Effects of cross-correlation between the real and imaginary parts of the quantum noise in a two-mode saturation laser system

A two-mode saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise is considered. The laser intensity Langevin equation and corresponding Fokker–Planck equation are derived by the phase-locking method. The effects of the cross-correlation strength λ between the real and imaginary parts of quantum noise and the cavity decay constant K   on the steady-state intensity distribution Q(I1,I2)Q(I1,I2), the mean light intensity 〈I〉〈I〉, the normalization autocorrelation λ11(0)λ11(0) and cross correlation λ12(0)λ12(0) are studied by numerical calculation. The results show that as λ   increases the Qs(I1,I2)Qs(I1,I2) show two extrema, and λ   almost does not affect the 〈I〉〈I〉, λ11(0)λ11(0) and λ12(0)λ12(0) when the laser system is operated far above threshold. Nevertheless, when the laser system is operated at and below threshold, λ   makes the curves of Qs(I1,I2)Qs(I1,I2) have the higher peak and drop faster. Furthermore, it enhances the deviation of λ11(0)λ11(0) and λ12(0)λ12(0) and lessens the mean light intensity 〈I〉〈I〉 when the laser system is operated at and below threshold.