Broadband acousto-optic modulators on Silicon Nitride

Abstract

Thin silicon nitride integrated photonics platforms rely on weakly confining waveguides and thick oxide cladding layers to enable ultra-low-optical losses on chip. Due to these favorable properties, this technology is seeing increased use in chip-scale systems tasked with manipulating and controlling classical and quantum optical systems. Phase-modulators play a crucial role in the low-noise control loops of such systems, but optically broadband phase modulators remain elusive as the same properties used to enable ultra-low-optical losses make interaction with the optical mode difficult. Here we show an unreleased and optically broadband acousto-optic modulator architecture on this platform enabled by long modulation lengths in a compact spiral structure. These devices achieve a V_π of 8.98 V at a modulation frequency of 704 MHz across an optical bandwidth exceeding 90 nm at telecom wavelengths. We demonstrate their use as part of the control loop in an optomechanical sensing system.

The authors demonstrate thin silicon nitride waveguide spirals that enable release-free phase-modulation. The presented modulators achieve a Vπ of 8.98 V with 1.13 dB of insertion loss at a modulation frequency of 704 MHz over a 90 nm optical bandwidth.

Introduction

Silicon nitride (SiN) photonics has enabled narrow linewidth lasers^1–5, record setting high-Q resonators^6,7, and sensing systems^8,9. With the further inclusion of piezoelectrics alongside SiN photonic integrated circuits (PICs)¹⁰, fast tunable lasers^11–13, microcomb tuning^14,15, optical isolators¹⁶, and quantum microwave-to-optical conversion¹⁷ have been demonstrated. All of these technologies are building blocks for PIC designers to use for producing mass-manufacturable integrated systems. However, SiN, a material platform noted for its broad optical transparency window¹⁸ reaching the visible spectrum^19,20, low optical losses⁶, and CMOS compatibility¹ suffers from a lack of optically broadband modulators. Modulators have been demonstrated through heterogeneous integration of electro-optic materials such as lithium niobate with SiN^21–24 but require substantial modifications to the cladding layer to bring electro-optic material within proximity to the SiN waveguide core. When broadband modulation frequencies are not necessary, acousto-optic modulators are an attractive choice. Laser locking schemes, such as the Pound-Drever-Hall technique²⁵, require optical modulators to generate the error signal used by the control system. PICs have been proposed^26,27 that utilize integrated modulators and lasers to interface with atomic transitions, serving as a necessary next step to developing PICs for light-atom interactions.

Currently, the few existing acousto-optic modulators on thin SiN rely on optical resonant enhancement of the stress optic interaction^28–30, limiting the optical bandwidth to that of the ring resonator. Recent thicker SiN work embeds aluminum nitride and air gaps within 710 nm of 300 nm thick SiN waveguides³¹ to optimize the overlap. However, the entire premise of the thin SiN platform is to drive down optical losses as far as possible by embedding the low-confining waveguide core in a pristine cladding layer. Introducing etched surfaces violates this premise and will drive up scattering losses on our thin SiN platform. Furthermore, avoiding release processes result in a simpler fabrication procedure.

A common technique to boost acousto-optic interactions is to exploit moving boundary effects in released high-contrast waveguide platforms. This technique has seen great success particularly in released silicon-on-insulator waveguide platforms, where it is commonly used to enhance Brillouin interactions^32–34 and modulator performance^35,36. Without release, waveguide boundaries cannot meaningfully shift in a thin SiN platform — a problem exacerbated by the low index contrast between cladding and core.

