Novel on chip rotation detection based on the acousto-optic effect in surface acoustic wave gyroscopes

An Acousto-Optic Gyroscope (AOG) consisting of a photonic integrated device embedded into two inherently matched piezoelectric surface acoustic wave (SAW) resonators sharing the same acoustic cavity is presented. This constitutes the first demonstration of a micromachined strain-based optomechanical gyroscope that uses the effective index of the optical waveguide due to the acousto-optic effect rather than conventional displacement sensing. The theoretical analysis comparing various photonic phase sensing techniques is presented and verified experimentally for the cases based on a Mach-Zehnder interferometer, as well as a racetrack resonator. This first prototype integrates acoustic and photonic components on the same lithium niobate on insulator (LNOI) substrate and constitutes the first proof of concept demonstration of the AOG. This approach enables the development of a new class of micromachined gyroscopes that combines the advantages of both conventional microscale vibrating gyroscopes and optical gyroscopes. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Existing gyroscopes for inertial navigation systems are based on either bulky mechanical implementations [1,2] or large volume and high power Optical Gyroscopes (OGs) [3][4][5].MEMS vibratory gyroscopes (MVGs) [6][7][8][9] are an interesting alternative, but have exhibited limitations on various fronts.The need for a large released mass makes MVGs vulnerable to shock [10].Since most MVGs operate at few kHz with quality factors > 1,000, their output bandwidth is limited to mHz for frequency matched operation [11] unless complex bandwidth extension techniques are used [12].Furthermore, the low operation frequency makes the gyroscope susceptible to environmental vibrations [13].On the other hand, OGs such as Fiber Optic Gyroscope (FOG) and Ring Laser Gyroscope (RLG) can achieve both high performance and operation stability [3].Unfortunately, miniaturization and power scaling of these implementations are challenging [14][15][16][17][18][19].In this work, we demonstrate the first prototype of an Acousto-Optic Gyroscope (AOG), which has the theoretical capability of addressing all the major issues encountered in MVGs or miniaturized OGs.The AOG is based on the concept of the Surface Acoustic Wave Gyroscope (SAWG) [20][21][22], in which the Coriolis force detection is performed optically instead of acousto-electrically.The use of SAW resonators enables the realization of a large unreleased mass and wide bandwidth operation.The optical sensing of the strain induced by the Coriolis force (via the acoustooptic effects) provides for extremely low noise levels, high sensitivity, and stable readout.In addition, the optical detection method significantly simplifies the electronic readout.The Coriolis-induced strain is mapped to a change in the effective index of the optical waveguide through the acousto-optic effect.Different photonic phase sensing techniques can be used to detect the index change such as a Mach-Zehnder Interferometer (MZI) [23] operated in the push pull operation or a racetrack (RT) resonator [24].In section 2 of this article, we describe the implementation of the proposed AOG in a lithium niobate on insulator (LNOI) substrate, which was selected because of its unique acoustic and photonic properties [25,26].The Scale Factor, SF, of a gyroscope is defined as the ratio of the output voltage to the input rotation.We derive the SF for the AOG in section 3. Section 3.2 compares the two aforementioned phase sensing techniques deriving the SF for each case.In section 4 we present the overall design of the AOG and in section 5 we discuss its fabrication.The theoretical analysis is verified experimentally in Section 6.Finally, we report the angular random walk (ARW) measurement for the MZI-AOG and compare it with the SAWG fabricated on the same platform.This work constitutes the very first demonstration of the AOG concept.F , is induced on the vibrating pillars in the direction orthogonal to both the input rotation direction and the drive vibration direction.The Coriolis force can be expressed as [25,27]: The pillars are arranged in a checkerboard configuration such that their constructive interference establishes a secondary SAW in the y (sense) direction.For Rayleigh SAW mode, the dominant strain component is the longitudinal one along the propagation direction, S, which can be expressed in terms of the stress, σ as

