  Control of dispersion in fibre optical waveguides is of critical importance
to optical fibre communications systems and more recently for continuum
generation from the ultraviolet to the mid-infrared. The wavelength at which
the group velocity dispersion crosses zero can be set by varying fibre core
diameter or index step. Moreover, sophisticated methods to manipulate
higher-order dispersion so as shape and even flatten dispersion over wide
bandwidths are possible using multi-cladding fibre. Here we introduce design
and fabrication techniques that allow analogous dispersion control in
chip-integrated optical microresonators, and thereby demonstrate higher-order,
wide-bandwidth dispersion control over an octave of spectrum. Importantly, the
fabrication method we employ for dispersion control simultaneously permits
optical Q factors above 100 million, which is critical for efficient operation
of nonlinear optical oscillators. Dispersion control in high Q systems has
taken on greater importance in recent years with increased interest in
chip-integrable optical frequency combs.
