  Recent advances in the design and fabrication of on-chip optical
microresonators has greatly expanded their applications in photonics, enabling
metrology, communications, and on-chip lasers. Designs for these applications
require fine control of dispersion, bandwidth and high optical quality factors.
Co-engineering these figures of merit remains a significant technological
challenge due to design strategies being largely limited to analytical tuning
of cross-sectional geometry. Here, we show that photonic inverse-design
facilitates and expands the functionality of on-chip microresonators;
theoretically and experimentally demonstrating flexible dispersion engineering,
quality factor beyond 2 million on the silicon-on-insulator platform with
single mode operation, and selective wavelength-band operation.
