Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times

We study a system for a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation. The analytical expression of the stationary intensity distribution (SID) for the laser is derived in the case of three different correlation times. The influences of each stochastic parameter on the SID are discussed, the effects of the noise "colour" and the cross-correlation of noises on the mean intensity , the variance, λ_2(0), and the skewness,λ_3(0) of the single-mode laser are investigated. We find that there are colourful phase transitions for the SID above a threshold, and re-entrant transitions induced by the "colour" of the additive noises. Further research of the curves of -τ_i, λ_2(0)-τ_i, and λ_3(0)-τ_i (i=1,2,3) (where τ_i is the correlation time) shows that the output intensity not only increases with the additive noise correlation time τ_2 and the cross-correlation time τ_3, but also the quality of the output of laser beams is optimized.     

Stochastic Multiresonance for Periodically Modulated Noise in a Single—Mode Laser

Multiplicatively introducing the noise and the signM into the gain-noise model of a single-mode laser system, we detect the two forms of stochastic resonance (the single-peak form stochastic resonance and stochastic multiresonance) in the curve of the dependence of signal-to-noise ratio upon the noise correlation time. Moreover, when the correlation coefficient and the intensities of both noises are changed, the two forms of stochastic resonance alternate.     

THE TRANSITION RATE OF A DOUBLE WELL SYSTEM DRIVEN BY CROSS-CORRELATED NOISES

The transition rate of a double well system driven by cross-correlated noises has been investigated, in when the correlation times between the noises are nonzero. From numerical computation, we find followings: (1) The transition rate decreases as the ,λ(λ is the strength of the correlations between noises) increases. (2) The transition rate increases as the τ(τ is the correlation time between noises) increases. It imglies that τ and λ play opposite roles in the transition rate of the system (3). For the case of perfectly correlated noises (λ= 1), there is no the suppressed phenomenon in the double well system with cross-correlated noise sources.     

Intensity Correlation Time of a Single-Mode Laser Driven by Two Coloured Noises with Coloured Cross-Correlation with Bias Signal Modulation

The intensity correlation time T is studied by employing a gain-noise model of a single-mode laser driven by coloured pump noise τ1 and coloured quantum noise τ2 with coloured cross-correlation τ3 with a bias signal modulation. By using the linear approximation method, we detect that a maximum （i.e. resonance） exists in the curves of the intensity correlation time T versus the noise intensities D and Q when the noise correlation coefficient A is positive; and a minimum （i.e. suppression） exists in the T - D and T - Q curves when A is negative. When A is zero, T increases monotonously with increase of D and decreases monotonically with increase of Q. Furthermore, the curve of T versus the pump noise self-correlation time τ1 is also studied. Our study shows that, no matter what the value of A is, there exist one maximum and one minimum in the T - τ1 curve.     

Influences of quantum noises on direct-modulated properties of 1.3-μm InGaAsP/InP laser diodes

Due to the zero dispersion point at 1.3μm in optical fibres, 1.3-μm InGaAsP/InP laser diodes have become main light sources in fibre communication systems recently. Influences of quantum noises on direct-modulated properties of single-mode 1.3-μm InGaAsP/InP laser diodes are investigated in this article. Considering the carrier and photon noises and the cross-correlation between the two noises, the power spectrum of the photon density and the signal-to-noise ratio (SNR) of the direct-modulated single-mode laser system are calculated using the linear approximation method. We find that the stochastic resonance (SR) always appears in the dependence of the SNR on the bias current density, and is strongly affected by the cross-correlation coefficient between the carrier and photon noises, the frequency of modulation signal, and the photon lifetime in the laser cavity. Hence, it is promising to use the SR mechanism to enhance the SNR of direct-modulated InGaAsP/InP laser diodes and improve the quality of optical fibre communication systems.     

Influence of the net gain on characteristic of stochastic resonance in a single-mode laser system

The phenomenon of stochastic resonance (SR) is found in a single-mode laser system driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. When the net gain a0 changes, it is found that, 1) the shape of the curve of the signal-to-noise ratio (SNR) versus the pump noise self-correlation time τ exhibits a changing process of multiform SR, from single-peak SR, to simultaneous existence of resonances and suppressions; 2) the curve of SNR. versus signal frequency Ω experiences a complicated changing process from the monotonous descending to the simultaneous appearances of a maximum and a minimum, and finally to monotonous descending; 3) the curve of SNR versus cross-correlation coefficient between the real and imaginary parts of the quantum noise λq appears an acute single-peak SR. Therefore, the net gain ao greatly influences the characteristic of SR of laser system.     

STATIONARY PROBABILITY DISTRIBUTION FOR COLORED-LOSS-NOISE MODEL OF A SINGLE-MODE DYE LASER

We apply the interpolation procedure to calculate the stationary probability distribution of the colored-loss-noise model of a single-mode dye laser operating above the threshold with correlation time τ covering a very wide range. By stochastic Runge-Kutta algorithm, we also carry out numerical simulations of steady-state properties. Comparing the results of the interpolation procedure and the unified colored-noise approximation with simulation results, we find that the agreement between the results of the interpolation procedure and the simulation results is much better than that of the unified colored-noise approximation when correlation time τ covers a range from moderate to large. We conclude that the interpolation procedure really improve the accuracy of predictions for this system.     

Stochastic resonance of bias signal-modulated noise in a single-mode laser＊

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.