Piezoelectrically actuated silicon-nitride-based high-speed spatial light modulator

Domain: physics
Published: 2025-11-26
Editorial outcome: major_revision

Abstract
Advancements in light modulator technology have been driving discoveries and progress across various fields. The problem of large-scale coherent optical control of atomic quantum systems—including cold atoms, ions, and solid-state color centers—presents among the most stringent requirements. This motivates a new generation of high-speed large-scale modulator technology operating in the visible to near-infrared wavelength range. We introduce a scalable modulator technology based on piezoelectrically actuated silicon nitride resonant waveguide gratings fabricated on 200 mm diameter silicon wafers with CMOS-compatible processes. We present a proof-of-concept device with 4×4 individually addressable 50 μm × 50 μm pixels or channels, each containing a resonant waveguide grating with a ~780 nm design wavelength, supporting >100 MHz modulation speeds, and a spectral response with >20 dB extinction.

Introduction
Devices that have the ability to control multiple optical modes at high speeds are revolutionizing many fields of science and technology, including laser ranging1, quantum information processing2, imaging3,4, optogenetics5, artificial intelligence6,7, and augmented and virtual reality(AR/VR)8,9. In particular, the availability of multimodal and/or high-speed light modulators has been instrumental in the rapid advancement of atom-based quantum technology over the last years2,10–13. Optical control of atomic quantum systems poses the following requirements: (R1) operation at a design wavelength of choice in the visible (VIS) to near-infrared (NIR) spectrum, (R2) a scalable technology with a high channel density (>100 mm−2), (R3) a high modulation speed (>100 MHz), and (R4) a high extinction ratio (>20 dB). This motivates the development of a new modulator technology, meeting these requirements to continue driving progress.

Requirement (R1) stems from the fact that many optical transitions in atoms or atom-like emitters in solids lie in the visible (VIS) to near-infrared (NIR) wavelength range. VIS to NIR wavelength operation is also essential for bioimaging14,15, optogenetics5, and AR/VR8. Requirement (R2), a scalable technology with a high channel density, originates from the need to individually control hundreds to thousands of atoms to unlock quantum technology’s full potential. High modulation speeds (R3) and high extinction ratios (R4) are required to optically control the state of atoms or atom-like emitters with high fidelity in a short time compared to the lifetime of the state13. A high-extinction and high-channel-density optical control technology acting as an ultrafast spatial light modulator is also an immediate benefit to the varied fields of research which already rely on devices with thousands to millions of times slower modulation rates.

Table 1 compares state-of-the-art multichannel light modulator technologies in terms of requirements (R1)-(R4). None of the existing technologies meets all requirements. Spatial light modulators (SLMs) operating in the VIS to NIR range based on microelectromechanical systems (MEMS)16–18 and liquid crystals19,20 are commercially available, but their modulation rates are limited. In the IR wavelength range, alternative SLM technologies with > 1 MHz modulation rates have been explored based on electrical gating of graphene21,22, the Pockels effect in organic electro-optic molecules23–25 and dielectric thin films26, the quantum-confined Stark effect in III-V semiconductor quantum-well-based material27,28, and charge carrier effects in indium tin oxide (ITO)29 and silicon30,31. The refractive index changes associated with these fast effects tend to be small, thus long interaction lengths are needed to realize devices with a high modulation efficiency. To create compact, free-space-coupled devices, one therefore often relies on optically resonant structures, such as metasurfaces21,22,24,28,29, Fabry-Perot cavities27, resonant waveguide gratings23,25,30, or photonic crystal cavities31.

To fulfill requirements (R1)-(R4), we introduce an SLM technology based on piezoelectrically actuated silicon nitride (SiN) resonant waveguide gratings (Fig. 1). The piezoelectric actuators induce strain in the gratings, resulting in a shift of the resonant wavelengths and thereby realizing free-space-coupled modulators. This technology not only enables SLMs with O(MHz) to O(GHz) modulation rates, it also operates in the VIS to NIR wavelength range. Moreover, our devices are fabricated on 200 mm diameter silicon wafers using deep ultraviolet (UV) optical lithography and CMOS-compatible (complementary-metal-oxide-semiconductor-compatible), low-temperature processes (see Methods for fabrication details). Hence, we can fabricate the piezoelectric actuators and resonant waveguide gratings directly on top of electronics to drive the devices32 or on (multiple) metal layers to enable large-scale electrical interconnects. These integration schemes are advantageous for the commercial production of large-scale SLMs.

Our work builds on a platform developed at Sandia National Laboratories consisting of a SiN optical waveguide layer on top of an aluminum-nitride-based (AlN) piezoelectric actuation layer33. While previous works on this platform focused on photonic integrated circuits13,33–35, here we demonstrate densely packed free-space-coupled modulators arranged in a 4×4 grid with a high fill factor of ~96% as a proof of concept for scalable SLM technology (Fig. 1). To boost the modulation efficiency of our devices we not only make use of optically resonant devices, namely resonant waveguide gratings36, but we also take advantage of the mechanical resonances of our pixels, which greatly enhances the piezoelectrically induced displacement37. Resonant waveguide gratings, also known as guided mode resonant gratings or waveguide-mode resonant gratings, couple light incident at specific wavelengths, incidence angles, and polarization to leaky guided modes, giving rise to resonances in the reflection and transmission spectra (in amplitude and phase)36.

Results
Design
We designed our SiN resonant waveguide gratings to operate at a wavelength λ of ~780 nm (R1), with a pitch Λ of 0.490 μm for a SiN thickness of 0.3 μm. The simulated reflection spectrum of our gratings, R[dB] = 10 × log10(|Eout(λ)|2 / |Eref(λ)|2), in Fig. 2a shows a steep dip at a wavelength of ~800 nm with an extinction ratio >50 dB (R4) with respect to the reflection at ~770 nm. We test our devices in a cross-polarized light setup, as schematically depicted below (see Supplementary Fig. 1 for more details). Our simulation of the reflection spectrum captures the cross-polarized testing method (see Methods for more information). The steep dip in the reflection spectrum results from the phase difference between TE and TM polarized reflected light shifting from 0 to π while the reflection amplitude of TE and TM fields remain similar (Fig. 2c), where TE polarized light corresponds to the electric field being parallel to the grating lines. When the TE and TM polarized light waves reflected off the grating are in phase with equal amplitude, the reflected light is polarized at 0° before the polarizing beam splitter and no light is reflected towards the detector. For a phase difference of π all light is reflected. Notably, the effective interferometer governing this effect is contained within ~1 μm of thickness of the device, requiring no long-path length stabilization.

A decrease in grating pitch blue-shifts the wavelength of the dip in the reflection spectrum (Fig. 2b). A pitch of 492 nm gives a maximum extinction ratio of >60 dB. The reduced extinction ratio at different pitches results from the ratio between the TE and TM reflection amplitudes being further away from 1 where the phase difference is 0. By reducing the grating pitch to 0.27 μm, we can shift the optical resonance all the way down to ~470 nm, the short wavelength end of the visible spectrum (see Supplementary Fig. 3). Our technology can operate at a design wavelength of choice in the VIS to near-IR spectrum simply by altering the pitch of the grating (R1).

Our simulations take into account the finite size of the gratings and the incident light beam. While the fabricated and tested devices have a grating size L of 49 μm (Fig. 1e), simulations indicate that we could reduce the size down to ~20 μm without significant changes in extinction ratio and the overall shape of the reflection spectrum (Fig. 2d), resulting in even higher channel densities (R2).

The material platform with which we are working allows fabrication of undercut devices (see Methods), giving us an additional degree of freedom in engineering the mechanical device properties. We can produce pixels of length L supported by a pillar of size l underneath (schematically shown in Fig. 3a, SEM image in Fig. 3b), where L and l can be chosen freely for every pixel. The pillar also contains electrical vias between the piezoelectric actuator and a bottom metal routing layer, connecting the pixels to bond pads (see Fig. 1d, e). Figure 3c shows the simulated mechanical mode with an eigenfrequency fr of 5.9 MHz for a device with L=49 μm and l=10 μm. This closely matches the resonance observed experimentally, Fig. 4b, c. By altering the pixel and pillar size L and l, we can set the mechanical resonance to a frequency of choice (Fig. 3d).

Characterization
Figures 4a and 2a show the measured reflection spectrum of a grating and its agreement with simulations, with a measured extinction ratio >20 dB (R4). We measure the modulation amplitude A and speed of the packaged devices by reflecting laser light off a pixel and detecting the reflected light (with electric field Eout) on a fast photodiode (Fig. 4e), which is connected to an electrical spectrum analyzer (ESA). When applying an AC voltage to the illuminated pixel, a peak appears on the ESA at the applied AC frequency f, as anticipated for our piezoelectrically actuated device. The height of this peak, i.e. the modulation amplitude A, depends on the laser wavelength. Figure 4a overlaps the reflection spectrum with the modulation amplitude as a function of wavelength λ. The peak of the modulation amplitude occurs where the slope in the reflection spectrum is steepest (~791 nm). The devices have an optical bandwidth of several nanometers (8 nm peak to trough of resonance, 3 dB bandwidth of 2.3 nm in the modulation amplitude measurement). This corresponds to photon-lifetime-limited modulation bandwidths on the order of 1 THz, which does not pose a limitation for the envisaged applications. Moreover, the target applications typically only require modulators with narrowband operation at a discrete set of wavelengths (e.g. a set of wavelengths corresponding to certain atomic transitions). Our modulator technology is very well suited to accommodate this requirement. Either one can use separate modulator chips designed to operate at different wavelengths, or pixels designed to operate at different wavelengths can be integrated on the same chip (in separate chip areas or interleaved).

Figure 4b compares the modulation amplitude and speed for two different types of devices, released and unreleased. Released devices are undercut and anchored to the substrate with a 10 μm wide silicon dioxide pillar in the middle of the pixel (see Methods for fabrication details and Fig. 3b for an SEM image of a device cross-section). Unreleased devices have no undercut. The goal of releasing is to make the devices more mechanically compliant, resulting in lower drive voltages for the same level of induced strain. Additionally, released devices have high-quality-factor mechanical resonances. Resonant enhancement reduces the required drive voltage even further. Figure 4b shows the wavelength shift Δλr/ΔV of the reflection spectrum versus the applied AC frequency f for a released and unreleased grating. We calculate the wavelength shift from the measured modulation amplitude and the slope of the reflection spectrum. The numerous peaks and troughs in Fig. 4b are attributed to mechanical resonances38,39. The more compliant nature of the released devices results in low-frequency wavelength shifts that are more than an order of magnitude larger compared to the unreleased devices. It also leads to the appearance of mechanical resonances at lower frequencies. Finite element analysis confirms the existence of mechanical resonances and identifies the mechanical mode at fr ≈ 5 MHz for the released device (Fig. 3c). The resonance at fr ≈ 5 MHz gives a large wavelength shift of 4 × 102 pm V−1, which corresponds to an enhancement of a factor k = (Δλr/ΔV)fr / (Δλ/ΔV) ≈ 50 compared to the low-frequency shift. Up to a frequency of ~ 10 MHz, the data shows wavelength shifts larger than the low-frequency response for the released device (R3). The stiffer nature of the unreleased device shifts the resonances to higher frequencies. Up to ~ 700 MHz, wavelength shifts are comparable to the low-frequency response. The frequency response measurements are limited by the photodetector bandwidths (DC-400 MHz for the released device and 5−1000 MHz for the unreleased device measurement) and the 900 MHz bandwidth of the voltage amplifiers on the printed circuit boards (see Methods).

From the frequency response measurements (Fig. 4b) and the measured reflection spectrum (Fig. 4a), we can estimate the voltages required to shift the spectrum by 8 nm, that is, the wavelength difference between the trough and peak in the spectrum. We find a voltage of ~ 20 V for a released device at the ~ 5 MHz mechanical resonance and ~ 1 × 103 V off-resonance (100 kHz driving frequency). For an unreleased device, we estimate a voltage of ~ 40 × 103 V off-resonance (at 10 MHz). We recognize that the off-resonance and unreleased device voltages are high in this proof-of-concept demonstration and suggest ways of lowering these significantly in the discussion. Also, we note that several technologies exist today to deliver voltages in the O(10 V) to O(kV) range at O(MHz) to O(GHz) frequencies, such as Si LDMOS (laterally-diffused metal-oxide semiconductor)40, SiC41, and GaN-based devices42.

Figure 4d shows the ring down measurement of the mechanical mode at ~ 5 MHz for a released device. Fitting the data gives a ring down time τ of 3.1 μs. This corresponds to a mechanical Q-factor of Qm = ωm τ = 52 (ωm = 2π × 5.3 MHz)43. This is in good agreement with the enhancement factor of ~ 50 observed in the frequency response measurement, as expected for a harmonic oscillator.

Pixel-to-pixel fabrication-induced variations lead to differences in resonance frequencies and enhancement factors, e.g. variations in pixel size, layer thicknesses, and depth of the undercut. For the pixels in our 4 × 4 device, we determined the mechanical resonance frequencies fr of the strong resonance around 5 MHz and the associated enhancement factor k (Fig. 4c). The average resonance frequency is 5.7 MHz (standard deviation of 0.9 MHz) and the average enhancement factor is 32 (standard deviation of 13). Established post-fabrication trimming techniques such as laser trimming44 and focused ion beam (FIB) milling45 can be used to tune up the resonances. A possible approach for closed-loop laser trimming consists of combining the trimming laser, probe laser (to be modulated by the device), and imaging optics in a single optical system, as has been demonstrated for photonic crystal cavities31 and ring resonators13. Image recognition methods can locate the pixel edges to be trimmed44. We can parallelize laser trimming of multiple pixels by e.g. using a liquid crystal SLM to generate arrays of laser spots and photodetector arrays for probe laser detection.

Methods
Fabrication
Our devices consist of a silicon nitride (SiN) optical waveguide layer on top of an aluminum-nitride-based (AlN) piezoelectric actuation layer with a silicon dioxide optical buffer layer in between33–35. The devices are fabricated on 200 mm diameter silicon wafers at Sandia National Laboratories using deep ultraviolet (UV) optical lithography. Low-temperature, CMOS-compatible processes are used for thin-film deposition, namely plasma-enhanced chemical vapor deposition (PECVD; for amorphous silicon, SiN and oxide deposition) and physical vapor deposition (PVD; for AlN and metal deposition). There are three metal layers in the stack to enable device actuation. From bottom to top, these are: a routing layer which we use to connect each of the pixels to bond pads, a bottom electrode layer, and a top electrode layer. In between the two electrode layers there is the AlN layer; together these comprise the piezoelectric actuation layer. The bottom electrode layer is separated from the routing layer by a silicon dioxide buffer. The three metal layers are connected by vias. Throughout the process flow, chemical-mechanical polishing (CMP) is used for planarization. In between the bottom electrode layer and routing layer there is also a patterned amorphous silicon layer to enable undercutting of devices. After having processed the entire device stack, a release etch in XeF2 gas removes the amorphous silicon to create undercut devices. The XeF2 gas can reach the amorphous silicon layer through deep, etched trenches.

Packaging
We dice the wafers into chips and wire bond them to printed circuit boards (Fig. 1d). The devices with 4 × 4 pixels have 17 bond pads, 1 pad for a shared ground and 16 pads for the signals applied to each of the pixels. Each of our PCBs contains 16 operational amplifiers (OPAMPs; Texas Instruments THS3491) to individually address 16 pixels. The OPAMPs provide a voltage gain of 5, have a 900 MHz bandwidth, and a ±16 V supply voltage. Ganged microscale RF plugs (Samtec) connect the PCBs to signal generators.

Simulation
We use Ansys Lumerical’s 2D FDTD solver for optical simulations. We run the simulation for two orthogonal polarizations. Afterwards, we use transfer matrix multiplication to implement the beamsplitter and waveplates together with the simulations of both polarizations.

