Time evolution of the intensity correlation function in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts

Using the linear approximation, we have studied the time evolution of intensity correlation function C(t) in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts. In the case of the pump noise with self-correlation time τ<<1, we find that the time evolution of C(t) varies with modulation signal frequency Ω, amplitude B and net gain a₀. (i) As Ω increases, the time evolution of C(t) changes from monotonically descending to flat descending and finally to damply oscillating; (ii) as B increases, it changes from monotonically descending to maximal; (iii) as net gain a₀ increases, it changes repeatedly from monotonically descending to monotonically ascending and to maximal, finally to monotonically descending again. However, in the case of τ>>1, the time evolution of C(t) only exhibits a form of damping oscillation.