Stochastic Resonance in a Single-Mode Laser Driven by Pump Noise and Quantum Noise with Cross-Correlated Real and Imaginary Parts

We present an analytic investigation of the signal-to-noise ratio (SNR) by studying a signal modulated model of a single-mode laser system driven by pump noise and quantum noise with correlated real and imaginary parts, and find there is a maximum in the curve of the dependence of SNR upon the cross-correlation coefficient $\lambda_q$ between the real part and the imaginary part, i.e., stochastic resonance appears in the SNR vs. $\lambda _q$ curve. Moreover, when the SNR is at the maximum, the cross-correlation coefficient $\lambda_q = 0$, which is coincidentally at the minimum of the mean normalized intensity fluctuation. The influences on stochastic resonance by the intensities of the pump and the quantum noise, the amplitude of the modulation signal, and the net gain of the laser are also studied. Furthermore, in order to ensure that the results obtained in this paper is reliable, the valid range for the linear approximation method is discussed.