Broadband acousto-optic modulators on Silicon Nitride

Domain: physics
Published: 2025-12-17
Editorial outcome: minor_revision

Abstract
Thinsiliconnitrideintegratedphotonicsplatformsrelyonweaklyconfiningwaveguidesandthickoxidecladdinglayerstoenableultra-low-opticallossesonchip.Duetothesefavorableproperties,thistechnologyisseeingincreaseduseinchip-scalesystemstaskedwithmanipulatingandcontrollingclassicalandquantumopticalsystems.Phase-modulatorsplayacrucialroleinthelow-noisecontrolloopsofsuchsystems,butopticallybroadbandphasemodulatorsremainelusiveasthesamepropertiesusedtoenableultra-low-opticallossesmakeinteractionwiththeopticalmodedifficult.Hereweshowanunreleasedandopticallybroadbandacousto-opticmodulatorarchitectureonthisplatformenabledbylongmodulationlengthsinacompactspiralstructure.ThesedevicesachieveaVπof8.98Vatamodulationfrequencyof704MHzacrossanopticalbandwidthexceeding90nmattelecomwavelengths.Wedemonstratetheiruseaspartofthecontrolloopinanoptomechanicalsensingsystem.

Introduction
Silicon nitride (SiN) photonics has enabled narrow linewidth lasers1–5,recordsettinghigh-Qresonators6,7,andsensingsystems8,9. WiththefurtherinclusionofpiezoelectricsalongsideSiNphotonic integrated circuits (PICs)10, fast tunable lasers11–13, microcomb tuning14,15, optical isolators16, and quantum microwave-to-optical conversion17havebeendemonstrated.Allofthesetechnologiesare building blocks for PIC designers to use for producing mass- manufacturableintegratedsystems.However,SiN,amaterialplatformnotedforitsbroadopticaltransparencywindow18reachingthe visible spectrum19,20, low optical losses6, and CMOS compatibility1 suffersfromalackofopticallybroadbandmodulators.Modulators have been demonstrated through heterogeneous integration of electro-optic materials such as lithium niobate with SiN21–24 but require substantial modifications to the cladding layer to bring electro-opticmaterialwithinproximitytotheSiNwaveguidecore.

When broadband modulation frequencies are not necessary, acousto-optic modulators are an attractive choice. Laser locking schemes,suchasthePound-Drever-Halltechnique25,requireoptical modulatorstogeneratetheerrorsignalusedbythecontrolsystem. PICshavebeenproposed26,27thatutilizeintegratedmodulatorsand lasers to interface with atomic transitions, serving as a necessary nextsteptodevelopingPICsforlight-atominteractions.

Currently, the few existing acousto-optic modulators on thin SiN rely on optical resonant enhancement of the stress optic interaction28–30, limiting the optical bandwidth to that of the ring resonator.RecentthickerSiNworkembedsaluminumnitrideandair gaps within 710nm of 300nm thick SiN waveguides31 to optimize theoverlap.However,theentirepremiseofthethinSiNplatformis todrivedownopticallossesasfaraspossiblebyembeddingthelow- confiningwaveguide corein a pristinecladdinglayer. Introducing etched surfaces violates this premise and will drive up scattering losses on our thin SiN platform. Furthermore, avoiding release processes resultinasimplerfabricationprocedure.

A common technique to boost acousto-optic interactions is to exploitmovingboundaryeffectsinreleasedhigh-contrastwaveguide platforms. This technique has seen great success particularly in released silicon-on-insulator waveguide platforms, where it is commonly used to enhance Brillouin interactions32–34 and modulator performance35,36. Without release, waveguide boundaries cannot meaningfullyshiftinathinSiNplatform—aproblemexacerbatedby thelow index contrast between cladding and core.

The low confinement, low index contrast, and unreleased waveguides culminating in weak acousto-optic modulation on thinSiNareasideeffectofengineeringaphotonicsplatformwith state-of-the-artultra-lowlosses.Wedemonstrateameanstobypass this deficiency by engineering long photon-photon interaction lengths enabled by ultra-low optical losses in the form of a multi- pass, release free, spiral acousto-optic modulator. Our modulators operate up to 706MHz, representing a 35 × increase in operation frequency over other work on thin SiN30 while achieving a Vπ of 8.98Vwith1.13dBofinsertionlossacrossabroadopticalbandwidth exceeding90nm.Trendsexpectedfromtheoryareexperimentally measuredtoconfirmthephase-matchingphysicsofthemodulators. Finally,wedemonstrateanimmediateapplicationofthetechnology to an optomechanical accelerometer basedon high-Qring resonatorsfabricatedatthesamecommercialfoundry.