Principle of operation
where L is the acousto-optical (AO) interaction length and H is the SAW penetration depth [28] (which is less than 10% of the acoustic wavelength, Λ [26]), then we can express the strain, S, as: In SAW gyroscopes [21,29], piezoelectric transducers are commonly used to sense the secondary waves.In this work, the secondary wave is detected through the elasto-optic effect in the photonic waveguides etched in the Lithium Niobate (LN) thin film, i.e. by monitoring the refractive index change, Δ n , due to the strain induced by the secondary wave.The change in the effective index of the optical waveguide is expressed as: where eff p is the effective acousto-optic coefficient in the specific propagation direction of the SAW.The photonic sensing technique shown in Fig. 2 uses a push-pull MZI (PP-MZI), which converts the phase modulation to intensity modulation at the photodetector output by mixing the optical beams from the two MZI arms.However, other phase sensing techniques like AOG RT can also be used, as we will discuss in the following sections.

AOG scale factor and comparison of photonic detection techniques
The SF (or sensitivity) of the AOG is determined by the change in the optical signal intensity, T, due to the phase variation, φ AOG, , , as a function of the external rotation, Ω z , / AOG AOG z β ϕ = ∂ ∂Ω , which directly relates to the SAW cavity design and the elasto-optic characteristics of the LN film.Overall, the SF can be expressed as: The induced phase shift due to rotation, AOG ϕ , can be expressed in terms of the refractive index change, Δn, and the waveguide length, L, as: where 1550 nm λ = is the optical wavelength.The SF is written in this way so that a direct comparison between various phase sensing techniques can be formulated by analyzing the gain factor, max AOG T G ϕ ∂ = ∂ .

Rotation induced phase changes
Placing the waveguides at the location of maximum strain for the standing wave pattern of the SAW cavity enhances the phase sensitivity by the resonator quality factor in the sense direction, Q S .This phenomenon can be accounted for by modifying Eq. ( 5) to be: The vibration velocity in Eq. ( 1) can be expressed in terms of the drive parameters: the electrical power, m P , the drive resonator quality factor, D Q , the resonator equivalent mass, r M [30], and the SAW resonance frequency, m f , as: Combining Eqs. ( 1) -( 7), the rotation induced phase can thus be derived to be equal to: where is the AO figure of merit of the material.

Photonic sensing techniques
Figure 2 shows the two phase sensing techniques considered for comparison in this study.Figure 2(a) represents a PP-MZI where E in represents the input electric field while E o1 and E o2 represent the output fields from the MMI coupler.For differential operation of the PP-MZI, its normalized transfer function is given by sin 2 The factor of two in the sin argument is due to the push-pull operation enabled by separating the MZI arms' centers by a distance equal to 3 / 2 Λ [31,32].This separation implies opposite phase modulation in the two arms such that when one waveguide is under compression, the other one is under tension.Thus, the AOG SF gain can be derived by evaluating the maximum of The AOG RT phase sensing technique is shown in Fig. 2(b) where an RT is coupled to a bus waveguide.We assume that only the two straight arms of the RT contribute to the phase modulation.For this reason the separation between the two straight arms in the RT is set to an even multiple of / 2 Λ , so that both waveguides will be either under compression or tension at the same time.Thus, the transfer function for the RT can be expressed in terms of the round trip intrinsic loss inside the RT, 2  a , the coupling coefficient, 2 r , and the round trip total phase shift, ϕ , as: .Accordingly, the maximum AOG sensitivity gain can be derived as: At this specific bias point, and assuming a low loss resonator, we can approximate in Eq. ( 11) to get: Also for low loss cavity near critical coupling, we can impose that a r ≈ and so as to find a very simple expression of the RT gain factor: To verify this analytical value, the derivative is computed numerically using Matlab and plotted in Fig. 4 as a function of r for two values of 0.85 a = and 0.99 a = . The first value 0.85 a = represents the round trip loss extracted from the RT resonator of this work and is equivalent to a propagation loss of 2.5 dB/cm.The second value of a = 0.99, corresponds to ultra-low losses (2.5 dB/m) that were recently reported for etched waveguide on the same LNOI substrate [33].Note that the finesse of the cavity is varying along that curve as r varies and the dashed lines point out the F value at the points of maximum slope.The numerical analysis confirms our analytical conclusion that the gain in the SF is bounded by 2 /5 F .It also shows that the RT has to be under-coupled for maximum phase sensitivity in agreement with [34].

