Operating an optical device at an EP causes small perturbations applied to the device’s optical path length to produce a greatly enhanced splitting of resonance frequencies due to the splitting being proportional to at the EP, instead of as for conventional devices. For increasingly small , the EP splitting can therefore be larger by several orders of magnitude by operating sufficiently close to the EP. This enhanced splitting has drawn great interest recently, in particular for the potential to miniaturize the optical gyroscope. However, a small but growing number of publications claim that EP sensors may not achieve a proportionally larger signal-to-noise ratio once the full readout system and noise is accounted for. Many different EP sensors have been proposed, some as passive resonators, others as resonators with internal gain operated either below or above lasing threshold. Each sensor class may use a different readout system to measure the splitting and is therefore subject to different noise, but the recent trend has been that once noise and readout system have been accounted for, the enhanced response cancels out and a signal-to-noise ratio proportional to is achieved. Despite this cancellation, enhanced precision in EP sensors has still been predicted, although there is disagreement in whether the enhancement arises from the EP or another aspect of the sensor’s architecture, such as the gain. In this paper, we demonstrate through simulations that the EP in two-coupled-mode resonant (below lasing threshold) gyroscopes plays no role in enhancing the signal-to-noise ratio. An all-passive EP gyro is simulated in the limits of shot noise and detector noise to show that in either of these noise limits, no improvement in SNR over the equivalent single-ring gyro is possible. One of the rings is then given gain to show that a large enhancement in detectornoise- limited SNR (~2400 fold) arises, but close proximity to the EP is not necessary to maximize this enhancement; the enhancement is actually significantly larger when the sensor is detuned from the EP. This gain-loss gyro is then compared to a single-ring gyro with gain to show that large sensitivity enhancements are possible in both architectures because the gain compensates the resonator loss, resulting in a narrowing of the resonance linewidth and a greater response to a rotation, but the coupled-ring gyro exhibits a much greater stability to gain fluctuations.
This review summarizes the status of three current efforts to develop optical gyroscopes with improved performance over state-of-the-art fiber optic gyroscopes (FOGs) in terms of accuracy, size, and/or cost. The first approach consists in replacing the temporally incoherent Er-doped fiber source used in FOGs withy a low-coherence laser whose linewidth is broadened to tens of GHz by an external phase modulator driven by noise. A FOG with a 3.24-km coil interrogated by such a source has recently produced a noise and a drift approaching strategic-grade performance, and exhibits a source mean-wavelength stability below 1 ppm. The second approach is the use of a hollow-core fiber (HCF) in the sensing coil of a FOG to reduce thermal drift. A FOG utilizing 250 m of polarization-maintaining HCF and interrogated with a broadened laser is shown to exhibit a noise of 0.135 deg/√h limited by backscattering arising from surface modes in the fiber, and a drift of 1.2 deg/h dominated by polarization coupling. The third investigation is an optical gyroscope made of two coupled ring resonators, one exhibiting loss and the other one gain, operated at or near an exceptional point. Time-domain simulations predict that when operated below threshold and interrogated with a conventional biasing and read-out scheme, this gyroscope exhibits a rotation sensitivity at least 170 times larger than an optimized single-ring resonator with the same radius (5 mm) and loss (0.5 dB). Such systems have a great potential for producing a new generation of gyroscopes with significantly smaller footprints than FOGs.
A new gyroscope architecture inspired by parity-time-symmetric optics is proposed and theoretically modeled. It consists of two ring resonators coupled together, one with loss and the other with gain, with a loss and gain selected such that the device does not lase. A narrow-linewidth laser is coupled into the loss ring to probe the coupled resonator’s rotation-dependent resonances, and a detector measures the rotation-induced change in the power transmitted by the device. Assuming that the small-signal gain is smaller than the loss, a common radius for the two rings of 5 cm, and imposing that the power in the gain medium never exceeds 10% of the saturation power to avoid gain saturation, we demonstrate that this structure has a sensitivity to rotation ~170 times larger than an optimized resonant fiber optic gyroscope of equal ring radius and loss. Such loss-gain coupled resonators are known to exhibit an exceptional point at a critical value of the coupling between resonators, at which point the device’s resonances become extremely sensitive to external perturbations such as a rotation. However, we demonstrate that the maximum rotation sensitivity of this paritytime- symmetric structure does not occur at the exceptional point. Instead, for the aforementioned parameter values and the imposition of a small circulating power, it is maximum when the inter-ring coupling is ~11% stronger than the exceptional-point coupling. This significant increase in rotation sensitivity is found to result to a much larger degree from a strong enhancement in the power circulating in the gain ring (although there is not a one-to-one correspondence), and to a much lower extent from an enhancement in the rotation-induced resonance-frequency shift.
A theoretical analysis of this little-studied resonator is performed, including a study of its sensitivity as a gyroscope and of transmission spectrum properties. When all its free parameters are optimized (the coupling ratio of the 3x3 coupler, the probe laser wavelength, and the length mismatch between the rings), this sensor is predicted to have the exact same maximum possible rotation sensitivity as a resonant fiber optic gyroscope (RFOG) with the same ring radius and fiber loss, for either a triangular or a planar a 3x3 fiber coupler. Changing the length mismatch (and re-adjusting the coupling ratio to maximize the sensitivity) has very little impact on the best sensitivity: all it does is redistribute the circulating light between rings, but the total number of recirculations is essentially unchanged, and so is the sensitivity. A second type of double-ring resonator is studied in which the output is collected via a 2x2 coupler placed on one of the rings. This two-coupler double-ring resonator gyroscope is found to have a larger rotation sensitivity than a two-coupler RFOG. For exceedingly small loss, the sensitivity enhancement is vanishingly small. For a ring loss of 1 dB, the enhancement is 1.8-fold. As the loss is increased, the enhancement increases asymptotically to either ~2.11 (triangular coupler) or ~1.78 (planar coupler), but the loss is then too high for either sensor to be practical. For small loss, the sensitivity of a two-coupler RFOG is 4 times lower than that of a conventional (one-coupler) RFOG. A two-coupler double-ring resonator gyroscope therefore never surpasses a single-coupler RFOG in sensitivity, but for applications requiring an additional 2x2 coupler, a two-coupler double-ring resonator has a higher rotation sensitivity than a twocoupler RFOG.