Velocity-matching in millimeter wave integrated optic modulators with periodic electrodes

One method of increasing the efficiency of a high-frequency integrated optic modulator is to use a periodic electrode to repeatedly “correct” the phase mismatch that results from unequal RF and optical propagation velocities. The center frequency of such a modulator´s passband can be determined analytically by expanding the traveling RF field in terms of space harmonics, and by then matching the phase velocity of the dominant space harmonic to the phase velocity of the optical carrier. The theory of space harmonic velocity-matching is presented for the simple case of periodic intermittent interaction and periodic phase reversal modulators having no back-reflections at electrode discontinuities. Velocity-matching with Bloch waves is then described for nonideal structures where significant back-reflections can occur. The measured modulation response for several 35-GHz periodic intermittent interaction modulators that were designed using these concepts is presented and compared with the theoretical predictions