Acousto-optic gyroscope design
Figure 5 and Fig. 6 show the layout views for the MZI-AOG and the RT-AOG respectively with zoomed-in SEMs of the various constitutive components.Four identical Interdigitated Transducers (IDTs), SAW reflectors and photonic waveguides are placed symmetrically with respect to a central pillar-filled cavity so as to ensure frequency matching between orthogonal SAW resonators.The IDTs in the sense direction are not excited electrically so that they have minimum effect on the secondary SAW standing wave pattern.The reason for having IDTs in the sense direction is to make sure that we have a fully symmetric design and are able to match the frequencies of the drive and sense resonators.The light is coupled in and out using grating couplers.The photonic readout shown in Fig. 5 is based on a (PP-MZI) where a Y junction is used for splitting the optical input into the two arms of the MZI [23] and a 2x2 multimode interference (MMI) 3-dB coupler is used as a beam combiner.The differential output is detected using a balanced photodetector.On the other hand, an RT is used in the photonic read-out where a butterfly MMI coupler [35] is used to couple the light to the RT.The following sub-sections will describe the design of each component forming the two AOGs.

SAW resonator design
The SAW resonator Q in the drive and sense directions can be fully harnessed when the frequencies of the orthogonal resonators are matched.Previous SAW gyroscope designs [20,29,36] targeted SAW propagation direction and LN wafer cuts that provide the highest electromechanical coupling coefficient by driving the SAW in the Z direction for a Y cut LN wafer.However, for such a cut, the material properties in the two orthogonal in-plane directions (X and Z) are not the same due the trigonal crystalline structure of LN.Such a configuration makes frequency matching difficult.In our AOG design, the two SAW resonators are rotated by ± 45° with respect to the Z-direction to preserve symmetry, hence inherently matching the drive and sense frequencies [37].The aperture length is equal to the total cavity length and is chosen to be L = 40Λ.The acoustic wavelength is selected to be 30 m μ Λ = so as to fit the gyroscope design in a 20x20 mm 2 die.This wavelength corresponds to an acoustic frequency of 115 MHz.The SAW reflector has 700 fingers to ensure proper confinement of the SAW inside the cavity.

Photonic components design
For both types of AOGs, grating couplers were used to couple light in and out of the photonic components.The grating coupler dimensions (shown in Fig. 7     The fabrication process flow is depicted in Fig. 8 starting with a Y-cut LNOI 4" wafer.The LN thin film (3" diameter and 500 nm in thickness) is bonded to silicon dioxide (SiO 2 , 1 m μ thick) on a LN substrate.The thin film was formed by means of ion-implantation, slicing and polishing (Fig. 8(A)) by an external vendor [39].The first fabrication step consists in the liftoff of evaporated Al thin film (Fig. 8(B)), which is set to be 100 nm thick and is used to define the IDT and reflector electrodes.After this step, a 140 nm Au layer lift-off is performed (Fig. 8(C)) for patterning of the pillars.Au is also used for coating the Al pads to facilitate wire bonding for testing purposes.The next step is the deposition of SiO 2 (1 µm thick) (Fig. 8(D)) , which is used as a mask layer during the LN etch.Chromium (Cr) (50 nm thick) is then deposited (Fig. 8(E)) and used as a mask for etching SiO 2 .This Cr layer is patterned twice.The first pattern is done with optical lithography to define the waveguides (WGs) (Fig. 8(F)).The second Cr patterning is performed at the die level using electron-beam lithography to define the grating couplers (Fig. 8(G)).Then SiO 2 is etched in an reactive ion etching (RIE) process using fluorine-based chemistry with the double-defined Cr mask (Fig.

