Higher-order exceptional points in parity-time symmetry and the optical gyroscope.

The practical application of integrated gyroscopes in engineering has not yet been fully realized due to the linear correlation between the Sagnac effect and dimensions. In recent demonstrations, gyroscopes operating near exceptional points (EPs) under parity-time (PT) symmetry have shown significant potential in enhancing their response to rotational rates. However, constructing higher-order EPs with refined physical properties poses a considerable challenge. Additionally, current methods for constructing higher-order EPs with robustness primarily rely on passive cavities, with almost no reports on constructing robust EPs using PT-symmetric systems that encompass both gain and loss. Here, we propose a robust design for a scalable fabrication of higher-order EP gyroscopes with PT-symmetric structure. We investigate the influence of perturbations on the frequency splitting of the higher-order EP gyroscope and demonstrate that it is possible to achieve a resonance splitting eight orders of magnitude higher than that obtained through the classical Sagnac effect. In comparison to the previously proposed PT-symmetric gyroscope, our solution allows a tunable frequency splitting by adjusting the phase shift, making it more measurable at the output power spectrum.