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We newly propose a photonic downconversion technique with optical frequency shift to detect millimeter-wave-band (mm-wave-band) radio-on-fiber (ROF) signals. In the proposed technique, the carrier and first-order sideband components of mm-wave-band ROF signal are differentially shifted closer to each other in the optical domain on the receiver side. The closely aligned optical components are filtered out and photodetected to generate a desired intermediate-frequency signal in the microwave band. We describe the theoretical basis for our proposal and the experimental transmission of a 60-GHz band 155-Mb/s differential phase-shift keying ROF signal over a 25-km-long standard single-mode fiber.