Our simulation takes into account the Gaussian shape of the excitation and collected beams. To directly compare the simulation with the measurement, we implement the same normalization method.

We perform a simulation without the grating structure to simulate the effect of reflection from the aluminum layer with the silicon dioxide and SiN layers on top (Eref). The resulting simulation is able to capture the entire measurement setup to accurately predict the results.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "After reviewing this paper, I do not recommend the paper to be publish in nature communications with this version. My questions are listed as follows:\n1.The claim of this paper is not correct. In the title, the author claims that the device can cover visible to near-infrared wavelengths. However, in the measurement, it only works ~ 800 nm.\n2.The modulation speed is not quite clear. It is better to show an eye-diagram to confirm the speed of light. As we can find in the paper, the ER is high. Thus, I think it can perform a very good eye-diagram.\n3.The principle of the device is note quite clear. Why it has a resonance? The author should explain about it.\n4.The figures are not well drawn, especially the experimental data.\n5.The paper is not well written. For instance, I cannot find inset in Fig. 4b. Meanwhile, Fig.4c is not illustrated.\n6.The author says this work demonstrated 4 × 4 individually addressable 50 µm × 50 µm pixels. However, in this paper, I can only find the results from one pixel.\n7.After all, I think Fig. 4b is not a good way to show the speed. For a modulator, we’d better use eye diagram.", "reviewer_2": "This manuscript presents a high-speed modulator technology targeting operation in the visible (VIS) to near-infrared (NIR) spectrum, with scalability to high density, high speed (>100 MHz), and a high extinction ratio. The proposed technology is based on piezoelectrically actuated silicon nitride resonant waveguide gratings fabricated using a CMOS-compatible process. Proof-of-concept results are demonstrated with a 4 × 4 spatial modulator operating at a wavelength of 780 nm, achieving modulation speeds >100 MHz and an extinction ratio >20 dB.\nThe technical content of this paper is of good quality and holds potential interest for a variety of applications, such as ranging, quantum information processing, atom control, display and imaging, and artificial intelligence, as mentioned by the authors in the motivation of the paper.\nHowever, there are significant issues that need to be addressed before the paper can be considered suitable for publication:\n1. Wavelength Range: The authors claim that the proposed technology enables operation at any wavelength in the VIS to NIR spectrum. This statement is not supported by experimental results or simulations. The only wavelength range considered in this paper is around 790 nm. What design or fabrication considerations need to be addressed when changing the wavelength? What performance can be expected at other wavelengths?\n2. Optical Bandwidth: The authors state that “The peak of the modulation amplitude occurs where the slope in the reflection spectrum is steepest (∼791 nm).” What is the optical bandwidth of the device? Could this pose a limitation for practical use in the applications mentioned?\n3. Performance Metrics: The performance of the device is not clearly reported. What voltage is required to achieve a π phase shift between TE and TM polarization? How is the modulation amplitude A, shown in Fig. 4a, related to the extinction ratio measured at the photodetector?\n4. Non-flat Frequency Response: The non-flat frequency response, with a strong peak due to the mechanical mode at 5 MHz, requires specific equalization of the driving signal. As mentioned in the discussion, variability in the response across different pixels (Fig. 4c) could make controlling spatial modulators with a large number of pixels extremely challenging. The authors should provide a more detailed analysis of this issue.\n5. Resonant Frequency Spread: In Fig. 4c, the resonant frequencies of different pixels are shown. Were these measured at the same optical wavelength? What causes the observed spread in the enhancement factor?\n6. Post-Fabrication Trimming: Post-fabrication trimming is proposed as a solution to fine-tune the resonances of different pixels. However, such trimming would require functionality monitoring for each pixel in a closed-loop manner. Is this a viable strategy for large arrays of pixels? More generally, what are the main limitations to scaling the proposed device to larger arrays? This should be elaborated on in the discussion section.\n7. Material Layer Stack: In Fig. 1b, the material layer stack is incomplete. The text mentions three metal layers, but these are not shown all in the figure.\n8. Fig. 4b Legend: The legend of Fig. 4b states, “The inset shows the simulated mechanical mode at the resonance frequency frf_rfr of ∼5 MHz.” However, no inset is present in this panel.\n9. Requirements R1–R4: In the introduction and Table 1, the authors refer to a list of requirements (R1–R4) first introduced in the abstract. It would be preferable to list and label these requirements (R1–R4) in the introduction rather than in the abstract.\n10. Fig. 3d Vertical Axis: In Fig. 3d, the bottom panel (“Simulated f_r as a function of L for l=5 μm (bottom)”) would be better presented with a logarithmic scale on the vertical axis to more clearly show the reduction in resonance frequency.\n11. Fig. 2 Caption: In Fig. 2, the caption includes the statement, “The 1/e field full width is kept at 45% of the grating size.” This phrasing is unclear and should be explained more clearly.\n12. Supplementary Information: In the supplementary information, the labels in Fig. 1 of the experimental setup (e.g., SLD, APD) should be better aligned with the descriptions provided in the text for clarity"}, "author_response": "Our devices operate around a wavelength of 780-800 nm. To our knowledge, there are no universally agreed boundaries to the visible spectrum. According to the International Commission on Illumination (CIE), the lower wavelength limit is generally taken between 360 and 400 nm and the upper limit between 760 and 830 nm1. Therefore, we conclude that our devices operate on the boundary between the visible and near-infrared wavelength range. Moreover, we can alter our design to shift the point of operation to shorter wavelengths (or longer wavelengths). Reducing/increasing the pitch or our gratings will lead to a shift towards shorter/longer wavelengths, as shown in Fig. 2b in our manuscript. Our resonant waveguide gratings are made of silicon nitride with a silicon oxide cladding. These materials are transparent in the visible and near-infrared wavelength range. Therefore we can freely alter the design to shift the wavelength of operation within this transparency range. To illustrate that we can shift the wavelength of operation all the way down to the short end of the visible spectrum, we included the simulated reflection spectrum in the supplementary information for a grating pitch of 0.27 μm (figure copied below), showing a resonance at ~470 nm (see also our reply to comment #1 of reviewer #2).\nTo emphasize that the exact wavelength of operation is a design choice, the introduction mentions “(R1) operation at a design wavelength of choice in the visible (VIS) to near-infrared (NIR) spectrum”.\nTo avoid any confusion, we changed the title of our manuscript from “Piezoelectrically actuated high-speed spatial light modulator for visible to near-infrared wavelengths” to “Piezoelectrically actuated silicon-nitride-based high-speed spatial light modulator”.\n2.The modulation speed is not quite clear. It is better to show an eye-diagram to confirm the speed of light. As we can find in the paper, the ER is high. Thus, I think it can perform a very good eye-diagram.\nThe modulation speed of our devices is shown in the frequency response measurement in Fig. 4b, which is a plot of the measured wavelength shift versus modulation frequency. Frequency response measurements are a standard method to measure modulation speed2.\nWe attribute the numerous peaks and troughs in our measurements to mechanical resonances. The frequency response measurements are limited by the photodetector bandwidths (DC-400 MHz for the released device and 5-1000 MHz for the unreleased device measurement) and the 900 MHz bandwidth of the voltage amplifiers on the printed circuit boards, as explained in the characterization section of the manuscript.\nEye diagrams are a typical and traditional way of measuring the behavior of communication links in datacom and telecom applications. We believe they add little value in this context. In general, they characterize entire communication links and are very much an indication of the noise figures of the detectors and amplifiers in the link and can show effects of dispersion and loss in the fibers in the link. They are traditionally also shown in modulator papers discussing specifically datacom or telecom high-speed modulators, but even there they add little quantitative value since they tell you very little about a single component in the entire optical link. At best, they show qualitatively that data transmission works in the link. In contrast, our devices are free-space-coupled spatial light modulators aimed at applications such as atom control and displays. We do not think that an eye diagram measurement would add meaningfully to the manuscript.\n3.The principle of the device is note quite clear. Why it has a resonance? The author should explain about it.\nOur devices belong to a class of devices described in literature as resonant waveguide gratings, also known as guided mode resonant gratings or waveguide-mode resonant gratings. Our manuscript contains several references to provide more background to the reader on the operating principles of resonant waveguide gratings3–6.\nAkin to standard grating couplers used in photonic integrated circuits, light waves incident on a resonant waveguide grating can couple to in-plane guided modes, provided the wavelength, polarization, and incidence angle are chosen correctly to match the grating design. Since the coupling to guided modes only occurs at certain wavelengths, we observe resonant behavior in the reflection and transmission spectra of these gratings. The resonant behavior can be observed both in the amplitude and phase spectra.\nWe added the following sentence to the introduction to clarify the device principle:\n“Resonant waveguide gratings, also known as guided mode resonant gratings or waveguide-mode resonant gratings, couple light incident at specific wavelengths, incidence angles, and polarization to leaky guided modes, giving rise to resonances in the reflection and transmission spectra (in amplitude and phase) [36].”\nOur device demonstration specifically relies on the resonant behavior in the phase spectra and simultaneous illumination with TE and TM polarized waves in a cross-polarized light setup, as detailed in the design section of the manuscript:\n“The steep dip in the reflection spectrum results from the phase difference between TE and TM polarized reflected light shifting from 0 to π while the reflection amplitude of TE and TM fields remain similar (Fig. 2c), where TE polarized light corresponds to the electric field being parallel to the grating lines (Fig. 4e). When the TE and TM polarized light waves reflected off the grating are in phase with equal amplitude, the reflected light is polarized at 0° before the polarizing beamsplitter and no light is reflected towards the detector. For a phase difference of π all light is reflected.”\nWe copied Fig. 2a, 2c, and 4e below for clarity.\n4.The figures are not well drawn, especially the experimental data.\nWe appreciate the reviewer’s feedback, but we are unsure which figures and which aspects of the figures the reviewer is referring to. The data has been plotted meticulously using conventional plotting methods (Matplotlib package in Python). We set up the plotting parameters to match the standard figure styles in scientific publications. To improve Fig. 4 showing the experimental measurement data, we added whitespace in between the subfigures and changed the fontsize of the labels a to e. We are open to suggestions to improve the style of our figures.\n5.The paper is not well written. For instance, I cannot find inset in Fig. 4b. Meanwhile, Fig.4c is not illustrated.\nIndeed, the mention of the inset in Fig. 4b was an artifact of previous versions. That figure is now included in more detail in Fig. 3c. We removed the mention of the inset in the manuscript.\nFig. 4c can be found in the upper right corner of page 5 of the manuscript. Fig. 4c shows the measured enhancement factor k versus the resonance frequency for the resonance near 5 MHz, for each pixel in a 4x4 SLM. Only 13 data points are shown because 3 pixels weren’t functioning electrically. We made the caption clearer by changing it from “Measurement of the mechanical resonance frequencies f of the strong resonance around 5 MHz and the associated enhancement factor k for each pixel. 13 of the 16 pixels were functioning in this device.” to “Measurement of the different mechanical resonance frequencies f for each pixel of the strong resonance around 5 MHz and the associated enhancement factor k. 13 of the 16 pixels were functioning in this device.” The figure is referenced at the end of the characterization section:\n“For the pixels in our 4×4 device, we determined the mechanical resonance frequencies f of the strong resonance around 5 MHz and the associated enhancement factor k (Fig. 4c).”\nWe also improved the wording of the final paragraph of the design section, explaining Fig. 3. We believe this makes it easier for the reader to understand the device concept. The new version of the paragraph reads:\n“The material platform with which we are working allows fabrication of undercut devices (see Methods), giving us an additional degree of freedom in engineering the mechanical device properties. We can produce pixels of length L supported by a pillar of size l underneath (schematically shown in Fig. 3a, SEM image in Fig. 3b), where L and l can be chosen freely for every pixel. The pillar also contains electrical vias between the piezoelectric actuator and a bottom metal routing layer, connecting the pixels to bond pads (see Fig. 1d and 1e). Fig. 3c shows the simulated mechanical mode with an eigenfrequency f of 5.9 MHz for a device with L = 49 μm and l = 10 μm. This closely matches the resonance observed experimentally, Fig. 4b and 4c. By altering the pixel and pillar size L and l, we can set the mechanical resonance to a frequency of choice (Fig. 3d).”\nWe are open to other recommendations to improve the quality of our manuscript.\n6.The author says this work demonstrated 4 × 4 individually addressable 50 µm × 50 µm pixels. However, in this paper, I can only find the results from one pixel.\nWhile Fig. 4a and 4b in the manuscript only show the results for one pixel in a 4x4 SLM, Fig. 4c shows the results of characterizing all pixels in a 4x4 SLM. Fig. 4c is also discussed in our reply to comment #5 of reviewer #1. We hope our reply above clarifies what is shown in Fig. 4c and where in the manuscript this figure is discussed.\n7.After all, I think Fig. 4b is not a good way to show the speed. For a modulator, we’d better use eye diagram.\nFor our reply to this comment, we refer to comment #2 of reviewer #1, which addresses the same topic.\nReviewer #2 (Remarks to the Author):\n1. Wavelength Range: The authors claim that the proposed technology enables operation at any wavelength in the VIS to NIR spectrum. This statement is not supported by experimental results or simulations. The only wavelength range considered in this paper is around 790 nm. What design or fabrication considerations need to be addressed when changing the wavelength? What performance can be expected at other wavelengths?\nThe reviewer is correct that we only demonstrate devices operating around 790 nm. As stated in the introduction, the exact wavelength of operation is a design choice: “(R1) operation at a design wavelength of choice in the visible (VIS) to near-infrared (NIR) spectrum”.\nWe can alter our design to shift the point of operation to shorter wavelengths (or longer wavelengths). Reducing/increasing the pitch of our gratings will lead to a shift towards shorter/longer wavelengths, as illustrated in Fig. 2b in our manuscript for wavelengths in the range ~780 nm - 820 nm. Our resonant waveguide gratings are made of silicon nitride with a silicon oxide cladding. These materials are transparent in the visible and near-infrared wavelength range. Therefore we can freely alter the design to shift the wavelength of operation within this transparency range.\nTo illustrate that we can shift the wavelength of operation all the way down to the short end of the visible spectrum, we included the simulated reflection spectrum in the supplementary information for a grating pitch of 0.27 μm (figure copied below), showing a resonance at ~470 nm. We refer to this simulation result in the design section of the main text:\n“By reducing the grating pitch to 0.27 μm, we can shift the optical resonance all the way down to ∼ 470 nm, the short wavelength end of the visible spectrum (see Supplementary Fig. 3). Our technology can operate at a design wavelength of choice in the VIS to near-IR spectrum simply by altering the pitch of the grating (R1).”\nWhen reducing the grating pitch, it is important to keep fabrication limits in mind. Fabrication limits depend on the foundry you are working with and the technology and toolset they have available. 