Results
Spiraldesign
Our thin SiN platform, illustrated in Fig. 1a, comprises of a 2.4μm×96.5nmwaveguideembeddedinsideasilicacladdinglayer.The passivewaveguidesarefabricatedatacommercialfoundryon200mm wafers and cored down to 100 mm. A piezoelectric layer stack comprisingofmolybdenum(Mo)andaluminumnitride(AlN)isdepositedon thecoredwafers.ThisMolayerincursmetal-inducedpropagationloss, andthetopcladdingthicknesswasselectedtoensureitstaysbelowan acceptable threshold. We observe additionallosses thatoccur due to processing of the wafer, likely during the piezoelectric deposition, bringingthetotalopticallossesto4.31dBm−1(SupplementaryNote1).

Achievinglongacousto-opticinteractionlengthsrequirescarefulchoiceofanacoustictransducer.Interdigitedtransducers(IDTs), whichlaunchatravelingacousticwavealongthesurfaceofamaterial, have previously been used in acousto-optic modulators on silicon-on-insulator37,aluminumnitride38,39,andlithiumniobate40–43. Importantly,theyhavebeenshowntoenablemulti-passAOMswhere thewaveguidecanbemeanderedtopassthelightthroughthesame acousticfieldmanytimes,drivingupmodulationefficiencywithout requiring more driving power44. Our IDTs were selected to have a pitch that is larger than the waveguide width to enable favorable overlap and can be fabricated using aluminum (Al) via a liftoff process.Acrosssectionscanningelectronmicroscope(SEM)image isshownofthislayerstackinFig.1b.

Thedominantmechanismofacousto-opticcouplinginourdevicesisthephotoelasticeffect.TheelectricfieldofthefundamentalTE mode,ofwhichwewishtophasemodulate,ispredominately xb-directedasshowninFig.1c.Basedoffofsilica’sphotoelastictensor, theS componentofthemechanicalstraintensorsimulatedinFig.1d yy contributesthemosttotheacousto-opticinteraction.Theoptimiza- tionofacousto-opticoverlapisdiscussedinSupplementaryNote2.

We select a waveguide spiral geometry because they have been showntoaffordlongphoton-phononinteractionlengthsinacompact form factor35,45–48.Ourproposedspirals,illustratedinFig.1e,arecom- pletely distinguished, to the best of our knowledge, from all other devicesinliteraturebecausetheyareparameterizedbytheintersection points(modulatedsegments)ofthelightwithatravelingacousticfield. Thesegeometricdegreesoffreedom,denotedbythefx g’sshownin n Fig. 1e, are explicitly calculated to phase-match the acousto-optic interactionviaaproceduredetailedinSupplementaryNote3.Motivated byultra-low loss integrated photonics platforms such as thin SiN, our design procedure allows for acousto-optic modulators of large pass counttobedesigned—bringingopticallybroadbandphasemodulation tothinSiN.Whenspiralsaredesignedinaccordancewiththisproce- dure,thesidebandamplitudegrowsinsuccessivemodulatedsegments, shownbyFig.1f.Thisleadstoamultiplicativeincreaseinmodulation indexwithincreasedmodulatedsegmentcountunderafixedRFpower. ForanextendedcomparisontootherspiralsinliteratureandthecalculationrequiredtodesignthesedevicesseeSupplementaryNote3.

Tounderstandhowthespiralstructureachievesaphase-matched acousto-optic interaction, it is helpful to draw an analogy to quasi- phase-matching (QPM)49,50, discussed extensively in Supplementary Note3.6.Inourdevices,thephase-mismatchaccruedperunitlengthis givenby

Δk=k(ω)−k(ω+Ωm)−Ωmng/c0, (1)

wherek(ω)isthefundamentalTEmode’sdispersioncurve,Ωm isthe radialmodulationfrequency,ng thegroupindex,andc0 thespeedof lightinvacuum.TheΔktermgivesrisetoacoherencelength,

Lcoh=2π/Δk (2)

which effectively places an upper length limit on the interaction length. This length is 13cm for our devices and on the order of microns for nonlinear processes like second harmonic generation (SHG).Tobreakthislimit,QPMalternatesthenonlinearcoefficient viapollingtocorrectforphase-mismatchinSHGandothernonlinear processes.Theanalogtothisinacousto-opticsisvaryingthephaseof the acoustic field encountered by the waveguide at different locations.UnlikeQPM,wehavecontinuouscontroloverthisphase, enabled in our devices by optimizing fx g. The acoustic phase for n each modulated segment is chosen to negate the optical phase- mismatchasshowninFig.1g.Usingacousticwavesthattravelacross thespiralareparamounttoachievingthis.Thisallowsincreasingly longspiralstobedesignedatthecostofadditionalinsertionlossand area(SupplementaryNote3.5foradiscussionofthisscaling).Useof otheracousticmodefamilies,suchasbulkacousticwaves(BAWs)29, wouldinherentlylimitthisscalingastheypresentauniformphase fronttothewaveguides.ThecoherencelengthfortheGHz-regime BAW modes is on the order of a few centimeters — limiting total modulated segment length unless multiple out-of-phase RF drives are used. Our devices only require one RF drive to modulate all waveguidepasses.

