Existing gyroscopes for inertial navigation systems are based on either bulky mechanical implementations or large volume and high power Optical Gyroscopes (OGs). MEMS vibratory gyroscopes (MVGs) are an interesting alternative but have exhibited limitations on various fronts. The need for a large released mass makes MVGs vulnerable to shock. Because most MVGs operate at few kHz with quality factors >1,000, their output bandwidth is limited to mHz for frequency matched operation unless complex bandwidth extension techniques are used. Furthermore, the low operation frequency makes the gyroscope susceptible to environmental vibrations. On the other hand, OGs such as Fiber Optic Gyroscope (FOG) and Ring Laser Gyroscope (RLG) can achieve both high performance and operation stability. Unfortunately, miniaturization and power scaling of these implementations are challenging.
Disclosed herein is 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), 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 acousto-optic 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) operated in the push pull operation or a racetrack (RT) resonator. Herein is described an implementation of the AOG in a lithium niobate on insulator (LNOI) substrate, which was selected because of its unique acoustic and photonic properties. The Scale Factor, SF, of a gyroscope is defined as the ratio of the output voltage to the input rotation. The derivation of the SF for the AOG and a comparison the two aforementioned phase sensing techniques are shown below. Various embodiments and a method of fabrication are presented. A theoretical analysis verified experimentally is also discussed.
F
c=−2MpΩz×vp (1)
The pillars are arranged in a checkerboard configuration such that their constructive interference establishes a secondary SAW in the sense (Y) 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, □ as S≈σ/(ρvR2) where ρ=4700 kg/m3 (for lithium niobate (LN)) is the substrate mass density and vR=3488 m/sec is the Rayleigh SAW phase velocity. Because the stress can be directly related to the Coriolis force as σ=Fc/(LH) where L is the acousto-optical (AO) interaction length and H is the SAW penetration depth, (which is less than 10% of the acoustic wavelength, Λ), then the strain, S, can be expressed as:
In one embodiment, the secondary wave is detected through the elasto-optic effect in the photonic waveguides etched in the Lithium Niobate (LN) thin film, that is, by monitoring the refractive index change, Δn, due to the strain induced by the secondary wave. The change in the effective index of the optical waveguide is expressed as:
Δn=½n3peffS (3)
where peff is the effective acousto-optic coefficient in the specific propagation direction of the SAW.
In an alternate embodiment, the device can be operated as a SAWG with acousto-electrical sensing, wherein the output is sensed through the sense SAW resonator.
FIG. shows one embodiment of the invention wherein the photonic sensing technique using 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. In other embodiments, other phase sensing techniques like AOG RT can also be used, as discussed below.
The SF (or sensitivity) of the AOG is determined by the change in the optical signal intensity, T, due to the phase variation, φAOG, G=∂T/∂φAOG, as a function of the external rotation, Ωz, βAOG=∂φAOG/∂Ωz, 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, φAOG, can be expressed in terms of the refractive index change, □n, and the waveguide length, L, as:
where λ=1550 nm is the optical wavelength. The SF is written in this way such that a direct comparison between various phase sensing techniques can be formulated by analyzing the gain factor,
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, Qs. This phenomenon can be accounted for by modifying Eq. (5) Error! Reference source not found. to be:
The vibration velocity in Eq. (1) can be expressed in terms of the drive parameters: the electrical power, Pm, the drive resonator quality factor, QD, the resonator equivalent mass, Mr and the SAW resonance frequency, fm, as:
Combining Eqs. (1)-(7), the rotation induced phase can thus be derived to be equal to:
where M2=(n6 (peff)2)/(ρvR3) is the AO figure of merit of the material.
