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

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