General Laser Intensity Langevin Equation in a Single-ModeLaser Model

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