Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope

Enhanced detection limit in an exceptional surface-based fiber resonator by manipulating Fano interference

An exceptional surface (ES) has advantages in improving sensing robustness and enhancing frequency splitting. Typically, the eigenvalue splitting must exceed the mode linewidth in order to be clearly visible in the spectrum, which limits the precision of the ES-based sensing structure. In this paper, a strategy for manipulating spectral line shape in an ES-based structure is experimentally realized. In addition, the limit of the minimum detectable displacement can be further reduced by monitoring the peak intensity of the Fano interference line shape. The demonstration of Fano interference in an ES-based system opens the way for a new class of ultrasensitive optical sensors.

Enhanced rotation sensing with high-order exceptional points in a multi-mode coupled-ring gyroscope

Exceptional points (EPs) of non-Hermitian systems are sensitive to perturbations and facilitate the development of highly sensitive gyroscopes. We propose a compact multi-mode optical gyroscope protocol that incorporates two coupled rings and exhibits a fourth-order EP, achieving higher sensitivity compared to gyroscopes based on second-order EPs. We show that the gyroscope sensitivity can be further improved by deviating from the fourth-order EP due to the gain dependence on the cavity intensity. Furthermore, our protocol exhibits resilience against backscattering from counter-propagating modes, which leads to a reduced angular random walk (ARW) factor and increased sensitivity. These features make our protocol highly promising for advancing high-performance optical gyroscopes and enhancing angular velocity sensing technologies.

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.

Dissipative coupling in a Bragg-grating-coupled single resonator with Fano resonance for anti-PT-symmetric gyroscopes

Anti-parity-time-symmetric Hamiltonians show an enhanced sensitivity to external perturbations that can be used for high-performance angular velocity sensing. Dissipative coupling is a valuable way for realizing anti-PT-symmetric Hamiltonians with optical resonators and is usually obtained by means of auxiliary waveguides. Here, we model and experimentally show the dissipative coupling between two counterpropagating modes of a single resonator, by means of a Bragg-grating placed in the feeding bus. The proposed solution enables the possibility of accurately designing the dissipative coupling strength in integrated non-Hermitian gyroscopes, thus providing high flexibility in the design of the proposed sensor. Moreover, we theoretically and experimentally demonstrate that the dissipative coupling between two counterpropagating modes of the same resonant cavity can give rise to an asymmetric Fano resonance.

Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem has long been interest in mathematical physics, however, only in the last decade entered the scope of experiments. In coupled systems, EPs give rise to unique physical phenomena, and enable the development of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and exploit the system's non-hermiticity. We observe amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which describes the main experimental features. The room temperature operation, and CMOS compatibility of our spintronic nanoscale oscillators means that they are ready to be employed in a variety of applications, such as field, current or rotation sensors, radiofrequeny and wireless devices, and in dedicated neuromorphic computing hardware. Furthermore, their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points expanding to strongly nonlinear systems.

Enhanced Sensing Mechanism Based on Shifting an Exceptional Point

Non-Hermitian systems associated with exceptional points (EPs) are expected to demonstrate a giant response enhancement for various sensors. The widely investigated enhancement mechanism based on diverging from an EP should destroy the EP and further limits its applications for multiple sensing scenarios in a time sequence. To break the above limit, here, we proposed a new enhanced sensing mechanism based on shifting an EP. Different from the mechanism of diverging from an EP, our scheme is an EP nondemolition and the giant enhancement of response is acquired by a slight shift of the EP along the parameter axis induced by perturbation. The new sensing mechanism can promise the most effective response enhancement for all sensors in the case of multiple sensing in a time sequence. To verify our sensing mechanism, we construct a mass sensor and a gyroscope with concrete physical implementations. Our work will deepen the understanding of EP-based sensing and inspire designing various high-sensitivity sensors in different physical systems.

Fundamental Sensitivity Limits for Non-Hermitian Quantum Sensors

Considering non-Hermitian systems implemented by utilizing enlarged quantum systems, we determine the fundamental limits for the sensitivity of non-Hermitian sensors from the perspective of quantum information. We prove that non-Hermitian sensors do not outperform their Hermitian counterparts (directly couple to the parameter) in the performance of sensitivity, due to the invariance of the quantum information about the parameter. By scrutinizing two concrete non-Hermitian sensing proposals, which are implemented using full quantum systems, we demonstrate that the sensitivity of these sensors is in agreement with our predictions. Our theory offers a comprehensive and model-independent framework for understanding the fundamental limits of non-Hermitian quantum sensors and builds the bridge over the gap between non-Hermitian physics and quantum metrology.

