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Communications in Theoretical Physics

Analyses of Valid Range for the Linear Approximation in a Single-Mode Laser

Cheng Qing-Hua, Cao Li, Wang Jun, Wu Da-Jin

Published Sep 15, 2004• 5 citations
Publisher

Abstract

Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctuation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part and imaginary part are cross-correlated. We analyzed the valid range for the linear approximation method by studying the influences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities of the quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that the valid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker, the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal has smaller amplitude and higher frequency.

DOI
10.1088/0253-6102/42/3/365

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Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctuation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part and imaginary part are cross-correlated. We analyzed the valid range for the linear approximation method by studying the influences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities of the quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that the valid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker, the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal has smaller amplitude and higher frequency.
Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctu-ation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part andimaginary part are cross-correlated. We analyzed the valid range for thelinear approximation method by studying theinfluences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities ofthe quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that thevalid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker,the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal hassmaller amplitude and higher frequency.
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.
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.
On the basis of calculating the steady-state mean normalized intensity fluctuation of a signal-mode laser system driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, we analyze the influence of modulation signal, noise, and its correlation form on the statistical fluctuation of the laser system. We have found that when the amplitude of modulation signal weakens and its frequency quickens, the statistical fluctuation will reduce rapidly. The statistical fluctuation of the laser system can be restrained by reducing the intensity of pump noise and quantum noise. Moreover, with prolonging of colored cross-correlation time, the statistical fluctuation of laser system experiences a repeated changing process, that is, from decreasing to augmenting, then to decreasing, and finally to augmenting again. With the decreasing of the value of cross-correlation coefficient, the statistical fluctuation will decrease too. When the cross-correlation form between the real part and imaginary part of quantum noise is zero correlation, the statistical fluctuation of laser system has a minimum. Compared with the influence of intensity of pump noise, the influence of intensity of quantum noise on the statistical fluctuation is smaller.
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.
An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imaginary parts of quantum noise is considered. The Fokker–Planck equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that: (i) The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; (ii) The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; (iii) The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.