The low confinement, low index contrast, and unreleased waveguides culminating in weak acousto-optic modulation on thin SiN are a side effect of engineering a photonics platform with state-of-the-art ultra-low losses. We demonstrate a means to bypass this deficiency by engineering long photon-photon interaction lengths enabled by ultra-low optical losses in the form of a multi-pass, release free, spiral acousto-optic modulator. Our modulators operate up to 706 MHz, representing a 35 × increase in operation frequency over other work on thin SiN³⁰ while achieving a V_π of 8.98 V with 1.13 dB of insertion loss across a broad optical bandwidth exceeding 90 nm. Trends expected from theory are experimentally measured to confirm the phase-matching physics of the modulators. Finally, we demonstrate an immediate application of the technology to an optomechanical accelerometer based on high-Q ring resonators fabricated at the same commercial foundry.

Results

Spiral design

Our thin SiN platform, illustrated in Fig. 1a, comprises of a 2.4 μm × 96.5 nm waveguide embedded inside a silica cladding layer. The passive waveguides are fabricated at a commercial foundry on 200 mm wafers and cored down to 100 mm. A piezoelectric layer stack comprising of molybdenum (Mo) and aluminum nitride (AlN) is deposited on the cored wafers. This Mo layer incurs metal-induced propagation loss, and the top cladding thickness was selected to ensure it stays below an acceptable threshold. We observe additional losses that occur due to processing of the wafer, likely during the piezoelectric deposition, bringing the total optical losses to 4.31 dB m⁻¹ (Supplementary Note 1).

Fig. 1. Overview of the modulator implementation and design.

a A illustration of the layer stack. Here, Al is aluminum, AlN is aluminum nitride, Mo is molybdenum, SiN is silicon nitride, SiO₂ is silica, and Si is silicon. The silica cladding above the waveguide is rendered transparent in the illustration so the waveguide is visible. b A false colored cross-section scanning electron microscope image of the layer stack illustrated in (a). c An optical mode profile with arrows indicating the electric field of the transverse electric (TE) mode is mostly $\widehat{x}$-directed. The z-component of the Poynting vector is shown as P_z. d Simulation of the relevant strain tensor components, S_xx and S_yy for the fundamental transducer acoustic mode. e An illustration of the design strategy. A total of C intersection points of the spiral waveguide with the acoustic wave, $\left\{x_n\right\}$, are optimized to maximize phase modulation and obey design rules such as the minimum bending radius, $r_{\min }$. f The field amplitude within a spiral with C = 38 modulated segments (the largest spiral experimentally measured later in this work) as a function of distance, s, along the waveguide normalized to the coherence length, L_coh. The modulated segment locations are colored in accordance with the acoustic field phase at each location. g. The acoustic field phase is compared to the optical phase-mismatch, revealing that the spirals are designed to counter the optical phase-mismatch through judicious selection of acoustic phase via placement of the spiral waveguides at locations $\left\{x_n\right\}$.

Achieving long acousto-optic interaction lengths requires careful choice of an acoustic transducer. Interdigited transducers (IDTs), which launch a traveling acoustic wave along the surface of a material, have previously been used in acousto-optic modulators on silicon-on-insulator³⁷, aluminum nitride^38,39, and lithium niobate^40–43. Importantly, they have been shown to enable multi-pass AOMs where the waveguide can be meandered to pass the light through the same acoustic field many times, driving up modulation efficiency without requiring more driving power⁴⁴. Our IDTs were selected to have a pitch that is larger than the waveguide width to enable favorable overlap and can be fabricated using aluminum (Al) via a liftoff process. A cross section scanning electron microscope (SEM) image is shown of this layer stack in Fig. 1b.

The dominant mechanism of acousto-optic coupling in our devices is the photoelastic effect. The electric field of the fundamental TE mode, of which we wish to phase modulate, is predominately $\widehat{x}$-directed as shown in Fig. 1c. Based off of silica’s photoelastic tensor, the S_yy component of the mechanical strain tensor simulated in Fig. 1d contributes the most to the acousto-optic interaction. The optimization of acousto-optic overlap is discussed in Supplementary Note 2.