Acousto-opticmodulator
AfullyfabricatedtestchipisshowninFig.2anexttoabarephotonic chipwherethespiralsarevisible.Thenumberofmodulatedsegments in each spiral,rangingfrom6to38,wasselectedtoexaminemod- ulation performance as the total spiral length grows to twice the coherencelengthspecifiedbyEquation(2).Figure2bshowsanoptical microscope image of the transducers annotated with geometric parameters such as aperture and finger count. They were designed usingananalyticelectricalmodeldetailedinSupplementaryNote4.

For the acoustic mode coupled to by the transducers at 468MHz, 5.02%ofincidentelectricalpowerisconvertedintoacousticpoweras measuredbytheelectrical|S11|2inFig.2c.Sidebandsmodulatedoffof thecarrierbytheacousticwavecanthenbedetectedinlightexiting thespiralusinganinterferometer(SupplementaryNote5).Modulation efficiency,definedastheratioinopticalpowerbetweenthecarrierand first sideband, quantifying modulation strength, is maximized near 468MHzinFig.2d.

Figure2dexhibitsafringingpatternduetoeitherconstructiveor destructiveinterferenceofthemodulationproducedbythenearand farsideofthespiralrelativetothetransducer.Astheacousticwave propagates2.8mmacrossthespiral,therelativeacousticphaseson thenearandfarsideofthespiralbecomefrequencydependentdueto thedispersionoftheacousticwave.TheRFbandwidthof0.57MHzis thereforesetbythisphenomenon.Inourchips,acousticlossesforthe fundamental acoustic mode are small (0.54dB/mm, Supplementary Note1)andthusthefarsideofthespiralsubstantiallycontributestothephasemodulation.

Thetheoryforourdevicespredictsthatthemeasuredmodulation indexisexpectedtomultiplicativelyincreasewithmodulatedsegment count,C,evenasthespirallengthexceedsthecoherencelengthof 13cm.Naturally,atradeoffbetweenspirallength,insertionloss,spiral area,andmodulationstrengtharises.Spiralgeometricinformationis presented in Fig. 2e, f to quantify devices sizes as a function of C. Figure2eindicatesthatthecoherencelengthof13cmcorrespondsto amodulatedsegmentcountofapproximately18.Bymeasuringmultiplespiralsonthechipwithvaryingmodulatedsegmentcountunder identicalRFdrivepower,amultiplicativeincreaseinthemodulation index isobserved in Fig. 2g. The phasemodulation index, β, corresponds to the parameter of the Bessel functions that model the amplitude and power of the sidebands. For phase modulation, we thereforeexpectthepowerinthefirstandsecondsidebandstoscale linearly and quadratically, respectively, in response to applied RF power.ThischaracteristicofphasemodulationisobservedinFig.2h.

Higherorderacousticmodes
In addition to the fundamental acoustic mode, the transducers couple to three more acoustic modes whose S strain tensor is yy simulated in Fig. 3a. These higher order acoustic modes may be beneficialinphotonicintegratedcircuitdesignifthelayerstackcan be tuned to optimize overlap for one of these modes. For these devices, the modulation indices achievable for each mode is experimentallymeasuredinFig.3bbyanRFdrivefrequencysweep. Ahighfrequencymodepresentat706MHzachievesthestrongest coupling,yetrequirestightlayerthicknesscontrolofthecladding (within1.5μm)asshownbythecorrespondingplotinFig.3a,lestthe waveguidefallintoastrainanti-node.Themodulationefficiencyof thismodepeaksnear −10dB(Fig.3c)under1Wofdrivingpower—a substantial increase over the modulation efficiency of the fundamentalacousticmode.

The higher order modes provide a mechanism to probe the degradationofphase-matching.Asthedrivefrequencydeviatesfrom thespiral’sdesigned454MHzidealoperationfrequency,apenaltyin modulation efficiency occurs due to phase-mismatch. The largest device presented in this work, with 38 modulated segments, has a phase-matched3dBbandwidthofseveralhundredMHzsimulatedin Fig. 3d. All higher order modes can therefore be viewed as phase- matchedgiventhis3dBmetric.Notethatthisdoesnotaccountfor different electromechanical and acousto-optic coupling for each mode.Acousticmodeswithinthe3dBrangeofFig.3dwilldemonstrate a nearlymultiplicative increaseof the modulation index with modulatedsegmentcountasshownbytheupperandlowerboundsof modulation index curve shapes expected by theory in Fig. 3e. The theoreticallycalculatedcurveformodulationindexscalingisfittothe measureddataforthethreeadditionalmodesandgoodagreement canbeseeninFig.3f,g.The706MHzmodeexhibitsthemostroll-off fromthetrendexpectedforperfectlyphase-matchedacousticmodes.

