High-Q ring resonators with contacts to the waveguide core provide a versatile platform for various applications in chip-scale optomechanics, thermo- and electro-optics. We propose and demonstrate a novel approach to implement azimuthally periodic co
ntacted ring resonators based on multi-mode Bloch matching that support contacts on both the inner and outer radius edges with small degradation to the optical Q. Radiative coupling between degenerate modes of adjacent transverse spatial order leads to imaginary frequency (Q) splitting and a scatterer avoiding high-Q wiggler supermode field. We experimentally measure Qs up to 258,000 in devices fabricated in a silicon device layer on buried oxide undercladding, and up to 139,000 in devices fully suspended in air using an undercut step. Wiggler supermodes are true modes of the microphotonic system that offer new degrees of freedom in electrical, thermal and mechanical design.
