Polarization fluctuation induced noise and backscattering-induced noise are the dominant noises in resonant fiber optic gyroscopes. This Letter proposes a new method to suppress the carrier and backscattering induced noise by the sideband locking technique. Besides choosing an optimized modulation depth and different clockwise and counterclockwise modulation frequencies, the sideband is locked to the cavity resonance. With the proper modulation frequency, the carrier frequency component locates