Optimizationofelectromechanicalimpedancematch
Withthespiralsobeyingtheexpectedtheory,themodulationindices ofthesedevicesmayfurtherbeincreasedthroughtransduceroptimization. As speculated by literature44, mm-aperture transducers may hold promise in improving acousto-optic modulation. Spirals presented in this work are uniquely positioned to examine this experimentally as the modulated segments in each spiral can accommodatetransducersthathavea1.6mmaperture.Thickening thebusbarsasshowninFig.4aimprovesimpedancematchingby drivingdownparasiticresistanceandcapacitance,inturnallowing forlargeraperturetransducers.The500nmaluminumthicknessof thebusbarsisselectedasitisthemaximumthicknessallowedforby our deposition tool. A fully fabricated transducer with relevant geometricparametersnexttoaspiralisshowninFig.4b.Geometric parametersforthedeviceshowninFig.4bwereobtainedthrough optimization of an electrical model (Supplementary Note 4) to improveelectromechanicalimpedancematchingforthetwolower frequencyacousticmodes.

The fraction of incident electrical power launched as an acoustic wave for the fundamental mode can be estimated by examining the |S11|2 measurements of the dual metal thickness transducers (Fig. 4c) and the single metal thickness transducers (Fig. 2c). A marginal increase of 19.1% is observed. More importantly,thispowerisdistributedoveralongerlengthofwaveguide by 1.6mm/378μm = 4.23. As such, we expect the modulation index for the fundamental acoustic mode to increase by 4.23×1.191=5.04. Measured optically, modulation index increases by a factor of 2.375 for the fundamental transducer mode,indicating good agreementbetween electrical and optical observations. Large transducers are therefore clearly beneficial for acousto-optic modulation.

Thehighestfrequencymodeforthedualmetalthicknesstransducersisat704MHzandachievesclosetoaβ=π/2radphaseshift. Reachingaπ/2peakphaseshiftisimportantasitadditionallymakes these devices candidates for the optically broadband modulators required for optical gyroscope drivers8,51. The incident RF power is increasedgraduallywhilesweepingoverthemaximumofthe704MHz acousticmode’sfringingpattern.Thephasevelocityoftheacoustic waveshiftsduetothermaleffects,asevidencedbytheshiftinfringing patternshowninFig.4e.AtPRF=34dBm,aβ=0.58π>π/2modulation index isachieved,whichapproximatelymaximizesthepowerinthe±1 sidebandsasshowninFig.4f.Theinterferometrybasedexperimental setup(SupplementaryNote5)manifeststhesidebands100MHzoffset fromtheRFdrivefrequencysuchthatpositiveandnegativesidebands canbedistinguished.

The thick bus bar devices provide the best modulation performance,yieldingVπof8.98Vat1550nm.Weadditionallyusethemto validateouropticallybroadbandclaim.Foreachacousticmode,we measuremodulationefficiencyasafunctionofwavelengthacrossthe 90nmtuningrange ofour laser inFig.4g.All four acoustic modes exhibit lessthan 3 dB variation inmodulation efficiencyacross this range,leadingtoanopticalbandwidthofatleast90nm.Thisoptically broadbandoperationisexpectedfromthedevicetheoryoutlinedin Supplementary Note 3.4 with additional analysis of experimental resultsprovidedinSupplementaryNote6.1.

Useofmodulatorsinaoptomechanicalsensingsystem
Themodulationindicesreportedinthisworkareimmediatelyuseful forimplementingaPound-Drever-Hall(PDH)lock25toanopticalring resonatorsensitivetoacceleration.Onaseparatechipproducedatthe same foundry with a similar waveguide layer stack, acceleration- sensitiveopticalringresonatorsarefabricatedthatfeatureareleased proofmassstructureontheinterior,asshowninFig.5a.Serpentine silicaspringsconnecttheproofmasstoalocationinproximitytothe ring resonator waveguide (Fig. 5b) enabling transduction of proof mass displacement into an optical resonance shift as illustrated in Fig. 5c. The experiment in Fig. 5d reads out this shift. An optical resonanceisshowninFig.5ealongsidethecorrespondingPDHerror signal. As the optical resonance frequency shifts in response to an appliedacceleration,anonzeroerrorsignalresultswhichismeasured bythesameLIAtodeterminethetransferfunctionoftheaccelerometerandnoiseequivalentacceleration(Fig.5f).Thefundamental bz displacement mode arises near 1.8 kHz and corresponds to the lowestnoiseequivalentaccelerationof6766ngHz−1/2.Amoredetailed experimentalprocedurediscussingcalibrationisavailableinSupplementaryNote7.

Methods
Phasemodulatorcharacterization
Theperformanceofthespiralphasemodulatorsaremeasuredusing theopticalheterodynetechnique.Lightoutputfromatunablelaser (TopticalCTL1550)issplitintotwopaths.Onepathpassesthroughthe phasemodulatorchipwhiletheotherpassesthroughabulkBrimrose acousto-optic frequency shifter to frequency shift the light by 100MHz. Thelight is recombinedand beaton a high-speed photodetector. An electronic spectrum analyzer measures the response whichcontainsuniquefrequencycomponentscorrespondingtothe sidebandsimpartedonthelightbythephasemodulator(seeFig.4f). Therelativemagnitudeofthesesidebandscanbefittoinferquantities suchasmodulationindex.

