Frédéric Boeuf
email: frederic.boeuf@st.com

Stéphane Monfray
email: stephane.monfray@st.com

Paul G Charette
email: paul.charette@usherbrooke.ca

Régis Orobtchouk
email: regis.orobtchouk@insa-lyon.fr

Design and Fabrication of a Ring-Coupled Mach-Zehnder Interferometer Gyroscope

Keywords: Integrated gyroscope, resonant gyroscope, SiN waveguide, Mach-Zehnder Interferometer

In this paper, we present a CMOScompatible integrated photonics resonant gyroscope incorporating active Si&Ge components with low-loss SiN waveguiding structures for the first time. The gyroscope design is based on a ring-coupled Mach-Zehnder interferometer (19.2 mm ring length). Based on numerical modelling, the estimated resolution is 1.08 deg/s, representing a 1.56-times improvement over a single ring all-pass design with the same footprint. Further improvement afforded by the MZI-based design is expected under Kerr effet limited conditions. Devices were fabricated with the STMicroelectronics DAPHNE (Datacom Advanced Photonics Nanoscale Environment) 300 mm Photonic R&D platform. Experimental measurements under static (nonrotating) conditions confirm the numerical modelling results.

I. INTRODUCTION

Optical gyroscopes are angular velocity sensors based on the Sagnac effect [START_REF] Lefèvre | The fiber optic gyroscope : second edition[END_REF], which causes a phase shift proportional to angular speed between two optical signals counter-propagating in a rotating loop. They have been used for decades in various domains, such as aeronautics, aerospace or military applications [START_REF] Dell'io | Recent advances in miniaturized optical gyroscopes[END_REF]. The most accurate gyroscopes are interferometric fiber optic gyroscopes (IFOG) and gyrolasers, which can reach inertial to tactical grade resolutions [START_REF] Lefèvre | Comprendre et apprécier le gyrofibre : le gyro aux performances ultimes ?[END_REF][START_REF] Ravaille | Gyromètre optique basé sur une cavité résonante passive en fibre à coeur creux[END_REF]. However, these gyroscopes are expensive and bulky, which makes them incompatible with mass-market production. More recently, emerging applications such as automotive, robotics, biomedical or consumer electronics have increased the demand for small footprints and low-cost gyroscopes [START_REF] Dell'io | Recent advances in miniaturized optical gyroscopes[END_REF][START_REF] Armenis | Advances in gyroscope technologies[END_REF]. Although microelectro-mechanical systems (MEMS) offer a compact alternative for cars and consumer electronics, they require vacuum packaging for high sensitivity [START_REF] Armenis | Advances in gyroscope technologies[END_REF] and cannot support high vibrations or accelerations [START_REF] Venediktov | Passive ring resonator micro-optical gyroscopes[END_REF].

Resonant fiber optic gyroscopes (RFOG), as their name implies, are based on fiber ring resonators and have twice the theoretical sensitivity of IFOGs for an equivalent footprint [START_REF] Terrel | Performance comparison of slowlight coupled-resonator optical gyroscopes[END_REF]. Indeed, shorter fiber lengths in RFOGs [START_REF] Armenis | Advances in gyroscope technologies[END_REF] without crossings result in lower losses [START_REF] Wu | Silicon Integrated Interferometric Optical Gyroscope[END_REF]. RFOGs require a high coherence laser source, however, unlike IFOGs [START_REF] Lefèvre | The fiber optic gyroscope : second edition[END_REF]. RFOG-type designs can be fabricated using integrated photonics, a leading technology for producing small footprint low-cost devices. Resonant gyroscope sensitivity, set by the slope of the response at resonance [START_REF] Guillén-Torres | Ring Resonator Optical Gyroscopes-Parameter Optimization and Robustness Analysis[END_REF], is generally limited in high-performance devices by the Kerr effect, resulting from a power imbalance between the counter-propagating beams [START_REF] Feugnet | Analysis of the design of a passive resonant miniature optical gyroscope based on integrated optics technologies[END_REF]. In 2009, Terrel et al. showed that coupling to a ring resonator via a Mach-Zehnder interferometer (MZI), termed a "Ring-coupled Mach-Zehnder interferometer" gyroscope, could improve the sensitivity of resonator-based gyroscopes as well as decrease the impact of the Kerr effect [START_REF] Terrel | Ring-coupled Mach-Zehnder interferometer optimized for sensing[END_REF].

In this paper, we present the design and characterization of a novel SiN ring-coupled Mach-Zehnder interferometer gyroscope incorporating active Si & Ge components for the first time. The design shows a 1.56× improvement compared to state-of-the-art singlering resonator integrated devices. The MZI-based design also leads to a decrease in noise due to the Kerr effect. The devices were fabricated on the STMicroelectronics 300 mm DAPHNE integrated photonics platform.

