  Supercontinuum generation in optical fibers is one of the most dramatic
nonlinear effects discovered, allowing short pulses to be converted into
multi-octave spanning coherent spectra. However, generating supercontinua that
are both coherent and broadband requires pulses that are simultaneously
ultrashort with high peak power. This results in a reducing efficiency with
increasing pulse repetition rate, that has hindered supercontinua at microwave
line spacing, i.e. 10s of GHz. Soliton microcombs by contrast, can generate
octave-spanning spectra, but with good conversion efficiency only at vastly
higher repetition rates in the 100s of GHz. Here, we bridge this efficiency gap
with resonant supercontinuum, allowing supercontinuum generation using input
pulses with an ultra-low 6 picojoule energy, and duration of 1 picosecond,
10-fold longer than what is typical. By applying synchronous pulse-driving to a
dispersion-engineered, low-loss Si$_3$N$_4$ photonic chip microresonator, we
generate dissipative Kerr solitons with a strong dispersive wave, both bound to
the input pulse. This creates a smooth, flattened 2,200 line frequency comb,
with an electronically detectable repetition rate of 28 GHz, constituting the
largest bandwidth-line-count product for any microcomb generated to date.
Strikingly, we observe that solitons exist in a weakly bound state with the
input pulse, stabilizing their repetition rate, but simultaneously allowing
noise transfer from one to the other to be suppressed even for offset
frequencies 100 times lower than the linear cavity decay rate. We demonstrate
that this nonlinear filtering can be enhanced by pulse-driving asynchronously,
in order to preserve the coherence of the comb. Taken together, our work
establishes resonant supercontinuum as a promising route to broadband and
coherent spectra.