Single-mode lasing by tailoring the excitation of localized surface plasmon resonances to whispering gallery modes in a microring laser

Cavity mode manipulation in lasers is urgent for the stable single-mode operation of a microring laser. Here, we propose and experimentally demonstrate the plasmonic whispering gallery mode microring laser for strong coupling between local plasmonic resonances and whispering gallery modes (WGM) on the microring cavity to achieve pure single-mode lasing. The proposed structure is fabricated based on integrated photonics circuits consisting of gold nanoparticles deposited on a single microring. Additionally, our numerical simulation provides deep insight into the interaction between the gold nanoparticles and WGM modes. The manufacture of microlasers for the advancement of lab-on-a-chip devices and all-optical detection of ultra-low analysts may benefit from our findings.

Polarization eigenstates analysis of helically structured thin films

The optical properties of thin films are generally determined by direct photometric quantities. We show that additional insight into the properties of anisotropic thin films can be obtained by computing the polarization eigenstates and eigenvalues of their Jones matrices. We consider helically structured thin films, which display intriguing optical response, such as the circular Bragg resonance. Using numerical simulations and actual measurements, we show that the eigenvectors are mutually orthogonal in most regions of the wavevector space, except near the circular Bragg and the oblique resonances. Special wavevector values, called exceptional points, are found where the Jones matrix becomes defective and its eigenvectors coalesce. Exceptional points are also found in pairs of wavevector values differing only by a sample rotation by π around the direction normal to the sample; this property is shown to arise from Saxton - de Hoop's reciprocity principle, which applies to lossy materials and contains time reversal symmetry, which only applies to lossless materials, as a special case.

Reconfigurable chiral exceptional point and tunable non-reciprocity in a non-Hermitian system with phase-change material

Non-Hermitian optics has emerged as a feasible and versatile platform to explore many extraordinary wave phenomena and novel applications. However, owing to ineluctable systematic errors, the constructed non-Hermitian phenomena could be easily broken, thus leading to a compromising performance in practice. Here we theoretically proposed a dynamically tunable mechanism through GST-based phase-change material (PCM) to achieve a reconfigurable non-Hermitian system, which is robust to access the chiral exceptional point (EP). Assisted by PCM that provides tunable coupling efficiency, the effective Hamiltonian of the studied doubly-coupled-ring-based non-Hermitian system can be effectively modulated to resist the external perturbations, thus enabling the reconfigurable chiral EP and a tunable non-reciprocal transmission. Moreover, such tunable properties are nonvolatile and require no static power consumption. With these superior performances, our findings pave a promising way for reconfigurable non-Hermitian photonic devices, which may find applications in tunable on-chip sensors, isolators and so on.

Exceptional Precision of a Nonlinear Optical Sensor at a Square-Root Singularity

Exceptional points (EPs)-spectral singularities of non-Hermitian linear systems-have recently attracted interest for sensing. While initial proposals and experiments focused on enhanced sensitivities neglecting noise, subsequent studies revealed issues with EP sensors in noisy environments. Here we propose a single-mode Kerr-nonlinear resonator for exceptional sensing in noisy environments. Based on the resonator's dynamic hysteresis, we define a signal that displays a square-root singularity reminiscent of an EP. However, our sensor has crucial fundamental and practical advantages over EP sensors: the signal-to-noise ratio increases with the measurement speed, the square-root singularity is easily detected through intensity measurements, and both sensing precision and information content of the signal are enhanced around the singularity. Our sensor also overcomes the fundamental trade-off between precision and averaging time characterizing all linear sensors. All these unconventional features open up new opportunities for fast and precise sensing using hysteretic resonators.

Non-Hermitian Sensing in Photonics and Electronics: A Review

Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided.

Intracavity Measurement Sensitivity Enhancement without Runaway Noise

A method to increase the sensitivity of an intracavity differential phase measurement that is not made irrelevant by a larger increase of noise is explored. By introducing a phase velocity feedback by way of a resonant dispersive element in an active sensor in which two ultrashort pulses circulate, it is shown that the measurement sensitivity is elevated without significantly increasing the Petermann excess noise factor. This enhancement technique has considerable implications for any optical phase based measurement; from gyroscopes and accelerometers to magnetometers and optical index measurements. Here we describe the enhancement method in the context of past dispersion enhancement studies including the recent work surrounding non-Hermitian quantum mechanics, justify the method with a theoretical framework (including numerical simulations), and propose practical applications.

