Spectral period doubling and encoding of dissipative optical solitons via gain control

Period-doubling bifurcation, as an intermediate state between order and chaos, is ubiquitous in all disciplines of nonlinear science. However, previous experimental observations of period doubling in ultrafast fiber lasers are mainly restricted to self-sustained steady state, controllable manipulation and dynamic switching between period doubling and other intriguing dynamical states are still largely unexplored. Here, we propose to expand the vision of dissipative soliton periodic doubling, which we illustrate experimentally by reporting original spontaneous, collisional, and controllable spectral period doubling in a polarization-maintaining ultrafast fiber laser. Specifically, the spontaneous period doubling can be observed in both single- and double-pulses. The mechanism of the switchable state and periodic doubling was revealed by numerical simulation. Moreover, state transformation of individual solitons can be resolved during the collision of triple solitons involving stationary, oscillating, and period doubling. Further, controllable deterministic switching between period doubling and other dynamical states, as well as exemplifying the application of period-doubling-based digital encoding, is achieved under programmable pump modulation. Our results open a new window for unveiling complex Hopf bifurcation in dissipative systems and bring useful insights into nonlinear science and applications.