  The generation of ultrashort pulses hinges on the careful management of
dispersion. Traditionally, this has exclusively involved second-order
dispersion, while higher-order dispersion was treated as a nuisance to be
minimized. Here we show that high-order dispersion can be strategically
leveraged to access an uncharted regime of ultrafast laser operation. In
particular, we demonstrate a mode-locked laser, with an intra-cavity spectral
pulse-shaper, that emits pure-quartic soliton pulses, which arise from the
interaction of the fourth-order dispersion and the Kerr nonlinearity. Using
phase-resolved measurements we demonstrate that the energy of these pulses is
proportional to the third power of the inverse pulse duration. This implies a
dramatic increase in the energy of ultrashort pulses compared to those emitted
by soliton lasers to date. These results not only demonstrate a novel approach
to ultrafast lasers, but more fundamentally, they clarify the use of
higher-order dispersion for optical pulse control, opening up a plethora of
possibilities in nonlinear optics and its applications.