II. RING-COUPLED MZI GYROSCOPE : PROPOSED DESIGN

A. Description of the Fabricated Device

The devices were fabricated on the STMicroelectronics 300 mm DAPHNE industrial platform, which is capable of

Eva Kempf

STMicroelectronics

Crolles, France eva.kempf@st.com Grenoble, France philippe.grosse@cea.fr co-integrating Si and SiN waveguides, active PN and PIN Si modulators, and Ge Photodiodes. A schematic of the design is given in Fig. 1. Light at λ 0 =1.31 µm (Pin) is injected into the input Si waveguide via a grating coupler and directed to the CCW(left)/CW(right) branches of the device with a 3dB coupler. Modulators (PIN/PN) in both branches are included for power balancing and modulation in future experiments. The signals are then split by Si-to-SiN tapers between the input power balance monitoring and normalization photodiodes (PDA, PDB) and the gyroscope SiN components (MZI and ring resonator). The upper (reference) arm of the MZI incorporates a heater that maintains a ±π/2 phase shift to maximize sensitivity [START_REF] Terrel | Ring-coupled Mach-Zehnder interferometer optimized for sensing[END_REF]. The lower arm of the MZI is coupled to the square-shaped ring resonator (4.8 mm on a side). Fig. 2 shows a picture of the device after SiN layer deposition for the fabrication of the SiN waveguides. The corner sections are 600×700 nm cross-section single-mode waveguides (propagation losses: ~0.5 dB/cm [START_REF] Guerber | Intégration d'un deuxième niveau de guidage photonique par dépôt de SiN au-dessus du SOI traditionnel[END_REF]). The straight sections are multimode waveguides designed to minimize losses from sidewall roughness (~0.4 dB/cm, width = 1.3 µm). The coupler between the lower arm of the MZI and the ring resonator was designed for critical coupling (κ²=15%). After counter-propagation in the ring, the two optical signals are routed to separate pairs of photodiodes (PD1/PD2, PD3/PD4) for differential measurements (see Pout1 and Pout2 in Fig. 1 for the CW propagating path).

Pierre Labeye

B. Mathematical Response

According to [START_REF] Zhou | Fano resonance-based electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers[END_REF], the normalized photocurrents measured by the photodiode pairs from the two counter-propagating signals in a static gyroscope are given by:

PD 2 PD B = PD 4 PD A = 1 4 • | | τ-e -i2πnL λ •e - αL 2
1-τ•e -i2πnL λ •e - αL 2 +√A•e iπϕ s | | 2 (1) PD 1 PD B = PD 3 PD A = 1 2 • 1 4 • | | - τ-e -i2πnL λ •e - αL 2
1-τ•e -i2πnL λ •e - αL 2 +√A•e iπϕ s | | 2 ( 2
)
where  is the ring round-trip transmission coefficient,  is the ring propagation loss coefficient, L is the ring roundtrip length, ϕ s is the MZI phase shift, A is a factor accounting for losses in the upper MZI arm, n is the effective index of the guided mode, and  is the wavelength. The quadrature arrangement of the PD1/PD2 and PD3/PD4 photodiode pairs at the opposite outputs of the interferometer enables differential measurements of the two counter-propagating signals, PD2-PD1 and PD4-PD3, yielding increased sensitivity [START_REF] Terrel | Ring-coupled Mach-Zehnder interferometer optimized for sensing[END_REF]. Gyroscope sensitivity is maximized by measuring the change between the normalized differential signals, (PD4-PD3)/PDA -(PD2-PD1)/PDB, as a function of rotation.

C. Device Parameters Estimation

Experimental data were obtained by monitoring the photocurrents from all photodiodes while sweeping the source wavelength in steps of 1 pm. Use of the heater was not required as s was already close to -π/2. Fig. 3 shows an example normalized transmission spectrum (PD4-PD3)/PDA and the corresponding fit to (1) and ( 2), where the maximum slope is 2.6•10 11 m -1 . For the (PD2-PD1)/PDB spectrum (not shown), the slope was slightly lower ( 2.1•10 11 m -1 ) due to a lower contrast, which may be corrected by optimizing the design. The ring parameters, τ = 85 ± 0.5%, α = 0.4 ± 0.02 dB/cm, and neff = 1.748 ± 0.01 (guided mode effective index) were estimated with a mode solver. Based on these parameters, (1) and ( 2) were multiplied by an amplitude variable P 0 bounded to [0.5,1.5], and fitted to the experimental data using nonlinear least squares to estimate the remaining unknown parameters, A = 3.5 ± 0.5dB and ϕ s = -0.4π ± 0.05π.

