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The indicatrix ellipsoid of an electrooptic crystal with a threefold rotation axis under the influence of an applied microwave field circularly polarized in a plane normal to the axis intersects this plane in a rotating ellipse of constant shape. A circularly polarized optical field in this plane produces an electric polarization at one sideband frequency only, upshifted if the optical field rotates in the opposite direction the indicatrix rotates, downshifted if the rotations are the same. Ideally, 100 percent conversion of the optical incident field into the up- or downshifted field may be achieved. A square waveguide containing a CdTe crystal is investigated as the structure appropriate for phase-matched single sideband conversion. Experiments are reported yielding a 67 percent conversion efficiency for shifting 10.6 μm laser radiation by 17 GHz. The efficiency was limited by crystal length and/or microwave breakdown. For longer crystals conversion efficiencies approaching 100 percent are extrapolated. Scaling laws for other microwave and laser frequencies are presented.