Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators

We analyze chromatic dispersion in tightly curved silicon strip and slot waveguides with high index contrast. It is found that the dispersion profile is changed dramatically at both polarization states, when bending radius is reduced to a few microns. Zero-dispersion wavelength may shift by more than 220 nm, which raises a critical issue in design and optimization of micro-resonator-based devices for nonlinear applications. We propose a slot structure to tailor in-cavity dispersion and obtain spectral lines with the standard deviation of frequency-dependent free spectral range of the slot-waveguide resonator made 460 times smaller than that of a strip-waveguide resonator, making it suitable for on-chip octave-spanning frequency comb generation in mid-infrared wavelength range.