III. RESONANT GYROSCOPE: PERFORMANCE ESTIMATION

A. Working Principle of Resonant Gyroscope

To compare gyroscope architectures, it is necessary to compute both sensitivity and resolution. Optical gyroscopes are based on the Sagnac effect. In ring-resonator based designs (Fig. 4), the resonance peaks in the transmission spectra for the counter-propagating optical signals incur equal and opposite shifts by ∆ν [START_REF] Malykin | Sagnac effect in ring lasers and ring resonators. How does the refractive index of the optical medium influence the sensitivity to rotation ?[END_REF]:

∆ν= 4A L•neff•λ 0 •Ω ( 3
)
where A is the ring area, L is its perimeter, neff is the guided mode effective index, λ 0 is the resonance wavelength in the absence of rotation, and Ω is the rotation speed.

In practice, one does not directly measure ∆ν, but rather the change in power output due to the shift at a fixed frequency ν p [START_REF] Grant | Loss-gain coupled ring resonator gyroscope[END_REF] (Fig. 5). This frequency corresponds to the gyroscope operating point, where the slope in the transmission spectrum is at a maximum, and the response is considered quasi-linear over the operating range. A differential measurement from both counter-propagating signals maximizes the signal-to-noise ratio.

B. Resolution Estimation

The measurement resolution is defined as the change in rotation speed, δΩ, corresponding to a signal level from the photodiodes that cannot be distinguished from the photocurrent standard deviation δi due to noise. Let T(ν p ,Ω) be the ring resonator transmission at frequency ν p and angular speed Ω . According to [START_REF] Guillén-Torres | Ring Resonator Optical Gyroscopes-Parameter Optimization and Robustness Analysis[END_REF], the gyroscope resolution can be written as:

δΩ=C• ( dT dν (ν p )) -1 • L•n•λ 0 4A • δi i D ( 4
)
where i D =RP in corresponds to the injected power, and C is a coefficient representing insertion losses. Sensitivity, S,

defined as S = C• ( dT dν (ν p )) -1 • Lnλ 0 4A
, is independent of the sources of noise and detection methods [START_REF] Grant | Loss-gain coupled ring resonator gyroscope[END_REF]. For a shotnoise limited system, δi is given by [START_REF] Guillén-Torres | Ring Resonator Optical Gyroscopes-Parameter Optimization and Robustness Analysis[END_REF]:

δi=√2qBR(P in •max(T)/C ( 5
)
where q is the elementary charge, B is the bandwidth, R is the photodiode responsivity and P in •max(T) is the maximum power received by the photodiodes. From ( 4), one can see that the higher the slope of the resonance, the better the gyro resolution.

Coupling a ring resonator to a MZI with a π/2 phase shift in the reference arm yields sharp asymmetric Fano resonances [START_REF] Terrel | Ring-coupled Mach-Zehnder interferometer optimized for sensing[END_REF][START_REF] Zhou | Fano resonance-based electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers[END_REF]. In their article [START_REF] Terrel | Ring-coupled Mach-Zehnder interferometer optimized for sensing[END_REF], M. Terrel et al. suggested that for low loss devices, the sharper slopes of Fano resonances compared to classical Lorentzian resonances could improve sensitivity by a factor of 1.305. In addition, they showed the interferometer-based design led to a 25% decrease in power circulating in the ring, which further reduced noise due to the Kerr effect. Fig. 6-TOP shows modeled CW transmission spectra in the case of a static gyroscope for photodiode signals PD1 and PD2 and the differential result PD2-PD1 (normalized by /PDB), assuming A=1 (no losses) and a MZI phase shift of -π/2 (all other ring parameters have estimated values stated above). Fig. 6-MID shows the modeled CW and CCW transmission spectra for cases of static and rotating gyroscopes (the 60k rads/s rotation rate is deliberately large for illustration purposes). Fig. 6-BOT shows the experimentally measured responses corresponding to Fig. 6-TOP, where the Fano resonance profiles are clearly visible. The shot noise limited resolution was computed using ( 4) and ( 5) with C = 4 (signal power is divided by four before reaching the MZI), λ = 1.31µm, L = 19.2 mm, and neff = 1.748. The photodiode parameters were taken from [START_REF] Guillén-Torres | Ring Resonator Optical Gyroscopes-Parameter Optimization and Robustness Analysis[END_REF]: responsivity R = 0.72, bandwidth B = 10 Hz, and the injected power in the grating coupler was taken to be P in = 1 mW . Since two photodiodes are used in each direction for detection, their noise will add quadratically. We therefore need to compute the value max(T) for signals PD1+PD2 and PD3+PD4 and inject it in [START_REF] Armenis | Advances in gyroscope technologies[END_REF]. For an all-pass ring resonator, the maximum value of transmission is determined by τ and is approximately equal to 1 when the losses are low. For this ring-coupled MZI, we computed the transmission maximum as max(PD2+PD1) ≈ 0.79.

