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Chinese Physics

Statistical fluctuations in a saturation laser model with correlated noises

Shibo Chen, Mei Dong-Cheng

Published Nov 2, 2006• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/15/12/016

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We consider a single-mode laser model driven by correlated quantum and pump noise and study the effects of the cross correlation time τ between noises on the steady-state intensity correlation function and the associated relaxation time. Based on an approximated Fokker–Planck description of the laser model and the Stratonovich-like ansatz, we find the steady-state probability distribution function P st ( I ), the steady-state intensity correlation function K ( s ) and the associated relaxation time T . From numerical computations we found the following: (1) τ suppresses the fluctuation of the laser intensity for the case of positively correlated noises (i.e. the correlation strength between noises λ > 0) and increases the intensity fluctuation for the case of negatively correlated noises (λ > 0); (2) τ slows down the decay of the intensity correlation for the case of λ > 0 but speeds up the decay for the case of λ < 0. The effects of τ on P st ( I ), K ( s ) and T are entirely opposite for λ < 0 and for λ > 0.
This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C(τ) and the associated relaxation time T (C) in the case of a stable locked phase resulting from the cross-correlation λ q between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.
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 study the effects of correlations between real and imaginary parts of pump noise on the correlation function and relaxation time of laser intensity in a saturation laser model driven by quadratic pump noise and quantum noise. Using the phase–locking method and the projection–operator method, we derived the stationary probability density, the relaxation time Tc and the intensity correlation function C(s) of the laser intensity, and then performing numerical computations, we find the following: (i) Tc monotonously increases as the correlation strength between the real and imaginary parts of quadratic pump noise λp increases and (ii) C(s) decreases exponentially as decay time s increases and C(s) increases as λp increases. The correlations between the real and imaginary parts of the quadratic pump noise slow down the rate of fluctuation decay of the laser intensity.
We study the effects of correlations between the real and imaginary parts of quantum noise on the intensity fluctuation for a single-mode laser. The analytic expressions of the intensity correlation function C (τ) and the associated relaxation time T c in the case of a stable locked phase resulting from the cross-correlation λ q between the real and imaginary parts of quantum noise are derived by means of projection operator method. Based on numerical computations it is found that the presence of cross-correlations between the real and imaginary parts of quantum noise causes the intensity fluctuation to increase. A slowing-down phenomenon exists in the sense that T c increases as a function of |λ q |. Thus the decay of intensity fluctuation becomes slower.