  Photonic crystals, material structures in which the dielectric function
varies periodically in one, two, or three dimensions, can provide exquisite
control over the propagation and confinement of light. By tailoring their band
structure, exceptional optical effects can be achieved, such as slow light
propagation or, through the creation of photonic bandgaps, optical cavities
with both a high quality factor and a small mode volume. Photonic crystal
cavities have been used to realize compact nano-lasers and achieve strong
coupling to quantum emitters, such as semiconductor quantum dots, color
centers, or cold atoms. A useful attribute of photonic crystals is the ability
to create chirped mirrors. Chirping has underpinned advances in ultra-fast
lasers based on bulk mirrors, but has yet to be fully exploited in integrated
photonics, where it could provide a means to engineer otherwise unattainable
dispersion profiles for a range of nonlinear optical applications, including
soliton frequency comb generation. The vast majority of integrated resonators
for frequency combs make use of microring geometries, where only waveguide
width and height are varied to engineer dispersion. Generation of frequency
combs has been demonstrated with one-dimensional photonic crystal cavities made
of silicon nitride, but the low index contrast prevents formation of broad
soliton combs. We overcome these challenges by using a photonic-crystal
Fabry-P\'erot resonator made of gallium phosphide, a material with a high
refractive index and a Kerr nonlinearity 200 times larger than that of silicon
nitride. We employ chirped photonic crystal mirrors to provide anomalous
dispersion. With subharmonic pulsed pumping at an average power of 23.6 mW, we
are able to access stable dissipative Kerr frequency combs. We demonstrate
soliton formation with a 3-dB bandwidth of 3.0 THz, corresponding to a pulse
duration of 60 fs.
