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Modern Physics Letters B

THE RELAXATION TIME OF A SINGLE-MODE LASER SYSTEM DRIVEN BY PUMP AND QUANTUM NOISES WITH REAL AND IMAGINARY PARTS CORRELATED

BING WANG, Yongxin Tang, Yan Shao-ping, Jianqiu Zhang

Published Aug 30, 2009• 2 citations
Publisher

Abstract

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).

DOI
10.1142/s0217984909020722

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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.
Based on the Fokker-Planck description of a single-mode laser model with correlations between the real and imaginary parts of the quantum noise as well as the pump noise,the dynamical properties of the laser system were studied by using of the mean relaxation time approximation method.The intensity correlation function and the associated mean relaxation time were calculated.It is found that the presence of correlations between the real and imaginary parts of the quantum noise always slows down the relaxation of the light intensity fluctuation when the laser is operated over the threshold.
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.
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(r) and the associated relaxation time Tc in the case of a stable locked phase resulting from the cross-correlation λq 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 Tc increases as a function of |λq|. Thus the decay o[ intensity fluctuation becomes slower.
Using the linear approximation, we have studied the time evolution of intensity correlation function C ( t ) in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts. In the case of the pump noise with self-correlation time τ<<1, we find that the time evolution of C ( t ) varies with modulation signal frequency Ω , amplitude B and net gain a 0 . (i) As Ω increases, the time evolution of C ( t ) changes from monotonically descending to flat descending and finally to damply oscillating; (ii) as B increases, it changes from monotonically descending to maximal; (iii) as net gain a 0 increases, it changes repeatedly from monotonically descending to monotonically ascending and to maximal, finally to monotonically descending again. However, in the case of τ>>1, the time evolution of C ( t ) only exhibits a form of damping oscillation.