A gyroscope includes a first optical resonator in optical communication with at least one optical waveguide and a second optical resonator in optical communication with the first optical resonator. One of the first optical resonator and the second optical resonator has a power loss rate L greater than zero and the other of the first optical resonator and the second optical resonator has a power gain rate G greater than zero. The at least one optical waveguide, the first optical resonator, and the second optical resonator are configured to be below lasing threshold. The gyroscope further includes at least one optical detector in optical communication with the at least one optical waveguide, and the at least one optical waveguide is configured to receive, from at least one light source, light having an input power P.sub.in at a frequency .sub.p and to transmit at least a portion of the light having an output power P.sub.out to the at least one optical detector.

A hyperbolic modulation offset reducer circuit for a resonator fiber optic gyro (RFOG) is provided. The circuit includes a first demodulation circuit that is configured to demodulate a received transmission signal from a resonator at twice a sideband heterodyne detection modulation frequency to reject signals due to backscatter. A slave resonance tracking loop of the circuit is coupled to an output of the first demodulation circuit. The slave resonance tracking loop is configured to create an offset frequency signal from the transmission signal that is applied to an optical phase lock loop of a RFOG. A hyperbolic modulator offset control loop is also coupled to the output of the first demodulation circuit. The hyperbolic modulator offset control loop is configured to create a subharmonic common modulation signal from the transmission signal that is coupled to a common phase module in a silicon photonics chip of the RFOG.

An apparatus, and corresponding method, includes a broadband light source configured to provide broadband source light and at least one optical phase modulator configured to receive the broadband source light and to deliver conditioned broadband output light having at least one of reduced spectral modulation depth and increased central degree of nth-order temporal coherence, characterized by a phase noise modulation enhancement factor, where n is an integer greater than or equal to 2, relative to the broadband source light.

An improved fiber-optic gyroscope (FOG) is proposed for enhancing the optical measurement sensitivity through the application of a heterodyne effect. The improved FOG is characterized by the use of a dual-injection polarization-maintaining 33 directional coupler which is configured to receive a pair of source light beams that are injected thereinto in a bi-directional manner. The forward-injected light beam is used to be split into a pair of interrogating beams for use by a coiled optical fiber to implement the detection and measurement of the Sagnac effect due to a rotational movement. On the other hand, the backward-injected light beam is used to be mixed with the paired interrogating beams that have passed through and returned from the coiled optical fiber to thereby provide a heterodyne effect that can boost the differential optical power amplitude of the paired interrogating beams, thereby enhancing the optical measurement sensitivity of the FOG application.

Lower noise and complexity techniques are disclosed for compensating for time varying phase changes in fiber optics in a resonant fiber optic gyroscope (RFOG). Orthogonal components derived from an electrical beat note signal and a difference between clockwise and counterclockwise resonant frequencies of an optical resonator coil of the RFOG are determined. The orthogonal products are converted to a phase which is differentiated with respect to time to obtain a beat note correction signal.