193 nm deep UV lithography is a widely available technology in commercial foundries that allows patterning of sub-100 nm features7, enabling the pitches needed for blue wavelength gratings (the exact feature size depends not only on pitch but also the duty cycle of the grating, e.g. for a 100 nm minimum feature size and 0.27 μm pitch, you can fabricate duty cycles in between 37% and 63%; the simulation shown above is for a duty cycle of 63%). The discussion of fabrication limits is also included in the supplementary information:\n“Reducing the pitch of the gratings leads to a resonance shift toward shorter wavelengths. The resonant waveguide gratings are made of silicon nitride with a silicon oxide cladding. These materials are transparent in the visible and near-infrared wavelength range. Therefore, we can freely alter the design to shift the wavelength of operation within this transparency range. As an example, Fig. 3 shows the simulated reflection spectrum for a grating pitch of 0.27 μm, with a resonance at ∼ 470 nm. When reducing the grating pitch, it is important to keep fabrication limits in mind. Fabrication limits depend on the foundry you are working with and the technology and toolset they have available. 193 nm deep UV lithography is a widely available technology in commercial foundries that allows patterning of sub-100 nm features [1], enabling the pitches needed for blue wavelength gratings. The exact feature size depends not only on pitch but also the duty cycle of the grating, e.g. for a 100 nm minimum feature size and 0.27 μm pitch, you can fabricate duty cycles in between 37 % and 63 % (the simulation shown below is for a duty cycle of 63 %).”\nSub-100 nm features can also easily be achieved with electron-beam lithography, but this technology is less amenable to high-volume production.\n2. Optical Bandwidth: The authors state that “The peak of the modulation amplitude occurs where the slope in the reflection spectrum is steepest (∼791 nm).” What is the optical bandwidth of the device? Could this pose a limitation for practical use in the applications mentioned?\nAs illustrated in Fig. 4a in the manuscript, the optical resonance is several nanometers wide (8 nm from peak to trough of resonance; 3 dB bandwidth of 2.3 nm in the modulation amplitude measurement), corresponding to photon-lifetime-limited modulation bandwidths on the order of 1 THz(!) (δν = c δλ/λ2). Therefore the optical bandwidths of our devices do not pose a limitation in terms of modulation speed for the envisaged applications.\nMoreover, the applications we envisage typically require modulators with narrowband operation at a discrete set of wavelengths (e.g. a set wavelengths corresponding to certain atomic or molecular transitions). Our modulator technology is very well suited to accommodate this requirement. Either one can use separate modulator chips designed to operate at different wavelengths, or pixels designed to operate at different wavelengths can be integrated on the same chip (in separate chip areas or interleaved).\nWe added this discussion to the manuscript:\n“The devices have an optical bandwidth of several nanometers (8 nm peak to trough of resonance, 3 dB bandwidth of 2.3 nm in the modulation amplitude measurement). This corresponds to photon-lifetime-limited modulation bandwidths on the order of 1 THz, which does not pose a limitation for the envisaged applications. Moreover, the target applications typically only require modulators with narrowband operation at a discrete set of wavelengths (e.g. a set wavelengths corresponding to certain atomic transitions). Our modulator technology is very well suited to accommodate this requirement. Either one can use separate modulator chips designed to operate at different wavelengths, or pixels designed to operate at different wavelengths can be integrated on the same chip (in separate chip areas or interleaved).”\n3. Performance Metrics: The performance of the device is not clearly reported. What voltage is required to achieve a π phase shift between TE and TM polarization? How is the modulation amplitude A, shown in Fig. 4a, related to the extinction ratio measured at the photodetector?\nThe voltage required to go from 0 to π phase difference between TE and TM polarization corresponds to the voltage required to shift the resonance by 8 nm, i.e. the wavelength difference between the trough and peak of the resonance (see Fig. 4a in the manuscript).\nIn Fig. 4b, we show the wavelength shift per volt (Δλ/ΔV) for a released and unreleased device as a function of modulation frequency. For a released device, we get a wavelength shift of 4x102 pm/V at a resonant driving frequency of ~5 MHz. Off resonance, at 100 kHz, we get a wavelength shift of ~7 pm/V for a released device. For an unreleased device, we get wavelength shifts of ~0.2 pm/V at 10 MHz (off resonance). This corresponds to voltages of 20 V, 1x103 V, and 40x103 V, respectively, to achieve the 0 to π phase difference change between TE and TM polarization, i.e. the voltage required to realize the extinction ratio of >20 dB measured in the reflection spectrum. We have added this information to the characterization section in the manuscript:\n“From the frequency response measurements (Fig. 4b) and the measured reflection spectrum (Fig. 4a), we can estimate the voltages required to shift the spectrum by 8 nm, that is, the wavelength difference between the trough and peak in the spectrum. We find a voltage of ∼ 20 V for a released device at the ∼ 5 MHz mechanical resonance and ∼ 1 × 103 V off-resonance (100 kHz driving frequency). For an unreleased device, we estimate a voltage of ∼ 40 × 103 V off-resonance (at 10 MHz). We recognize that the off-resonance and unreleased device voltages are high and suggest ways of lowering these significantly in the discussion.”\nWe recognize the voltages required for high-extinction-ratio modulation are high and suggest several ways to improve this in the discussion section of the manuscript:\n“One of the main challenges ahead is to reduce the voltages required to achieve high-extinction-ratio modulation. We see several ways to achieve this. Firstly, we can use a piezoelectric material with an enhanced response. Scandium aluminum nitride, for instance, has a piezoelectric response up to 5 times larger compared to AlN [43]. Secondly, instead of resonant waveguide gratings, we can use other compact, optically resonant structures with narrower optical linewidths. Vertically coupled photonic crystal cavities with high quality factors and small mode volumes are a promising candidate. These have been demonstrated in silicon with linewidths <10 pm at a wavelength of 1.6 μm [21]. Silicon nitride photonic crystal cavities with linewidths down to 0.1 nm at 760 nm have been reported [44], though these were not vertically coupled. By combining narrow-linewidth photonic crystal cavities with piezoelectric materials with an enhanced response, we can potentially reduce the drive voltages by three to four orders of magnitude.”\nThe modulation amplitude A in Fig. 4a is the result of a small-signal modulation measurement and is not meant to demonstrate the extinction ratio of our devices. The modulation amplitude versus wavelength measurement demonstrates that our devices behave as expected, namely that the amplitude peaks on the slope of the reflection spectrum R (since A ~ (dR/dλ)*Δλ), as demonstrated in the manuscript.\n4. Non-flat Frequency Response: The non-flat frequency response, with a strong peak due to the mechanical mode at 5 MHz, requires specific equalization of the driving signal. As mentioned in the discussion, variability in the response across different pixels (Fig. 4c) could make controlling spatial modulators with a large number of pixels extremely challenging. The authors should provide a more detailed analysis of this issue.\nThe reviewer is correct that for the generation of arbitrary waveforms, signal equalization is required. While we do not demonstrate this in our manuscript, we would like to point out that signal equalization has already been demonstrated for integrated modulators with mechanical resonances in the MHz to GHz range8. We acknowledge the need for signal equalization in the case of arbitrary waveform generation in the discussion section of our manuscript and point the reader to a reference demonstrating signal equalization for a modulator with mechanical resonances:\n“Our modulator technology could even generate arbitrary waveforms requiring the full device bandwidth (i.e. not only driving at resonance frequencies) by using signal equalization techniques to compensate for the non-flat frequency response. Signal equalization has been demonstrated for photonic integrated circuit modulators with mechanical resonances in the MHz to GHz range [39].”\nAs the reviewer points out, there are indeed variations in the frequency response from pixel to pixel (see Fig. 4c in the manuscript). We can set up automated measurements of every pixel (see comment #6 of reviewer #2 for more details), to characterize the frequency response before using the spatial light modulator in an application. In addition, we can also tune up the resonances of all pixels using post-fabrication trimming techniques (e.g. laser trimming, a standard technique used in the semiconductor industry), as detailed in our response to comment #6 of reviewer #2 and added to the revised manuscript.\nFinally, we’d like to mention that not every application requires arbitrary waveform generation (and therefore equalization). For instance, one can drive the modulators at resonance to generate strong sidebands to the incident laser beam. The generation of these sidebands can be switched on and off (individually controlled for every pixel) with response times on the order of microseconds, with the exact response time depending on the mechanical quality factor. This has applications in the optical control of atomic systems, where one wishes to address certain atomic transitions in large-scale arrays of atoms, ions, or solid-state color centers9.\nAnother way of using this SLM technology is to drive different pixels at different resonance frequencies. The beams reflected by the SLM overlap in the far field. By driving each pixel at a certain frequency and phase, we can generate predictable time-varying and even periodically repeating patterns in the far field, i.e. our SLM acts as a high-speed laser scanner. This principle has been described conceptually in literature for photonic integrated circuit phased arrays10. For instance, by driving the nth channel at frequency ω + n∆ω 0 (preferably corresponding to a resonance frequency to enable low-voltage driving), one can generate a pattern repeating itself every T = 2π/∆ω. Our SLM technology enables MHz speeds, compared to conventional MEMS scanners being limited to sub-MHz speeds11. High-speed laser scanners have applications in atom control12, display technology11, and laser ranging13.\nThe above mentioned examples and applications are summarized in the discussion section of the manuscript:\n“We see many potential applications for this SLM technology. Depending on the target application, we can configure our modulator technology in different ways. For instance, driving the modulators at a strong mechanical resonance generates strong sidebands to the incident laser light (the sidebands could be resonant with an atomic transition). The generation of these sidebands can be switched on and off (individually controlled for every pixel) with response times on the order of microseconds, with the exact response time depending on the mechanical quality factor. This has applications in the optical control of atomic systems, where one wishes to address certain atomic transitions in large-scale arrays of atoms, ions, or solid-state color centers [13]. We can use different mechanical resonances to generate sidebands at different frequencies or engineer the pixels to alter the mechanical resonances, e.g. by varying the grating size or the depth of the undercut. Laser trimming [21, 41] or focused ion beam milling [42] can alter the resonance frequencies post-fabrication. Predictable time-varying and even periodically repeating light patterns can be generated in the far field [38] by driving each of the pixels at a particular mechanical resonance frequency, enabling low-voltage driving, with a particular phase. The generated pattern will depend on the chosen frequencies and phases. This concept has been described for photonic integrated circuit phased arrays [38] and has applications in atom control [46], display technology [47], and laser ranging [48]. The proposed SLM technology enables MHz speeds, compared to conventional MEMS laser scanners limited to sub-MHz speeds [47].”\n5. Resonant Frequency Spread: In Fig. 4c, the resonant frequencies of different pixels are shown. Were these measured at the same optical wavelength? What causes the observed spread in the enhancement factor?\nYes, these were all measured at 791 nm, we have added this information to the caption.\nWe suspect that the spread in enhancement factor and resonance frequency are caused by fabrication-induced variations from pixel to pixel, such as variations in the size of the pixel, layer thicknesses, and depth of the undercut. As shown in Fig. 3d (and copied below), the resonance frequency shifts rather quickly as a function of the pixel size L and the supporting pillar width l (and therefore the undercut distance). We expect variations in resonance frequency to be correlated with variations in enhancement factor, but the exact relationship is complex (e.g. a wider pillar increases the resonance frequency; the wider pillar leads to more clamping loss so a lower enhancement/quality factor, but a wider pillar also increases the stiffness which is associated with an increase in enhancement/quality factor).\nThe following sentence in the characterization section of the manuscript clarifies this to the reader:\n“”Pixel-to-pixel fabrication-induced variations lead to differences in resonance frequencies and enhancement factor, e.g. variations in pixel size, layer thicknesses, and depth of the undercut.”\n6. Post-Fabrication Trimming: Post-fabrication trimming is proposed as a solution to fine-tune the resonances of different pixels. However, such trimming would require functionality monitoring for each pixel in a closed-loop manner. Is this a viable strategy for large arrays of pixels? More generally, what are the main limitations to scaling the proposed device to larger arrays? This should be elaborated on in the discussion section.\nWe believe post-fabrication trimming of large arrays is a viable strategy. Laser trimming is widely used in the semiconductor industry to e.g. tune resistors by selectively removing material. Large-scale laser trimming systems with sub-micrometer alignment accuracy are commercially available14. Moreover, closed-loop trimming can easily be achieved by combining the trimming laser, probe laser (to be modulated by the device), and imaging optics in a single optical system, as we have demonstrated before in our research group for photonics crystal cavity15 and ring resonator trimming9. To trim one of our pixels, one would repeatedly measure the mechanical resonances (using a probe laser, detector, electrical signal generator and analyzer) while trimming material from the edges of the pixel. The edges of the pixel can be detected using image recognition techniques16. Fig. 3d in the manuscript shows how small changes in pixel size lead to large resonance shifts, e.g. a change in pixel size from 40 μm to 35 μm shifts the resonance frequency from 8 MHz to 11 MHz. So removing small amounts of material would be sufficient to tune up the resonances (for our 4x4 SLM we observed a standard deviation of 0.9 MHz for an average resonance frequency of 5.7 MHz, see manuscript). Potentially, one could parallelize laser trimming of multiple pixels, e.g. by using a liquid crystal SLM to generate arrays of laser spots (instead of a single laser spot) combined with photodiode arrays for probe laser detection. Similar to laser trimming, one could use focused ion beam (FIB) milling to trim away material, as has been demonstrated e.g. for MEMS gyroscopes17. The probe laser and associated optical system could reside outside of the FIB chamber and optical signals could enter the chamber through windows.\nWe added the following discussion to the manuscript to clarify a potential approach for trimming:\n“Established post-fabrication trimming techniques such as laser trimming [41] and focused ion beam (FIB) milling [42] can be used to tune up the resonances. A possible approach for closed-loop laser trimming consists of combining the trimming laser, probe laser (to be modulated by the device), and imaging optics in a single optical system, as has been demonstrated for photonic crystal cavities [21] and ring resonators [13]. Image recognition methods can locate the pixel edges to be trimmed [41]. We can parallelize laser trimming of multiple pixels by e.g. using a liquid crystal SLM to generate arrays of laser spots and photodetector arrays for probe laser detection.”\nIn our opinion, the main challenge in scaling the proposed device to larger arrays is to get all the required electrical signals in to drive the pixels. In our prototype device, we used wire bonds to get the electrical signals from the printed circuit board into the chip. But, the number of bond pads is limited by the perimeter of the chip. Assuming we have a square chip with side S, the number of bond pads scales with S, while the number of pixels scales with the area S2. Therefore the number of pixels we can put on a chip goes up quicker than the number of electrical signals we can get in. So in order to get enough signals in, we’d have to make very large chips on which only a small area is filled with pixels (which is expensive and ultimately limited by the wafer size). For example, on a 1 cm by 1 cm chip, with pixel size of 50 μm and a typical bond pad spacing of 100 μm, we can fit 40000 pixels but only 400 bond pads around the edge of the chip. A possible solution to the electrical IO problem is to make use of through-silicon vias, a well-known technology in the semiconductor industry, to get the signals from the front to the back of the chip. The backside of the chip can then be bonded to an interposer which takes care of the electrical fanout (using cheaper technology compared to the SLM chip). This interposer could also hold some of the electronic driving ICs.\nAn even more advanced solution would be to integrate (some of) the electronics to drive the pixels on the SLM chip, as also suggested in the introduction of the manuscript. For example, one could integrate a demultiplexer on chip to limit the number of electrical inputs required.