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Physica Scripta

Intensity correlation function and relaxation time of a single-mode laser driven by quadratic pump noise and quantum noise

You-Lin Xiang, Dong-Cheng Mei

Published May 21, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0031-8949/77/06/065003

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Based on the Fokker–Planck description of a single-mode laser system and the projection operator method, the mean relaxation time T of a single-mode laser system with correlations between the real and imaginary parts of the quantum noise as well as the pump noise is studied. It is found that the mean relaxation time T increases with the increasing net gain a0 and decreases with the increasing self-saturation coefficient A. T increases with the increasing pump noise strength Q but decreases with the increasing quantum noise strength D. The mean relaxation time T increases (decreases) with the increasing pump noise self-correlation time τ if a0 > 0 (a0 < 0). T decreases with the increasing |λ| (λ is the coefficient of cross-correlation between the real and imaginary parts of the quantum noise).
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.
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.
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.
Treated at the quantum noise of the real and imaginary parts of crosscorrection and saturation laser mode,an analysis of the intensity correlation function and the associated relaxation time is made in the case of a stable locked phase resulting from the cross-correlation between the real and imaginary parts of 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 increases as a function of.Thus the decay of intensity fluctuation becomes slow.