Main

For many applications proposed for programmable optical systems1,2,3, the key requirements are (1) large scale; (2) fast response: sub-microsecond for applications in machine learning4,5,6,7 and quantum control8,9,10,11; and (3) power efficiency to enable operation in the cryogenic environment for integration with superconducting detectors12,13 and artificial atoms14,15,16. Leading Mach–Zehnder mesh (MZM) platforms17 consist of cascaded Mach–Zehnder interferometers (MZIs) to perform the general special unitary SU(N) group requiring N(N – 1)/2 MZIs (ref. 18), as illustrated in Fig. 1a for a four-mode programmable SU(4) in a rectangular mesh arrangement19. To meet the scalability requirement, for even a modest mode count N, the most demanding technical challenge is reliable manufacturing and a clear path to electronics co-integration. Although presently only modern complementary metal–oxide–semiconductor (CMOS)-compatible VLSI processes offer these capabilities through foundry services, material choices are practically limited to Si (refs. 20,21) and silicon nitride (SiN) technologies22. For the high-bandwidth requirement within these materials, silicon-free carrier modulation23 is problematic for MZMs because of the inherently coupled phase and amplitude. Silicon electric-field-induced χ(2) (ref. 24) modulators are promising, but they have not been realized at scale and have a restricted operating wavelength power. A recently introduced alternative relies on piezo-optomechanical actuation of SiN waveguides25,26,27,28, which in the case of another study25 has enabled narrow-band operation up to 250 MHz with SiN waveguides for visible–near-infrared (NIR) operation and high optical power handling. Finally, the energy requirement is incompatible with any thermal modulation schemes, which dissipate an average of >800 mW for doped SiO2 (ref. 21), >20 mW per modulator for SOI (ref. 29) and >40 mW per modulator for SiN (ref. 17). Electrostatic MEMS devices meet the power requirement (promising sub-picowatt hold power)30,31, but modulation timescales have thus far been limited to the microsecond regime.

Fig. 1: High-speed, visible-wavelength and cryogenic-compatible PICs.
figure 1

a, Schematic of a four-mode programmable circuit consisting of cascaded MZIs for SU(4) operations. b, Trade space diagram of the power–reconfiguration rate for other CMOS-compatible photonic technologies and our piezo-actuated photonics. c, Microscopy images of a fully processed 200 mm wafer with insets showing the zoomed-in view of a reticle and a 4 × 4 MZM. d, Three-dimensional concept art of an MZI with piezo-optomechanical phase shifters. e, Cross-sectional diagram of our phase shifter, illustrating how an applied voltage across the piezo results in strain imparted to the optical waveguide.

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Figure 1b summarizes this power–modulation bandwidth trade space for SiN and Si platforms compatible with the scalability requirement mentioned earlier. For a cross-platform comparison, Fig. 1b plots the power dissipated for π-phase shifts as a function of the circuit reconfiguration rate. In the thermal regime, the power dissipated is constant up to the maximum reconfiguration bandwidth, whereas piezo-actuation contains a trade-off between faster programming speeds and power dissipated on chip. The piezo-optomechanical approach offers up to three orders of magnitude improvement in programming time with lower power consumption as that of thermal approach and three to five orders of magnitude improvement in power dissipation at the maximum thermal reconfigurability rate, showing the exceptional suitability of this technology for MZM systems. Motivated by these considerations, we advance our wafer-scale process for SiN photonic integrated circuits (PICs) (Fig. 1c) with phase-only piezo-optomechanical tuners, whose basic design and operation are shown in Fig. 1d,e, through the co-design and development of photonics, electromechanics, electrical and mechanical control systems, and driver software. We combine the best attributes of the different devices discussed in our previous work25 into a proof-of-principle MZM architecture capable of achieving 20 ns reconfiguration time, on-chip power dissipation per modulator below 200 µW when switching on average for every 1 µs and 6 nW hold power, operation at 700–780 nm with optical transmission up to 1,550 nm, and improved power efficiency at 5 K.

