Transition between optical turbulence and dissipative solitons in a complex Ginzburg-Landau equation with quasi-cw noise

Noise-induced phase transition between chaos and ordered states plays an important role in the self-organization of dissipative structures. Here, we numerically simulate the phase transitions between statistically stationary regimes in a laser cavity by using a stochastic complex cubic-quintic Ginzburg-Landau equation with a phase-diffusion model. Depending on the linear and nonlinear gains, the dissipative system converges from the initial noise floor to different regimes, including continuous wave, phase turbulence, amplitude turbulence (AT), and stable soliton structure. Around the regime boundaries, we found that only certain phase noise can cause the instability of phase turbulence. The defects formed due to the noise will continue to spread out and self-organize to form AT or stabilize the soliton structure in the defect area. Our results are helpful in understanding the dynamics of the buildup of mode locking and noiselike pulses in passively mode-locked lasers.

Figure 1

Phase diagram of different dynamics regimes in parameter plane ($\delta ,\varepsilon$).

Figure 2

(a), (c) are the evolution of temporal intensity profile and spectrum of $P1$ in Fig. 1 ($\delta =0.9,\varepsilon =0.33$), respectively. (b), (d) are the time profile and corresponding spectrum of $z=1000$ and $z=5000$, respectively. (e) The cavity energy and the degree of coherence are a function of the propagation distance z.

Figure 3

Several typical round trips of the transition state from PT to AT. (a1)–(a5) are the time profiles of $z=2160$, 2195, 2198, 2245, and 2400, respectively. (b1)–(b5) are the corresponding phase profile, and (c1)–(c5) are the corresponding traces in ($\left|E\right|cos\psi {,}_{}^{}\left|E\right|sin\psi$) space, respectively.

Figure 4

(a), (b) are the temporal and spectrum evolution of $P2$ in Fig. 1, respectively. (c) The enlarged temporal domain of (a). (d) The XFROG traces during the formation of a new soliton. (e) The cavity energy and the degree of coherence.

Figure 5

Several typical round trips in the transition state from PT to the transition regime between AT and PS. (a1)–(a5) are the time profiles of $z=2570$, 2576, 2620, 2688, and 2710, respectively. (b1)–(b5) are the corresponding phase profiles, and (c1)–(c5) are the corresponding traces in ($\left|E\right|cos\psi {,}_{}^{}\left|E\right|sin\psi$) space, respectively.

Figure 6

(a), (c), (d) are the evolution of temporal intensity profile of $P3, P4$, and $P5$ in Fig. 1 ($\delta =0{,}_{}^{}\varepsilon =0.76$; $\delta =-0.41{,}_{}^{}\varepsilon =0.87$; $\delta =-0.3{,}_{}^{}\varepsilon =0.84$), respectively. (b), (d), (f) are the corresponding several typical round trips in the transition state from PT to stable states of (a), (b) and (c), respectively.