  Conversion of microwave radiation into the optical range has been predicted
to reach unity quantum efficiency in whispering gallery resonators made from an
optically nonlinear crystal and supporting microwave and optical modes
simultaneously. In this work we theoretically explore and experimentally
demonstrate a resonator geometry that can provide the required phase matching
for such a conversion at any desired frequency in the sub-THz range. We show
that such a ring-shaped resonator not only allows for the phase matching, but
also maximizes the overlap of the interacting fields. As a result,
unity-efficient conversion is expected in a resonator with feasible parameters.