Accelerometerexperiment
AsimplifiedblockdiagramofthisexperimentisshowninFig.5d. Thespiralphase-modulatorsareusedtoimplementaPDHlocktoa releasedopticalringresonator(picturedinFig.5a,b)thatissensitivetoacceleration.AZurichUHFLIlock-inamplifier(LIA)drivesthe spiralmodulator’s502MHzacousticmodethroughaRFamplifierto generateaPDHerrorsignalviademodulationofthebeatsignalon thephotodetector.Thiserrorsignalisfedintothelasercontroller, whichimplementsaproportion-integration-derivativecontrolloop to lock the laser to the minimum of the ring resonator transfer function. The experiment then shakes the optical accelerometer, causing the resonance frequency to shift under the applied acceleration. This shift is also measured by the lock-in-amplifier by demodulatingtheerrorsignalgeneratedbythecontrolloopatthe shake frequency. Simultaneously, a commercial accelerometer (ADXL 354) located next to the optical chip on the shaker table reportstheaccelerationappliedbytheshakertable.Thissystemis further calibrated with a bulk acousto-optic frequency shifter through a procedure documented in the Supplementary Information to obtain the transfer function in units of MHz g−1 shown in Fig.5f.Thiscalibrationprocedureisnotrequiredtomeasurenoise- equivalentacceleration.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript \"Broadband acousto-optic modulators on Silicon Nitride\" describes the development and implementation of a novel, traveling wave optically broadband acousto-optic modulator using thin silicon nitride waveguides. These modulators, capable of achieving a π/2 phase shift at a wavelength of 1550 nm, offer significant advantages due to their avoidance of complex fabrication processes and heterogeneous integration, capitalizing instead on ultra-low-loss waveguides to achieve long interaction lengths necessary for efficient modulation. The architecture utilizes spiraling waveguides that allow light to repeatedly pass through an acoustic field up to 38 times within a compact area, facilitating effective modulation with a Vπ of 8.98 V at 704 MHz and an insertion loss of just 1.13 dB. This manuscript also highlights the modulators' immediate applicability in optomechanical sensing systems. I recommend publication of this manuscript with a few minor comments:\n1. In the abstract, “As silicon nitride has favorable optical properties, such as ultra-low-loss and a large optical transparency window, a rich ecosystem of potential photonic integrated circuits are therefore inhibited.” This sentence does not read well.\n2. Figure 1, green, yellow, gray, materials not specified in figure or caption. From the text later one can sort of figure it out, but I recommend labeling those materials in the figure.\n3. On phase matching, it mentions the basic idea of that in the text when introducing Figure 1e, and the results of increasing of numbers of loops in Figure 2. Could the author show more intermediate results in between of the design philosophy and final results? This is very important technical content for readers to understand, appreciate, and repeat the design.\n4. The authors mention the loss of 1.1 dB is primarily because of metal layer; can they explain more how they reach this conclusion?\n5. Could the authors provide more information regarding the material properties and method for AlN and Mo?\n6. Could the authors comment on how to further how to further increase the acoustic-optical interaction in the future?", "reviewer_2": "The article under review describes broadband acousto-optic modulators on silicon nitride. In this work, the authors utilize ultra-low loss thin silicon nitride (<100nm) to realize the modulators. The modulator design is optimized by maximizing the optical and acoustic interaction through the use of a long spiral. This device avails modulators to the SiN photonics toolkit. The manuscript is interesting and I recommend publishing the manuscript after addressing the following points:\n1) Integrated photonics technologies have a variety of modulator types (eg. electro-optic, free-carrier based). The modulator described in this work uses the acousto-optic effect. A table which allows a comparison of modulator merics such as half wave voltage / bandwidth / loss/ foot print etc. should be added to the paper.\n2) Currently, the half wave voltage in the paper is higher than other technologies. Can the authors discuss what can be done to reduce it? The interaction length through ultra-low loss silicon nitride requires a 26cm length. There should be a fundamental limit to how long the waveguide can be that is loss limited. Can the authors comment on whether increasing the length is a feasible approach to reduce Vpi\n3) Within the context of comment (2), there should be a trade off with the modulator footprint which may be useful to discuss as well.\n4) Other than in Fig. 8 (d), can the authors comment on whether any data averaging was done to obtain the plots in the article? If so, how did they decide on the number of measurements used for the averaging?\n5) To further improve the transducer, a greater thickness is required. More commentary around potential design improvements to enhance the modulator performance is warranted given that LiNbO3 modulators are currently very competitive. For example (but not limited to these), can the overlap be improved, and if so how much, could any other material integration give better performance etc.