General laser intensity Langevin equation in a single-mode laser model

A two-dimensional single-mode laser model is investigated, with cross-correlations between the real and imaginary parts of the quantum noise as well as the pump noise. The general closed form of the laser intensity Langevin equation (GILE) is obtained under a stable locked phase resulting from the cross-correlation lambda (q) between the real and imaginary parts of the quantum noise. Because of the presence of a new term containing lambda (q), we can unify the two opposite intensity Langevin equations which correspond to the two special cases for \lambda (q)\ --> 0 and \lambda (q)\ --> 1 in the GILE. It is expected that the transient and stationary properties of the laser model can be changed qualitatively when lambda (q) varies.