8(H))
. Chlorine-based chemistry is used in an inductively coupled plasma (ICP) RIE process to partially etch the LN with the SiO 2 mask (Fig. 8(I)).The Cr mask is also removed during the ICP etch step.The final step is dry etch (Fig. 8(J)) of SiO 2 to expose the metallic pads and completely remove it from the SAW resonator surface.

Characterization of SAW resonators
The frequency responses of the drive and sense acoustic resonators are measured using a vector network analyzer (PNA N5230A) and RF probing.The measurement result showing the magnitude of the cross coupling admittance, Y 21 , between the two ports of each resonator is reported in Fig. 9.The ~40 kHz mismatch between sense and drive frequencies can be attributed to fabrication misalignments.This mismatch is still within the resonator bandwidth,    The slight shift in the wavelength might be attributed to differences in the actual dimensions of the etched waveguides with respect to the design values.The envelope reflects the transfer function of the grating couplers.On the other hand, the RT transfer function with respect to the wavelength is plotted in Fig. 10(b) together with the fitting (to Eq. ( 10)) to extract the round trip loss, a, and the coupling coefficient, r, as well as the Finesse, F. Despite some discrepancies in the fitting of the RT transfer function due mostly to the assumption of having a single mode waveguide (note that the waveguides are 2 µm wide due to fabrication constraints and well above the width required for single-mode operation), it was possible to confidently extract the values of a and r for the fabricated RT.The fiber to chip coupling loss for the MZI was about −35 dB while that for the RT was about −36 dB.The minimum insertion loss for the RT was found at an optical wavelength near 1528 nm, which is different from the design wavelength of the butterfly MMI coupler.The high coupling loss is attributed mostly to the accuracy of the fiber alignment to the photonic chip and to the fabrication tolerance of the gratings couplers dimensions.In fact, our prior work on LNOI gratings couplers has demonstrated insertion loss of about 12 dB per coupler [38].To compensate for such high coupling loss in the AOG measurement, an Erbium Doped Fiber Amplifier (EDFA) is used as described in the next section.Although the butterfly MMI coupler was designed to achieve slightly under-coupling conditions, the extracted value for r at the wavelength of operation is instead reflecting an over-coupling condition (r < a), which ended up impacting the SF negatively.Figure 11 plots the RT transfer function and its derivative for the coupling condition that was achieved experimentally and shows the bias point for maximum sensitivity.Although the attained losses match the one simulated in Fig. 4, it is clear that because of the achieved value of r, the RT configuration is not expected to yield a net enhancement in the sensitivity of the AOG.The plot also shows the bias point at the phase offset of one quarter of the full width half maximum.In term of wavelength, the bias point can be derived as

