In this paper we propose a robust method for the optical generation of two bands of continuously tunable, microwave and millimeter-wave (mm-wave) signals. The proposed configuration consists of an optical phase modulator (PM), a fiber Bragg grating (FBG) optical notch filter and a tunable, electrical signal source. One band originates from the beating of the two first-order harmonics generated by the phase modulator, while the other band results from the beating of the two second-order harmonics. The phase modulator is driven by a low-frequency, tunable electrical reference source in order to produce the required harmonics. A notch filter is employed to remove the optical fundamental at the output of the phase modulator. It is mathematically shown, and experimentally verified, that the beating of the remaining optical harmonics in a square-law photo-detector can generate only even-orders of the electrical drive signal; all the odd-orders are canceled. In our measurements, the modulator drive signal is tuned from 18.8 GHz to 25 GHz. As a result, the frequency of the measured, electrical output signal is continuously tunable from 37.6 GHz to 50 GHz in the first band and from 75.2 GHz to 100 GHz in the second band.