Observation of exceptional points in helically structured thin films

Exceptional points (EPs) in the polarization space were observed in reflection on helically structured thin films. These films have form anisotropy at the nanoscale introduced through dynamic control of crystalline growth geometry by changing the orientation of the substrate with respect to the impinging vapor. They are simpler alternatives to metasurfaces, because they can be produced at low cost using conventional thin-film deposition techniques. The EPs were experimentally confirmed by eigenstate swapping on a closed circuit surrounding them and were predicted by numerical calculations. Reflective surfaces operating at an EP could be used to make ultrasensitive sensors.

Rotation sensitivity and shot-noise-limited detection in an exceptional-point coupled-ring gyroscope

A theoretical study is performed of the sensitivity and quantum-noise limit of a passive coupled-ring optical gyroscope operated at and detuned from its exceptional point (EP) and interrogated with a practical conventional readout system. When tuned to its EP, the Sagnac frequency splitting is proportional to the square root of the applied rotation rate, but the signal generated by the sensor is shown to be proportional to the applied rotation rate. The sensitivity is never larger, and the minimum detectable rotation rate in the quantum-noise limit never lower, than that of a standard single-ring gyro of the same radius and loss, even when the coupled-ring gyro is tuned exactly to its EP. As pointed out elsewhere for other EP sensors, in this particular passive sensor at least, there is no sensitivity or resolution benefit in operating at an EP.

Rotation Active Sensors Based on Ultrafast Fibre Lasers

Gyroscopes merit an undeniable role in inertial navigation systems, geodesy and seismology. By employing the optical Sagnac effect, ring laser gyroscopes provide exceptionally accurate measurements of even ultraslow angular velocity with a resolution up to 10-11 rad/s. With the recent advancement of ultrafast fibre lasers and, particularly, enabling effective bidirectional generation, their applications have been expanded to the areas of dual-comb spectroscopy and gyroscopy. Exceptional compactness, maintenance-free operation and rather low cost make ultrafast fibre lasers attractive for sensing applications. Remarkably, laser gyroscope operation in the ultrashort pulse generation regime presents a promising approach for eliminating sensing limitations caused by the synchronisation of counter-propagating channels, the most critical of which is frequency lock-in. In this work, we overview the fundamentals of gyroscopic sensing and ultrafast fibre lasers to bridge the gap between tools development and their real-world applications. This article provides a historical outline, highlights the most recent advancements and discusses perspectives for the expanding field of ultrafast fibre laser gyroscopes. We acknowledge the bottlenecks and deficiencies of the presented ultrafast laser gyroscope concepts due to intrinsic physical effects or currently available measurement methodology. Finally, the current work outlines solutions for further ultrafast laser technology development to translate to future commercial gyroscopes.

Enhanced rotation sensing and exceptional points in a parity-time-symmetric coupled-ring gyroscope

Enhancement in rotation sensitivity is achieved in a parity-time-symmetric gyroscope consisting of a ring with gain coupled to a lossy ring, operated below laser threshold and in the vicinity of its exceptional point (EP). An external laser and a conventional readout system are used to measure the large rotation-induced shifts in resonance frequency known to occur in this device. A complete model of the rotation sensitivity is derived that accounts for gain saturation caused by the large circulating power. Compared to a single-ring gyro, the sensitivity is enhanced by a factor of ∼300 when the inter-ring coupling is tuned to its EP value κ_EP, and ∼2400 when it is decreased from κ_EP, even though the Sagnac frequency shift is then much smaller. ∼40% of this 2400-fold enhancement is assigned to a new sensing mechanism where rotation alters the gain saturation. These results show that this compact gyro has a far greater sensitivity than a conventional ring gyro, and that this improvement arises mostly from the gain compensating the loss, as opposed to the enhanced Sagnac frequency shift from the EP. This gyro is also shown to be much more stable against gain fluctuations than a single-ring gyro with gain.

Resonant micro-optical gyro based on self-injection locking

We propose the idea and design of a novel resonant micro-optical gyro based on a self-injection locking technique. By enhancing the reciprocity and measuring beat frequency, the sensitivity of gyro is improved effectively, which is usually limited by two main factors: low signal-to-noise ratio and immature signal detecting technique. In addition, a small size distributed feedback semiconductor laser with megahertz linewidth is used for miniaturization, instead of the narrow linewidth and tunable laser in traditional resonant gyros. Sensitivity of this resonant micro-optical gyro depends, in fact, on the accuracy of time measurement. In this paper, theory sensitivity is demonstrated to be at the order of 10^-4 deg/h under a 6 KHz modulation frequency.