AOG SF measurement
The AOG measurement setup is shown in Fig. 12 where each of the AOG samples is mounted on the rate table (Ideal Aerosmith 1291RB) together with the optical positioners and connected to the measurement instruments.The gyroscope die is packaged in a Pin Grid Array (PGA) ceramic package.An Ultra-High Frequency Lock-In (UHFLI) amplifier from Zurich Instruments is used to phase lock the SAW drive resonator using a built-in Phase Locked Loop (PLL).In addition, a built-in Proportional Integral Derivative (PID) controller is used to amplitude-control the drive signal for the SAW resonator and reject any variations due to vibration or temperature drift.An optical carrier generated by a benchtop tunable laser (SANTEC TSL-510) is coupled into the optical grating via a vertical groove array (VGA).A polarization controller is used after the laser to make sure that we excite the TE polarization for which the gratings couplers were optimized.The same VGA is also used to couple out the modulated gyroscope signal through another set of fibers in the array.The EDFA is placed after the output coupler to compensate for the coupling loss.The optical alignment is optimized by adjusting a six degree of freedom manipulator while looking for maximum transmission as the laser wavelength is being swept.The photonic output is fed to the lock-in amplifier where the Coriolis component is separated from the quadrature component.Due to the RF cables and fibers, full 360° rotations for the rate table are not allowed.The input rotation is applied as a sinusoidal oscillation to the rate table.To make sure the optical alignment between the fibers and the gratings couplers does not affect the measurement results, the input rotation frequency is limited to 2 Hz and the amplitude to 8 degrees.
The SF can be extracted for each AOG as the slope of the straight line in Fig. 13(a).The measured SF PP-MZI = 48 nV / ( o /sec) in the case of the PP-MZI is higher than that of the RT SF RT = 9 nV / ( o /sec) with the ratio / 5 .3

PP MZI RT
SF SF − ≈ .Due to variations in the coupling efficiency, the values of the SF vary from measurement to measurement within ± 58% of the average value of 48 nV / ( o /sec) and 9 nV / ( o /sec) respectively for the PP-MZI and the RT detection methods.The expected theoretical values for the SFs can be obtained directly from Eqs. ( 8), ( 9) and ( 14) as SF PP-MZI = 58 nV / ( o /sec) and SF RT = 20 nV / ( o /sec).Since the two SAW resonators behave identically for both AOGs, the theoretically predicted ratio between the two SFs can be calculated as the ratio between the two gain factors (see Fig. 13(b)) 2 2.9 0.7 The discrepancy between the theoretical prediction and the measured values is attributed mostly to the uncertainty on the repeatability of the coupling.Furthermore, the actual placement of the pillars and fabrication variations have minor impact on that discrepancy.It is important to note that the RT-based detection method yielded a SF lower than the one of the MZI-based method because of the specific losses and the value of r achieved by the RT resonator in this demonstration.In theory, if lower losses and appropriate values of r are attained, then higher gains are possible from the RT-based detection method.These experimental results showcase the first demonstration of an AOG and confirm the validity of our proposed analytical model for the different photonic sensing techniques.The theoretical projections hint that with the appropriate design of the couplers and reduced losses, the AOG sensitivity could be significantly improved, making it a competitive solution beyond MVGs.

AOG ARW measurement
The zero-rate output (ZRO) of the MZI-AOG was recorded for 4 hours and its Allan deviation is plotted in Fig. 14 from where we can extract ARW of 60 / o hr and bias instability less than 1° / sec.The figure also compares the noise performance of the AOG with the same gyroscope, but operated as a SAWG with acousto-electrical sensing (i.e. the output is sensed through the sense SAW resonator).The results highlight the better stability of the AOG due to the decoupling between the acoustic drive signal and the optical sensing signal.Although far from coming close to the best performance MVGs or OGs, this first prototype shows the feasibility of the proposed idea and lays the foundations for further engineering of a high performance component.

Conclusion
A novel rotation sensing technique based on the acousto-optic effect is developed.Two different photonic phase sensing techniques are considered and compared both theoretically and experimentally.The manufacturability of this novel device is made possible by the development of a fabrication process that integrates acoustic and photonic components on the same LNOI platform.The experimental results demonstrate the feasibility of the proposed AOG and, most importantly, verify the theoretical description of its principle of operation.In this paper, we have presented proof-of-concept results for the first prototype of the AOG.Despite the limited performance, it can be theoretically shown that the technology could yield more than 20 x improvements by reducing the losses on the photonic components (shown to be possible in [33]) and properly designing the MMI coupler.Such improvements yields enhancement of about 20x in the SF and the ARW.Furthermore, additional 20x improvement is possible by increasing the SAW resonators Q and operating at a larger acoustic wavelength.Thus, a new class of highly sensitive strain-based acousto-optic gyroscopes can be developed.