We select a waveguide spiral geometry because they have been shown to afford long photon-phonon interaction lengths in a compact form factor^35,45–48. Our proposed spirals, illustrated in Fig. 1e, are completely distinguished, to the best of our knowledge, from all other devices in literature because they are parameterized by the intersection points (modulated segments) of the light with a traveling acoustic field. These geometric degrees of freedom, denoted by the $\left\{x_n\right\}$’s shown in Fig. 1e, are explicitly calculated to phase-match the acousto-optic interaction via a procedure detailed in Supplementary Note 3. Motivated by ultra-low loss integrated photonics platforms such as thin SiN, our design procedure allows for acousto-optic modulators of large pass count to be designed — bringing optically broadband phase modulation to thin SiN. When spirals are designed in accordance with this procedure, the sideband amplitude grows in successive modulated segments, shown by Fig. 1f. This leads to a multiplicative increase in modulation index with increased modulated segment count under a fixed RF power. For an extended comparison to other spirals in literature and the calculation required to design these devices see Supplementary Note 3.

To understand how the spiral structure achieves a phase-matched acousto-optic interaction, it is helpful to draw an analogy to quasi-phase-matching (QPM)^49,50, discussed extensively in Supplementary Note 3.6. In our devices, the phase-mismatch accrued per unit length is given by

$$\mathrm{\Delta }k=k\left(\omega \right)-k\left(\omega +{\mathrm{\Omega }}_m\right)\approx \frac{{\mathrm{\Omega }}_m{n}_g}{c_0},$$ 1

where k(ω) is the fundamental TE mode’s dispersion curve, Ω_m is the radial modulation frequency, n_g the group index, and c₀ the speed of light in vacuum. The Δk term gives rise to a coherence length,

$$L_{\mathrm{coh}}=\frac{2}{\mathrm{\Delta }k}$$ 2

which effectively places an upper length limit on the interaction length. This length is 13 cm for our devices and on the order of microns for nonlinear processes like second harmonic generation (SHG). To break this limit, QPM alternates the nonlinear coefficient via polling to correct for phase-mismatch in SHG and other nonlinear processes. The analog to this in acousto-optics is varying the phase of the acoustic field encountered by the waveguide at different locations. Unlike QPM, we have continuous control over this phase, enabled in our devices by optimizing $\left\{x_n\right\}$. The acoustic phase for each modulated segment is chosen to negate the optical phase-mismatch as shown in Fig. 1g. Using acoustic waves that travel across the spiral are paramount to achieving this. This allows increasingly long spirals to be designed at the cost of additional insertion loss and area (Supplementary Note 3.5 for a discussion of this scaling). Use of other acoustic mode families, such as bulk acoustic waves (BAWs)²⁹, would inherently limit this scaling as they present a uniform phase front to the waveguides. The coherence length for the GHz-regime BAW modes is on the order of a few centimeters — limiting total modulated segment length unless multiple out-of-phase RF drives are used. Our devices only require one RF drive to modulate all waveguide passes.

Acousto-optic modulator

A fully fabricated test chip is shown in Fig. 2a next to a bare photonic chip where the spirals are visible. The number of modulated segments in each spiral, ranging from 6 to 38, was selected to examine modulation performance as the total spiral length grows to twice the coherence length specified by Equation (2). Figure 2b shows an optical microscope image of the transducers annotated with geometric parameters such as aperture and finger count. They were designed using an analytic electrical model detailed in Supplementary Note 4. For the acoustic mode coupled to by the transducers at 468 MHz, 5.02% of incident electrical power is converted into acoustic power as measured by the electrical ∣S₁₁∣² in Fig. 2c. Sidebands modulated off of the carrier by the acoustic wave can then be detected in light exiting the spiral using an interferometer (Supplementary Note 5). Modulation efficiency, defined as the ratio in optical power between the carrier and first sideband, quantifying modulation strength, is maximized near 468 MHz in Fig. 2d.

