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We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the output modulation to determine the conditions for enhanced gyroscopic sensitivities. The element is treated as both a phase and amplitude filter, and the time-dependence of the cavity field is considered. Both atomic gases (two-level and multi-level) and optical resonators (single and coupled) are considered and compared as dispersive elements. We find that it is possible to simultaneously enhance the gyro scale factor sensitivity and suppress the dead band by using an element with anomalous dispersion that has greater loss at the carrier frequency than at the side-band frequencies, i.e., an element that simultaneously pushes and intensifies the perturbed cavity modes, e.g. a two-level absorber or an under-coupled https://ntrs.nasa.gov/search.jsp?R=20090019025 2018-05-12T12:35:45+00:00Z 2 optical resonator. The sensitivity enhancement is inversely proportional to the effective group index, becoming infinite at a group index of zero. However, the number of round trips required to reach a steady-state also becomes infinite when the group index is zero (or two). For even larger dispersions a steady-state cannot be achieved, and nonlinear dynamic effects such as bistability and periodic oscillations are predicted in the gyro response.

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We present an entirely linear all-optical method of cavity scale factor enhancement that relies on mode coupling between the orthogonal polarization modes of a single optical cavity, eliminating the necessity of using an atomic medium to produce the required anomalous dispersion, which decreases the dependence of the scale factor on temperature and increases signal-to-noise ratio by reducing absorption and nonlinear effects. The use of a single cavity results in common mode rejection of the noise and drift that would be present in a system of two coupled cavities. We show that the scale-factor-to-mode-width ratio is increased above unity for this system, and demonstrate tuning of the scale factor by (i) directly varying the polarization mode coupling via rotation of an intracavity half-wave plate, and (ii) coherent control of the cavity reflectance which is achieved simply by varying the incident polarization superposition. These tuning methods allow us to closely approach the critical anomalous dispersion condition and achieve unprecedented enhancements in scale factor and in the scale-factor-to-mode-width ratio. Based on these findings, we propose an adaptation of the traditional optical cavity gyroscope that takes advantage of polarization mode coupling to enhance the gyro scale factor, and demonstrate how the bandwidth of the scale factor enhancement for this gyroscope can be effectively broadened in comparison with fast-light gyroscopes based on atomic media.