Figure 1
Figure 1 depicts a schematic view of the AOG and offers an overview of its principle of operation.Two orthogonal SAW resonators are shown (only reflectors are shown in the y direction to avoid cluttering the image) with metallic pillars placed at the center acting as the moving mass, p M , of the gyroscope.A SAW standing wave pattern is established along the x (drive) direction.The pillars are placed inside the cavity at the anti-nodes of the SAW standing wave pattern (location of maximum x-directed velocity).The pillars are driven longitudinally with vibration velocity, p v .When out-plane rotation, z Ω , is applied, Coriolis force, c F , is induced on the vibrating pillars in the direction orthogonal to both the input rotation direction and the drive vibration direction.The Coriolis force can be expressed as [25,27]:

Fig. 1 .
Fig. 1. 3D sketch of the AOG (PD = Photo-detector, IDT = Interdigitated transducer).IDT on the sense cavity are not shown to avoid cluttering the drawing, but reflectors are present to point out that a high Q acoustic cavity is also present on the sense side.
SAW phase velocity.Since the stress can be directly related to the Coriolis force as ( )

Fig. 2 .
Fig. 2. Phase sensing techniques for the AOG where the secondary acoustic induced due to rotation is sensed as strain variation in the photonic waveguides: (a) The strained waveguides are part of a PP-MZI and (b) The strained waveguides are part of an RT resonator.

Figure 3
Figure 3 plots RT T and its derivative as function of AOG ϕ .The finesse, F, can be derived

Fig. 3 .Fig. 4 .
Fig. 3. RT transfer function and its derivative as function of phase.Maximum phase sensitivity is obtained at one quarter of the full width half maximum.

Fig. 5 .Fig. 6 .
Fig. 5. Layout view of the MZI AOG with zoomed-in SEMs of the various components forming it.
(a)) were optimized using FDTD LUMERICAL tool for maximum coupling efficiency for the TE polarized light.1 assuming θ m = 8 degrees as the coupling angle were selected.The length of the waveguides of the MZI arms and the RT straight arm is chosen to be equal to the cavity length.The waveguides are placed at the positions of maximum strain in the SAW cavity.The MZI arms' separation is set to 3Λ/2 for push-pull operation while the RT straight arms' separation is set to 7Λ to double the phase sensitivity.The length and width of the 3-dB MMI coupler in the MZI-AOG are chosen to be 3 see Fig.7(b)), to ensure 3-dB splitting around 1550 nm (optical wavelength).The dimensions of the butterfly MMI coupler[35] in the RT-AOG were chosen to be equal to 1

40 Fig. 9 .
Fig. 9. Frequency response for the drive and sense cavities showing a mismatch of 40 kHz which is within the resonator bandwidth (100 kHz).

Figure 10 (
Figure 10(a) plots the MZI transfer function for the two outputs as a function of the wavelength.A balanced output is achieved near the design value of 1550 nm.

Fig. 10 .
Fig. 10.(a) Measured insertion loss for the two output ports of the MZI as function of the wavelength.(b)Measured insertion loss for the RT as function of wavelength together with fitting.a, r and F were extracted from the fitting.

Fig. 11 .
Fig. 11.RT transfer function and its derivative as a function of phase for the actual losses and coupling condition.

Fig. 12 .
Fig. 12. AOG measurement setup.The optical setup with the positioners and manipulators are mounted on top of the rate table.

Fig. 13 .
Fig. 13.(a) Measured output voltage as a function of rotation rate together with fitting to extract the scale factor for each AOG.(b) Theoretical comparison between the two photonic sensing techniques.The value of the expected gain factor for the experimentally demonstrated value of r is indicated on the plot.

Fig. 14 .
Fig. 14.Measured Allan deviation for the zero-rate output of the AOG compared with the experimental results for the same device tested as a SAWG (electro-acoustic read-out instead of acousto-optic).