Rotation Sensing Ring Resonator

• Rotation sensing ring resonators are closed-loop systems that convert angular motion into measurable shifts using the Sagnac effect and other transduction mechanisms.
• Optical implementations leverage both active and passive architectures, balancing geometric scaling with high-Q, finesse, and robust readout strategies.
• Recent advances include matter-wave and quantum extensions that employ innovative stabilization and phase locking to enhance sensitivity and resolution.

A rotation sensing ring resonator is a closed-loop resonant system in which angular motion is transduced into a measurable spectral, phase, or modal observable by virtue of circulation around a ring. In optical implementations, the dominant mechanism is usually the Sagnac effect: clockwise and counterclockwise waves acquire different effective path times or resonance conditions, producing a beat note, resonance splitting, or phase shift proportional to rotation. The term also encompasses matter-wave and quantum-ring realizations in which rotation is encoded in standing-wave precession, cavity transmission spectra, or a rotation-dependent phase-transition edge rather than in an optical beat frequency. Across the literature, the concept ranges from meter-scale ring laser gyroscopes and passive resonant gyroscopes to whispering-gallery-mode microresonators, hollow-core-fiber cavities, silicon photonic rings, and ring-shaped Bose–Einstein condensates (Belfi et al., 2011, Liu et al., 2019, Maccioni et al., 2022, Mao et al., 2022, Fsaifes et al., 2016, Mou et al., 2021, Woffinden et al., 2022, Pradhan et al., 2023).

1. Fundamental transduction mechanisms

In free-space and integrated optical gyroscopes, the standard transduction law is the Sagnac relation. For a ring laser gyroscope, one reported form is

$f_s = \frac{4A}{\lambda P}\,\Omega \cos\theta,$

where $A$ is the enclosed area, $P$ the perimeter, $\lambda$ the intracavity wavelength, and $\theta$ the angle between the area vector and the rotation axis. Equivalent vector forms, such as

$$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$

appear in passive ring gyroscope formulations. In both cases the scale factor is set by $A/P$, so geometry is not an implementation detail but part of the sensing physics itself (Maccioni et al., 2022, Gereons et al., 18 Jun 2026).

The distinction between active and passive optical rings is operational rather than conceptual. In an active ring laser gyroscope, the cavity itself lases in the two counterpropagating directions and the output is the beat frequency between them. In a passive resonant gyroscope, an external laser is injected and locked to the ring resonances in both directions; the rotation signal is then extracted from the difference between the clockwise and counterclockwise resonance conditions. A representative passive formulation writes the measured Sagnac frequency as

$f_s = f_{AOM} - f_{FSR},$

so the observable is the deviation of the acousto-optic-modulator frequency from the cavity free spectral range rather than a direct free-running laser beat (Liu et al., 2019).

For whispering-gallery-mode resonators, the optical-frequency shift is հաճախ expressed as a Sagnac–Fizeau correction to the cavity resonance,

$$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$

which is effectively linear in $\Omega$ when the dispersion term is small. In the millimeter-scale wedged resonator gyroscope, this shift is measured as a bidirectional beat whose sign distinguishes clockwise from counterclockwise rotation (Mao et al., 2022).

Matter-wave ring resonators implement the same general idea with different observables. In a ring-shaped Bose–Einstein condensate, two counter-propagating phonon modes form a standing wave in the superfluid frame, and in the laboratory frame the standing-wave pattern rotates at angular rate $A$0 for azimuthal mode number $A$1. The rotation signal is read from the phase of the complex Fourier amplitude $A$2 rather than from an optical beat note (Woffinden et al., 2022). In the Bose–Hubbard ring model, rotation enters as a Peierls phase in the hopping term,

$A$3

shifting the superfluid–Mott-insulator phase boundary; the proposed sensing observable is the change in the order parameter near the critical edge (Jiang et al., 2022).

A further cavity-assisted matter-wave variant uses a ring Bose–Einstein condensate inside an optical cavity driven by orbital-angular-momentum modes. There, a rotating angular lattice modifies the cavity transmission spectrum through side-mode frequencies

$A$4

making the output sensitive either to condensate chirality or, if the winding number is known, to laboratory rotation (Pradhan et al., 2023).