Fig. 2. Acousto-optic modulator.

a A chip without AlN deposited so the waveguides are visible (left) and a completely fabricated chip with AlN and transducers (right). b An optical microscope image of a transducer next to a spiral. There are 19 waveguides visible on the transducer side of the spiral, corresponding to C = 38 modulated segments when counting both sides. Contrast and color has been modified to make the waveguides next to the transducer more visible. c ∣S₁₁∣² of the transducer reveals electromechanical coupling as the RF drive frequency is swept. d. Modulation efficiency as a function of transducer RF drive frequency for the spiral with C = 38 modulated segments. The RF drive power, P_RF, and optical wavelength, λ, are fixed. e Scaling of the waveguide length as a function of modulated segment count. f Scaling of the spiral area as a function of modulated segment count. Note that the spiral area is defined as the area of the smallest rectangle it can fit in. g Multiple spirals of varying modulated segment count are measured with identical transducer designs under the same drive power to ensure the measured modulation index increases multiplicatively with modulated segment count. h Scaling of the modulation efficiency for the first and second sidebands with respect to applied incident RF power following the expected trend for phase-modulation. The negative sidebands track identically to their positive counterparts.

Figure 2d exhibits a fringing pattern due to either constructive or destructive interference of the modulation produced by the near and far side of the spiral relative to the transducer. As the acoustic wave propagates 2.8 mm across the spiral, the relative acoustic phases on the near and far side of the spiral become frequency dependent due to the dispersion of the acoustic wave. The RF bandwidth of 0.57 MHz is therefore set by this phenomenon. In our chips, acoustic losses for the fundamental acoustic mode are small (0.54 dB/mm, Supplementary Note 1) and thus the far side of the spiral substantially contributes to the phase modulation.

The theory for our devices predicts that the measured modulation index is expected to multiplicatively increase with modulated segment count, C, even as the spiral length exceeds the coherence length of 13 cm. Naturally, a tradeoff between spiral length, insertion loss, spiral area, and modulation strength arises. Spiral geometric information is presented in Fig. 2e, f to quantify devices sizes as a function of C. Figure 2e indicates that the coherence length of 13 cm corresponds to a modulated segment count of approximately 18. By measuring multiple spirals on the chip with varying modulated segment count under identical RF drive power, a multiplicative increase in the modulation index is observed in Fig. 2g. The phase modulation index, β, corresponds to the parameter of the Bessel functions that model the amplitude and power of the sidebands. For phase modulation, we therefore expect the power in the first and second sidebands to scale linearly and quadratically, respectively, in response to applied RF power. This characteristic of phase modulation is observed in Fig. 2h.

Higher order acoustic modes

In addition to the fundamental acoustic mode, the transducers couple to three more acoustic modes whose S_yy strain tensor is simulated in Fig. 3a. These higher order acoustic modes may be beneficial in photonic integrated circuit design if the layer stack can be tuned to optimize overlap for one of these modes. For these devices, the modulation indices achievable for each mode is experimentally measured in Fig. 3b by an RF drive frequency sweep. A high frequency mode present at 706 MHz achieves the strongest coupling, yet requires tight layer thickness control of the cladding (within 1.5 μm) as shown by the corresponding plot in Fig. 3a, lest the waveguide fall into a strain anti-node. The modulation efficiency of this mode peaks near  − 10 dB (Fig. 3c) under 1 W of driving power — a substantial increase over the modulation efficiency of the fundamental acoustic mode.