\n6) Though higher order acoustic modes may be advantageous, it is not clear how one can control which modes are excited. The authors should clarify this. If there is a difficulty in exciting a specific higher order mode and the design is typically optimized for a specific mode, then is there an inherent tradeoff?", "reviewer_3": "In this manuscript, the authors demonstrate an acousto-optic phase modulator based on a spiral waveguide in thin-film silicon nitride, using travelling acoustic waves from IDTs on a Mo/AlN top layer. In contrast to prior work on silicon nitride, this modulator design does not use optical resonant enhancement, or suspended structures as in other recent work [31]. Using up to a 26 cm spiral waveguide, along with careful phase control over dozens of segments in the acoustic wave path, a V_pi of ~9 V is achieved for acousto-optic phase modulation at 704 MHz with ~1.1 dB insertion loss.\nIn general the work is interesting and seems technically to mostly be of high quality, except for a key issue addressed below. That aside, I am a bit uncertain if the manuscript represents the degree of novelty that the authors seem to claim, in part because the design is primarily based on principles that have already been reported in other recent work, and otherwise because I have some doubts about the applicability and practicality of using such a large structure and high RF power for producing phase modulation at a single RF frequency, particularly related to the next point:\nCritically, I am not certain that I believe the authors' claim that the device is \"broadband.\" It certainly is not broadband in the RF/acoustic sense, and I do not think it is broadband in the optical sense as well. When two (or more) modulators at the same frequency are placed in series, there can be constructive or destructive interference of the modulation index depending on the phase delay. The authors explore this in the supplement, and use this to design specific delay lengths between each segment. However I am not sure that their conclusion of the negligible impact of group index. Perhaps this can be true for operation around a certain theoretical design wavelength, but I do not see how this can produce broadband operation over 100+ nm. In any case, much more narrowband/continuous wavelength data would be needed to be provided to justify any claim about bandwidth.\nI am not certain that the level of lithographic control to match phase delays to sub-radian levels over centimeter lengths is possible without post-fabrication trimming, due to variations in waveguide width and film stress and thickness across the wafer. However, perhaps given the weak confinement of thin silicon nitride waveguides and the use of a foundry process, this is possible in principle.\nEven if constructive interference between all the segments is achieved, then it is still achieved for only certain wavelength bands due to material and waveguide dispersion. This is understood from basic modulator theory. If you have two modulators in series so that there is a phase difference theta between them:\nphi(t) = beta*cos(omega*t) + beta*cos(omega*t+theta)\nthen this can be rewritten as\nphi(t) = 2*beta*cos(theta/2)*cos(omega*t+theta/2).\nIf the phase theta is pi between the two modulation segments, then the modulation cancels. So, we want to keep theta to a multiple of 2*pi. This can be achieved, but it cannot be entirely \"broadband\" unless phi doesn't vary as a function of wavelength. I have a hard time believing that v_g varies so little over 100 nm that light does not accumulate an appreciable phase difference over tens of cm.\nIn the case of multiple segments, the interference becomes more complicated, but the principle is the same. Even with random phases between each segment, it should be possible to find \"good\" wavelengths where most of the interference is constructive. Conversely, there are \"bad' wavelengths where most of the interference is destructive. This is already reported in detail in many papers, e.g. [33] and [37]. Another way of thinking about it is that, from the standpoint of light waves, experiencing many discrete modulation segments in series is not temporally very different from experiencing modulation at a discrete point in a resonator that it traverses numerous times, except that phase matching is more perfectly achieved for the latter via the resonance condition.\nAs far as I can tell, the only figure in the entire paper that is used to justify the claim of optical bandwidth is Fig. 2g, which shows modulation data at a series of coarse, discrete points across 100 nm. The same plot could be constructed from measurements of modulation in a resonator, as long as the laser was tuned to the resonant frequencies (equivalent to \"good wavelengths\" mentioned above). So in that sense the resonator approach would also seem to meet the authors' criterion for \"broadband.\"\nIf the authors are not able to experimentally demonstrate broadband operation over a continuous wavelength band that contradicts this assessment, then the results of this paper are all a bit hard to interpret--since V_pi is going to vary as a function of wavelength, and the result of 9 V may occur only at certain magic wavelengths. I do think that the device may be able to achieve \"broadband\" operation over smaller continuous bands, but I believe that it cannot be continuously broadband over the 100 nm band shown in Fig. 2e given the design parameters.\nUsing the index of refraction of silica to estimate the optical wavevector difference between 1500 and 1600 nm, a 1 mm path length will produce a phase difference of 2*pi*(1.4446-1.443)*(1 mm)/(1550 nm) = 6.5 rad over this range. A 25 cm path length would produce a phase difference of ~1600 rad. Within one operation band, we probably need the phase to vary by ~1 rad or less over the bandwidth, so for the 25 cm device that might mean that the actual continuous bandwidth we can operate over at once is on the rough order of 1/16 nm. This is certainly more wideband than many resonant devices, but is quite narrowband compared to many other AOM demonstrations. The other recent work in [31] does achieve broad bandwidth because it consists of a single travelling-wave modulator, by comparison.