2. Principal architectures and geometric realizations

The architecture of a rotation sensing ring resonator determines its scale factor, linewidth, nonreciprocity budget, and feasible stabilization strategy. The following implementations illustrate the range of established and proposed platforms.

Platform	Representative implementation	Reported characteristics
Active ring laser gyroscope	Square He–Ne cavity with side length 1.35 m, perimeter $A$5, area $A$6 (Belfi et al., 2011)	Continuous operation longer than 30 days
Passive resonant gyroscope	Heterolithic 1 m × 1 m square ring cavity (Liu et al., 2019)	Finesse about 141,000; quality factor $A$7
Geometrically locked ring laser gyroscope	Square cavity $A$8 with diagonal Fabry–Perot resonators (Maccioni et al., 2022)	Fully operative for 14 days
3D passive ring gyroscope	Tetrahedral array with four triangular cavities, side length $A$9, perimeter $P$0 (Gereons et al., 18 Jun 2026)	Free spectral range $P$1
Wedged WGM resonator gyroscope	Silica resonator of diameter 2.5 mm (Mao et al., 2022)	Loaded $P$2 for the sensing unit
Hollow-core-fiber test resonator	15 cm diameter semi-bulk ring using Kagome HC-PCF (Fsaifes et al., 2016)	Linewidth 3.2 MHz; contrast 89%
SOI ring resonator for gyroscopic use	17.3 mm strip-waveguide ring on 220 nm SOI (Mou et al., 2021)	$P$3; FSR 0.036 nm; resonance depth 0.9810

Large active and passive free-space rings maximize $P$4 and therefore maximize raw Sagnac scaling. This is explicit in the Earth-rotation and seismology instruments, which use square or tetrahedral geometries with mirror-defined cavities and high mechanical rigidity (Liu et al., 2019, Maccioni et al., 2022, Gereons et al., 18 Jun 2026). Their design problem is dominated by geometry preservation, backscatter management, and long-term operation rather than by fabrication compatibility.

Microresonator and integrated-photonics platforms invert those priorities. The wedged silica WGM gyroscope exploits clockwise and counterclockwise circulation in a millimeter-scale resonator with high $P$5 and taper phase matching (Mao et al., 2022). The large-area SOI strip-waveguide ring seeks photon-gyroscopic suitability through low-loss multimode straight sections, single-mode bends and couplers, 90° Bezier bends, and linear tapers, thereby combining single-mode spectral purity with a 17.3 mm cavity length (Mou et al., 2021).

Fiber resonators occupy an intermediate regime. The Kagome hollow-core-photonic-crystal-fiber test resonator was built specifically to assess resonant rotation sensing. Its stated motivation is the suppression of Kerr-induced non-reciprocity by guiding light mostly in air rather than silica. The reported linewidth, contrast, and coupling efficiency are presented as compatible with medium-to-high-performance rotation sensing, even though the paper explicitly treats the device as a test resonator rather than a complete gyroscope (Fsaifes et al., 2016).

A plausible implication is that ring-resonator gyroscope design is organized by two competing routes to sensitivity: enlarging the geometrical scale factor, or increasing resonance discrimination through $P$6, finesse, and contrast. The literature does not reduce those routes to a single universal optimum; instead, each platform balances them against a different dominant nonideality.

3. Stabilization, locking, and readout strategies

Because the sensed quantity is typically much smaller than the uncontrolled drift of the resonator, readout architecture is inseparable from sensing architecture. In the geometrically locked GP2 ring laser gyroscope, two diagonal Fabry–Perot cavities formed by the same mirrors as the square ring are locked to a reference metrological He–Ne laser using a Pound–Drever–Hall-type method. An acousto-optic modulator sweeps the injected frequency, the error signal drives piezoelectric transducers, and the correction is applied symmetrically on each diagonal so that cavity length is changed without distorting the square geometry. The same paper emphasizes that this symmetric correction also helps preserve the relative backscattering phases from the mirrors, thereby suppressing nonlinear laser-dynamics errors in the Sagnac signal (Maccioni et al., 2022).

In the 1 m × 1 m passive resonant gyroscope, both counterpropagating beams are phase modulated and PDH-locked to adjacent longitudinal modes of the square ring cavity. The secondary loop uses an acousto-optic modulator at about 75 MHz, matching the cavity FSR, and the rotation signal is the residual difference $P$7. The paper also reports the use of a reference ultra-stable laser and an adaptive filter to subtract cavity-drift-correlated noise from the Sagnac readout, illustrating a passive-cavity strategy in which common-mode cavity motion remains a first-order concern because the two locks are separated by one FSR rather than perfectly common-mode (Liu et al., 2019).

