Narrow Results

Based on the single-mode laser noise model driven by quadratic colored pump noise and quantum noise with cross-correlation between real and imaginary parts of noise proposed in International Journal of Modern Physics B20, 5383 (2006) and Phys. Rev. E 73, 023802 (2006), the stochastic resonance (SR) of laser intensity is investigated by virtue of the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ_p and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency for the model. It is shown that there are three different types of SR in the model: the conventional form of SR, the SR in the broad sense and the bona fide SR.

The output power and the signal-to-noise ratio (SNR) of a single-mode laser system are calculated in the case of the laser model with periodically modulated noise. The corresponding stochastic resonance (SR) phenomena are discussed and compared with the case without periodically modulated noise. It is shown that the main difference between the two noise laser models exists in the SNR as a function of signal period. There appears resonance and suppression coexisting phenomenon for the model with periodically modulated noise, which can be utilized to restrain or optimize the output SNR of the system. Whereas, SR is absent for the model without periodically modulated noise, and the SNR just increases monotonously with signal period.

Using linear approximation method, we calculate the intensity correlation time of a single-mode laser driven by both colored pump noise with signal modulation and quantum noise with cross-correlation between its real and imaginary parts, and analyze the influence of the signal, noise and its cross-correlation form on the statistical fluctuation of the laser system. We detect that the "color" of pump noise is an important factor that affects the statistical fluctuation of the laser system. When the colored pump noise is short time correlation, within a determinate parameter range, the intensity correlation time can be prolonged, and the statistical fluctuation of the laser system can be restrained by increasing the amplitude of modulation signal. The specific frequency of input signal will result in intensity correlation time to appear maximum, and the statistical fluctuation of the laser system is least here. When the colored pump noise is long time correlation, within a determinate parameter range, the intensity correlation time can be also prolonged by increasing the frequency of modulation signal and decreasing its amplitude, and the statistical fluctuation of the laser system will decrease. In particular, when the intensity of quantum noise increases and the cross-correlation between its real and imaginary parts enhance, the intensity correlation time will prolong, and the statistical fluctuation of the laser system is restrained.

The effects of the correlations between real and imaginary parts of the quadratic pump noise on the normalized intensity correlation function and the associated relaxation time of a single-mode laser model were investigated. The expressions of the intensity correlation function C(s) and the relaxation time T_c were derived. Based on numerical computations, we found that T_c monotonously increases as the strength λ_p of correlation between the real and imaginary parts of quadratic pump noise increases and the larger λ_p value is, the slower C(s) decays. The presence of correlations between the real and imaginary parts of the quadratic pump noise causes the intensity fluctuation to increase.

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).