\nThis analysis is of course somewhat speculative and based mostly on back-of-the-envelope math and prior published work, but in any case, the characterization of device performance as a function of wavelength is currently inadequate to support any claims of bandwidth at all.\nIt also makes me worry that some of the other assertions that are so confidently made in the paper may not have actually been fully thought through. It does not mean that the results are not interesting, but if it is difficult to produce a device for operation at a specific wavelength without extensive trial and error, then the results may not be too practical.\nThe tone and writing style of the paper is also at times quite stiff--many paragraphs are just a series of terse declarative sentences, without relationships or connections explained between them. Numerous sentences in a row start with \"The\" at several points in the paper, and some statements seem like non sequiturs.\nI apologize for the harsh review, as the work is technologically impressive and it's clear that a lot of thought and hard work went into it. I just do not think the experimental data presented justify all of the claims made, particularly based on prior literature, and that a more detailed experimental investigation is warranted. I would love to be proven wrong, but I'm worried that the data presented do not tell the full story.\nSome other minor comments are enumerated below:\n1. It would be better to have a theoretical line plotted behind the data in Fig. 2f, instead of a random linear fit. In addition, the phrase \"Indeed, the linear trend does continue with the experimentally collected data in Figure 2f\" does not really mean anything. A linear increase does not \"validate\" the design methodology. A linear fit can have a slope of zero. Basically any curve is linear if you zoom in enough. A linear fit where 10 segments has 10x the modulation index of 1 segment, and where 30 segments have 30x the modulation index of 1 segment and 3x the modulation index of 10 segments, would validate the design methodology. Anything else is a false conclusion.\n2. On page 3, the listing of equations (2-6) seems a bit awkward, since none of them are really motivated from theory or the text, or cited with references to the supplement or whatever, besides the reference for \"coherence length\" which is a bit of an interesting definition and might merit a bit more description to the reader in terms of what it actually means for this study.\n3. On line 284, the phrase \"The key to large transducers is to thicken the bus bars,\" does not really mean anything. It'd be better to say that adding thick bus bars lower resistance to improve impedance matching.\n4. On line 365, I think that the phase matching technique does not seem as \"completely novel\" as the authors claim. The use of a spiral waveguide to enhance efficiency is not new, and in a bunch of the silicon a-o work, phase matching is explored in great detail. The arc length calculation for the bends is neat, but depending on fabrication tolerances it may not be required at that precision.\n5. In the phrase \"Insertion loss can be driven down further through removal of the AlN above the waveguides and recovering the foundry loss [56],\" what does recovering mean? I thought losses were dominated by the Mo metal layer? Do you mean that the Mo and AlN could be deposited only in specific areas via a mask or liftoff, and that would make the insertion losses lower, similar to the best foundry values? I wonder if that might be a bit more feasible than removing it if it's already on top of the oxide clad.\n6. The following sentences are somewhat incorrect: \"The acousto-optic nature of the interaction can be seen by examining the slope of modulation efficiency for the 1st and 2nd order sidebands in response to an RF power sweep, shown in Figure 2h. The first and second sidebands scale with 1× and 2× the applied RF power in dBm.\" The modulation efficiency slopes do not say anything at all about the interaction being acousto-optic. Those power laws are the same for all linear sinusoidal modulation in all systems. It suggests that you are seeing phase modulation as expected. Saying the sidebands scale with 1x and 2x the power in dBm is true, but it's probably more correct to say that the first and second sideband powers scale linearly and quadratically with the applied RF power, in accordance with the expected trend (from the Jacobi–Anger Bessel expansion).\nSome more line edits...\n7. Line 219 page 4 - \"coherent modulation\" might not be the most descriptive term, since it's specifically interference between the modulation in the different segments that creates the peaks and nulls, I believe?\n8. \"The photonics is fabricated at a commercial foundry on 200 mm wafers. They are cored down to 100 mm and...\" Using \"photonics\" in this way is a bit unusual, in part because I'd consider the entire device part of the photonics, not just the passive waveguides. In any case, subject-verb agreement would dictate \"photonics are.\" The phrase \"They are cored down\" I assume is of course referring to the processed wafers, but based on the sentence structure it would be referring to the photonics themselves, not the wafers, when the wafers are what are being cut down. It would also be helpful to readers to mention which foundry process if that's not proprietary.\n9. \"fabricated on a foundry SiN photonics process to increase the acousto-optic interaction length in a compact area.\" Interjecting the foundry process here again makes it sound like that is the part that increases the interaction length. We already know it is from a foundry process since that was mentioned in the prior paragraph. If it is to be included, that phrase should be between commas here. Later in this paragraph you refer to this approach as \"novel,\" which I am not sure is so true any there are several works that have introduced similar multi-pass designs."