Stochastic soliton quantization in mode-locked fibre laser

Soliton quantization is a natural, intrinsic and random consequence property of localized pulses in nonlinear systems. It is formed in the fiber laser in the form of dissipative solitons due to the gain competition between the solitons in the laser cavity. The observation of quantized separations between the solitons was predicted either due to the interaction between far separated solitons or due to the interaction between weakly overlapping pulses [1, 2]. It was first found experimentally in a nonlinear amplified loop mirror mode-locked fiber laser [3] and then in a nonlinear polarization rotation mode locking fiber laser [4, 5] with a requirement of high pump power of >400 mW. Here, we report for the first time the experimental demonstration of the stochastic temporal soliton quantization state regimes at a low range of the pump powers (∼41 mW) using a carbon nanotube's saturable absorber mode-locked fiber laser [6]. We found that the regimes and the total number of pulses in the cavity are highly sensitive to the pump power and the state of the polarization which could lead to several distinct regimes of pulse formation. However, for certain pumping powers which were 41 mW and specific orientation of the laser cavity polarization controller (PC), we observed pulse trains of several tenths of pulses as shown in the real-time spatiotemporal measurements in Fig. 1a. The pulse train consists of a stochastic quantized distribution with separation between pulses starting from about 3 ns to tenths of ps with a nonlinearly quantized separation, behaving between the localized soliton pulses as shown in Fg. 1b. The pulses are localized with a much broader temporal separation far from the main soliton pulse and condensed to a very narrow seperations nearer to it. By slightly increasing the pump power to ∼88 mW and varying the PC, we obtained the second order of the stochastic soliton which also have a quantized temporal distribution without any undesirable distribution of types or interactions between neighboring solitons along 5000 roundtrip pulse train. The quantized soliton, actually, has formed intrinsically in the form of dissipative solitons due to large binding soliton states.