Fig. 3. Higher-order acoustic modes.

a. S_yy strain tensor components for three other acoustic modes that can be excited by the transducer. Note that the waveguide location is marked with dashed lines. The frequencies are labeled to be consistent with (f) and (g), but the actual simulated values differ slightly. b A broadband RF drive frequency sweep with incident RF power, P_RF, and optical wavelength, λ, fixed reveals higher order acoustic modes coupling to the optical mode in the spiral with C = 38 modulated segments. c Modulation efficiency for the 706 MHz mode. It is the strongest performing acoustic mode due to the favorable overlap of the S_yy strain tensor component with the waveguide shown in (a). d Theoretical calculations illustrating relative degradation of modulation efficiency as acoustic mode frequency differs from the spiral’s designed frequency. The shaded blue region shows the 3 dB range, indicating all acoustic modes in (a, b) are still expected to nearly satisfy phase-matching considerations. e. Theoretical calculation showing the range of possible modulation index trends expected across the 3 dB shaded region in (d) as a function of modulated segment count. The 706 MHz mode in (f) exhibits behavior similar to the lower dashed black line. f. Scaling of the modulation index for the 706 MHz mode contrasted against the fundamental mode. The provided frequencies are the average of the measured devices, and there is slight variation from device to device. The agreement between the theory and the data validates the behavior claimed in (d). g Modulation index scaling of the 502 MHz and 639 MHz modes. The modulation index multiplicatively increases, as expected from theory.

The higher order modes provide a mechanism to probe the degradation of phase-matching. As the drive frequency deviates from the spiral’s designed 454 MHz ideal operation frequency, a penalty in modulation efficiency occurs due to phase-mismatch. The largest device presented in this work, with 38 modulated segments, has a phase-matched 3 dB bandwidth of several hundred MHz simulated in Fig. 3d. All higher order modes can therefore be viewed as phase-matched given this 3 dB metric. Note that this does not account for different electromechanical and acousto-optic coupling for each mode. Acoustic modes within the 3 dB range of Fig. 3d will demonstrate a nearly multiplicative increase of the modulation index with modulated segment count as shown by the upper and lower bounds of modulation index curve shapes expected by theory in Fig. 3e. The theoretically calculated curve for modulation index scaling is fit to the measured data for the three additional modes and good agreement can be seen in Fig. 3f, g. The 706 MHz mode exhibits the most roll-off from the trend expected for perfectly phase-matched acoustic modes.

Optimization of electromechanical impedance match

With the spirals obeying the expected theory, the modulation indices of these devices may further be increased through transducer optimization. As speculated by literature⁴⁴, mm-aperture transducers may hold promise in improving acousto-optic modulation. Spirals presented in this work are uniquely positioned to examine this experimentally as the modulated segments in each spiral can accommodate transducers that have a 1.6 mm aperture. Thickening the bus bars as shown in Fig. 4a improves impedance matching by driving down parasitic resistance and capacitance, in turn allowing for larger aperture transducers. The 500 nm aluminum thickness of the bus bars is selected as it is the maximum thickness allowed for by our deposition tool. A fully fabricated transducer with relevant geometric parameters next to a spiral is shown in Fig. 4b. Geometric parameters for the device shown in Fig. 4b were obtained through optimization of an electrical model (Supplementary Note 4) to improve electromechanical impedance matching for the two lower frequency acoustic modes.

Fig. 4. Optimization of acousto-optic impedance match.

a An illustration of transducers with thickened bus bars. The layer stack is otherwise identical to Fig. 1a. b An optical microscope image of the new transducer design with relevant geometric parameters denoted. Contrast and color has been modified to make the waveguides below the transducer more visible. c The ∣S₁₁∣² of these transducers. This subfigure can be directly compared to Fig. 2c to see a greater fraction of incident power being dissipated into the acoustic wave. d The modulation index for all acoustic modes present, showing a substantial performance increase when compared to Fig. 3b. Incident RF power, P_RF, and optical wavelength, λ, are fixed while measuring this spiral with C = 38 modulated segments. e Sweep of RF frequency, f_RF, over a node of the highest frequency acoustic mode while incident RF power, P_RF, is gradually increased after each frequency sweep. The coloring expresses the modulation efficiency. The contours indicate the modulation index, β, achieved. f. The carrier,  ± 1, and  ± 2 sidebands resulting in a β = 0.58π rad modulation index are displayed. The power in the  ± 1 sidebands are maximized near this modulation index. The measurement setup (Supplementary Note 5) manifests the sidebands 100 MHz from harmonics of the RF drive frequency, f_RF. The y-axis is normalized such that 0 dB corresponds to the total optical power present in all sidebands. Note that this is the same device as (d), but the RF power has been increased from 30 dBm to 34 dBm. g A measurement of modulation efficiency as a function of wavelength for the four acoustic modes. There are 1000 equally spaced data points for each mode. The RF drive frequency, f_RF, is fixed at the f_RF value denoted on the plot for the collection of these 1000 data points.