Results

Device fabrication, design and theory of operation

Our devices are designed and fabricated on a 200 mm wafer following an improved process flow based on our previous work25. The optical layer consists of a 300-nm-thick SiN layer in a silicon dioxide cladding, located on top of aluminium nitride (AlN) piezoelectric actuators with functionality for selective release and metal routing; Supplementary Section 1 provides additional fabrication details. This process enables high-speed and broadband active modulators. Specifically, Fig. 2a shows a full MZI with strain-actuated phase shifters both internal and external to the directional couplers, as indicated by the unfolded layout in Fig. 1d. Each arm of the internal phase shifter contains an optical-path-length-matched piezo-actuated segment (imparting a phase Θ1,2) and same for the external phase shifter (imparting a phase Φ1,2). Each phase shifter consists of a 400-nm-width SiN waveguide passing through an adiabatic taper, expanding to a width of 5 µm for improved strain transfer25, propagating for a distance of 1.1 mm, and then through a second adiabatic taper back down to a 400-nm-wide single-mode turn. This loop repeats nine times, as shown in Fig. 2b, for a total path length of ~1 cm per phase shifter. The cross section shown in Fig. 2c,d reveals a slightly undercut 10-µm-wide pillar around the oxide-clad 5-µm-wide SiN waveguide and AlN actuators. Applying a potential difference across AlN transfers strain to the waveguide (a finite element simulation is shown in Fig. 2e), imparting a shift in the refractive index predominantly due to the strain-optic effect32 in addition to moving boundary effects33.

Fig. 2: Design of piezo-actuated modulators.
figure 2

a, Microscopy photo of an MZI with labelled SiN waveguides, metal routing (M1), phase shifters and directional couplers. b, Model of a phase shifter with labelled optical input/output, waveguide taper and actuation regions with finite element simulations of the 400 nm and 5-µm-wide waveguide transverse-electric (TE) modes. c, Schematic of the cross section of a phase shifter with materials labelled as shown. d, Scanning electron microscopy image of the cross section of the fabricated device, where the waveguides (purple), AlN (blue) and metal routing (white) are labelled. e, Finite element simulation of the first mechanical eigenfrequency at 253 MHz with the plotted displacement exaggerated for visibility.

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When applying a potential difference, the strain imparts phase change Δθ to the optical mode for a given length L of the phase shifter as follows:

$${\Delta}\theta = (2\uppi /\lambda )({\Delta}n_{\mathrm{eff}}L + n_{\mathrm{eff}}{\Delta}L),$$
(1)

where λ is the free-space wavelength, neff is the static effective mode index, ΔL is the strain-induced path-length change in the phase shifter and Δneff is the total effective strain-induced change in the refractive index:

$${\Delta}n_{\mathrm{eff}} = {\Delta}n_{\mathrm{eff},\varepsilon } + {{{\mathrm{{\Delta}}}}}n_{\mathrm{eff,wg}},$$
(2)
$${\Delta}n_{\mathrm{eff},\varepsilon } = - p_{11}(n_{\mathrm{eff}}^3/2)\varepsilon _{xx},$$
(3)

which includes contributions from strain-optic (Δneff,ε) effects and moving boundary (Δneff,wg) that contributes to waveguide modal dispersion. Here p11 is the diagonal component of the strain-optic coefficient for SiN, and εxx is the tensile strain component in the horizontal (x) direction parallel to the substrate surface (Fig. 2e). We estimate the strain values transferred to the SiN from a finite element model using approximate values of AlN piezoelectric coupling coefficients25, layer-stack geometries and material properties, indicating that the dominant strain is tensile in the horizontal (x) direction and of magnitude εxx ≈ 1.5 × 10–6 per volt applied. The change in effective index due to strain (as shown in equation (3)) is a signed quantity depending on the direction of induced strain, meaning opposite strains produced by a negative applied voltage produce an opposite-shift effective index. This effect allows for a push–pull or differential operation34 of the phase shifts Θ1,2, Φ1,2 ∈ [–π/2, π/2] in Fig. 2a for an applied Vs ∈ [–Vπ/2, Vπ/2], defined as the potential relative to ground with Vπ being the required voltage for a π phase shift.

