Steady-State Analysis of a Single-Mode Laser Driven by ColoredPump Noise with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ_q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Q_st(I), the mean 〈I〉, and the variance λ₂(0) of the laser intensity. It is shown thatcross-correlation intensity λ_q of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠0), improving the pump parameters monotonously will make the curves of Q_st(I) exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λ_q and τ when thelaser is operated near or below threshold. Especially when τ≠0, the heights of the peaks of the curves ofλ₂(0)-a₀ and λ₃(0)-a₀, (here a₀ is the net gain coefficient) go up asλ_q increases. However the entire curves of λ₂(0)-a₀ and λ₃(0)-a₀ are abruptly suppressed when λ_q=1, in similarity to phase transition of stationaryintensity distribution.