Approximate Fokker-Planck equation for a single-mode laser driven by quadratic pump noise and quantum noise with cross-correlation between real and imaginary parts of noise

A single-mode laser noise model driven by quadratic pump noise and quantum noise with cross-correlation between the real and imaginary parts of the noises is proposed. The approximate Fokker-Planck equation (AFPE) of the model for the laser phase and the laser amplitude is derived. It is found that the laser phase is controlled intensively by the correlation between the real and imaginary parts of the pump noise and that of the quantum noise. The correlation between the real and imaginary parts of quantum noise {lambda}{sub q} tends to lead the laser phase to be locked at some values and the correlation between the real and imaginary parts of the pump noise {lambda}{sub p} tends to destroy or confine the laser phase lock. Quantitative results are presented and discussed in detail. As an important application of the above-mentioned results, we take a phase lock approximation to get a Langevin equation for the laser field amplitude and an AFPE of the laser intensity.