Room-temperature operation

Figure 3 summarizes the modulator performance at room temperature (300 K). Figure 3a,b shows the operation across a broadband range of wavelengths (700–780 nm). The plots shown here take advantage of the push–pull operation for optical loss balance (typical insertion loss of −3.5 dB at 737 nm; Supplementary Section 2 provides the loss characterization details) of the phase shifters by applying opposite-polarity voltages to each arm. We estimate VπL from the sinusoidal fits, yielding values from 50 V ⋅cm (700 nm) to 65 V ⋅cm (780 nm) in the push–pull configuration or a corresponding VπL in the range of 100–130 V cm per phase shifter. We attribute the variance in VπL to material and waveguide dispersion. From Fig. 3a, we observe an inherent static phase shift in our MZIs. This shift does not highly depend on the wavelength and is a result of local stress and refractive-index differences seen by the two arms of the MZI due to fabrication. We note that the peak of the MZI’s cross-port transmission (Fig. 3a) depends on the splitting ratios of our passive directional couplers and decreases as the wavelength increases, thus moving further away from the 50:50 point. An improved 2 × 2 × 2 MZI design35,36 in conjunction with wavelength-tolerant directional couplers37 would enable full tunability across the range of wavelengths tested.

Fig. 3: MZI modulator characterization at 300 K.
figure 3

a, Cross-port power transmission coefficient of several wavelengths versus differential driving voltage of the MZI. b, Extracted phase shifts from sinusoidal fits at the same wavelengths. c, Photodiode response at 737 nm with a 5 MHz, 20 V peak-to-peak (pk–pk) square wave applied. d, Photodiode output with 15 ns full-width at half-maximum, 20 V pk–pk Gaussian pulse applied. e, Zoomed-in view of the falling edge of 5 MHz square in c, showing a fall time of ~5 ns. f, Normalized modulator response for a 3 V sinusoidal signal showing mechanical resonance at 241 MHz.

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Time-resolved measurements shown in Fig. 3c–e indicate short rise and fall times of ~5 ns. Figure 3c plots the transmission when averaging over 16 square-wave voltage pulses applied through an arbitrary waveform generator (AWG), indicating a fall time of 5 ns. As shown in Fig. 3d, the modulator follows a Gaussian pulse with a full-width at half-maximum of 15 ns. We do not observe substantial hysteresis during active modulation, estimating a <1% deviation from single-shot traces limited by detector noise and stability of our measurement setup. Figure 3f plots the small-signal frequency-resolved modulator response, indicating a −3 dB cutoff at ν3dB = 120 MHz. This cutoff is consistent with the RC time constant during measurement, consisting of the device capacitance of 17 pF and series resistance of ~80 Ω arising from the voltage source and on-chip routing metal. We attribute the peak at 241 MHz to the fundamental mechanical resonance, which is 253 MHz as per our finite element model (Fig. 2e). The shape of the peak exhibits a characteristic resonance and anti-resonance feature typical of mechanical resonators38,39. We note that the AWG used for these tests does not produce the full 20 V swing across its entire bandwidth (500 MHz), which accounts for the distorted Gaussian envelope and atypical falling edge shown in Fig. 3d,e, respectively. The contrast in these measurements is low, as this device is optimized for cryogenic operation, as described later.

Cryogenic operation at 5 K

We performed the cryogenic characterization in a 4 K closed-cycle cryostat (Montana Instruments). Using a fibre array and radio-frequency probe mounted on nanopositioners inside the cryostat (Supplementary Section 5), we applied various voltage waveforms. The transmission curves in Fig. 4 show no degradation in the switching operation, with an overall similar performance at a base temperature of 5 K (Fig. 4a,b) compared with room temperature. Figure 4c indicates an extinction of approximately 30 dB. We remark that compared with Fig. 3a, the static phase offset shown in Fig. 4c shifts due to differences in thermal contraction and stress-optic effects in the two MZI arms at cryogenic temperatures. Figure 4d plots a time trace when holding Vs = 20 V, indicating very stable open-loop operation (<0.5% drift) on the timescale of minutes. The corresponding hold power of 2 nW is nearly eight orders of magnitude smaller than the cooling power (90 mW) of the Montana cryostat. This low power consumption is a critical benefit, as even state-of-the-art thermal SiN waveguide modulators (Fig. 1b) would easily overwhelm the cryostat’s cooling power. We note that the actual extinction ratio of the modulator is larger than 30 dB; however, limited volume in the cryostat prevented the use of differential driving (as demonstrated at room temperature) and limited the phase change to approximately π/2 rather than π.

Fig. 4: Cryogenic operation of the modulator at 5 K at 737 nm wavelength.
figure 4

a, A 16-sample averaged photodiode response for a 5 MHz, 20 V pk–pk square-wave driving signal. b, Zoomed-in falling edge of the square wave, showing the same ~5 ns fall time as that at room temperature. c, Direct current sweep of a single phase shifter in our modulator, showing the maximum extinction ratio of ~30 dB. d, Stability of our modulator held at 5 K and constant 20 V, showing <0.5% drift of the MZI set point over several minutes.

