  We propose and analyze a new type of a resonator in an annular geometry which
is based on a single defect surrounded by radial Bragg reflectors on both
sides. We show that the conditions for efficient mode confinement are different
from those of the conventional Bragg waveguiding in a rectangular geometry. A
simple and intuitive approach to the design of optimal radial Bragg reflectors
is proposed and employed, yielding chirped gratings. Small bending radii and
strong control over the resonator dispersion are possible by the Bragg
confinement. A design compromise between large Free Spectral Range (FSR)
requirements and fabrication tolerances is suggested.