Using the measured value of maximum slope from section II.C, we find an initial resolution estimate of δΩ = 2.13°/s. Note, however, that the frequency sampling resolution in Fig. 3 was insufficient to fully resolve the resonance peaks, leading to an under-estimation of the maximum slope. Using the numerical model (Fig. 6-MID) with A = 1 (assuming no losses in the MZI), ϕ s = -π/2, the maximum resonance slope dT/dν was re-calculated, leading to a more realistic resolution estimate of 1.08°/s.

C. Resolution Improvement Compared to a Single Ring

All-pass Gyroscope Compared to a single ring all-pass resonator without an interferometer with a similar footprint, the resonance slope, and thus the sensitivity, of the MZI-coupled design is multiplied by 1.305 [START_REF] Terrel | Ring-coupled Mach-Zehnder interferometer optimized for sensing[END_REF]. To quantify the improvement in resolution, both the increase in slope and decrease in SNR must be taken into account. Considering the effect of the 3 dB couplers in both directions (25% power loss after circulating in the ring compared to 50% loss for an all-pass ring that would use two fewer photodiodes), the SNR is improved by a factor 0.75/0.5=1.5. In addition, compared to a figure of 0.79 for the MZI-coupled gyro, the maximum transmission for an all-pass ring design would be around 0.5 because of the presence of a third 3 dB coupler before the detection photodiodes. This results in a combined SNR degradation of √0.79/0.5=1.257. As a result, the resolution improvement for the MZI-coupled design is 1.305•1.5/1.257 = 1.56. This improvement is even greater considering that the maximum injected power P max is limited by the Kerr effect: since 25% less power is circulating in the ring for the MZI-coupled design compared to a single all-pass ring, we could inject 25% more power before being limited by the Kerr effect, and the total resolution improvement would therefore be 1.56•√1.25 = 1.74.

IV.CONCLUSION

A CMOS-compatible integrated SiN gyroscope based on a ring resonator coupled to a Mach-Zehnder interferometer manufactured on the STMicroelectronics 300 mm DAPHNE industrial platform was presented. A detailed characterization of the gyro performance was given, showing an estimated SNR improvement of 19.3% over a single ring all-pass design. Combined with the sensitivity gain from the sharp Fano resonances due to the MZI, the resolution at an input power of 1 mW was estimated at 2.13 °/s. By refining the characterization measurements and optimizing the device, an estimated resolution of 1.08 °/s is expected. As a result, compared to a single ring all-pass with the same footprint, our design is expected to enhance the resolution by a factor ×1.56. In addition, since 25% less power is circulating in the ring due to the MZI [START_REF] Guerber | Intégration d'un deuxième niveau de guidage photonique par dépôt de SiN au-dessus du SOI traditionnel[END_REF], this improvement could rise to ×1.74 under conditions where the Kerr effect is the limiting noise factor. Experimental measurements under static conditions confirm the numerical modelling results.

Fig. 1 .

 1 Fig. 1. Schematic of the ring-coupled Mach-Zehnder interferometer gyroscope. The PD1/PD2 and PD3/PD4 photodiode pairs enable quadrature measurements of the two counterpropagating optical signals in the ring, while photodiodes PDA and PDB are used for input power balance monitoring and normalization between the CW & CCW signals.

Fig. 2 .

 2 Fig. 2. TOP: Optical microscope picture of the gyroscope before deposition of the metal layers. BOTTOM: Si-to-SiN transition sections and Ge photodiodes.

Fig. 3 .

 3 Fig. 3. Experimental data and corresponding fit to (1) and (2).

Fig. 4 .

 4 Fig. 4. Principle of resonant gyroscope.

Fig. 5 .

 5 Fig. 5. Ring transmission T as a function of frequency with and without rotation

Fig. 6 .

 6 Fig.6. TOP: Modeled CW transmission spectra without rotation for photodiode outputs PD1 & PD2 and the differential signal PD2-PD1; MID: Modeled CW and CCW transmission spectra for the normalized differential signal pairs, PD1-PD2 and PD3-PD4, for static and rotating gyroscopes (60k rads/s CW); BOT: Experimental measurements corresponding to TOP.

V. ACKNOWLEDGMENTS

This work was supported by a European IPCEI program and IRT Nanoelec.

VI.REFERENCES