Bidirectional Soliton Rain Dynamics Induced by Casimir-Like Interactions in a Graphene Mode-Locked Fiber Laser

We study experimentally and theoretically the interactions among ultrashort optical pulses in the soliton rain multiple-pulse dynamics of a fiber laser. The laser is mode locked by a graphene saturable absorber fabricated using the mechanical transfer technique. Dissipative optical solitons aggregate into pulse bunches that exhibit complex behavior, which includes acceleration and bidirectional motion in the moving reference frame. The drift speed and direction depend on the bunch size and relative location in the cavity, punctuated by abrupt changes under bunch collisions. We model the main effects using the recently proposed noise-mediated pulse interaction mechanism, and obtain a good agreement with experiments. This highlights the major role of long-range Casimir-like interactions over dynamical pattern formations within ultrafast lasers.

Figure 1

Experimental environment. (a) Bilayer graphene flake following transfer on the top of the fiber facet, covering the entire core, forming a graphene-based saturable absorber (scale bar $10\mu \mathrm{m}$). Inset: The same graphene flake before transfer, on top of PDMS (scale bar $20\mu \mathrm{m}$). (b) The ultrafast fiber laser setup, integrating the graphene saturable absorber (GSA). See text for abbreviations. (c) Autocorrelation trace, 1.1 ps wide and approximately hyperbolic-secant shaped (fit). (d) Optical spectrum, and (e) oscilloscope trace of the pulse train.

Figure 2

Experimental recording of accelerated soliton dynamics. (a) Slow time vs fast time plot, optical power color-coded. Color code chosen to create contrast among smaller bunches. The two strong peaks near the edges are the condensed soliton phase anchor repeated after one cavity roundtrip (76.5 ns). Trajectories exhibit bi-directional accelerated motion relative to the anchor. The red dashed lines mark the times of individual oscilloscope traces displayed in panels (b)–(e) from bottom to top, with an arrow on top of each pulse showing its relative direction of motion.

Figure 3

Analysis of accelerated pulse dynamics. (a) Simulation of pulse-bunch trajectories located to the right (blue curve) and left (red curve) of the stagnation point. A schematic illustration of NMI mechanism is overlaid, showing the pulse bunches in black and the gain level in orange (not to scale). The stagnation point is found where gain levels reach the gain value before the anchor (horizontal dashed line). (b) Typical experimental traces of pulse bunch trajectories, measured in the fast time scale, as a function of slow time evolution [extracted at different initial times from Fig. 2]. The slow time is relative to each initial motion start time (fluctuations in the trajectories at early slow times caused by pulse collisions).

Figure 4

Complex many-pulse trajectories, displayed as color-coded oscilloscope readout vs fast and slow times, comparing the experiments [left panels (a),(c)] with simulations [right panels (b),(d)]. Simulations are based on the NMI theory, assuming the annihilation of a fixed fraction of bunch energy during collisions. The anchor is positioned at the edges of the waveform. The pulses are marked either at zero slow time or at the time of their formation, with red or yellow points, respectively.