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Temporal solitons are optical pulses that arise from the balance of negativegroup-velocity dispersion and self-phase modulation. For decades only quadraticdispersion was considered, with higher order dispersion thought of as anuisance. Following the recent reporting of pure-quartic solitons, we hereprovide experimental and numerical evidence for an infinite hierarchy ofsolitons that balance self-phase modulation and arbitrary negative pure,even-order dispersion. Specifically, we experimentally demonstrate theexistence of solitons with pure-sextic ($\beta_6$), -octic ($\beta_8$) and-decic ($\beta_{10}$) dispersion, limited only by the performance of ourcomponents, and show numerical evidence for the existence of solitons involvingpure $16^{\rm th}$ order dispersion. Phase-resolved temporal and spectralcharacterization reveals that these pulses, exhibit increasing spectralflatness with dispersion order. The measured energy-width scaling laws suggestdramatic advantages for ultrashort pulses. These results broaden thefundamental understanding of solitons and present new avenues to engineerultrafast pulses in nonlinear optics and its applications.

The interaction of Kerr nonlinearity with even-orders of dispersion: an infinite hierarchy of solitons