The fraction of incident electrical power launched as an acoustic wave for the fundamental mode can be estimated by examining the ∣S₁₁∣² measurements of the dual metal thickness transducers (Fig. 4c) and the single metal thickness transducers (Fig. 2c). A marginal increase of 19.1% is observed. More importantly, this power is distributed over a longer length of waveguide by 1.6 mm/378 μm = 4.23. As such, we expect the modulation index achievable for the fundamental acoustic mode to increase by $\sqrt{4.23\times 1.191}=2.25$. Measured optically, modulation index increases by a factor of 2.375 for the fundamental transducer mode, indicating good agreement between electrical and optical observations. Large transducers are therefore clearly beneficial for acousto-optic modulation.

The highest frequency mode for the dual metal thickness transducers is at 704 MHz and achieves close to a β = π/2 rad phase shift. Reaching a π/2 peak phase shift is important as it additionally makes these devices candidates for the optically broadband modulators required for optical gyroscope drivers^8,51. The incident RF power is increased gradually while sweeping over the maximum of the 704 MHz acoustic mode’s fringing pattern. The phase velocity of the acoustic wave shifts due to thermal effects, as evidenced by the shift in fringing pattern shown in Fig. 4e. At P_RF = 34 dBm, a β = 0.58π > π/2 modulation index is achieved, which approximately maximizes the power in the  ± 1 sidebands as shown in Fig. 4f. The interferometry based experimental setup (Supplementary Note 5) manifests the sidebands 100 MHz offset from the RF drive frequency such that positive and negative sidebands can be distinguished.

The thick bus bar devices provide the best modulation performance, yielding V_π of 8.98 V at 1550 nm. We additionally use them to validate our optically broadband claim. For each acoustic mode, we measure modulation efficiency as a function of wavelength across the 90 nm tuning range of our laser in Fig. 4g. All four acoustic modes exhibit less than 3 dB variation in modulation efficiency across this range, leading to an optical bandwidth of at least 90 nm. This optically broadband operation is expected from the device theory outlined in Supplementary Note 3.4 with additional analysis of experimental results provided in Supplementary Note 6.1.

Use of modulators in a optomechanical sensing system

The modulation indices reported in this work are immediately useful for implementing a Pound-Drever-Hall (PDH) lock²⁵ to an optical ring resonator sensitive to acceleration. On a separate chip produced at the same foundry with a similar waveguide layer stack, acceleration-sensitive optical ring resonators are fabricated that feature a released proof mass structure on the interior, as shown in Fig. 5a. Serpentine silica springs connect the proof mass to a location in proximity to the ring resonator waveguide (Fig. 5b) enabling transduction of proof mass displacement into an optical resonance shift as illustrated in Fig. 5c. The experiment in Fig. 5d reads out this shift. An optical resonance is shown in Fig. 5e alongside the corresponding PDH error signal. As the optical resonance frequency shifts in response to an applied acceleration, a nonzero error signal results which is measured by the same LIA to determine the transfer function of the accelerometer and noise equivalent acceleration (Fig. 5f). The fundamental $\widehat{z}$ displacement mode arises near 1.8 kHz and corresponds to the lowest noise equivalent acceleration of 6766 ngHz^−1/2. A more detailed experimental procedure discussing calibration is available in Supplementary Note 7.

