We report on measurement of small displacements with sub-nanometer precision using an optoelectronic oscillator (OEO) with an intra-loop Michelson interferometer. In comparison with conventional homodyne and heterodyne detection methods, where displacement appears as a power change or a phase shift, respectively, in the OEO detection, the displacement produces a shift in the oscillation frequency. In comparison with typical OEO sensors, where the frequency shift is proportional to the OEO oscillation frequency in radio-frequency domain, the frequency shift in our method with an intra-loop interferometer is proportional to an optical frequency. We constructed a hybrid apparatus and compared characteristics of the OEO and heterodyne detection methods.

The frequency pulling effect in an optoelectronic oscillator (OEO) due to the high dispersion produced by coherent population trapping (CPT) resonance in an intraloop Rb85 cell has been experimentally measured. With the direct modulation of the injection current of an extended-cavity diode laser, we construct the OEO and a beating signal with a frequency of 3.036 GHz is filtered by CPT resonance. The effective total loop length of the OEO under the CPT resonance condition can be significantly increased. As the optical path length of the OEO is changed, the microwave-frequency shift of the OEO corresponding to the effective total loop length is measured and reported.