Steady-state analysis of a single-mode laser with cross-correlation between the real and imaginary parts of pump noise

A gain laser model is investigated in consideration of colored quadratic pump noises term. Accordingly the cross-correlation coefficient λp between the real and imaginary parts of the pump noise is successfully introduced to the amplitude equation. We present a thorough discussion of how the noise cross-correlation intensity λp, measured as a new important parameter, determines the behaviors of the stationary intensity distribution Qst(I), the mean intensity 〈I〉, and variance λ2(0). The cross-correlation coefficient λp has a notable influence on the stationary intensity distribution and variance, however, when λp is changed, there is almost no difference in the mean intensity. If λp is assumed to be the different value (λp1,λp2), and they satisfy the formula λp12+λp22=1, the Qst(I)∼I curves and the λ2(0)∼a0 curves for λp1 and λp2 will overlap, respectively.