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Journal of the Optical Society of America B

Optical instabilities: new theories for colored-noise-driven laser instabilities

Peter Jung, Peter Hänggi A

Published May 1, 1988• 64 citations
Publisher

Abstract

Novel colored-noise theories for optical instabilities are presented and compared with conventional approaches. In contrast to the conventional approaches, valid for small noise correlation times only, these new theories allow for a description of moderate-to-strong noise color and are of relevance particularly for the dye-laser instability and noise-dithered ring-laser gyroscopes. The theories are applied to the dye-laser instability and optical bistability. For the dye laser we evaluate the stationary probability and the integral of the stationary intensity correlation function (relaxation time), which both compare favorably with exact numerical results. For optical bistability we present the stationary probability and the switching rates.

DOI
10.1364/josab.5.000979

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Novel colored-noise theories for optical instabilities are presented and compared with conventional approaches. In contrast to the conventional approaches, valid for small noise correlation times only, these new theories allow for a description of moderate-to-strong noise color and are of relevance particularly for the dye-laser instability and noise-dithered ring-laser gyroscopes. The theories are applied to the dye-laser instability and optical bistability. For the dye laser we evaluate the stationary probability and the integral of the stationary intensity correlation function (relaxation time), which both compare favorably with exact numerical results. For optical bistability we present the stationary probability and the switching rates.
Predictions for dye-laser intensity correlation functions of a stochastic model incorporating colored gain-noise fluctuations are discussed and compared with the predictions of the model incorporating loss-noise fluctuations. It is shown that differences between the two models are generally masked by the finite correlation time of the noise. Important differences are shown to exist well above threshold when the correlation time of the colored noise is of the same order or smaller than the cavity decay time. A new algorithm for the simulation of stochastic equations with colored noise is used and discussed.
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 intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times \ensuremath{\tau} larger than the deterministic relaxation time td{\mathit{t}}_{\mathit{d}}td​, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.
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.