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Physical Review A

Saturation effect in a laser at steady state

Shiqun Zhu, Jianping Yin

Published Apr 1, 1992• 19 citations
Publisher

Abstract

The saturation properties of a single-mode laser are fully taken into account. The analytic expressions of the mean, variance, and skewness of the steady-state laser intensity are calculated. Compared with third-order laser theory and with experimental measurements, good agreement is obtained on the variance of the intensity, but noticeable deviations occur in the mean and skewness when the laser is operated far above threshold.

DOI
10.1103/physreva.45.4969

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The saturation properties of a single-mode laser are fully taken into account. The analytic expressions of the mean, variance, and skewness of the steady-state laser intensity are calculated. Compared with third-order laser theory and with experimental measurements, good agreement is obtained on the variance of the intensity, but noticeable deviations occur in the mean and skewness when the laser is operated far above threshold.
We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker–Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that (i) the correlation strength λ of correlated noises always enhances the fluctuation of laser intensity; (ii) the correlation time τ of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.
The saturation effects in a single-mode laser with multiplicative white noise are investigated through a full saturation laser model. The corresponding Fokker-Planck equation is transformed to a radial Schr\"odinger equation and the intensity correlation time and effective eigenvalues are calculated. Compared with experimental measurements, excellent agreement is obtained and the cavity decay rate is also determined. Relatively large errors occur in the third-order theory and the measured data.
The steady-state fluctuations of an inhomogeneously broadened two-mode laser with both additive and multiplicative white noise are investigated theoretically. A Fokker-Planck equation of the intensity-distribution function is presented. Analytic expressions of the autocorrelation and cross correlation of the steady-state two-mode intensities are derived for equal pump parameters of the two modes. Large intensity fluctuations occur when the laser is operated below threshold. However, when the laser is operated far above threshold, there is almost no difference between the laser models with and without multiplicative noise.
We investigate the statistical properties of two single-mode dye-laser models—the colored-loss-noise model and the colored-gain-noise model. Analytic expressions of the probability, the mean and the variance of the steady-state laser intensity are obtained through the unified expansion theory [Phys. Rev. A43 (1991) 700]. By comparison we find that when the cavity decay rate for the electric field is large and the pump parameter is small, the differences of the results of the two laser models are small. Otherwise, the differences are large. And the correlation time of the noise has very obvious influence on the results of the two models.
The statistical properties of a homogeneously broadened ring laser with an injected signal are investigated and the normalized two-mode intensity auto- and cross-correlation functions are calculated by a full saturation laser theory with backscattering. The theoretical predictions are in good agreement with the experimental measurements. Further investigation reveals that the backscattering can reduce the fluctuations in the system while the full saturation effect plays a major role when the laser is operated above threshold. It is also quite important to notice that the injected signal can drive the weak mode from incoherent light to coherent light.