Optical annular resonators based on radial Bragg and photonic crystal reflectors

A ring resonator based on Bragg reflection is studied in detail. Closed form expressions for the field and dispersion curves for radial Bragg gratings and photonic crystals based resonators are derived and compared to FDTD simulations. For strong confinement, the required gratings exhibit a chirped period and a varying index profile. Small bending radii and low radiation losses are shown to be possible due to the Bragg confinement. The sensitivity of the resonator characteristics to fabrication errors is analyzed quantitatively. A mixed confinement configuration utilizing both Bragg reflection and total internal reflection is also suggested and analyzed.