The active He–Ne gyroscope developed for nano-rotational motion sensing uses a distinct but related control philosophy. Its perimeter is stabilized with piezoelectric actuators moving mirror boxes along a diagonal, and a double-PZT configuration moves two opposite mirrors symmetrically. The same system stabilizes the beam intensities through a PID analog controller acting on the RF plasma excitation. Offline correction then estimates null shift through $P$8 and backscatter pulling through a diagnostic based on

$P$9

followed by $\lambda$0. The paper explicitly attributes the strongest low-frequency improvement to this combination of active stabilization and offline systematics subtraction (Belfi et al., 2011).

In the millimeter-scale wedged WGM gyroscope, readout is built around a bidirectional pump-probe scheme rather than cavity locking in the meter-scale gyroscope sense. A narrow-linewidth tunable diode laser near 1550 nm is split 50/50 and launched into the same fiber taper from opposite directions. One arm contains an acousto-optic modulator to avoid direct interference and create a measurable offset, and the beat is monitored with a lock-in amplifier. The experimentally extracted beat of interest is $\lambda$1, which directly tracks rotation and changes sign between clockwise and counterclockwise rotation (Mao et al., 2022).

A more recent integrated proposal couples a rotation-sensing single-mode optical ring resonator to an inverse weak value amplified Sagnac interferometer. In that design the ring produces a Sagnac phase

$\lambda$2

while the dark-port readout yields

$\lambda$3

with effective amplification by $\lambda$4 under post-selection. The paper argues that the advantage is not merely formal amplification but the ability to use larger input power while keeping the detector near saturation-limited detected power (Yanik et al., 22 Jul 2025).

Three-dimensional passive ring gyroscopes introduce an additional layer of readout: vector reconstruction. In the tetrahedral free-space system, three non-coplanar cavities provide projected rotation rates, and the Cartesian rotation vector is obtained through inversion of the normal-vector matrix, $\lambda$5. This makes the resonator array itself part of the estimator (Gereons et al., 18 Jun 2026).

4. Reported performance and dominant limitations

Reported performance spans many orders of magnitude and should be interpreted in the context of bandwidth, axis, platform size, and noise model rather than as directly comparable headline numbers. The geometrically locked GP2 ring laser gyroscope reports long-term stability of about $\lambda$6 over one day and short-term sensitivity of about $\lambda$7 in the $\lambda$8–$\lambda$9 Hz band, with 14 days of continuous unattended operation and no data points lost in locked mode (Maccioni et al., 2022). The 1 m × 1 m passive resonant gyroscope reports rotation resolution of about $\theta$0 at an integration time of 1000 s and sensitivity of about $\theta$1 in the 5–100 Hz band (Liu et al., 2019). The 1.82 m$\theta$2 active He–Ne ring laser demonstrates an angular sensitivity at the level of $\theta$3 below 1 Hz in the horizontal-plane configuration, with earlier operation already at few $\theta$4 in the 10–100 mHz band (Belfi et al., 2011).

Compact and transportable architectures report different performance envelopes. The 3D passive ring gyroscope for seismology reaches white-noise-limited sensitivities of $\theta$5, $\theta$6, and $\theta$7 on the $\theta$8, $\theta$9, and $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$0 axes, respectively, with minimum Allan deviations of $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$1, $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$2, and $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$3 at short averaging times (Gereons et al., 18 Jun 2026). The Kagome hollow-core-fiber test resonator does not report inertial rotation data, but from the measured linewidth and contrast the authors estimate a shot-noise-limited angular random walk of about $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$4 for the Kagome A resonator with $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$5 cm and $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$6 mW (Fsaifes et al., 2016). The chip-scale optical gyroscope with inverse weak value amplified readout is presently a proposal rather than an experimental sensor; under the stated conservative and idealized parameter choices it reports a minimum detectable angular rotation rate of $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$7 and Allan deviation of $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$8, with more than 10× improvement over its baseline ring-plus-Sagnac comparator at fixed detected power (Yanik et al., 22 Jul 2025).

