A high quality factor optical resonator structure includes a substrate, a center disc formed on the substrate, and a plurality of concentric grating rings surrounding the center disc. The concentric rings are spaced apart from the center disc and from one another by regions of lower index of refraction material with respect thereto, and wherein spacing between the grating rings and the center disc is non-periodic such that a magnitude of a displacement distance of a given grating ring with respect to a λ/4 Bragg reflector geometry is largest for a first of the grating rings immediately adjacent the center disk and decreases in a radially outward direction.