Nonlinear transition between PT-symmetric and PT-broken modes in coupled fiber lasers

We present a systematic analysis of the stationary regimes of nonlinear parity-time (PT) symmetric laser composed of two coupled fiber cavities. We find that power-dependent nonlinear phase shifters broaden regions of existence of both PT-symmetric and PT-broken modes, and can facilitate transitions between modes of different types. We show the existence of non-stationary regimes and demonstrate an ambiguity of the transition process for some of the unstable states. We also identify the presence of higher-order stationary modes, which return to the initial state periodically after a certain number of round-trips.

Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope

Exceptional points are singularities of open systems, and among their many remarkable properties, they provide a way to enhance the responsivity of sensors. Here we show that the improved responsivity of a laser gyroscope caused by operation near an exceptional point is precisely compensated by increasing laser noise. The noise, of fundamental origin, is enhanced because the laser mode spectrum loses the oft-assumed property of orthogonality. This occurs as system eigenvectors coalesce near the exceptional point and a bi-orthogonal analysis confirms experimental observations. While the results do not preclude other possible advantages of the exceptional-point-enhanced responsivity, they do show that the fundamental sensitivity limit of the gyroscope is not improved through this form of operation. Besides being important to the physics of microcavities and non-Hermitian photonics, these results help clarify fundamental sensitivity limits in a specific class of exceptional-point sensor.

Operating a laser gyroscope near an exceptional point has been shown to enhance its responsivity. However, here the authors demonstrate in theory and experiment that the enhanced responsivity is exactly compensated by increased noise that is inherent to this system near the exceptional point.

Quantum Sensing with a Single-Qubit Pseudo-Hermitian System

Quantum sensing exploits the fundamental features of a quantum system to achieve highly efficient measurement of physical quantities. Here, we propose a strategy to realize a single-qubit pseudo-Hermitian sensor from a dilated two-qubit Hermitian system. The pseudo-Hermitian sensor exhibits divergent susceptibility in a dynamical evolution that does not necessarily involve an exceptional point. We demonstrate its potential advantages to overcome noises that cannot be averaged out by repetitive measurements. The proposal is feasible with the state-of-art experimental capability in a variety of qubit systems, and represents a step towards the application of non-Hermitian physics in quantum sensing.

Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity

Gyroscopes are essential to many diverse applications associated with navigation, positioning and inertial sensing¹. In general, most optical gyroscopes rely on the Sagnac effect-a relativistically induced phase shift that scales linearly with the rotational velocity^2,3. In ring laser gyroscopes (RLGs), this shift manifests as a resonance splitting in the emission spectrum, which can be detected as a beat frequency⁴. The need for ever more precise RLGs has fuelled research activities aimed at boosting the sensitivity of RLGs beyond the limits dictated by geometrical constraints, including attempts to use either dispersive or nonlinear effects^5-8. Here we establish and experimentally demonstrate a method using non-Hermitian singularities, or exceptional points, to enhance the Sagnac scale factor^9-13. By exploiting the increased rotational sensitivity of RLGs in the vicinity of an exceptional point, we enhance the resonance splitting by up to a factor of 20. Our results pave the way towards the next generation of ultrasensitive and compact RLGs and provide a practical approach for the development of other classes of integrated sensor.

Parity-time-symmetry-breaking gyroscopes: lasing without gain and subthreshold regimes

We show that the lasing threshold for two coupled resonators (CRs) corresponds to lasing without gain (LWG), a phenomenon analogous to lasing without inversion in atomic systems, when parity-time (PT) symmetry is broken. The use of LWG for gyroscopes may resolve some of the difficulties associated with PT-symmetric gyroscopes. In particular, we find that PT-symmetric systems suffer from undamped Rabi oscillations, whereas LWG systems are overdamped. In addition, observation of enhanced sensitivity should be more straightforward in LWG gyros because the enhancement remains above unity even at couplings far from the exceptional point (EP). Finally, LWG gyros operate more like conventional laser gyroscopes with one frequency for each output direction, and therefore there is no ambiguity in the direction of rotation. Gain saturation in CR systems is found to dramatically boost the size of the sensitivity enhancement, eliminate the Rabi oscillations, and enlarge the parameter space around the EP over which the enhancement is expected to occur. A second situation with broken symmetry is also examined: CR systems below threshold. Whereas the pole in sensitivity coincides with the EP at threshold, the pole can occur far away from the EP for subthreshold systems. Our analysis also puts previous results on passive and active fast-light cavities using atomic vapor cells into the context of EP-enhanced sensing with non-Hermitian Hamiltonians.