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4 × 4 programmable interferometer

Having characterized the MZIs, we now consider a proof-of-principle SU(4) programmable unitary transformation, which consists of N(N − 1)/2 = 6 MZIs. The MZM is fully programmable, where all the phase shifters are computer controlled (Supplementary Section 3).

Figure 5 summarizes the MZM characterization. After a basic voltage calibration, we run voltage sweeps across all the six MZIs, producing internal phase-shifter transmissions as shown in Fig. 5d. The optical input and output combinations (Fig. 5c) here for each plotted MZI show maximum power differences on actuation; a full dataset of all the 12 phase shifters is shown in Supplementary Section 4. Figure 5d plots the transmission of output port 3 on actuating ‘MZI3’, which indicates an optical extinction ratio in excess of 40 dB. The total loss through the MZM ranges from −14 to −21 dB at 737 nm, depending on the optical path taken, primarily due to waveguide bending losses in the phase shifters, which could be completely eliminated with an unfolded implementation or larger-radii waveguide bends. We confirm that our MZM maintains the 100 MHz bandwidth as demonstrated in single MZI devices by applying a 10 V, 100 MHz sinusoid to the internal phase shifter of MZI2 and monitor the optical outputs 5 and 6 with a laser coupled through optical input 3. We utilize a lock-in detection scheme on the output photodiodes to extract the signal at 100 MHz (Fig. 5e,f) for both channels and a relative phase offset of 0.59π; the small deviation from π/2 is likely due to the 125 MHz bandwidth of the photodiode being close to the driving frequency.

Fig. 5: Proof-of-principle MZM operation at 737 nm.
figure 5

a, Scanning electron microscopy image of the device. b, Photograph of the photonic chip, wire bonds, printed circuit board, and optical input/output for testing. c, Diagram of MZI list and labels for optical input/output; fibre channels 1 and 8 are not connected and channels 2 and 7 are straight-through waveguides for alignment and calibration. d, Actuation of numbered MZI while plotting optical outputs 3 and 4 or 5 and 6; optical inputs used are input 3 for MZIs 2, 3 and 5; input 4 for MZI6; and input 6 for MZI1 and MZI4. The plotted optical power is normalized to the input laser power after accounting for facet coupling losses. e, Measured signal amplitude from fibre outputs 5 and 6 of the 4 × 4 MZM with a 10 V, 100 MHz driving sinusoid on MZI2. f, Signal amplitude as a function of lock-in phase; integration time for the lock-in measurements is 4 ms.

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Although the results shown in Fig. 5 demonstrate the programmability of our MZM as a single packaged device, voltage-handling limitations of our on-chip vias (see Discussion below) currently prevent accessing the full scope of SU(4) operations and thus the use of certain calibration procedures34,40,41 to discern 4 × 4 matrices or unitary fidelities produced by the chip. However, with expected improvements in overall loss, loss balance between MZIs, and a full 2π-phase actuation (enabled by a combination of better via design, fabrication processes, and control electronic systems), we will explore such measurements in future experiments.

Discussion

We have demonstrated a four-mode programmable interferometer in a 200 mm CMOS foundry. The MZM comprises cryogenically compatible, piezo-optomechanical phase shifters with >100 MHz bandwidth operating in the visible–NIR wavelengths, which should be immediately applicable to many hybrid photonic architectures16, quantum protocols8,42 and machine-learning algorithms6.

Although the devices presented here show promise for universal linear-optic programmable photonics in new performance regimes and application spaces, there are still some non-idealities that will be improved in future work. First, the dominant source of loss in all devices presented is the bends induced by waveguide meanders and directional couplers, measured to be −2.7 dB of the −3.5 dB MZI insertion loss (Supplementary Section 2). Waveguide propagation losses (−0.39 dB cm–1) and adiabatic taper losses of −0.022 ± 0.038 dB per taper account for the remaining loss of −0.8 dB. We estimate that implementing less tightly folded versions of the same devices that have fewer bends and tapers would allow us to achieve MZI insertion losses substantially lower than −1 dB. Second, in these particular devices, small voids in AlN in the vicinity of electrical vias produced metal filamentation that degraded the device breakdown voltage and prevented the application of voltages above Vs = 25 V. Although we found individual vias in the test structures on the same wafer that allowed Vs > 90 V, the yield was insufficient for an MZI comprising 90 vias. After a systematic failure analysis and cross-sectional imaging, the process yield improved greatly so that full SU(N) devices appear likely with maximum Vs > 90 V (Supplementary Section 6). Besides the electrical vias, we have not observed any causes of systematic failure (such as mechanical failure or fatigue) in our devices, likely attributed to the relatively low strain and stress values under operation.