FIG. shows the two-phase sensing techniques considered for comparison in this study. FIG. (a) represents a PP-MZI where Ein represents the input electric field while Eo1 and Eo2 represent the output fields from the MMI coupler. For differential operation of the PP-MZI, its normalized transfer function is given by TPP-MZI=sin 2φAOG. The factor of two in the argument of the sin function is due to the push-pull operation enabled by separating the MZI arms' centers by a distance equal to 3Λ/2. 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 ∂T/∂φAOG, which is equal to:
G
PP-MZI=2 (9)
The AOG RT phase sensing technique is shown in FIG. (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 Λ/2, such that both waveguides will be either under compression or under 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, a2, the coupling coefficient, r2, and the round trip total phase shift, φ, as:
where φ=φo+2φAOG,
is the round trip phase shift, and LT is the total racetrack length. Thus:
FIG. plots TRT and its derivative as function of φAOG. The finesse, F, can be derived also in terms of a and r as
The plot in
has a maximum at a specific phase offset that equals to one quarter of the full width half maximum (Δφ
Accordingly, the maximum AOG sensitivity gain can be derived as:
At this specific bias point, and assuming a low loss resonator, we can approximate sin φ≈Δφ1/2/4 and
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 ∂RT/∂φAOG is computed numerically using Matlab and plotted in FIG. as a function of r for two values of a=0.85 and a=0.99. The first value a=0.85 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. 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 2F/5. It also shows that the RT has to be under-coupled for maximum phase sensitivity.
FIG. and FIG. 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 such 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 design is fully symmetric, and the frequencies of the drive and sense resonators are able to be matched. The light is coupled in and out using grating couplers.
The photonic readout shown in FIG. is based on a (PP-MZI) where a Y junction is used for splitting the optical input into the two arms of the MZI and a 2×2 multimode interference (MMI) 3-dB coupler is used as a beam combiner. The differential output is detected using a balanced photodetector. An RT is used in the photonic read-out where a butterfly MMI coupler is used to couple the light to the RT.
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 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 the design of the AOG, 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. The aperture length is equal to the total cavity length and is chosen to be L=40Λ. The acoustic wavelength is selected to be Λ=30 μm so as to fit the gyroscope design in a 20×20 mm2 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.
Frequency matching between the drive and sense directions can also be attained by separately tuning the center frequencies of each acoustic cavity by modifying the electrical boundary conditions for the acoustic gratings (reflectors). By varying the electrical load attached to the reflectors between open circuit and short circuit conditions a continuous range of frequencies within a few 1,000 s parts per million of the resonator center frequencies can be attained.
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
The length of the waveguides of the MZI arms and the RT straight arm are chosen to be equal to the cavity length. The waveguides are placed at the positions of maximum strain in the SAW cavity. The separation of the MZI 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 L3dB-MMI=118.1 μm and W3dB-MMI=11.6 μm, respectively, as shown in
Electrodes can be placed next to the waveguides so as to apply an electric field across it and induce an index of refraction change through the electro-optic effect and tune the wavelength of operation of either the MZI or the RT.
The fabrication process flow is depicted in FIG. starting with a Y-cut LNOI 4″ wafer. The LN thin film (3″ diameter and 500 nm in thickness) is bonded to silicon dioxide (SiO2, 1 μm thick) on a LN substrate. The thin film was formed by means of ion-implantation, slicing and polishing (A) by an external vendor. The first fabrication step consists in the lift-off of evaporated Al thin film, as shown in (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 (C) for patterning of the pillars. Au may also be used for coating the Al pads to facilitate wire bonding for testing purposes. The next step is the deposition of SiO2 (1 μm thick) (D), which is used as a mask layer during the LN etch. Chromium (Cr) (50 nm thick) is then deposited (E) and used as a mask for etching SiO2. This Cr layer is patterned twice. The first pattern is done with optical lithography to define the waveguides (WGs) (F). The second Cr patterning is performed at the die level using electron-beam lithography to define the grating couplers (G). Then SiO2 is etched in a reactive ion etching (RIE) process using fluorine-based chemistry with the double-defined Cr mask (H). Chlorine-based chemistry is used in an inductively coupled plasma (ICP) RIE process to partially etch the LN with the SiO2 mask (I). The Cr mask is also removed during the ICP etch step. The final step is dry etch (J) of SiO2 to expose the metallic pads and completely remove it from the SAW resonator surface.
