GoKawiilCompared with traditional two-frequency RLGs, the beat frequency of the chiral RLG needs to be modified as equation (1): (the derivation can be found in the Methods)
$$\Delta v=\sqrt{{[\eta ({I}_{{\rm{cw}}}-{I}_{{\rm{ccw}}})+2{\varOmega }_{S}]}^{2}-\left(\frac{{I}_{{\rm{cw}}}}{{I}_{{\rm{ccw}}}}+\frac{{I}_{{\rm{ccw}}}}{{I}_{{\rm{cw}}}}+2\right){r}^{2}}$$ (1)
where \(\Delta v\) is the beat frequency of the chiral RLG; r is the backscattering coupling coefficient; \(\eta \) is the nonlinear frequency pulling coefficient (refer to the Supplementary Information for the derivation), which represents the overall effect of the laser intensity on its own frequency.
Benefiting from common-mode noise suppression, conventional RLGs can directly extract the Sagnac frequency splitting from the beat signal with balanced CW and CCW intensities, whereas equation (1) demonstrates that the intensity-dependent nonlinear frequency pulling introduces an additional term \(\eta ({I}_{{\rm{cw}}}-{I}_{{\rm{ccw}}})\) when \({I}_{{\rm{cw}}}
e {I}_{{\rm{ccw}}}\). Considering a typical value of the backscattering coefficient \(r=30\) Hz, for a chiral RLG operating at the point of maximum frequency bias (for example, \({
u =
u }_{3}\) in Fig. 4a) with an intensity ratio \({I}_{{\rm{cw}}}/{I}_{{\rm{ccw}}}\approx 2.4\), the introduced frequency bias is about 364 Hz, which is far greater than the lock-in threshold \(\sqrt{\left(\frac{{I}_{{\rm{cw}}}}{{I}_{{\rm{ccw}}}}+\frac{{I}_{{\rm{ccw}}}}{{I}_{{\rm{cw}}}}+2\right)}r\approx 66\) Hz. The chiral RLG will therefore always have a real and nearly linear frequency response with rotation, provided that \(\eta ({I}_{{\rm{cw}}}-{I}_{{\rm{ccw}}})\) and \({\varOmega }_{{\rm{S}}}\) have the same sign. Moreover, although the intensity asymmetry at this operating point reduces the interference fringe contrast by approximately 10%, leading to a decrease in the signal-to-noise ratio from 35.5 dB under achiral conditions to 34.9 dB under chiral conditions, this value remains well above the typical SNR limit (about 20 dB) required for high-precision laser gyroscope frequency counting. Therefore, such a chiral bias does not adversely affect the readout of the gyroscope signal.
Fig. 4: Frequency response characteristics of the chiral RLG. Full size image a, The CW or CCW mode intensity, nonlinear frequency pulling coefficient \(\eta \) (top) and the corresponding frequency bias with tuning frequency \(
u \) around the 20Ne gain centre \({
u }_{0}\) (bottom). b, The frequency response to low rotational speed of the RLG under different operating points and chirality states. Here, \({
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