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Physical Review A

Steady-state analysis of strongly colored multiplicative noise in a dye laser

Ronald F. Fox, Rajarshi Roy

Published Feb 1, 1987• 124 citations
Publisher

Abstract

A new Langevin equation for dye-laser fluctuations below and near threshold is used to obtain the intensity distribution function in closed form. The effect of strongly colored multiplicative pump noise is incorporated by means of an ansatz of Hanggi et al. [Phys. Rev. A 32, 695 (1985)] for an effective diffusion coefficient at steady states. Excellent agreement with the measurements of Lett, Short, and Mandel [Phys. Rev. Lett. 52, 341 (1984)] is obtained.

DOI
10.1103/physreva.35.1838

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A new Langevin equation for dye-laser fluctuations below and near threshold is used to obtain the intensity distribution function in closed form. The effect of strongly colored multiplicative pump noise is incorporated by means of an ansatz of Hanggi et al. [Phys. Rev. A 32, 695 (1985)] for an effective diffusion coefficient at steady states. Excellent agreement with the measurements of Lett, Short, and Mandel [Phys. Rev. Lett. 52, 341 (1984)] is obtained.
The steady-state properties of a dye laser model with white quantum noise and strongly colored pump noise are investigated. An effective diffusion coefficient in the steady state is presented. Our coefficient differs from that of Fox and Roy [Phys. Rev. A 35, 1838 (1987)]. We compare our results with the measurements and simulations of Lett, Short, and Mandel [Phys. Rev. Lett. 52, 341 (1984)], and the results of Fox and Roy, respectively. We find that the quantum noise plays an important role in the steady-state analysis of laser fluctuations below and near threshold.
We carry out numerical simulations of the evolution and steady-state properties of a dye laser operating near resonance. The model we use is fully two dimensional (i.e., it includes the intensity and the phase of the radiation) and does not involve the usual low-intensity expansions commonly used in the literature. The equation for the complex electric field is driven by white additive noise (quantum fluctuations due to spontaneous emission) and by colored multiplicative noise (fluctuations of the gain parameter). We note that the simulations agree with the experimental results of Zhu, Yu, and Roy [Phys. Rev. A 34, 4333 (1986)] for parameter values used in their experiments. We compare the simulation results with predictions of the ``best Fokker-Planck equation'' (BFPE) for the steady-state distribution of the laser intensity and find remarkable quantitative agreement for large ranges of parameters values, even for values that are in principle beyond the range of validity of this equation. We conclude that the BFPE can be safely invoked to make predictions for this system.
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.
Recent theoretical analyses of the single-mode laser with colored-noise pump fluctuations have allowed the detailed prediction of the short-time behavior of the intensity autocorrelations of such a laser. In particular, a rounding off of the intensity correlation function on the time scale of the correlation time of the pump fluctuations has been predicted. We present results from experiments performed on a single-mode dye-laser system that clearly confirm these predictions. Numerical simulations of the laser Langevin equations including the colored-noise pump fluctuations are used to fit the experimental results.
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.