In addition to device performance improvements, design variations and prospects for large-scale photonics remain to be explored. With our current technology and SU(2) device footprint (approximately 1.3 mm × 0.6 mm), we can conceivably fit >500 components on a single die without any lithographic modifications (such as stitching between reticle fields), enough to make an SU(32) device. Simply lengthening the phase shifters would also allow them to operate at CMOS-level voltages at the cost of actuation bandwidth due to increased device capacitance (a 10-cm-length phase shifter would potentially have Vπ ≈ 5–10 V and ν3dB ≈ 12 MHz). Alternatively, strain-concentrating structures or mechanical resonance effects would help shrink our current device size by reducing the required driving voltage. Moreover, high-scandium-concentration Sc(1–x)AlxN has shown a fivefold increase in piezoelectric responsivity43, promising a further five times reduction in Vπ or device length.

Finally, the layer stack of our PIC (Supplementary Table 1 and Fig. 2c), which places the optical layers on top, enables many extensions to the platform. The optical layer—on top of all the metal and piezoelectric layers—allows for alternative optical layers to expand the transparency window into the ultraviolet regime44,45,46. Moreover, heterogeneously integrated thin films for either photon generation14,47,48 and detection13 or nonlinear interactions49,50,51,52 could be placed directly on top of the optical layer with photons coupling evanescently to the rest of the integrated photonics. The AlN-actuator-based photonic platform is also entirely post-CMOS compatible and therefore can be directly fabricated on fully formed CMOS integrated circuits53 for direct biasing or control of hybrid systems54,55,56; thus, the architecture presented here can be scaled to both very large photonic circuit sizes and very small photonic circuit pitches without electrical control bottlenecks.

Methods

Hold-power consumption and reconfiguration energy calculations

We first calculate the device capacitance C and on-chip routing metal resistance Rchip based on the measured RC roll-off in our frequency response curve, yielding C = 17 pF and Rchip = 30 Ω in addition to a series voltage source resistance of 50 Ω. The device leakage resistance based on previous measurements25 is estimated to be 500 MΩ and 200 GΩ at 300 and 5 K, respectively. The hold power P = IV, where I and V are the leakage current and applied voltage across the device, respectively, is found for two phase shifters holding 25 V to maintain a phase shift of π. The reconfiguration energy dissipated on chip is calculated using the formula E = (Rchip/Rtot)CV2, where Rtot is the total series resistance of the circuit including external resistors in the AWG and Vs = 50 V. This equation accounts for two phase shifters with a 50 V swing and represents energy dissipated from on-chip resistances from vias and routing metal lines. To reduce on-chip energy dissipation for slower reconfiguration rates, Rtot is adjusted such that the corner frequency 1/(2πRtotC) matches the current reconfiguration frequency (which is done off chip at the voltage source). This minimizes the on-chip energy dissipation as well as maintaining the necessary reconfiguration rate. The total power dissipated (Fig. 1b) is simply the hold power plus the reconfiguration energy times the reconfiguration rate.

Device characterization

We characterize individual MZI modulators both at room temperature and cryogenic temperature with a 250-µm-pitch optical fibre array that is coupled through gratings to the on-chip waveguides. We use a 150-µm-pitch radio-frequency probe (in the ground–signal–ground–signal–ground configuration at room temperature and ground–signal–ground at cryogenic temperature) to apply high-frequency electrical signals.

Digital lock-in amplifier

A time trace of output channels 5 and 6 of the MZM is directly digitized by a high-speed oscilloscope. The time traces are digitally integrated (for 4 ms) with sinusoids of varying frequencies and phases, whose resulting amplitudes form the data for the plots in Fig. 5e,f. The two photodiodes used for both channels have bandwidths of 125 and 600 MHz. Please see Supplementary Information for more detailed experimental methods.