Matter-wave platforms currently operate at a much coarser absolute scale. In the ring-BEC phonon interferometer, the experimentally achievable single-shot sensitivity is about $$\delta f = \frac{4A}{\lambda P}\,\mathbf{\Omega}\cdot \mathbf{n},$$9, while the atomic-shot-noise-limited estimate is $A/P$0 (Woffinden et al., 2022). The ring-BEC-in-cavity scheme identifies $A/P$1 as the approximate practical limit for clearly resolving the side-mode peaks corresponding to $A/P$2 in the configuration studied for $A/P$3 (Pradhan et al., 2023).

The limitation mechanisms are highly platform-specific but structurally similar. In large passive and active optical rings, the limiting terms reported across the literature are detection noise, residual amplitude modulation, cavity mechanical instability, air currents, acoustic coupling, temperature instability, backscatter-induced pulling, and geometric drift (Liu et al., 2019, Belfi et al., 2011, Gereons et al., 18 Jun 2026). In GP2, high-frequency locking efficiency is limited by piezoelectric actuators that must move more than 2 kg, restricting servo bandwidth to only a few tenths of a hertz, while the stated laboratory environment adds vibrational, thermal, electromagnetic, and electronic noise (Maccioni et al., 2022). In the wedged WGM gyroscope, the effective silica index varies from about 1.44 to 1.48 due to environment, contributing a small band around the linear beat-versus-rotation curve (Mao et al., 2022). In the phonon interferometer, by contrast, the dominant limitation is intrinsic many-body damping rather than technical noise, with thermal Landau damping and nonlinear high-harmonic generation identified as the principal decay channels (Woffinden et al., 2022).

A recurring misconception is that the highest raw $A/P$4 or finesse alone determines gyroscope performance. The hollow-core-fiber study explicitly argues otherwise by introducing a shot-noise figure of merit proportional to $A/P$5 rather than to finesse alone, thereby emphasizing linewidth and contrast jointly (Fsaifes et al., 2016). This suggests that usable rotation sensitivity is best understood as a systems quantity combining scale factor, resonance discrimination, nonreciprocity suppression, and stable readout.

5. Quantum, hybrid, and matter-wave extensions

Rotation sensing ring resonators have increasingly been generalized beyond classical two-beam cavity gyroscopes. One theoretical direction uses non-Hermitian coupled resonators. In the proposal based on two coupled whispering-gallery-mode resonators with loss and gain, the rotating active resonator experiences the Sagnac–Fizeau shift

$A/P$6

and the coupled supermode eigenfrequencies

$A/P$7

become rotation-dependent. The proposed observables are the steady-state average photon number and the output-field fluctuation spectra, and the paper explicitly states that operation near an exceptional point is not required (Tian et al., 2019).

A distinct quantum-metrological proposal treats a spinning WGM microresonator as an effective SU(2) interferometer. A large-detuned two-level atom mediates an effective coupling between the clockwise and counterclockwise modes, producing an effective Hamiltonian

$A/P$8

The reported result is Heisenberg-limit scaling in the linear case, with $A/P$9, and beyond-Heisenberg scaling in a nonlinear extension with Kerr-type terms, where $f_s = f_{AOM} - f_{FSR},$0. The paper attributes this enhancement to the fact that with atom-induced mode coupling the rotation parameter is encoded in both phase and amplitude rather than in phase alone (Cheng et al., 2021).

The ring-shaped BEC phonon interferometer is the most direct matter-wave analogue of a hemispherical resonator gyroscope in the dataset. Counter-propagating azimuthal phonons create a standing wave,

$f_s = f_{AOM} - f_{FSR},$1

which in the laboratory frame becomes

$f_s = f_{AOM} - f_{FSR},$2

The observable is the phase of

$f_s = f_{AOM} - f_{FSR},$3

so the slope of $f_s = f_{AOM} - f_{FSR},$4 yields $f_s = f_{AOM} - f_{FSR},$5. The same work reports rapid decay with measured quality factors up to $f_s = f_{AOM} - f_{FSR},$6, a typical $f_s = f_{AOM} - f_{FSR},$7 case with $f_s = f_{AOM} - f_{FSR},$8, and an idealized numerical regime in which early-time interrogation could reach $f_s = f_{AOM} - f_{FSR},$9 (Woffinden et al., 2022).

