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Period doubling is a universal bifurcation of central importance in alldisciplines of nonlinear science, which generally signals the existence ofchaotic dynamics in the vicinity of the system parameters. Although observed indiverse ultrafast laser configurations, there is still no consensus on itsphysical origin. The observations also include other types of pulsatingdissipative solitons, with either short or long periods. Real time spectralcharacterization allows to investigate optical spectral oscillations, whosefeatures reveal the intracavity dynamics leading to instabilities. Following acontextual review, this article presents a variety of period doubling dynamicsmanifesting in the spectral domain of dissipative solitons. These dynamics areobtained with ultrafast fiber lasers featuring either anomalous or normaldispersion. It reveals a sequence of period doubling bifurcations andinstabilities within transient dynamics, unveiling intertwined bifurcations andthe entrainment of new pulsating frequencies. The oscillating frequencies tendto lock to the integral of roundtrip numbers as well as coexist with perioddoubling, demonstrating new combinations of the period doubling bifurcationwith other bifurcations. These experimental findings are confirmed by numericalsimulations, emphasizing both the universality of the period doublingbifurcations and their potentially highly complicated manifestations withinultrafast laser systems.

Spectral pulsations of dissipative solitons in ultrafast fiber lasers: period doubling and beyond