Fig. 5. Application of modulators to optomechanical sensing system.

a A picture of an optomechanical accelerometer. Four optical ring resonators are accessible via packaging, with two being released and sensitive to acceleration. The chip was produced with a similar layer stack to Fig. 1a (however, no piezoelectric was deposited). b An optical microscope image of the SiO₂ serpentine spring structure that allows the ring resonator to be sensitive to acceleration. c A diagram explaining device operation. As the proof mass displaces, the ring resonator is perturbed, shifting the optical resonance frequency. d The experiment used to characterize the optomechanical accelerometer. e Using P_RF = 0.25 W of RF power, a PDH error signal can be generated using the modulators. f The transfer function and noise equivalent acceleration (NEA) is measured. The fundamental resonance of the released mechanical structure is near 1.8 kHz.

Optomechanical accelerometers have been demonstrated on various platforms previously^9,52–55, but readout schemes rely on side-of-fringe locking schemes and involve a number of components off chip such as photodetectors. PDH locking, enabled on-chip by our modulators, rejects intensity noise to first order. Noting that photodetectors and lasers are possible on-chip with thin SiN platforms², the addition of a simple modulator architecture shown in this work enables fully integrated thin SiN optomechanical accelerometers.

Discussion

Our spiral structures are designed to trade off insertion loss and device area with V_π through selection of a modulated segment count. When compared to state-of-the-art SiN acousto-optic modulators in Table 1, our technique enables the only optically broadband, unreleased, and high frequency acousto-optic modulators on thin SiN. We achieve a V_π of 8.98 V at a wavelength of 1550 nm with an optical bandwidth exceeding 90 nm.

Table 1.

A comparison of technologies for modulating SiN waveguides

Reference	Waveguide thickness [nm]	Optically broadband	Modulation frequency	Released	Wavelength	VπL [V ⋅ cm]	Vπ [V]	VπLα [V ⋅ dB]	Size
Hosseini60	25	Yes	DC-629 kHz	No	640 nm	12.5	12.5a	-	10 mm
Freedman31	300	Yes	2.31 GHz	Yes	730 nm	0.26	1.3b	-	2 mm
Jin28	175	No	DC-300 kHz	Yes	1550 nm	3.6	8	1.1	1.2 mm × 1.2 mmc
Wang30	175	No	DC-20 MHz	No	1550 nm	43	-	1.3	1.2 mm × 1.2 mm
Tian29	810	No	~3 GHz	Yes	1550 nm	-	-	-	200 μm × 200 μm
Dong61	300	Yes	DC-120 MHz	Yes	780 nm	100d	100d	39e	1.3 mm × 0.6 mm
This work	96.5	Yes	704 MHz	No	1550 nm	54.7	9	10.17	23 mm2

V_πL for our multi-pass devices is defined using the length of waveguide modulated by the acoustic wave (38 × 1.6 mm = 6.08 cm). Thus, our V_πL reflects a property of the waveguide cross section and can be used to compare various waveguide platforms. V_πLα uses the total spiral length of 26 cm as all 26 cm of the spiral contribute to insertion loss. See Supplementary Note 5 for further comments. Device size is estimated based on information available in the associated reference. Some devices^31,60 have negligible width. In this case, size is reported as a length.

^aCalculated using an active length of 10 mm.

^bCalculated from modulation length and V_πL.

^cEstimated based on the ring resonator radius using single stripe waveguides.

^dPer phase shifter (i.e., it is not configured as push-pull) at room temperature.

^eCalculated using V_πL and a waveguide propagation loss of 0.39 dB cm⁻¹.