The Bose–Hubbard ring model proposes a different sensing principle: rotation shifts the quantum phase-transition edge by modifying the hopping term through $$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$0, with mean-field decoupling yielding an effective local Hamiltonian that depends on $$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$1. The authors state that at the exact critical edge the sensing resolution depends on the rotation velocity, the particle numbers, and the ring radius, while being independent of the hopping constant and on-site interaction. This is not a resonator in the optical-finesse sense, but it is a ring-resonator-like rotation sensor in the broader sense of a closed-loop phase-sensitive system (Jiang et al., 2022).

The ring-BEC-in-cavity work introduces a hybrid optomechanical interpretation. The cavity is both probe and readout, the condensate acts as a mechanical rotor, and the relevant signal is the cavity phase-quadrature spectrum

$$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$2

Rotating the optical lattice breaks chirality and makes the spectrum sensitive to the sign as well as the magnitude of the winding number. Conversely, with known winding number the same configuration serves as a laboratory rotation sensor (Pradhan et al., 2023).

6. Related ring-resonator phenomena and common distinctions

Not every ring-resonator phenomenon that involves frequency splitting, mode rotation, or polarization rotation constitutes inertial rotation sensing. This distinction is explicit in several adjacent works. The subwavelength-grating ring resonator that generates transverse optical spin is relevant because it uses quasi-degenerate modes, mode hybridization, avoided crossings, and a ring geometry with azimuthal circulation, but the reported splitting is caused by bending-induced symmetry breaking rather than by Sagnac rotation. The paper states directly that it does not discuss gyroscope operation, inertial rotation measurement, or rotation-induced resonance splitting (Iukhtanov et al., 10 Feb 2026).

The superconducting four-port ring resonator is similarly adjacent rather than direct. It supports two orthogonal lowest-order modes and shows that transmission-line inhomogeneities cause frequency splitting and modal-axis rotation relative to the ports. The mode-rotation angle is given by

$$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$3

but this “mode rotation” is a rotation in modal basis, not measurement of mechanical angular velocity. The paper is best read as a precursor study of the dual-mode physics that a superconducting rotation sensor would need, rather than as a completed gyroscope (Sun et al., 30 Jun 2025).

The Vernier-effect ring and racetrack resonator study is also not a rotation-sensing paper. Its stated contribution is FSR extension and resonance suppression through cascaded and parallel resonator architectures, with the effective FSR governed by a Vernier relation such as

$$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$4

Its relevance to gyroscopes is therefore indirect: larger effective FSR and stronger suppression could reduce readout ambiguity and intra-channel cross-talk, but the paper explicitly notes that the Vernier effect does not increase the fundamental Sagnac response (Zhang et al., 2023).

A different source of confusion arises from optical rotation that is not inertial rotation sensing. The twisted split-ring-resonator photonic metamaterial exhibits pure optical activity, retrieved index differences as large as $$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$5, rotation angles of about $$\Delta_{\mathrm{Sagnac}} = \frac{n r \Omega \omega_a}{c}\left( 1-\frac{1}{n^2} -\frac{\lambda}{n}\frac{dn}{d\lambda} \right),$$6 for 205 nm sample thickness, and circular dichroism of about 33%. Its mechanism is chiral mode splitting between left- and right-handed circular polarizations, not angular-velocity sensing (Decker et al., 2010). A plausible implication is that such strong polarization-dependent phase response could serve as a compact transduction element in a broader sensing architecture, but that implication is not itself a claim of the paper.

The field as a whole therefore contains two distinct uses of the phrase “rotation” in ring systems. One use refers to physical angular motion measured through Sagnac nonreciprocity, standing-wave precession, or a rotation-dependent quantum phase boundary. The other refers to rotation of polarization, handedness of local field circulation, or rotation of modal axes in a degenerate-mode subspace. Treating these as equivalent obscures the actual sensing mechanism. Within the stricter inertial-sensing sense, the defining feature of a rotation sensing ring resonator remains a closed-loop resonant system whose measurable output is calibrated to angular velocity or rotational state through a nonreciprocal or frame-dependent ring response (Belfi et al., 2011, Liu et al., 2019, Maccioni et al., 2022, Mao et al., 2022, Woffinden et al., 2022).