The novel aspect of the fabrication process is that the transducers, the reflectors and the pillars are all fabricated in the same metallic layer. The metallic material of the layer can be one of a number of materials, such as tungsten (W), gold (Au), aluminum (Al), platinum (Pt), nickel (Ni), molybdenum (Mo), copper (Cu), iridium (Ir), ruthenium (Ru), palladium (Pd), and silver (Ag) or any alloy of the same. Beyond lithium niobate, the SAW components may be composed of GaAs, AlN, Sc-doped AlN, PZT, GaN, ZnO. These materials may comprise the entire wafer or can be a thin film on silicon. The photonic components may be composed of LN, As2S3, GaAs, GaN, AlN, InGaAs, AlGaAs, InP, or any other material which can produce the acousto-optic effect.
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, Y21, between the two ports of each resonator is reported in FIG. The ˜40 kHz mismatch between sense and drive frequencies can be attributed to fabrication misalignments. This mismatch is still within the resonator bandwidth, which is approximately 100 kHz since the loaded QD=QS=1000. The quality factor and mismatch can be considered as the limiting aspect for the AOG bandwidth (50 kHz) which is well beyond what can be accomplished by MVGs.
Characterization of the Photonic MZI and RT—
FIG. (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.
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. (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 is 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. Prior work on LNOI gratings couplers has demonstrated insertion loss of about 12 dB per coupler. 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.
The AOG measurement setup is shown in FIG. where each of the AOG samples is mounted on a rate table 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 is coupled into the optical grating via a vertical groove array (VGA). A polarization controller is used after the laser to make sure that the TE polarization is excited, 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 if 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 possible. 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. (a). The measured SFPP-MZI=48 nV/(°/sec) in the case of the PP-MZI is higher than that of the RT SFRT=9 nV/(°/sec) with the ratio SFPP-MZI/SFRT≈5.3. 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/(°/sec) and 9 nV/(°/sec) respectively for the PP-MZI and the RT detection methods. The expected theoretical values for the SFs can be obtained directly from Eq. (8), (9) and (14) as SFPP-MZI=58 nV/(°/sec) and SFRT=20 nV/(°/sec). Because 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, as shown in
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.
The zero-rate output (ZRO) of the MZI-AOG was recorded for 4 hours and its Allan deviation is plotted in
A novel rotation sensing technique based on the acousto-optic effect has been disclosed herein. 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.
Despite the limited performance, it can be theoretically shown that the invention could yield more than 20× improvements by reducing the losses on the photonic components and properly designing the MMI coupler. Such improvements yield enhancement of about 20× in the SF and the ARW. Furthermore, additional 20× 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.
To those skilled in the art to which the invention relates, many modifications and adaptations of the invention will suggest themselves. Implementations provided herein, including sizes, shapes, ratings and specifications of various components or arrangements of components, and descriptions of specific manufacturing processes, should be considered exemplary only and are not meant to limit the invention in any way. As one of skill in the art would realize, many variations on implementations discussed herein which fall within the scope of the invention are possible. Accordingly, the method and apparatus disclosed herein are not to be taken as limitations on the invention but as an illustration thereof.
This application claims the benefit of U.S. Provisional Application No. 62/606,676, filed Oct. 3, 2017.
This invention was made with government support under a contract from the Defense Advanced Research Projects Agency (DARPA) entitled Precise Robust Inertial Guide for Munitions (PRIGM)-Advanced Inertial Micro Sensor (AIMS) program (Award No. N66001-16-1-4025). The U. S. Government has certain rights in the invention.
Number | Date | Country | |
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62606676 | Oct 2017 | US |