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Rigorous expressions of resonant frequency shift (RFS) in anomalous dispersion enhanced resonant optical gyroscopes (ADEROGs) are deduced without making approximation, which provides a precise theoretical guidance to achieve ultra-sensitive ADEROGs. A refractive index related modification factoris introduced when considering special theory of relativity (STR). We demonstrate that the RFS will not be ”infinitely large” by using critical anomalous dispersion (CAD) and negative modification does not exist, which make the mechanism of anomalous dispersion enhancement clear and coherent. Although step change of RFS will happen when the anomalous dispersion condition varies, the amplification of RFS is limited by attainable variation of refractive index in practice. Moreover, it is shown that the properties of anomalous dispersion will influence not only the amplification of RFS, but also the detection range of ADEROGs.

Theoretical analyses of resonant frequency shift in anomalous dispersion enhanced resonant optical gyroscopes