\nWe added the following to the discussion section of the manuscript to address this challenge:\n“Another challenge is to get all the required electrical driving signals onto the SLM chip as we scale up the number of pixels. In our proof-of-concept device we use wire bonds. The number of wire bonds is limited by the available chip perimeter. For example, on a 1 cm by 1 cm chip, for a pixel size of 50 μm and a typical bond pad spacing of 100 μm, we can fit 40 000 pixels, but only 400 bond pads around the chip perimeter. One approach to increase the number of electrical inputs is to make use of through-silicon vias [45] and bond the SLM chip to an interposer. This interposer could also hold electronic driving ICs. An even more advanced solution is to integrate some of the electronics on the SLM chip.”\n7. Material Layer Stack: In Fig. 1b, the material layer stack is incomplete. The text mentions three metal layers, but these are not shown all in the figure.\nIndeed, the methods section mentions three metal layers. Fig. 1b only shows two metal layers. The third layer mentioned in the methods is a routing layer, used to connect the pixels to bond pads (see Fig. 1d and 1e). The bottom metal routing layer is connected to the top two metal layers through vias, as explained in the methods section: “There are three metal layers in the stack to enable device actuation. From bottom to top, these are: a routing layer which we use to connect each of the pixels to bond pads, a bottom electrode layer, and a top electrode layer. In between the two electrode layers there is the AlN layer; together these comprise the piezoelectric actuation layer. The bottom electrode layer is separated from the routing layer by a silicon dioxide buffer. The three metal layers are connected by vias.” Because the device principle can be understood without this third routing layer, we did not add it to the conceptual schematic in Fig. 1b. We agree with the reviewer that the layer stack including all metal layers should be made clearer in the manuscript. Therefore, we have adjusted Fig. 3a to show all three metal layers and the vias (figure copied below).\n8. Fig. 4b Legend: The legend of Fig. 4b states, “The inset shows the simulated mechanical mode at the resonance frequency frf_rfr of ∼5 MHz.” However, no inset is present in this panel.\nIndeed, the mention of the inset in Fig. 4b is an artifact of previous versions. That figure is now included in more detail in Fig. 3c. We have removed the mention of the inset in the caption.\n9. Requirements R1–R4: In the introduction and Table 1, the authors refer to a list of requirements (R1–R4) first introduced in the abstract. It would be preferable to list and label these requirements (R1–R4) in the introduction rather than in the abstract.\nWe thank the reviewer for their feedback. We have rewritten the introduction and the abstract. The requirements are now listed in the introduction instead of the abstract.\n10. Fig. 3d Vertical Axis: In Fig. 3d, the bottom panel (“Simulated f_r as a function of L for l=5 μm (bottom)”) would be better presented with a logarithmic scale on the vertical axis to more clearly show the reduction in resonance frequency.\nWe thank the reviewer for their suggestion. We have changed the bottom panel of Fig. 3d to have a logarithmic scale on the vertical axis. We copied the modified figure below.\n11. Fig. 2 Caption: In Fig. 2, the caption includes the statement, “The 1/e field full width is kept at 45% of the grating size.” This phrasing is unclear and should be explained more clearly.\nIn order to fairly compare the different grating sizes, we rescaled the size of the Gaussian beam in the simulation to the pixel size. Otherwise different proportions of the beam would interact with the grating. For example, if we would keep the beam size the same and decrease the pixel size, the reflection amplitude would drop massively (as a large part of the beam would not interact with the grating). To clarify this we have adjusted the caption accordingly: “For a fair comparison the Guassian input beam was rescaled such that the 1/e field full width is kept at 45% of the grating size. This way, equal proportions of the input beam interact with the grating structure at all pixel sizes.”\n12. Supplementary Information: In the supplementary information, the labels in Fig. 1 of the experimental setup (e.g., SLD, APD) should be better aligned with the descriptions provided in the text for clarity\nWe adjusted the labels in the figure to better align with the terminology in the text above."}, {"round": 2, "reviewer_comments": {"reviewer_1": "After reviewing the revised manuscript and response letter, I still think this work is not good enough and is not suitable for nature communications. My concerns is listed as follows:\n1.I do agree with the author’s clam about eye diagram. The eye diagram shows both the speed and extinction ratio, which is very important. In the first version, the author just show the Wavelength shift (dlambda/dV) under different frequency. However, the modulation efficiency is not shown. For a typical modulation work, i.e. the first graphene modulator paper published in nature 474, 64(2011), the modulation efficiency is shown, although the eye diagram is not shown.\n2.In the revised manuscript, the author adds the detail information about the resonance. It is about 8 nm peak to trough of resonance, 3 dB bandwidth of 2.3 nm in the modulation amplitude measurement. From this data, we can find that the FWFH is large. In the measurement, the shift efficiency is 4 × 10^2 pm/V at 5 MHz while it is only about 10 pm/V in higher frequency. This means that it needs 20 V for 5 MHz and about 1000 V for other high frequency. However, it is unreasonable. Note that, for typical high frequency amplifier, the voltage is < 7.5V.\n3.To solve above issue, the author also added discussion about high Q resonance in Ref[2] and ref[44]. But in ref[2], it is in a difference material platform and it have very small optical volume. In ref[44], this is a planar waveguide which is difference from vertical coupling in this work. I think with such material platform and relative large optical mode volume, it is hard to get a high Q. Based on [Nano letters 13,691 (2013)] from the same group, the Q of a vertical coupling silicon resonator is about 2000, which is still not large enough for this work.\n4.Based on above calculation, I guess the author can not get very good modulation diagram or clear waveforms in high frequency, since the modulation efficiency and extinction ratio is too low. Meanwhile, in Fig.4a, the author shows the modulation amplitude A, which is not a traditional way. In a typical modulator, we need the modulation depth or ER of the diagram. The modulation amplitude A is just filter out the DC part and thus only AC part is left. This can not show the performance of the device in high speed modulation.\nBased on the above discussion, I think this work can not get very clear modulation diagram or modulation depth with current data. Thus, I think it is not suitable for Nature communications.", "reviewer_2": "The authors have addressed all of my comments with detailed responses. The manuscript has been revised accordingly, with the addition of numerous technical details that enhance both the quality and readability of the paper.\nHowever, a few issues remain that should be addressed to make the paper suitable for publication.\nThe authors acknowledge that the voltages required for achieving high extinction ratio modulation are high. To address this issue, they propose the use of optically resonant structures with linewidths as narrow as a few tens of nanometers. While this approach could reduce the required driving voltage, it would also increase the device’s sensitivity to fabrication imperfections—particularly critical when the modulator must operate at precise wavelengths ( such as those corresponding to specific atomic or molecular transitions).\nFurthermore, it is unclear whether the enhancement of the resonant effect necessary to lower the driving voltage would also impact the modulator's already non-flat frequency response, as shown in Fig. 4b. This could complicate the signal equalization process in applications that require the device to operate across a broad frequency range.\nThe authors should include a discussion of the limitations associated with using high-Q resonant structures with extremely narrow linewidths."}, "author_response": "Literature reports on modulators, whether free-space-coupled or photonic-integrated-circuit-based modulators, typically show the static transmission or reflection spectrum and the frequency response of the device1-7. Frequency response measurements are typically shown in the form of normalized S measurements. The addition of eye diagrams is less common, as also remarked by the reviewer, and they are often only measured in the context of modulators specifically targeting optical communication links, which is not the target application of our technology.\nA measure of the modulation efficiency is frequently mentioned in modulator reports, as mentioned by the reviewer. Contrary to the reviewer’s statement and as we outline below, we do provide the modulation efficiency in our manuscript.\nIn our manuscript, we show the reflection spectrum (Fig. 4a) and the wavelength shift (△λ/△V) vs modulation frequency (Fig. 4b). The reflection spectrum shows the achievable extinction ratio. The wavelength shift is effectively a measure of the modulation efficiency of our devices. Our wavelength shift vs frequency measurement gives the reader more information compared to a conventional normalized S measurement, which only gives a measure of the speed of the device, not the modulation efficiency. Our measurement effectively gives the reader a measure of both the speed and modulation efficiency of the devices, combined in one plot. Additionally, we also estimate the voltage needed for a full shift of the resonance (to achieve >20 dB extinction as measured in the spectral response). This gives the reader another measure of the modulation efficiency, which combines the wavelength shift and reflection spectrum data in one figure of merit.\nThe section in the manuscript outlining the voltage needed for a full shift of the resonance is the following (see characterization section):\n“From the frequency response measurements (Fig. 4b) and the measured reflection spectrum (Fig. 4a), we can estimate the voltages required to shift the spectrum by 8 nm, that is, the wavelength difference between the trough and peak in the spectrum. We find a voltage of ∼ 20 V for a released device at the ∼ 5 MHz mechanical resonance and ∼ 1 × 103 V off-resonance (100 kHz driving frequency). For an unreleased device, we estimate a voltage of ∼ 40 × 103 V off-resonance (at 10 MHz). We recognize that the off-resonance and unreleased device voltages are high and suggest ways of lowering these significantly in the discussion.”\n2.In the revised manuscript, the author adds the detail information about the resonance. It is about 8 nm peak to trough of resonance, 3 dB bandwidth of 2.3 nm in the modulation amplitude measurement. From this data, we can find that the FWFH is large. In the measurement, the shift efficiency is 4 × 10^2 pm/V at 5 MHz while it is only about 10 pm/V in higher frequency. This means that it needs 20 V for 5 MHz and about 1000 V for other high frequency. However, it is unreasonable. Note that, for typical high frequency amplifier, the voltage is < 7.5V.\nWe acknowledge that the off-resonance and unreleased device voltages are high in the current implementation of our technology. We clearly state in the abstract that this is a proof-of-concept device. Moreover, in the discussion section of our manuscript we provide solutions to lower these voltages by three to four orders of magnitude, which brings them in the volt-level realm:\n“One of the main challenges ahead is to reduce the voltages required to achieve high-extinction-ratio modulation. We see several ways to achieve this. Firstly, we can use a piezoelectric material with an enhanced response. Scandium aluminum nitride, for instance, has a piezoelectric response up to 5 times larger compared to AlN [43]. Secondly, we can use optical resonators with reduced optical linewidths. Recently, a silicon-nitride-based resonant waveguide grating with a linewidth of only ∼ 0.7 pm at 779 nm has been demonstrated [44]. Vertically coupled photonic crystal cavities with high quality factors are another promising candidate. These have been demonstrated in silicon with linewidths <10 pm at a wavelength of 1.6 μm [21]. Silicon nitride photonic crystal cavities with linewidths down to 0.1 nm at 760 nm have been reported [45], though these were not vertically coupled. By combining narrow-linewidth optical resonators with piezoelectric materials with an enhanced response, we can potentially reduce the drive voltages by three to four orders of magnitude.”\nIn addition, we note that several solutions already exist today to deliver high voltages at high frequencies. LDMOS (laterally-diffused metal-oxide-semiconductor) devices typically operate between 24 V and 50 V and can deliver up to 50 dBm of output power at 2 GHz8. MHz-level operation of kilovolt SiC MOSFETs (metal-oxide-semiconductor field-effect transistors) has also been reported in literature9. Moreover, GaN-based electronics can operate at ~100 V in the GHz frequency range10.\n3.To solve above issue, the author also added discussion about high Q resonance in Ref[2] and ref[44]. But in ref[2], it is in a difference material platform and it have very small optical volume. In ref[44], this is a planar waveguide which is difference from vertical coupling in this work. I think with such material platform and relative large optical mode volume, it is hard to get a high Q. Based on [Nano letters 13,691 (2013)] from the same group, the Q of a vertical coupling silicon resonator is about 2000, which is still not large enough for this work.\nRef. [2] the reviewer is referring to is [Panuski, C. L. et al. A full degree-of-freedom spatiotemporal light modulator. Nat. Photonics 16, 834–842 (2022)]. This is a paper out of our research group demonstrating vertically coupled silicon photonic crystal cavities with linewidths <10 pm (Q>1e5) at a wavelength of 1.6 μm. The reviewer is correct that it is a different material platform and a longer wavelength of operation compared to our manuscript. However, it demonstrates that we can design and fabricate vertically coupled photonic crystal cavities with extremely high Q-factors, a non-trivial feat. It is a massive improvement compared to earlier work out of our group [Nano letters 13,691 (2013)] where the Q-factor was limited to ~3000, as correctly observed by the reviewer. This is thanks to major improvements in both design and fabrication.\nRef. [44] the reviewer is referring to is [Fryett, T. K. et al. Encapsulated silicon nitride nanobeam cavity for hybrid nanophotonics. ACS Photonics 5, 2176 (2018)]. In this paper, the authors demonstrate a simulated Q-factor as large as 1e5 and a measured Q-factor of 7e3 for a silicon nitride photonic crystal cavity at a wavelength of ~0.8 μm. The discrepancy between simulation and fabrication is attributed to fabrication imperfections. The reviewer is correct that this paper does not demonstrate a vertically coupled photonic crystal cavity, as also mentioned in our manuscript (vertical coupling would require design modifications). But, it does demonstrate that very high Q-factors can be achieved in silicon nitride photonic crystal cavities, even when they are cladded with a material with an index of ~1.5.\nLet’s look at the Q-factors we would need to lower the driving voltage of our devices by several orders of magnitude. For our released devices, we’ve measured a wavelength shift of ~7 pm/V off-resonance (at 100 kHz driving frequency). To get high-extinction-ratio modulation, we want to shift the optical resonance by its full width. That means that for a 1 V driving voltage, we want an optical resonance of at most ~7 pm wide (Q~1e5). A 10 V driving voltage would correspond to a ~70 pm wide optical resonance (Q~1e4). Given the above-mentioned demonstrations of silicon nitride and silicon photonic crystal cavities, Q-factors in the 1e4-1e5 range appear within reach.\nMoreover, a silicon-nitride-based resonant waveguide grating (vertically coupled) with an optical Q-factor of 1.1e6 at 779 nm has recently been demonstrated11. This work demonstrates that extremely high Q-factors can indeed be achieved in silicon-nitride-based resonant waveguide gratings. This is another indication that the Q-factors required to get to 1-10 V driving voltages can be realized in vertically coupled silicon-nitride-based devices.\nWe have added the above-mentioned reference, which shows that vertically coupled silicon-nitride-based resonators can have extremely high Q-factors, to the discussion section:\n“Secondly, we can use optical resonators with reduced optical linewidths. Recently, a silicon-nitride-based resonant waveguide grating with a linewidth of only ∼ 0.7 pm at 779 nm has been demonstrated [44]. Vertically coupled photonic crystal cavities with high quality factors are another promising candidate. These have been demonstrated in silicon with linewidths < 10 pm at a wavelength of 1.6 μm [21]. Silicon nitride photonic crystal cavities with linewidths down to 0.1 nm at 760 nm have been reported [45], though these were not vertically coupled. By combining narrow-linewidth optical resonators with piezoelectric materials with an enhanced response, we can potentially reduce the drive voltages by three to four orders of magnitude.”\n4.Based on above calculation, I guess the author can not get very good modulation diagram or clear waveforms in high frequency, since the modulation efficiency and extinction ratio is too low. Meanwhile, in Fig.4a, the author shows the modulation amplitude A, which is not a traditional way. In a typical modulator, we need the modulation depth or ER of the diagram. The modulation amplitude A is just filter out the DC part and thus only AC part is left. This can not show the performance of the device in high speed modulation.\nBased on the above discussion, I think this work can not get very clear modulation diagram or modulation depth with current data. Thus, I think it is not suitable for Nature communications.