the signal and image frequencies via a modulation of the population inversion. Particular attention is paid to the residual noise flux that persists in the laser output above threshold and to the typical characteristics of a second-order phase transition displayed by the gain in the threshold region. The results for the above-threshold laser amplifier are compared with experimental measurements of both gain and noise for the argon-ion (class-A) and CO2{\mathrm{CO}}_{2}CO2​ (class-B) lasers. The signal-to-noise ratios for both heterodyne and direct-detection measurements are evaluated, and the conditions are determined under which optical amplification can lead to an enhancement of sensitivity.
We have measured the gain and statistical-noise properties of a weak probe beam amplified through two-beam coupling in atomic-potassium vapor for both the Rabi and stimulated Rayleigh gain features. The probe-beam gain was observed to be as large as 125 for the Rabi feature, whereas the gain was typically less than 2 for the Rayleigh feature. The rms noise at the Rabi gain feature was approximately three times greater than the ideal amplifier quantum-noise limit. For the Rayleigh gain feature, the rms noise was 12 to 15 times greater than the ideal amplifier quantum-noise limit. We present a fully quantum-mechanical theory of two-beam coupling in a system of two-level atoms which includes the effects of atomic motion and pump-beam absorption. The predictions of this theory are in good agreement with the experimental data. \textcopyright{} 1996 The American Physical Society.