Without increasing spiral size, V_π and insertion loss may be reduced further through several improvements. Insertion loss can be decreased by removing AlN and Mo everywhere except for underneath the IDT fingers via alternative transducer designs⁵⁶. Since traveling waves enable modulation at a distance, loss inducing materials can be kept far away from the waveguides. Paired with an investigation of the origin of processing-induced optical losses⁵⁷, it may be possible to achieve a 16 × decrease in insertion loss. V_π may simultaneously be improved through transducers with an aperture larger than demonstrated in this work. Alternative piezoelectric materials featuring higher electromechanical coefficients, such as lithium niobate²¹, lead zirconate titanate (PZT)¹¹, and aluminum scandium nitride (AlScN)³⁷ may be favorable depending on the application, modulation frequency requirements, and fabrication constraints if acoustic impedance matching between the piezoelectric and silica can be achieved. Additionally, the silica cladding thickness and spiral can be engineered to be optimized for the highest frequency acoustic mode of which we determined to perform the best in this work.

The devices presented in this work lend immediate use to applications requiring PDH locking, demonstrated through a prototype optomechanical accelerometer. Our high-frequency modulators enable sideband-resolved PDH locking as the modulation frequency exceeds the cavity decay rate. Use cases extend further to include low-noise microwave oscillators⁵⁸ and lasers⁵⁹ implemented on thin SiN. Such technologies are still dependent on external phase modulators and our modulators now provide an on chip solution. The π/2 modulation index achieved at high frequency in our devices certainly exceeds what is required for PDH locking, but was targeted as an important milestone as it is necessary for fully integrated thin SiN optical gyroscopes^8,51. Such an exciting development would mean fully integrated optical inertial measurement units, combining optomechanical accelerometer and optical gyroscope technology, is within reach.

Methods

Phase modulator characterization

The performance of the spiral phase modulators are measured using the optical heterodyne technique. Light output from a tunable laser (Toptical CTL 1550) is split into two paths. One path passes through the phase modulator chip while the other passes through a bulk Brimrose acousto-optic frequency shifter to frequency shift the light by 100 MHz. The light is recombined and beat on a high-speed photodetector. An electronic spectrum analyzer measures the response which contains unique frequency components corresponding to the sidebands imparted on the light by the phase modulator (see Fig. 4f). The relative magnitude of these sidebands can be fit to infer quantities such as modulation index.

Accelerometer experiment

A simplified block diagram of this experiment is shown in Fig. 5d. The spiral phase-modulators are used to implement a PDH lock to a released optical ring resonator (pictured in Fig. 5a, b) that is sensitive to acceleration. A Zurich UHFLI lock-in amplifier (LIA) drives the spiral modulator’s 502 MHz acoustic mode through a RF amplifier to generate a PDH error signal via demodulation of the beat signal on the photodetector. This error signal is fed into the laser controller, which implements a proportion-integration-derivative control loop to lock the laser to the minimum of the ring resonator transfer function. The experiment then shakes the optical accelerometer, causing the resonance frequency to shift under the applied acceleration. This shift is also measured by the lock-in-amplifier by demodulating the error signal generated by the control loop at the shake frequency. Simultaneously, a commercial accelerometer (ADXL 354) located next to the optical chip on the shaker table reports the acceleration applied by the shaker table. This system is further calibrated with a bulk acousto-optic frequency shifter through a procedure documented in the Supplementary Information to obtain the transfer function in units of MHz g⁻¹ shown in Fig. 5f. This calibration procedure is not required to measure noise-equivalent acceleration.

Author contributions

S.E.K. and W.J. conceptualized the modulator architecture. S.E.K. designed the spirals, transducers, and experiments with input from all authors. T.H.C. and A.G.A. fabricated the transducers. T.H.C. fabricated the accelerometers. Y.T provided guidance for the accelerometer experiment. A.F., M.P., and S.A.B. supervised the project.

Peer review

Peer review information

Nature Communications thanks Dawn Tan, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data generated in this study has been deposited in the repository Zenodo at 10.5281/zenodo.17409114.

Competing interests

S.E.K., T.H.C., W.J., A.F., and S.A.B. have a patent pending. The other authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-67618-3.