\nThe modulation amplitude A in Fig. 4a is the result of a small-signal modulation measurement and is not meant to demonstrate the modulation depth or extinction ratio of our devices. The modulation amplitude versus wavelength measurement demonstrates that our devices behave as expected, namely that the amplitude peaks on the slope of the reflection spectrum R (since A ~ (dR/dλ)*Δλ), as shown in the manuscript.\nContrary to the reviewer’s statement, the manuscript does show a clear waveform at high frequency, namely in Fig. 4d. Fig. 4d shows a ringdown measurement; that is an exponentially decaying sine wave after applying a ~5 MHz signal to the device.\nGiven that we are not targeting optical communication as an application, we did not procure the high-voltage, high-frequency sources required to measure an eye diagram.\nWe refer to our answers above as to how we plan on reducing the driving voltages and which solutions exist today to generate high voltages at high frequencies.\nWe’d like to emphasize again that many applications do not require arbitrary waveform generation as characterized in eye diagrams.\nFor instance, one can drive the modulators at mechanical resonance to generate strong sidebands to the incident laser beam (driving at resonance reduces the voltage requirements massively). The generation of these sidebands can be switched on and off (individually controlled for every pixel) with response times on the order of microseconds, with the exact response time depending on the mechanical quality factor. This has applications in the optical control of atomic systems, where one wishes to address certain atomic transitions in large-scale arrays of atoms, ions, or solid-state color centers14.\nAnother way of using this SLM technology is to drive different pixels at different resonance frequencies. The beams reflected by the SLM overlap in the far field. By driving each pixel at a certain frequency and phase, we can generate predictable time-varying and even periodically repeating patterns in the far field, i.e. our SLM acts as a high-speed laser scanner. This principle has been described conceptually in literature for photonic integrated circuit phased arrays15. For instance, by driving the nth channel at frequency ω + n∆ω 0 (corresponding to a resonance frequency to enable low-voltage driving), one can generate a pattern repeating itself every T = 2π/∆ω. Our SLM technology enables MHz speeds, compared to conventional MEMS scanners being limited to sub-MHz speeds16. High-speed laser scanners have applications in atom control17, display technology16, and laser ranging18.\nThe above mentioned examples and applications are summarized in the discussion section of the manuscript:\n“We see many potential applications for this SLM technology. Depending on the target application, we can configure our modulator technology in different ways. For instance, driving the modulators at a strong mechanical resonance generates strong sidebands to the incident laser light (the sidebands could be resonant with an atomic transition). The generation of these sidebands can be switched on and off (individually controlled for every pixel) with response times on the order of microseconds, with the exact response time depending on the mechanical quality factor. This has applications in the optical control of atomic systems, where one wishes to address certain atomic transitions in large-scale arrays of atoms, ions, or solid-state color centers [13]. We can use different mechanical resonances to generate sidebands at different frequencies or engineer the pixels to alter the mechanical resonances, e.g. by varying the grating size or the depth of the undercut. Laser trimming [21, 41] or focused ion beam milling [42] can alter the resonance frequencies post-fabrication. Predictable time-varying and even periodically repeating light patterns can be generated in the far field [38] by driving each of the pixels at a particular mechanical resonance frequency, enabling low-voltage driving, with a particular phase. The generated pattern will depend on the chosen frequencies and phases. This concept has been described for photonic integrated circuit phased arrays [38] and has applications in atom control [48], display technology [49], and laser ranging [50]. The proposed SLM technology enables MHz speeds, compared to conventional MEMS laser scanners limited to sub-MHz speeds [49].”\nReviewer #2 (Remarks to the Author):\nThe reviewer is correct that an increase in optical Q-factor, or equivalently, a decrease in optical linewidth, makes the devices more sensitive to fabrication imperfections. This can lead to discrepancies between the desired operating wavelengths and the as-fabricated resonant wavelengths. The solution to this issue is post-fabrication tuning. Some of the most commonly used post-fabrication tuning mechanisms in integrated optics are on-chip heaters14,19 and laser trimming7,14. Both induce a change in effective index, leading to a resonance shift. On-chip heaters typically induce a non-permanent index change, meaning they need to be kept on continuously during device operation, leading to high power consumption. Laser trimming can induce a permanent change in index, thereby avoiding the need for power hungry on-chip heaters. Whereas laser trimming of mechanical resonators typically relies on ablating material to shift the mechanical resonance, laser trimming of optical resonators usually operates in a different regime, with the aim of altering the effective index14.\nWe do not expect an increase in optical Q-factor to complicate the signal equalization process. The non-flat frequency response is a consequence of the existence of mechanical resonances. Our intention is to increase the Q-factor of the optical resonances by altering the design of the resonator in the thin, top silicon nitride layer. This does not directly impact the mechanical resonances. However, a very high optical Q-factor could limit the modulation bandwidth due to the long associated photon lifetimes. This should be taken into consideration when designing the optical resonator. If we target a Q-factor in the range 1e4 to 1e5, as discussed above in our answer to comment 3 of reviewer #1, the photon-lifetime-limited bandwidths would be in the range of ~4 to 40 GHz. These bandwidths are still way larger than our target of 100 MHz (see requirement R3 in manuscript), therefore this is not a concern.\nTo address the limitations associated with high-Q optical resonances, we added the following sentences to the discussion section in the manuscript:\n“A significant reduction in linewidth will increase the need for post-fabrication optical resonance tuning, as the resonant wavelength is likely to deviate from the target operating wavelength. This is a common problem in integrated optics for which multiple solutions have been reported, e.g. laser trimming [13, 21] and on-chip heaters [13, 46].”"}, {"round": 3, "reviewer_comments": {"reviewer_1": "After reviewing this revised manuscript, I think it would be OK for Nature communications, since the author indicates that the application would be the sideband generation except the optical communications. I have the following concerns which the author still should be addressed:\n1.The applied voltage is very high. As the author said in the response letter, it is a proof of concept demonstration. The author should indicate “proof of concept demonstration” in the revised manuscript.\n2.Although the author discuss a lot of ways to enhance the quality factor, I think it is better to provide some schemes for obtaining high applied voltage. As he discusses in the response to Question 1, there are several schemes for obtaining high voltage at high frequency, such as GaN-based electronics. This should be included in the manuscript.", "reviewer_2": "Response letter manuscript NCOMMS-24-74249\nBelow, you can find our responses to the reviewers' comments, highlighted in blue for clarity.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nAfter reviewing this paper, I do not recommend the paper to be publish in nature\ncommunications with this version. My questions are listed as follows:\n1.The claim of this paper is not correct. In the title, the author claims that the device can\ncover visible to near-infrared wavelengths. However, in the measurement, it only works ~\n800 nm.\nOur devices operate around a wavelength of 780-800 nm. To our knowledge, there are no\nuniversally agreed boundaries to the visible spectrum. According to the International\nCommission on Illumination (CIE), the lower wavelength limit is generally taken between 360\nand 400 nm and the upper limit between 760 and 830 nm1. Therefore, we conclude that our\ndevices operate on the boundary between the visible and near-infrared wavelength range.\nMoreover, we can alter our design to shift the point of operation to shorter wavelengths (or\nlonger wavelengths). Reducing/increasing the pitch or our gratings will lead to a shift towards\nshorter/longer wavelengths, as shown in Fig. 2b in our manuscript. Our resonant waveguide\ngratings are made of silicon nitride with a silicon oxide cladding. These materials are\ntransparent in the visible and near-infrared wavelength range. Therefore we can freely alter\nthe design to shift the wavelength of operation within this transparency range. To illustrate\nthat we can shift the wavelength of operation all the way down to the short end of the visible\nspectrum, we included the simulated reflection spectrum in the supplementary information\nfor a grating pitch of 0.27 μm (figure copied below), showing a resonance at ~470 nm (see\nalso our reply to comment #1 of reviewer #2).\nTo emphasize that the exact wavelength of operation is a design choice, the introduction\nmentions “(R1) operation at a design wavelength of choice in the visible (VIS) to\nnear-infrared (NIR) spectrum”.\nTo avoid any confusion, we changed the title of our manuscript from “Piezoelectrically\nactuated high-speed spatial light modulator for visible to near-infrared wavelengths” to\n“Piezoelectrically actuated silicon-nitride-based high-speed spatial light modulator”.\n2.The modulation speed is not quite clear. It is better to show an eye-diagram to confirm the\nspeed of light. As we can find in the paper, the ER is high. Thus, I think it can perform a very\ngood eye-diagram.\nThe modulation speed of our devices is shown in the frequency response measurement in\nFig. 4b, which is a plot of the measured wavelength shift versus modulation frequency.\nFrequency response measurements are a standard method to measure modulation speed2.\nWe attribute the numerous peaks and troughs in our measurements to mechanical\nresonances. The frequency response measurements are limited by the photodetector\nbandwidths (DC-400 MHz for the released device and 5-1000 MHz for the unreleased device\nmeasurement) and the 900 MHz bandwidth of the voltage amplifiers on the printed circuit\nboards, as explained in the characterization section of the manuscript.\nEye diagrams are a typical and traditional way of measuring the behavior of communication\nlinks in datacom and telecom applications. We believe they add little value in this context. In\ngeneral, they characterize entire communication links and are very much an indication of the\nnoise figures of the detectors and amplifiers in the link and can show effects of dispersion\nand loss in the fibers in the link. They are traditionally also shown in modulator papers\ndiscussing specifically datacom or telecom high-speed modulators, but even there they add\nlittle quantitative value since they tell you very little about a single component in the entire\noptical link. At best, they show qualitatively that data transmission works in the link. In\ncontrast, our devices are free-space-coupled spatial light modulators aimed at applications\nsuch as atom control and displays. We do not think that an eye diagram measurement would\nadd meaningfully to the manuscript.\n3.The principle of the device is note quite clear. Why it has a resonance? The author should\nexplain about it.\nOur devices belong to a class of devices described in literature as resonant waveguide\ngratings, also known as guided mode resonant gratings or waveguide-mode resonant\ngratings. Our manuscript contains several references to provide more background to the\nreader on the operating principles of resonant waveguide gratings3–6.\nAkin to standard grating couplers used in photonic integrated circuits, light waves incident on\na resonant waveguide grating can couple to in-plane guided modes, provided the\nwavelength, polarization, and incidence angle are chosen correctly to match the grating\ndesign. Since the coupling to guided modes only occurs at certain wavelengths, we observe\nresonant behavior in the reflection and transmission spectra of these gratings. The resonant\nbehavior can be observed both in the amplitude and phase spectra.\nWe added the following sentence to the introduction to clarify the device principle:\n“Resonant waveguide gratings, also known as guided mode resonant gratings or\nwaveguide-mode resonant gratings, couple light incident at specific wavelengths, incidence\nangles, and polarization to leaky guided modes, giving rise to resonances in the reflection\nand transmission spectra (in amplitude and phase) [36].”\nOur device demonstration specifically relies on the resonant behavior in the phase spectra\nand simultaneous illumination with TE and TM polarized waves in a cross-polarized light\nsetup, as detailed in the design section of the manuscript:\n“The steep dip in the reflection spectrum results from the phase difference between TE and\nTM polarized reflected light shifting from 0 to π while the reflection amplitude of TE and TM\nfields remain similar (Fig. 2c), where TE polarized light corresponds to the electric field being\nparallel to the grating lines (Fig. 4e). When the TE and TM polarized light waves reflected off\nthe grating are in phase with equal amplitude, the reflected light is polarized at 0° before the\npolarizing beamsplitter and no light is reflected towards the detector. For a phase difference\nof π all light is reflected.”\nWe copied Fig. 2a, 2c, and 4e below for clarity.\n4.The figures are not well drawn, especially the experimental data.\nWe appreciate the reviewer’s feedback, but we are unsure which figures and which aspects\nof the figures the reviewer is referring to. The data has been plotted meticulously using\nconventional plotting methods (Matplotlib package in Python). We set up the plotting\nparameters to match the standard figure styles in scientific publications. To improve Fig. 4\nshowing the experimental measurement data, we added whitespace in between the\nsubfigures and changed the fontsize of the labels a to e. We are open to suggestions to\nimprove the style of our figures.\n5.The paper is not well written. For instance, I cannot find inset in Fig. 4b. Meanwhile, Fig.4c\nis not illustrated.\nIndeed, the mention of the inset in Fig. 4b was an artifact of previous versions. That figure is\nnow included in more detail in Fig. 3c. We removed the mention of the inset in the\nmanuscript.\nFig. 4c can be found in the upper right corner of page 5 of the manuscript. Fig. 4c shows the\nmeasured enhancement factor k versus the resonance frequency for the resonance near\n5 MHz, for each pixel in a 4x4 SLM. Only 13 data points are shown because 3 pixels weren’t\nfunctioning electrically. We made the caption clearer by changing it from “Measurement of\nthe mechanical resonance frequencies f of the strong resonance around 5 MHz and the\nr\nassociated enhancement factor k for each pixel. 13 of the 16 pixels were functioning in this\ndevice.” to “Measurement of the different mechanical resonance frequencies f for each pixel\nr\nof the strong resonance around 5 MHz and the associated enhancement factor k. 13 of the\n16 pixels were functioning in this device.” The figure is referenced at the end of the\ncharacterization section:\n“For the pixels in our 4×4 device, we determined the mechanical resonance frequencies f of\nr\nthe strong resonance around 5 MHz and the associated enhancement factor k (Fig. 4c).”\nWe also improved the wording of the final paragraph of the design section, explaining Fig. 3.\nWe believe this makes it easier for the reader to understand the device concept. The new\nversion of the paragraph reads:\n“The material platform with which we are working allows fabrication of undercut devices (see\nMethods), giving us an additional degree of freedom in engineering the mechanical device\nproperties. We can produce pixels of length L supported by a pillar of size l underneath\n(schematically shown in Fig. 3a, SEM image in Fig. 3b), where L and l can be chosen freely\nfor every pixel. The pillar also contains electrical vias between the piezoelectric actuator and\na bottom metal routing layer, connecting the pixels to bond pads (see Fig. 1d and 1e). Fig.\n3c shows the simulated mechanical mode with an eigenfrequency f of 5.9 MHz for a device\nr\nwith L = 49 μm and l = 10 μm. This closely matches the resonance observed experimentally,\nFig. 4b and 4c. By altering the pixel and pillar size L and l, we can set the mechanical\nresonance to a frequency of choice (Fig. 3d).”\nWe are open to other recommendations to improve the quality of our manuscript.\n6.The author says this work demonstrated 4 × 4 individually addressable 50 µm × 50 µm\npixels. However, in this paper, I can only find the results from one pixel.\nWhile Fig. 4a and 4b in the manuscript only show the results for one pixel in a 4x4 SLM, Fig.\n4c shows the results of characterizing all pixels in a 4x4 SLM. Fig. 4c is also discussed in\nour reply to comment #5 of reviewer #1. We hope our reply above clarifies what is shown in\nFig. 4c and where in the manuscript this figure is discussed.\n7.After all, I think Fig. 4b is not a good way to show the speed. For a modulator, we’d better\nuse eye diagram.\nFor our reply to this comment, we refer to comment #2 of reviewer #1, which addresses the\nsame topic.