Methods and apparatus are provided for determining the rotational rate of an optical gyro. An optical gyro comprises at least one substrate, a multi-frequency light source (MFLS) mounted on the substrate, and a resonator coupled to the MFLS. The MFLS is configured to produce a first light beam having a first frequency and a second light beam having a second frequency and phase locked with the first light beam. The resonator comprises an optical fiber coil having a hollow core. The resonator is configured to circulate a portion of each of the first and second light beams through the hollow core. The portion of the first light beam propagates in a first counter-propagating direction, and the portion of the second light beam propagates in a second counter-propagating direction. A measured difference between the first and second frequencies indicates a frequency shift proportional to the rotation rate of the optical gyro.