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Journal of Optoelectronics·laser

Dynamical Properties of a Single-mode Laser with Correlations Between Real and Imaginary Parts of Quantum Noise~*

Xie Chong-wei, Mei Dong-Cheng

Published Jan 1, 2004• 1 citation
OpenAlex

Abstract

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.

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With the linear approximation method, the intensity correlation function C(t) and normalized mean intensity fluctuation C(0) are calculated, which reflects dynamic properties of the laser. The time evolution of C(t) is discussed in a loss noise model of single mode laser system by pump noise and quantum noise with cross correlation real and imaginary parts. The influences on the time evolution of C(t) are analyzed from cross correlation coefficient between the real and imaginary of quantum noise λ q, intensities of the pump noise P and quantum noise Q, respectively. The time evolution of C(t) is a monotonous descending process, while the whole C(t) versus t curve falls down with noises intensity reducing and the cross correlation between real and imaginary parts of the quantum noise weakening, which shows that the great influence of the noises intensity and the cross correlation between real and imaginary parts of the quantum noise on the time evolution of C(t). When t increases, an extremum or three extrema appears in the C(t) versus λ q curve. Finally, the valid range for the linear approximation method is discussed.

Chinese Journal of Lasers•Jan 1, 2004•0 citations
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.
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).
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.
Adopting the linear approximation method, a loss model for a single-mode laser driven by pump noise and quantum noise whose real and imaginary parts are correlated is studied. We investigated the intensity correlation function, which describes the dynamic property of a laser and varies with time. Moreover, the valid range for the linear approximation method is obtained, and the effects of the intensities of the pump noise and quantum noise on the variance of the laser intensity, and the correlation coefficient between the real and imaginary parts of the quantum noise, are discussed in detail. We find that the valid range is extended in the case of small quantum noise and far form threshold, and it is the largest in the case of small quantum noise, far form threshold and no correlation between the real and imaginary parts of the quantum 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.
With the linear approximation method, the intensity correlation function C(t) and normalized mean intensity fluctuation C(0) are calculated, which reflects dynamic properties of the laser. The time evolution of C(t) is discussed in a loss noise model of single mode laser system by pump noise and quantum noise with cross correlation real and imaginary parts. The influences on the time evolution of C(t) are analyzed from cross correlation coefficient between the real and imaginary of quantum noise λ q, intensities of the pump noise P and quantum noise Q, respectively. The time evolution of C(t) is a monotonous descending process, while the whole C(t) versus t curve falls down with noises intensity reducing and the cross correlation between real and imaginary parts of the quantum noise weakening, which shows that the great influence of the noises intensity and the cross correlation between real and imaginary parts of the quantum noise on the time evolution of C(t). When t increases, an extremum or three extrema appears in the C(t) versus λ q curve. Finally, the valid range for the linear approximation method is discussed.