\nReviewer #2 (Remarks to the Author):\nThis manuscript presents a high-speed modulator technology targeting operation in the\nvisible (VIS) to near-infrared (NIR) spectrum, with scalability to high density, high speed\n(>100 MHz), and a high extinction ratio. The proposed technology is based on\npiezoelectrically actuated silicon nitride resonant waveguide gratings fabricated using a\nCMOS-compatible process. Proof-of-concept results are demonstrated with a 4 × 4 spatial\nmodulator operating at a wavelength of 780 nm, achieving modulation speeds >100 MHz\nand an extinction ratio >20 dB.\nThe technical content of this paper is of good quality and holds potential interest for a variety\nof applications, such as ranging, quantum information processing, atom control, display and\nimaging, and artificial intelligence, as mentioned by the authors in the motivation of the\npaper.\nHowever, there are significant issues that need to be addressed before the paper can be\nconsidered suitable for publication:\n1. Wavelength Range: The authors claim that the proposed technology enables operation at\nany wavelength in the VIS to NIR spectrum. This statement is not supported by experimental\nresults or simulations. The only wavelength range considered in this paper is around 790\nnm. What design or fabrication considerations need to be addressed when changing the\nwavelength? What performance can be expected at other wavelengths?\nThe reviewer is correct that we only demonstrate devices operating around 790 nm. As\nstated in the introduction, the exact wavelength of operation is a design choice: “(R1)\noperation at a design wavelength of choice in the visible (VIS) to near-infrared (NIR)\nspectrum”.\nWe can alter our design to shift the point of operation to shorter wavelengths (or longer\nwavelengths). Reducing/increasing the pitch of our gratings will lead to a shift towards\nshorter/longer wavelengths, as illustrated in Fig. 2b in our manuscript for wavelengths in the\nrange ~780 nm - 820 nm. Our resonant waveguide gratings are made of silicon nitride with a\nsilicon oxide cladding. These materials are transparent in the visible and near-infrared\nwavelength range. Therefore we can freely alter the design to shift the wavelength of\noperation within this transparency range.\nTo illustrate that we can shift the wavelength of operation all the way down to the short end\nof the visible spectrum, we included the simulated reflection spectrum in the supplementary\ninformation for a grating pitch of 0.27 μm (figure copied below), showing a resonance at\n~470 nm. We refer to this simulation result in the design section of the main text:\n“By reducing the grating pitch to 0.27 μm, we can shift the optical resonance all the way\ndown to ∼ 470 nm, the short wavelength end of the visible spectrum (see Supplementary Fig.\n3). Our technology can operate at a design wavelength of choice in the VIS to near-IR\nspectrum simply by altering the pitch of the grating (R1).”\nWhen reducing the grating pitch, it is important to keep fabrication limits in mind. Fabrication\nlimits depend on the foundry you are working with and the technology and toolset they have\navailable. 193 nm deep UV lithography is a widely available technology in commercial\nfoundries that allows patterning of sub-100 nm features7, enabling the pitches needed for\nblue wavelength gratings (the exact feature size depends not only on pitch but also the duty\ncycle of the grating, e.g. for a 100 nm minimum feature size and 0.27 μm pitch, you can\nfabricate duty cycles in between 37% and 63%; the simulation shown above is for a duty\ncycle of 63%). The discussion of fabrication limits is also included in the supplementary\ninformation:\n“Reducing the pitch of the gratings leads to a resonance shift toward shorter wavelengths.\nThe resonant waveguide gratings are made of silicon nitride with a silicon oxide cladding.\nThese materials are transparent in the visible and near-infrared wavelength range.\nTherefore, we can freely alter the design to shift the wavelength of operation within this\ntransparency range. As an example, Fig. 3 shows the simulated reflection spectrum for a\ngrating pitch of 0.27 μm, with a resonance at ∼ 470 nm. When reducing the grating pitch, it is\nimportant to keep fabrication limits in mind. Fabrication limits depend on the foundry you are\nworking with and the technology and toolset they have available. 193 nm deep UV\nlithography is a widely available technology in commercial foundries that allows patterning of\nsub-100 nm features [1], enabling the pitches needed for blue wavelength gratings. The\nexact feature size depends not only on pitch but also the duty cycle of the grating, e.g. for a\n100 nm minimum feature size and 0.27 μm pitch, you can fabricate duty cycles in between\n37 % and 63 % (the simulation shown below is for a duty cycle of 63 %).”\nSub-100 nm features can also easily be achieved with electron-beam lithography, but this\ntechnology is less amenable to high-volume production.\n2. Optical Bandwidth: The authors state that “The peak of the modulation amplitude occurs\nwhere the slope in the reflection spectrum is steepest (∼791 nm).” What is the optical\nbandwidth of the device? Could this pose a limitation for practical use in the applications\nmentioned?\nAs illustrated in Fig. 4a in the manuscript, the optical resonance is several nanometers wide\n(8 nm from peak to trough of resonance; 3 dB bandwidth of 2.3 nm in the modulation\namplitude measurement), corresponding to photon-lifetime-limited modulation bandwidths on\nthe order of 1 THz(!) (δν = c δλ/λ2). Therefore the optical bandwidths of our devices do not\npose a limitation in terms of modulation speed for the envisaged applications.\nMoreover, the applications we envisage typically require modulators with narrowband\noperation at a discrete set of wavelengths (e.g. a set wavelengths corresponding to certain\natomic or molecular transitions). Our modulator technology is very well suited to\naccommodate this requirement. Either one can use separate modulator chips designed to\noperate at different wavelengths, or pixels designed to operate at different wavelengths can\nbe integrated on the same chip (in separate chip areas or interleaved).\nWe added this discussion to the manuscript:\n“The devices have an optical bandwidth of several nanometers (8 nm peak to trough of\nresonance, 3 dB bandwidth of 2.3 nm in the modulation amplitude measurement). This\ncorresponds to photon-lifetime-limited modulation bandwidths on the order of 1 THz, which\ndoes not pose a limitation for the envisaged applications. Moreover, the target applications\ntypically only require modulators with narrowband operation at a discrete set of wavelengths\n(e.g. a set wavelengths corresponding to certain atomic transitions). Our modulator\ntechnology is very well suited to accommodate this requirement. Either one can use\nseparate modulator chips designed to operate at different wavelengths, or pixels designed to\noperate at different wavelengths can be integrated on the same chip (in separate chip areas\nor interleaved).”\n3. Performance Metrics: The performance of the device is not clearly reported. What voltage\nis required to achieve a π phase shift between TE and TM polarization? How is the\nmodulation amplitude A, shown in Fig. 4a, related to the extinction ratio measured at the\nphotodetector?\nThe voltage required to go from 0 to π phase difference between TE and TM polarization\ncorresponds to the voltage required to shift the resonance by 8 nm, i.e. the wavelength\ndifference between the trough and peak of the resonance (see Fig. 4a in the manuscript).\nIn Fig. 4b, we show the wavelength shift per volt (Δλ/ΔV) for a released and unreleased\ndevice as a function of modulation frequency. For a released device, we get a wavelength\nshift of 4x102 pm/V at a resonant driving frequency of ~5 MHz. Off resonance, at 100 kHz,\nwe get a wavelength shift of ~7 pm/V for a released device. For an unreleased device, we\nget wavelength shifts of ~0.2 pm/V at 10 MHz (off resonance). This corresponds to voltages\nof 20 V, 1x103 V, and 40x103 V, respectively, to achieve the 0 to π phase difference change\nbetween TE and TM polarization, i.e. the voltage required to realize the extinction ratio of\n>20 dB measured in the reflection spectrum. We have added this information to the\ncharacterization section in the manuscript:\n“From the frequency response measurements (Fig. 4b) and the measured reflection\nspectrum (Fig. 4a), we can estimate the voltages required to shift the spectrum by 8 nm, that\nis, the wavelength difference between the trough and peak in the spectrum. We find a\nvoltage of ∼ 20 V for a released device at the ∼ 5 MHz mechanical resonance and ∼ 1 × 103\nV off-resonance (100 kHz driving frequency). For an unreleased device, we estimate a\nvoltage of ∼ 40 × 103 V off-resonance (at 10 MHz). We recognize that the off-resonance and\nunreleased device voltages are high and suggest ways of lowering these significantly in the\ndiscussion.”\nWe recognize the voltages required for high-extinction-ratio modulation are high and suggest\nseveral ways to improve this in the discussion section of the manuscript:\n“One of the main challenges ahead is to reduce the voltages required to achieve\nhigh-extinction-ratio modulation. We see several ways to achieve this. Firstly, we can use a\npiezoelectric material with an enhanced response. Scandium aluminum nitride, for instance,\nhas a piezoelectric response up to 5 times larger compared to AlN [43]. Secondly, instead of\nresonant waveguide gratings, we can use other compact, optically resonant structures with\nnarrower optical linewidths. Vertically coupled photonic crystal cavities with high quality\nfactors and small mode volumes are a promising candidate. These have been demonstrated\nin silicon with linewidths <10 pm at a wavelength of 1.6 μm [21]. Silicon nitride photonic\ncrystal cavities with linewidths down to 0.1 nm at 760 nm have been reported [44],\nthough these were not vertically coupled. By combining narrow-linewidth photonic crystal\ncavities with piezoelectric materials with an enhanced response, we can potentially reduce the drive\nvoltages by three to four orders of magnitude.”\nThe modulation amplitude A in Fig. 4a is the result of a small-signal modulation\nmeasurement and is not meant to demonstrate the extinction ratio of our devices. The\nmodulation amplitude versus wavelength measurement demonstrates that our devices\nbehave as expected, namely that the amplitude peaks on the slope of the reflection\nspectrum R (since A ~ (dR/dλ)*Δλ), as demonstrated in the manuscript.\n4. Non-flat Frequency Response: The non-flat frequency response, with a strong peak due\nto the mechanical mode at 5 MHz, requires specific equalization of the driving signal. As\nmentioned in the discussion, variability in the response across different pixels (Fig. 4c) could\nmake controlling spatial modulators with a large number of pixels extremely challenging. The\nauthors should provide a more detailed analysis of this issue.\nThe reviewer is correct that for the generation of arbitrary waveforms, signal equalization is\nrequired. While we do not demonstrate this in our manuscript, we would like to point out that\nsignal equalization has already been demonstrated for integrated modulators with\nmechanical resonances in the MHz to GHz range8. We acknowledge the need for signal\nequalization in the case of arbitrary waveform generation in the discussion section of our\nmanuscript and point the reader to a reference demonstrating signal equalization for a\nmodulator with mechanical resonances:\n“Our modulator technology could even generate arbitrary waveforms requiring the full device\nbandwidth (i.e. not only driving at resonance frequencies) by using signal equalization\ntechniques to compensate for the non-flat frequency response. Signal equalization has been\ndemonstrated for photonic integrated circuit modulators with mechanical resonances in the\nMHz to GHz range [39].”\nAs the reviewer points out, there are indeed variations in the frequency response from pixel\nto pixel (see Fig. 4c in the manuscript). We can set up automated measurements of every\npixel (see comment #6 of reviewer #2 for more details), to characterize the frequency\nresponse before using the spatial light modulator in an application. In addition, we can also\ntune up the resonances of all pixels using post-fabrication trimming techniques (e.g. laser\ntrimming, a standard technique used in the semiconductor industry), as detailed in our\nresponse to comment #6 of reviewer #2 and added to the revised manuscript.\nFinally, we’d like to mention that not every application requires arbitrary waveform generation\n(and therefore equalization). For instance, one can drive the modulators at resonance to\ngenerate strong sidebands to the incident laser beam. The generation of these sidebands\ncan be switched on and off (individually controlled for every pixel) with response times on the\norder of microseconds, with the exact response time depending on the mechanical quality\nfactor. This has applications in the optical control of atomic systems, where one wishes to\naddress certain atomic transitions in large-scale arrays of atoms, ions, or solid-state color\ncenters9.\nAnother way of using this SLM technology is to drive different pixels at different resonance\nfrequencies. The beams reflected by the SLM overlap in the far field. By driving each pixel at\na certain frequency and phase, we can generate predictable time-varying and even\nperiodically repeating patterns in the far field, i.e. our SLM acts as a high-speed laser\nscanner. This principle has been described conceptually in literature for photonic integrated\ncircuit phased arrays10. For instance, by driving the nth channel at frequency ω + n∆ω\n0\n(preferably corresponding to a resonance frequency to enable low-voltage driving), one can\ngenerate a pattern repeating itself every T = 2π/∆ω. Our SLM technology enables MHz\nspeeds, compared to conventional MEMS scanners being limited to sub-MHz speeds11.\nHigh-speed laser scanners have applications in atom control12, display technology11, and\nlaser ranging13.\nThe above mentioned examples and applications are summarized in the discussion section\nof the manuscript:\n“We see many potential applications for this SLM technology. Depending on the target\napplication, we can configure our modulator technology in different ways. For instance,\ndriving the modulators at a strong mechanical resonance generates strong sidebands to the\nincident laser light (the sidebands could be resonant with an atomic transition). The\ngeneration of these sidebands can be switched on and off (individually controlled for every\npixel) with response times on the order of microseconds, with the exact response time\ndepending on the mechanical quality factor. This has applications in the optical control of\natomic systems, where one wishes to address certain atomic transitions in large-scale arrays\nof atoms, ions, or solid-state color centers [13]. We can use different mechanical resonances\nto generate sidebands at different frequencies or engineer the pixels to alter the mechanical\nresonances, e.g. by varying the grating size or the depth of the undercut. Laser trimming [21,\n41] or focused ion beam milling [42] can alter the resonance frequencies post-fabrication.\nPredictable time-varying and even periodically repeating light patterns can be generated in\nthe far field [38] by driving each of the pixels at a particular mechanical resonance frequency,\nenabling low-voltage driving, with a particular phase. The generated pattern will depend on\nthe chosen frequencies and phases. This concept has been described for photonic\nintegrated circuit phased arrays [38] and has applications in atom control [46],\ndisplay technology [47], and laser ranging [48]. The proposed SLM technology enables MHz\nspeeds, compared to conventional MEMS laser scanners limited to sub-MHz speeds [47].”\n5. Resonant Frequency Spread: In Fig. 4c, the resonant frequencies of different pixels are\nshown. Were these measured at the same optical wavelength? What causes the observed\nspread in the enhancement factor?\nYes, these were all measured at 791 nm, we have added this information to the caption.\nWe suspect that the spread in enhancement factor and resonance frequency are caused by\nfabrication-induced variations from pixel to pixel, such as variations in the size of the pixel,\nlayer thicknesses, and depth of the undercut. As shown in Fig. 3d (and copied below), the\nresonance frequency shifts rather quickly as a function of the pixel size L and the supporting\npillar width l (and therefore the undercut distance). We expect variations in resonance\nfrequency to be correlated with variations in enhancement factor, but the exact relationship is\ncomplex (e.g. a wider pillar increases the resonance frequency; the wider pillar leads to\nmore clamping loss so a lower enhancement/quality factor, but a wider pillar also increases\nthe stiffness which is associated with an increase in enhancement/quality factor).\nThe following sentence in the characterization section of the manuscript clarifies this to the\nreader:\n“”Pixel-to-pixel fabrication-induced variations lead to differences in resonance frequencies\nand enhancement factor, e.g. variations in pixel size, layer thicknesses, and depth of the\nundercut.”\n6. Post-Fabrication Trimming: Post-fabrication trimming is proposed as a solution to fine-tune\nthe resonances of different pixels. However, such trimming would require functionality\nmonitoring for each pixel in a closed-loop manner. Is this a viable strategy for large arrays of\npixels? More generally, what are the main limitations to scaling the proposed device to larger\narrays? This should be elaborated on in the discussion section.