Modeling an exceptional point gyroscope utilizing a single ring resonator and a loss-modulated grating

In this paper, we present a theoretical study of a nonreciprocal exceptional-point (EP) gyroscope first proposed some time ago that utilizes a single ring resonator in which an EP is formed by coupling the clockwise (CW) and counterclockwise (CCW) modes with a grating. The grating has a weak reflectivity selected so that it couples the two modes at the rate required to enable an EP. A key challenge of this EP structure is its inherent reciprocity. To overcome this limitation, we introduce a small difference between the resonance frequencies of the CW and CCW modes. We demonstrate that an EP can then exist only if the grating has a loss modulation and no index modulation. This is confirmed by modeling this grating-ring EP gyro using temporal coupled-mode equations. This analysis reveals that, at the EP, the two eigenfrequencies split proportionally to the square-root of the applied rotation rate, a hallmark of EP gyros. However, when interrogated at the point of steepest slope in its transmission spectrum—a technique that maximizes sensitivity—the transmitted power of the grating-ring gyro still has a linear, rather than square-root, dependence on rotation rate. Furthermore, this linear response to a rotation has a smaller slope (and therefore smaller rotation sensitivity) than a conventional non-EP resonant gyro with the same ring perimeter and minimum loss. The overall conclusion is that while this EP gyro configuration has inherently a significantly higher thermal stability than two-ring EP gyros, it offers no inherent sensitivity advantage over a conventional resonant gyro. These results are consistent with the published sensitivity performance of other non-laser EP gyros.