High-sensitivity real-splitting anti-PT-symmetric microscale optical gyroscope

Optical gyroscopes measure the angular velocity using the Sagnac effect. However, the resonance splitting due to the Sagnac effect is directly proportional to the linear dimensions of the device. Consequently, integrated optical gyroscopes are still the subject of research. We propose the idea and the design of an anti-parity-time (APT)-symmetric optical gyroscope exhibiting a resonance splitting independent from the dimensions of the device. With a 80  μm×40  μm footprint integrated device, we demonstrated that it is possible to achieve a resonance splitting 10⁶ times higher than the one obtained through the classical Sagnac effect. With respect to the previously proposed parity-time (PT)-symmetric gyroscope, our solution exhibits a real frequency splitting, directly measurable at the output power spectrum. Moreover, it can be kept at its exceptional point more accurately than the PT-symmetric counterpart. Finally, the anti-PT-symmetric gyroscope presented here can detect the sign of the angular velocity differently from the PT-symmetric one.

Mechanical exceptional-point-induced transparency and slow light

Recently, the conception of PT symmetry has attracted considerable attention in various fields such as optics, acoustics, and atomic physics because of the existence of exceptional point (EP) and its importance in understanding non-Hermitian physics. Here, we propose a new scheme of investigating the mechanical-EP-induced transparency and tunable fast-to-slow light phenomena in PT-symmetric mechanical systems. We find that (i) the transmission of the probe field changes from singleto double transparency windows via the transition from a broken mechanical PT-symmetric phase to an unbroken mechanical PT-symmetric phase; (ii) the efficiency of transparency can be significantly enhanced about three orders of magnitude in the vicinity of the mechanical EP, compared to passive mechanical resonators system; and (iii) the mechanical EP can not only amplify the group delay, but also manipulate the switch from slow light to fast light, which may offer an approach to achieve the practical application of slow light and relevant to the optical switcher and communication network. Our results reveal that the exotic properties of the mechanical EP can result in enormous enhancement of the transmitted probe power and novel steering of fast and slow light.

Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing

Unconventional properties of non-Hermitian systems, such as the existence of exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes however remains unclear. In this work, we analyze the parametric-sensing properties of linear coupled-mode systems that are described by effective non-Hermitian Hamiltonians. Our analysis fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal power and signal-to-noise ratio for any such sensor. We use these to demonstrate that enhanced signal power requires gain, but not necessarily any proximity to an exceptional point. Further, when noise is included, we show that nonreciprocity is a powerful resource for sensing: it allows one to exceed the fundamental bounds constraining any conventional, reciprocal sensor.

Unidirectional light emission in PT-symmetric microring lasers

The synergetic use of gain and loss in parity-time symmetric coupled resonators has been shown to lead to single-mode lasing operation. However, at the corresponding resonance frequency, an ideal ring resonator tends to support two degenerate eigenmodes, traveling along the cavity in opposite directions. Here, we show a unidirectional single-moded parity-time symmetric laser by incorporating active S-bend structures with opposite chirality in the respective ring resonators. Such chiral elements break the rotation symmetry of the ring cavities by providing an asymmetric coupling between the clockwise (CW) and the counterclockwise (CCW) traveling modes, hence creating a new type of exceptional point. This property, consequently, leads to the suppression of one of the counter-propagating modes. In this paper, we first measure the extinction ratio between the CW and CCW modes in a single ring resonator in the presence of an S-bend waveguide. We then experimentally investigate the unidirectional emission in PT-symmetric systems below and above the exceptional point. Finally, unidirectional emission will be shown in systems of two S-bend ring resonators coupled through a link structure.

Closed-loop superluminal passive cavity

We demonstrate the operation of a closed-loop fast-light cavity that allows rapid (~10 ms) measurements of the cavity mode frequency and its uncertainty. We vary the scale factor by temperature tuning the atomic density of an intracavity vapor cell. The cavity remains locked even as the system passes through the critical anomalous dispersion where a pole is observed in the scale factor. Positive and negative scale-factor enhancements as large as |S| ≈70 were obtained. To our knowledge, these are the first experiments that demonstrate a scale-factor enhancement in a closed-loop fast-light device by changing the optical path length, laying the groundwork for the improvement of cavity-based metrology instruments such as optical gyroscopes.