\nWe believe post-fabrication trimming of large arrays is a viable strategy. Laser trimming is\nwidely used in the semiconductor industry to e.g. tune resistors by selectively removing\nmaterial. Large-scale laser trimming systems with sub-micrometer alignment accuracy are\ncommercially available14. Moreover, closed-loop trimming can easily be achieved by\ncombining the trimming laser, probe laser (to be modulated by the device), and imaging\noptics in a single optical system, as we have demonstrated before in our research group for\nphotonics crystal cavity15 and ring resonator trimming9. To trim one of our pixels, one would\nrepeatedly measure the mechanical resonances (using a probe laser, detector, electrical\nsignal generator and analyzer) while trimming material from the edges of the pixel. The\nedges of the pixel can be detected using image recognition techniques16. Fig. 3d in the\nmanuscript shows how small changes in pixel size lead to large resonance shifts, e.g. a\nchange in pixel size from 40 μm to 35 μm shifts the resonance frequency from 8 MHz to 11\nMHz. So removing small amounts of material would be sufficient to tune up the resonances\n(for our 4x4 SLM we observed a standard deviation of 0.9 MHz for an average resonance\nfrequency of 5.7 MHz, see manuscript). Potentially, one could parallelize laser trimming of\nmultiple pixels, e.g. by using a liquid crystal SLM to generate arrays of laser spots (instead of\na single laser spot) combined with photodiode arrays for probe laser detection. Similar to\nlaser trimming, one could use focused ion beam (FIB) milling to trim away material, as has\nbeen demonstrated e.g. for MEMS gyroscopes17. The probe laser and associated optical\nsystem could reside outside of the FIB chamber and optical signals could enter the chamber\nthrough windows.\nWe added the following discussion to the manuscript to clarify a potential approach for\ntrimming:\n“Established post-fabrication trimming techniques such as laser trimming [41] and focused\nion beam (FIB) milling [42] can be used to tune up the resonances. A possible approach for\nclosed-loop laser trimming consists of combining the trimming laser, probe laser (to be\nmodulated by the device), and imaging optics in a single optical system, as has been\ndemonstrated for photonic crystal cavities [21] and ring resonators [13]. Image recognition\nmethods can locate the pixel edges to be trimmed [41]. We can parallelize laser trimming of\nmultiple pixels by e.g. using a liquid crystal SLM to generate arrays of laser spots and\nphotodetector arrays for probe laser detection.”\nIn our opinion, the main challenge in scaling the proposed device to larger arrays is to get all\nthe required electrical signals in to drive the pixels. In our prototype device, we used wire\nbonds to get the electrical signals from the printed circuit board into the chip. But, the\nnumber of bond pads is limited by the perimeter of the chip. Assuming we have a square\nchip with side S, the number of bond pads scales with S, while the number of pixels scales\nwith the area S2. Therefore the number of pixels we can put on a chip goes up quicker than\nthe number of electrical signals we can get in. So in order to get enough signals in, we’d\nhave to make very large chips on which only a small area is filled with pixels (which is\nexpensive and ultimately limited by the wafer size). For example, on a 1 cm by 1 cm chip,\nwith pixel size of 50 μm and a typical bond pad spacing of 100 μm, we can fit 40000 pixels\nbut only 400 bond pads around the edge of the chip. A possible solution to the electrical IO\nproblem is to make use of through-silicon vias, a well-known technology in the\nsemiconductor industry, to get the signals from the front to the back of the chip. The\nbackside of the chip can then be bonded to an interposer which takes care of the electrical\nfanout (using cheaper technology compared to the SLM chip). This interposer could also\nhold some of the electronic driving ICs.\nAn even more advanced solution would be to integrate (some of) the electronics to drive the\npixels on the SLM chip, as also suggested in the introduction of the manuscript. For\nexample, one could integrate a demultiplexer on chip to limit the number of electrical inputs\nrequired.\nWe added the following to the discussion section of the manuscript to address this\nchallenge:\n“Another challenge is to get all the required electrical driving signals onto the SLM chip as\nwe scale up the number of pixels. In our proof-of-concept device we use wire bonds. The\nnumber of wire bonds is limited by the available chip perimeter. For example, on a 1 cm by 1\ncm chip, for a pixel size of 50 μm and a typical bond pad spacing of 100 μm, we can fit\n40 000 pixels, but only 400 bond pads around the chip perimeter. One approach to increase\nthe number of electrical inputs is to make use of through-silicon vias [45] and bond the SLM\nchip to an interposer. This interposer could also hold electronic driving ICs. An even more\nadvanced solution is to integrate some of the electronics on the SLM chip.”\n7. Material Layer Stack: In Fig. 1b, the material layer stack is incomplete. The text mentions\nthree metal layers, but these are not shown all in the figure.\nIndeed, the methods section mentions three metal layers. Fig. 1b only shows two metal\nlayers. The third layer mentioned in the methods is a routing layer, used to connect the\npixels to bond pads (see Fig. 1d and 1e). The bottom metal routing layer is connected to the\ntop two metal layers through vias, as explained in the methods section: “There are three\nmetal layers in the stack to enable device actuation. From bottom to top, these are: a routing\nlayer which we use to connect each of the pixels to bond pads, a bottom electrode layer, and\na top electrode layer. In between the two electrode layers there is the AlN layer; together\nthese comprise the piezoelectric actuation layer. The bottom electrode layer is separated\nfrom the routing layer by a silicon dioxide buffer. The three metal layers are connected by\nvias.” Because the device principle can be understood without this third routing layer, we did\nnot add it to the conceptual schematic in Fig. 1b. We agree with the reviewer that the layer\nstack including all metal layers should be made clearer in the manuscript. Therefore, we\nhave adjusted Fig. 3a to show all three metal layers and the vias (figure copied below).\n8. Fig. 4b Legend: The legend of Fig. 4b states, “The inset shows the simulated mechanical\nmode at the resonance frequency frf_rfr of ∼5 MHz.” However, no inset is present in this\npanel.\nIndeed, the mention of the inset in Fig. 4b is an artifact of previous versions. That figure is\nnow included in more detail in Fig. 3c. We have removed the mention of the inset in the\ncaption.\n9. Requirements R1–R4: In the introduction and Table 1, the authors refer to a list of\nrequirements (R1–R4) first introduced in the abstract. It would be preferable to list and label\nthese requirements (R1–R4) in the introduction rather than in the abstract.\nWe thank the reviewer for their feedback. We have rewritten the introduction and the\nabstract. The requirements are now listed in the introduction instead of the abstract.\n10. Fig. 3d Vertical Axis: In Fig. 3d, the bottom panel (“Simulated f_r as a function of L for\nl=5 μm (bottom)”) would be better presented with a logarithmic scale on the vertical axis to\nmore clearly show the reduction in resonance frequency.\nWe thank the reviewer for their suggestion. We have changed the bottom panel of Fig. 3d to\nhave a logarithmic scale on the vertical axis. We copied the modified figure below.\n11. Fig. 2 Caption: In Fig. 2, the caption includes the statement, “The 1/e field full width is\nkept at 45% of the grating size.” This phrasing is unclear and should be explained more\nclearly.\nIn order to fairly compare the different grating sizes, we rescaled the size of the Gaussian\nbeam in the simulation to the pixel size. Otherwise different proportions of the beam would\ninteract with the grating. For example, if we would keep the beam size the same and\ndecrease the pixel size, the reflection amplitude would drop massively (as a large part of the\nbeam would not interact with the grating). To clarify this we have adjusted the caption\naccordingly: “For a fair comparison the Guassian input beam was rescaled such that the 1/e\nfield full width is kept at 45% of the grating size. This way, equal proportions of the input\nbeam interact with the grating structure at all pixel sizes.”\n12. Supplementary Information: In the supplementary information, the labels in Fig. 1 of the\nexperimental setup (e.g., SLD, APD) should be better aligned with the descriptions provided\nin the text for clarity\nWe adjusted the labels in the figure to better align with the terminology in the text above.\nReferences\n1. Sliney, D. H. What is light? The visible spectrum and beyond. Eye 30, 222–229 (2016).\n2. Xue, S. et al. Full-spectrum visible electro-optic modulator. Optica 10, 125 (2023).\n3. Benea-Chelmus, I.-C. et al. Gigahertz free-space electro-optic modulators based on Mie\nresonances. Nat Commun 13, 3170 (2022).\n4. Benea-Chelmus, I.-C. et al. Electro-optic spatial light modulator from an engineered\norganic layer. Nat Commun 12, 5928 (2021).\n5. Shuai, Y.-C. et al. Coupled bilayer photonic crystal slab electro-optic spatial light\nmodulators. IEEE Photonics J. 9, 1–11 (2017).\n6. Quaranta, G., Basset, G., Martin, O. J. F. & Gallinet, B. Recent advances in resonant\nwaveguide gratings. Laser Photon. Rev. 12, 1800017 (2018).\n7. Deep UV Photolithography. https://www.newport.com/n/deep-uv-photolithography.\n8. Xue, S. et al. Full-spectrum visible electro-optic modulator. Optica 10, 125 (2023).\n9. Menssen, A. J. et al. Scalable photonic integrated circuits for high-fidelity light control.\nOptica, OPTICA 10, 1366–1372 (2023).\n10. Dong, M. et al. Synchronous micromechanically resonant programmable photonic\ncircuits. Nat Commun 14, 7716 (2023).\n11. Holmstrom, S. T. S., Baran, U. & Urey, H. MEMS Laser Scanners: A Review. J.\nMicroelectromech. Syst. 23, 259–275 (2014).\n12. Dong, M. et al. Programmable photonic integrated meshes for modular generation of\noptical entanglement links. Npj Quantum Inf. 9, (2023).\n13. Zhang, X., Kwon, K., Henriksson, J., Luo, J. & Wu, M. C. A large-scale\nmicroelectromechanical-systems-based silicon photonics LiDAR. Nature 603, 253–258\n(2022).\n14. Laser Micro Trimming Equipment LMT-HR Series.\nhttps://www.toray-eng.com/products/semicon/sem_016.html.\n15. Panuski, C. L. et al. A full degree-of-freedom spatiotemporal light modulator. Nat.\nPhotonics 16, 834–842 (2022).\n16. Liu, Y., Zhao, Q., Zhang, D. & Cui, J. Automatic Pico laser trimming system for silicon\nMEMS resonant devices based on image recognition. IEEE Trans. Semicond. Manuf.\n36, 260–267 (2023).\n17. Mechanical trimming with focused ion beam for permanent tuning of MEMS dual-mass\ngyroscope. Sensors and Actuators A: Physical 313, 112189 (2020).\nResponse letter manuscript NCOMMS-24-74249A\nBelow, you can find our responses to the reviewers' comments, highlighted in blue for clarity.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nAfter reviewing the revised manuscript and response letter, I still think this work is not good\nenough and is not suitable for nature communications. My concerns is listed as follows:\n1.I do agree with the author’s clam about eye diagram. The eye diagram shows both the\nspeed and extinction ratio, which is very important. In the first version, the author just show\nthe Wavelength shift (dlambda/dV) under different frequency. However, the modulation\nefficiency is not shown. For a typical modulation work, i.e. the first graphene modulator\npublished in nature 474, 64(2011), the modulation efficiency is shown, although the\neye diagram is not shown.\nLiterature reports on modulators, whether free-space-coupled or\nphotonic-integrated-circuit-based modulators, typically show the static transmission or\nreflection spectrum and the frequency response of the device1-7. Frequency response\nmeasurements are typically shown in the form of normalized S measurements. The\n21\naddition of eye diagrams is less common, as also remarked by the reviewer, and they are\noften only measured in the context of modulators specifically targeting optical\ncommunication links, which is not the target application of our technology.\nA measure of the modulation efficiency is frequently mentioned in modulator reports, as\nmentioned by the reviewer. Contrary to the reviewer’s statement and as we outline below, we\ndo provide the modulation efficiency in our manuscript.\nIn our manuscript, we show the reflection spectrum (Fig. 4a) and the wavelength shift\n(△λ/△V) vs modulation frequency (Fig. 4b). The reflection spectrum shows the achievable\nr\nextinction ratio. The wavelength shift is effectively a measure of the modulation efficiency of\nour devices. Our wavelength shift vs frequency measurement gives the reader more\ninformation compared to a conventional normalized S measurement, which only gives a\n21\nmeasure of the speed of the device, not the modulation efficiency. Our measurement\neffectively gives the reader a measure of both the speed and modulation efficiency of the\ndevices, combined in one plot. Additionally, we also estimate the voltage needed for a full\nshift of the resonance (to achieve >20 dB extinction as measured in the spectral response).\nThis gives the reader another measure of the modulation efficiency, which combines the\nwavelength shift and reflection spectrum data in one figure of merit.\nThe section in the manuscript outlining the voltage needed for a full shift of the resonance is\nthe following (see characterization section):\n“From the frequency response measurements (Fig. 4b) and the measured reflection\nspectrum (Fig. 4a), we can estimate the voltages required to shift the spectrum by 8 nm, that\nis, the wavelength difference between the trough and peak in the spectrum. We find a\nvoltage of ∼ 20 V for a released device at the ∼ 5 MHz mechanical resonance and ∼ 1 × 103\nV off-resonance (100 kHz driving frequency). For an unreleased device, we estimate a\nvoltage of ∼ 40 × 103 V off-resonance (at 10 MHz). We recognize that the off-resonance and\nunreleased device voltages are high and suggest ways of lowering these significantly in the\ndiscussion.”\n2.In the revised manuscript, the author adds the detail information about the resonance. It is\nabout 8 nm peak to trough of resonance, 3 dB bandwidth of 2.3 nm in the modulation\namplitude measurement. From this data, we can find that the FWFH is large. In the\nmeasurement, the shift efficiency is 4 × 10^2 pm/V at 5 MHz while it is only about 10 pm/V in\nhigher frequency. This means that it needs 20 V for 5 MHz and about 1000 V for other high\nfrequency. However, it is unreasonable. Note that, for typical high frequency amplifier, the\nvoltage is < 7.5V.\nWe acknowledge that the off-resonance and unreleased device voltages are high in the\ncurrent implementation of our technology. We clearly state in the abstract that this is a\nproof-of-concept device. Moreover, in the discussion section of our manuscript we provide\nsolutions to lower these voltages by three to four orders of magnitude, which brings them in\nthe volt-level realm:\n“One of the main challenges ahead is to reduce the voltages required to achieve\nhigh-extinction-ratio modulation. We see several ways to achieve this. Firstly, we can use a\npiezoelectric material with an enhanced response. Scandium aluminum nitride, for instance,\nhas a piezoelectric response up to 5 times larger compared to AlN [43]. Secondly, we can\nuse optical resonators with reduced optical linewidths. Recently, a silicon-nitride-based\nresonant waveguide grating with a linewidth of only ∼ 0.7 pm at 779 nm has been\ndemonstrated [44]. Vertically coupled photonic crystal cavities with high quality factors are\nanother promising candidate. These have been demonstrated in silicon with linewidths <10\npm at a wavelength of 1.6 μm [21]. Silicon nitride photonic crystal cavities with linewidths\ndown to 0.1 nm at 760 nm have been reported [45], though these were not vertically\ncoupled. By combining narrow-linewidth optical resonators with piezoelectric materials with\nan enhanced response, we can potentially reduce the drive voltages by three to four orders\nof magnitude.”\nIn addition, we note that several solutions already exist today to deliver high voltages at high\nfrequencies. LDMOS (laterally-diffused metal-oxide-semiconductor) devices typically operate\nbetween 24 V and 50 V and can deliver up to 50 dBm of output power at 2 GHz8. MHz-level\noperation of kilovolt SiC MOSFETs (metal-oxide-semiconductor field-effect transistors) has\nalso been reported in literature9. Moreover, GaN-based electronics can operate at ~100 V in\nthe GHz frequency range10.\n3.To solve above issue, the author also added discussion about high Q resonance in Ref[2]\nand ref[44]. But in ref[2], it is in a difference material platform and it have very small optical\nvolume. In ref[44], this is a planar waveguide which is difference from vertical coupling in this\nwork. I think with such material platform and relative large optical mode volume, it is hard to\nget a high Q. Based on [Nano letters 13,691 (2013)] from the same group, the Q of a vertical\ncoupling silicon resonator is about 2000, which is still not large enough for this work.\nRef. [2] the reviewer is referring to is [Panuski, C. L. et al. A full degree-of-freedom\nspatiotemporal light modulator. Nat. Photonics 16, 834–842 (2022)]. This is a paper out of\nour research group demonstrating vertically coupled silicon photonic crystal cavities with\nlinewidths <10 pm (Q>1e5) at a wavelength of 1.6 μm. The reviewer is correct that it is a\ndifferent material platform and a longer wavelength of operation compared to our\nmanuscript. However, it demonstrates that we can design and fabricate vertically coupled\nphotonic crystal cavities with extremely high Q-factors, a non-trivial feat. It is a massive\nimprovement compared to earlier work out of our group [Nano letters 13,691 (2013)] where\nthe Q-factor was limited to ~3000, as correctly observed by the reviewer. This is thanks to\nmajor improvements in both design and fabrication.\nRef. [44] the reviewer is referring to is [Fryett, T. K. et al. Encapsulated silicon nitride\nnanobeam cavity for hybrid nanophotonics. ACS Photonics 5, 2176 (2018)]. In this paper,\nthe authors demonstrate a simulated Q-factor as large as 1e5 and a measured Q-factor of\n7e3 for a silicon nitride photonic crystal cavity at a wavelength of ~0.8 μm. The discrepancy\nbetween simulation and fabrication is attributed to fabrication imperfections. The reviewer is\ncorrect that this paper does not demonstrate a vertically coupled photonic crystal cavity, as\nalso mentioned in our manuscript (vertical coupling would require design modifications). But,\nit does demonstrate that very high Q-factors can be achieved in silicon nitride photonic\ncrystal cavities, even when they are cladded with a material with an index of ~1.5.