Nonlinear phase shift of solitons with pulse duration spanning four orders under a period-doubling bifurcation

Following the soliton area theorem, solitons with pulse durations from hundreds of femtoseconds to tens of nanoseconds could be achieved by applying different anomalous dispersion in the open part of a fiber laser while fixing the fiber segments. By increasing the pump power represented by the small-signal gain, period-doubling bifurcation of solitons with pulse durations of femtosecond, picosecond, and nanosecond is realized, respectively. The nonlinear phase shift of a pulse, when the pulse propagates along the cavity, is retrieved to represent the amplitude of the cavity nonlinearity. The threshold effect for the appearance of period-doubling bifurcation is directly confirmed by the change of nonlinear phase shift based on solitons with pulse duration of either femtosecond, picosecond, or nanosecond. The threshold of the nonlinear phase shift of the femtosecond soliton and that of the picosecond soliton are close. However, when the soliton pulse duration is in the range of nanosecond, a much smaller nonlinear phase shift is required for the appearance of period-doubling bifurcation compared with femtosecond/picosecond solitons. Thresholds for the appearance of period-quadrupling and period-octupling are demonstrated as well.