\nLet’s look at the Q-factors we would need to lower the driving voltage of our devices by\nseveral orders of magnitude. For our released devices, we’ve measured a wavelength shift\nof ~7 pm/V off-resonance (at 100 kHz driving frequency). To get high-extinction-ratio\nmodulation, we want to shift the optical resonance by its full width. That means that for a 1 V\ndriving voltage, we want an optical resonance of at most ~7 pm wide (Q~1e5). A 10 V driving\nvoltage would correspond to a ~70 pm wide optical resonance (Q~1e4). Given the\nabove-mentioned demonstrations of silicon nitride and silicon photonic crystal cavities,\nQ-factors in the 1e4-1e5 range appear within reach.\nMoreover, a silicon-nitride-based resonant waveguide grating (vertically coupled) with an\noptical Q-factor of 1.1e6 at 779 nm has recently been demonstrated11. This work\ndemonstrates that extremely high Q-factors can indeed be achieved in silicon-nitride-based\nresonant waveguide gratings. This is another indication that the Q-factors required to get to\n1-10 V driving voltages can be realized in vertically coupled silicon-nitride-based devices.\nWe have added the above-mentioned reference, which shows that vertically coupled\nsilicon-nitride-based resonators can have extremely high Q-factors, to the discussion\nsection:\n“Secondly, we can use optical resonators with reduced optical linewidths. Recently, a\nsilicon-nitride-based resonant waveguide grating with a linewidth of only ∼ 0.7 pm at 779 nm\nhas been demonstrated [44]. Vertically coupled photonic crystal cavities with high quality\nfactors are another promising candidate. These have been demonstrated in silicon with\nlinewidths < 10 pm at a wavelength of 1.6 μm [21]. Silicon nitride photonic crystal cavities\nwith linewidths down to 0.1 nm at 760 nm have been reported [45], though these were not\nvertically coupled. By combining narrow-linewidth optical resonators with piezoelectric\nmaterials with an enhanced response, we can potentially reduce the drive voltages by three\nto four orders of magnitude.”\n4.Based on above calculation, I guess the author can not get very good modulation diagram\nor clear waveforms in high frequency, since the modulation efficiency and extinction ratio is\ntoo low. Meanwhile, in Fig.4a, the author shows the modulation amplitude A, which is not a\ntraditional way. In a typical modulator, we need the modulation depth or ER of the diagram.\nThe modulation amplitude A is just filter out the DC part and thus only AC part is left. This\ncan not show the performance of the device in high speed modulation.\nBased on the above discussion, I think this work can not get very clear modulation diagram\nor modulation depth with current data. Thus, I think it is not suitable for Nature\ncommunications.\nThe modulation amplitude A in Fig. 4a is the result of a small-signal modulation\nmeasurement and is not meant to demonstrate the modulation depth or extinction ratio of\nour devices. The modulation amplitude versus wavelength measurement demonstrates that\nour devices behave as expected, namely that the amplitude peaks on the slope of the\nreflection spectrum R (since A ~ (dR/dλ)*Δλ), as shown in the manuscript.\nContrary to the reviewer’s statement, the manuscript does show a clear waveform at high\nfrequency, namely in Fig. 4d. Fig. 4d shows a ringdown measurement; that is an\nexponentially decaying sine wave after applying a ~5 MHz signal to the device.\nGiven that we are not targeting optical communication as an application, we did not procure\nthe high-voltage, high-frequency sources required to measure an eye diagram.\nWe refer to our answers above as to how we plan on reducing the driving voltages and\nwhich solutions exist today to generate high voltages at high frequencies.\nWe’d like to emphasize again that many applications do not require arbitrary waveform\ngeneration as characterized in eye diagrams.\nFor instance, one can drive the modulators at mechanical resonance to generate strong\nsidebands to the incident laser beam (driving at resonance reduces the voltage requirements\nmassively). The generation of these sidebands can be switched on and off (individually\ncontrolled for every pixel) with response times on the order of microseconds, with the exact\nresponse time depending on the mechanical quality factor. This has applications in the\noptical control of atomic systems, where one wishes to address certain atomic transitions in\nlarge-scale arrays of atoms, ions, or solid-state color centers14.\nAnother way of using this SLM technology is to drive different pixels at different resonance\nfrequencies. The beams reflected by the SLM overlap in the far field. By driving each pixel at\na certain frequency and phase, we can generate predictable time-varying and even\nperiodically repeating patterns in the far field, i.e. our SLM acts as a high-speed laser\nscanner. This principle has been described conceptually in literature for photonic integrated\ncircuit phased arrays15. For instance, by driving the nth channel at frequency ω + n∆ω\n0\n(corresponding to a resonance frequency to enable low-voltage driving), one can generate a\npattern repeating itself every T = 2π/∆ω. Our SLM technology enables MHz\nspeeds, compared to conventional MEMS scanners being limited to sub-MHz speeds16.\nHigh-speed laser scanners have applications in atom control17, display technology16, and\nlaser ranging18.\nThe above mentioned examples and applications are summarized in the discussion section\nof the manuscript:\n“We see many potential applications for this SLM technology. Depending on the target\napplication, we can configure our modulator technology in different ways. For instance,\ndriving the modulators at a strong mechanical resonance generates strong sidebands to the\nincident laser light (the sidebands could be resonant with an atomic transition). The\ngeneration of these sidebands can be switched on and off (individually controlled for every\npixel) with response times on the order of microseconds, with the exact response time\ndepending on the mechanical quality factor. This has applications in the optical control of\natomic systems, where one wishes to address certain atomic transitions in large-scale arrays\nof atoms, ions, or solid-state color centers [13]. We can use different mechanical resonances\nto generate sidebands at different frequencies or engineer the pixels to alter the mechanical\nresonances, e.g. by varying the grating size or the depth of the undercut. Laser trimming [21,\n41] or focused ion beam milling [42] can alter the resonance frequencies post-fabrication.\nPredictable time-varying and even periodically repeating light patterns can be generated in\nthe far field [38] by driving each of the pixels at a particular mechanical resonance frequency,\nenabling low-voltage driving, with a particular phase. The generated pattern will depend on\nthe chosen frequencies and phases. This concept has been described for photonic\nintegrated circuit phased arrays [38] and has applications in atom control [48],\ndisplay technology [49], and laser ranging [50]. The proposed SLM technology enables MHz\nspeeds, compared to conventional MEMS laser scanners limited to sub-MHz speeds [49].”\nReviewer #2 (Remarks to the Author):\nThe authors have addressed all of my comments with detailed responses. The manuscript\nhas been revised accordingly, with the addition of numerous technical details that enhance\nboth the quality and readability of the paper.\nHowever, a few issues remain that should be addressed to make the paper suitable for\npublication.\nThe authors acknowledge that the voltages required for achieving high extinction ratio\nmodulation are high. To address this issue, they propose the use of optically resonant\nstructures with linewidths as narrow as a few tens of nanometers. While this approach could\nreduce the required driving voltage, it would also increase the device’s sensitivity to\nfabrication imperfections—particularly critical when the modulator must operate at precise\nwavelengths ( such as those corresponding to specific atomic or molecular transitions).\nFurthermore, it is unclear whether the enhancement of the resonant effect necessary to\nlower the driving voltage would also impact the modulator's already non-flat frequency\nresponse, as shown in Fig. 4b. This could complicate the signal equalization process in\napplications that require the device to operate across a broad frequency range.\nThe authors should include a discussion of the limitations associated with using high-Q\nresonant structures with extremely narrow linewidths.\nThe reviewer is correct that an increase in optical Q-factor, or equivalently, a decrease in\noptical linewidth, makes the devices more sensitive to fabrication imperfections. This can\nlead to discrepancies between the desired operating wavelengths and the as-fabricated\nresonant wavelengths. The solution to this issue is post-fabrication tuning. Some of the most\ncommonly used post-fabrication tuning mechanisms in integrated optics are on-chip\nheaters14,19 and laser trimming7,14. Both induce a change in effective index, leading to a\nresonance shift. On-chip heaters typically induce a non-permanent index change, meaning\nthey need to be kept on continuously during device operation, leading to high power\nconsumption. Laser trimming can induce a permanent change in index, thereby avoiding the\nneed for power hungry on-chip heaters. Whereas laser trimming of mechanical resonators\ntypically relies on ablating material to shift the mechanical resonance, laser trimming of\noptical resonators usually operates in a different regime, with the aim of altering the effective\nindex14.\nWe do not expect an increase in optical Q-factor to complicate the signal equalization\nprocess. The non-flat frequency response is a consequence of the existence of mechanical\nresonances. Our intention is to increase the Q-factor of the optical resonances by altering\nthe design of the resonator in the thin, top silicon nitride layer. This does not directly impact\nthe mechanical resonances. However, a very high optical Q-factor could limit the modulation\nbandwidth due to the long associated photon lifetimes. This should be taken into\nconsideration when designing the optical resonator. If we target a Q-factor in the range 1e4\nto 1e5, as discussed above in our answer to comment 3 of reviewer #1, the\nphoton-lifetime-limited bandwidths would be in the range of ~4 to 40 GHz. These bandwidths\nare still way larger than our target of 100 MHz (see requirement R3 in manuscript), therefore\nthis is not a concern.\nTo address the limitations associated with high-Q optical resonances, we added the following\nsentences to the discussion section in the manuscript:\n“A significant reduction in linewidth will increase the need for post-fabrication optical\nresonance tuning, as the resonant wavelength is likely to deviate from the target operating\nwavelength. This is a common problem in integrated optics for which multiple solutions have\nbeen reported, e.g. laser trimming [13, 21] and on-chip heaters [13, 46].”\nReferences\n1. Xue, S. et al. Full-spectrum visible electro-optic modulator. Optica 10, 125 (2023).\n2. Desiatov, B., Shams-Ansari, A., Zhang, M., Wang, C. & Lončar, M. Ultra-low-loss\nintegrated visible photonics using thin-film lithium niobate. Optica 6, 380 (2019).\n3. Benea-Chelmus, I.-C. et al. Gigahertz free-space electro-optic modulators based on\nMie resonances. Nat Commun 13, 3170 (2022).\n4. Benea-Chelmus, I.-C. et al. Electro-optic spatial light modulator from an engineered\norganic layer. Nat Commun 12, 5928 (2021).\n5. Liu, M. et al. A graphene-based broadband optical modulator. Nature 474, 64 (2011).\n6. Shuai, Y.-C. et al. Coupled bilayer photonic crystal slab electro-optic spatial light\nmodulators. IEEE Photonics J. 9, 1–11 (2017).\n7. Panuski, C. L. et al. A full degree-of-freedom spatiotemporal light modulator. Nat.\nPhotonics 16, 834–842 (2022).\n8. Johansson, T. & Fritzin, J. A review of Watt-level CMOS RF power amplifiers. IEEE\nTrans. Microw. Theory Tech. 62, 111 (2014).\n9. Jørgensen, A. B., Aunsborg, T. S., Bęczkowski, S., Uhrenfeldt, C., Munk-Nielsen, S.\nHigh-frequency resonant operation of an integrated medium-voltage SiC MOSFET\npower module. IET Power Electron. 13, 475 (2020).\n10. Krause, S., Brückner, P., Dammann, M. & Quay, R. High-power-density AlGaN/GaN\ntechnology for 100-V operation at L-band frequencies. 2019 IEEE International\nElectron Devices Meeting (IEDM), pp. 17.4.1-17.4.4 (2019).\n11. Fang, J. et al. Million-Q free space meta-optical resonator at near-visible\nwavelengths. Nat. Commun. 15, 10341 (2024).\n12. Block, I. D., Mathias, P. C., Jones, S. I., Vodkin, L. O., Cunningham, B. T. Optimizing\nthe spatial resolution of photonic crystal label-free imaging. Appl. Opt. 48, 6567\n(2009).\n13. Grepstad, J. O. et al. Finite-size limitations on quality factor of guided resonance\nmodes in 2D photonic crystals. Opt. Express 21, 23640 (2013).\n14. Menssen, A. J. et al. Scalable photonic integrated circuits for high-fidelity light\ncontrol. Optica 10, 1366–1372 (2023).\n15. Dong, M. et al. Synchronous micromechanically resonant programmable photonic\ncircuits. Nat Commun 14, 7716 (2023).\n16. Holmstrom, S. T. S., Baran, U. & Urey, H. MEMS Laser Scanners: A Review. J.\nMicroelectromech. Syst. 23, 259–275 (2014).\n17. Dong, M. et al. Programmable photonic integrated meshes for modular generation of\noptical entanglement links. Npj Quantum Inf. 9, 42 (2023).\n18. Zhang, X., Kwon, K., Henriksson, J., Luo, J. & Wu, M. C. A large-scale\nmicroelectromechanical-systems-based silicon photonics LiDAR. Nature 603,\n253–258 (2022).\n19. Van Campenhout, J., Green, W. M. J., Assefa, S. & Vlasov, Y. A., Integrated NiSi\nwaveguide heaters for CMOS-compatible silicon thermo-optic devices. Opt. Lett. 35,\n1013-1015 (2010).\nResponse letter manuscript NCOMMS-24-74249B\nBelow, you can find our responses to the reviewer’s comments, highlighted in blue for clarity.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nAfter reviewing this revised manuscript, I think it would be OK for Nature communications,\nsince the author indicates that the application would be the sideband generation except the\noptical communications. I have the following concerns which the author still should be\naddressed:\n1.The applied voltage is very high. As the author said in the response letter, it is a proof of\nconcept demonstration. The author should indicate “proof of concept demonstration” in the\nrevised manuscript.\nThe proof-of-concept nature of the work is emphasized in the abstract, the introduction, and\nthe discussion:\n“We present a proof-of-concept device with 4 × 4 individually addressable 50 μm × 50 μm\npixels or channels, …”\n…\n“While previous works on this platform focused on photonic integrated circuits [13, 33–35],\nhere we demonstrate densely packed free-space-coupled modulators arranged in a 4 × 4\ngrid with a high fill factor of ∼ 96 % as a proof of concept for scalable SLM technology (Fig.\n1).“\n…\n“In our proof-of-concept device we use wire bonds.”\nIn addition to the statements above, we have now also stressed this fact in the context of the\nhigh voltage discussion (see characterization section):\n“We recognize that the off-resonance and unreleased device voltages are high in this\nproof-of-concept demonstration and suggest ways of lowering these significantly in the\ndiscussion.”\n2.Although the author discuss a lot of ways to enhance the quality factor, I think it is better to\nprovide some schemes for obtaining high applied voltage. As he discusses in the response\nto Question 1, there are several schemes for obtaining high voltage at high frequency, such\nas GaN-based electronics. This should be included in the manuscript.\nWe thank the reviewer for their suggestion and have added the following sentence to the\nmanuscript (see characterization section) in line with our discussion in the previous response\nletter:\n“Also, we note that several technologies exist today to deliver voltages in the O(10 V) to\nO(kV) range at O(MHz) to O(GHz) frequencies, such as Si LDMOS (laterally-diffused\nmetal-oxide semiconductor) [40], SiC [41], and GaN-based devices [42].”"}, "author_response": "The proof-of-concept nature of the work is emphasized in the abstract, the introduction, and the discussion:\n“We present a proof-of-concept device with 4 × 4 individually addressable 50 μm × 50 μm pixels or channels, …”\n…\n“While previous works on this platform focused on photonic integrated circuits [13, 33–35], here we demonstrate densely packed free-space-coupled modulators arranged in a 4 × 4 grid with a high fill factor of ∼ 96 % as a proof of concept for scalable SLM technology (Fig. 1).“\n…\n“In our proof-of-concept device we use wire bonds.”\nIn addition to the statements above, we have now also stressed this fact in the context of the high voltage discussion (see characterization section):\n“We recognize that the off-resonance and unreleased device voltages are high in this proof-of-concept demonstration and suggest ways of lowering these significantly in the discussion.”\n2.Although the author discuss a lot of ways to enhance the quality factor, I think it is better to provide some schemes for obtaining high applied voltage. As he discusses in the response to Question 1, there are several schemes for obtaining high voltage at high frequency, such as GaN-based electronics. This should be included in the manuscript.\nWe thank the reviewer for their suggestion and have added the following sentence to the manuscript (see characterization section) in line with our discussion in the previous response letter:\n“Also, we note that several technologies exist today to deliver voltages in the O(10 V) to O(kV) range at O(MHz) to O(GHz) frequencies, such as Si LDMOS (laterally-diffused metal-oxide semiconductor) [40], SiC [41], and GaN-based devices [42].”"}]

Decision letter