}, "author_response": "Response to Reviewers for: Broadband acousto-optic modulators on Silicon\n4\n1OxideMEMS Lab, Purdue University, West Lafayette, Indiana 47907, USA\n5\n2Anello Photonics, Santa Clara, California 95054, USA\n8\n9\n10\n11\n12\n13\n14\nOriginal Main Text oMT\nOriginal Supplementary Information oSI\nRevised Main Text rMT\nRevised Supplementary Information rSI\nThis response to reviewers document RR\nRR Table 1: Abbreviations used in this document to clarify which document is being referenced.\n16\n1. Reviewercommentsareseparatedpoint-by-point, witheach“point”beinglabeledby“Reviewer:”. Sometimeshighlights\n17\nwill appear to emphasize key conditions required to respond to the Reviewer’s question.\n18\n2. Detailed responses follow each point and are labeled with “Author:”. Responses to key conditions highlighted in the\n20\n3. At the end of the response to each point, we present the “Action Taken:” section which details how we improved the\n22\nnumbers referring to the revised Main Text or Supplementary Information will be included here to point to the changes.\n23\n4. Due to the large number of responses to the Reviewers we integrated into the manuscript, we have edited for clarity\n24\nand conciseness. Structural changes made as a result of these edits are highlighted in RR Section 5 and linked to the\n25\ncorresponding reviewer comment motivating the revisions.\n27\nthe revised Main Text or revised Supplementary Information. Some will also appear in this response document for convenience.\n29\nabbreviations in Table 1.\n30\n2\n32\nmentation of a novel, traveling wave optically broadband acousto-optic modulator using thin silicon nitride waveguides. These\n33\nmodulators,capableofachievingaπ/2phaseshiftatawavelengthof1550nm,offersignificantadvantagesduetotheiravoidance\n34\nofcomplexfabricationprocessesandheterogeneousintegration, capitalizinginsteadonultra-low-losswaveguidestoachievelong\n35\ninteraction lengths necessary for efficient modulation. The architecture utilizes spiraling waveguides that allow light to repeat-\n36\nedly pass through an acoustic field up to 38 times within a compact area, facilitating effective modulation with a V of 8.98 V\nπ 37\nat 704 MHz and an insertion loss of just 1.13 dB. This manuscript also highlights the modulators’ immediate applicability in\n38\noptomechanical sensing systems. I recommend publication of this manuscript with a few minor comments:\n39\n41\n43\ntransparency window, a rich ecosystem of potential photonic integrated circuits are therefore inhibited.” This sentence does not\n44\nread well.\n45\n47\nlimit. The corresponding sentence now reads “Thin silicon nitride (SiN), offering some of the lowest optical losses achievable on\n48\nchip, lacks optically broadband modulators as the low confining waveguide core is buried in a thick oxide cladding.”\n49\n51\n1. The abstract has been revised (rMT Page 1).\n52\n54\nfigure it out, but I recommend labeling those materials in the figure.\n55\n57\n59\n1. Revised rMT Figure 1a to have a color-coded material legend.\n60\n2. Revised rMT Figure 1b to explicitly call out geometric dimensions and materials.\n61\n3. Revised rMT Figure 1’s caption to clearly communicate the materials used.\n62\n64\nincreasingofnumbersofloopsinFigure2. Couldtheauthorshowmoreintermediateresultsinbetweenofthedesignphilosophy\n65\nand final results? This is very important technical content for readers to understand, appreciate, and repeat the design.\n66\n68\nquasi-phase-matching. In rSI Page 17 Figure 7, we pictorially illustrate this link starting from quasi-phase-matching as pre-\n69\nsentedinanonlinearopticstextbook[1]. WehaveadditionallyrevisedtherMTtodescribetheoperationprincipleofourdevices\n70\nwithin this framework (rMT Page 3 Lines 134-164). Note that the introduction and first results section have been revised and\n71\nreorganized in accordance to this comment without any changes to the reported experimental data.\n72\n74\n1. Added a new Supplementary Information section (rSI Note 3.6) with a new figure (rSI Page 17 Figure 7) that details the\n75\nrelationship between the spirals and quasi-phase-matching.\n76\n3\n2. Included this discussion in the rMT as an explanation of the spiral design (rMT Page 3 Lines 134-164).\n77\n79\nthis conclusion?\n80\n82\ninformation about processing induced losses in rMT Page 2 Lines 85-90. A more detailed discussion of the experiments con-\n83\nducted to reach these conclusions is included in rSI Note 1.\n85\nacross the 100nm Molybdenum layer. Therefore, layers above the Mo layer will not meaningfully contribute to the additional\n86\noptical losses we observe. Following release of the wafers from the foundry, we performed the following steps to understand the\n87\nadditional optical losses.\n88\n1. Opticallossesat1550nmarespecifiedbythefoundryat0.25dB/m. Dicingacontrolwafer(withnosubsequentprocessing\n89\nsteps after leaving the photonics fab) into chips, we corroborate this claim with our own measurements.\n90\n2. Send the bare photonic wafers to AMS Inc. [3] for deposition of the 100nm Molybdenum layer and 1.5µm Aluminum\n92\n3. Dice the resulting wafers into chips for transducer prototyping. Here, we measure optical losses by fitting the transmission\n93\nspectrumofaopticalringresonatorlocatedonthechip. WeshowthisdatainrSIPage2Figure1basthebluedotslabeled\n94\n“AlN, Mo present”. The upper bound on the measured loss (blue shaded rectangle) is used to calculate the insertion loss\n95\nof the spiral based on the spiral length.\n96\n4. Using a plasma etch, the Mo and AlN layers are stripped off of a test chip such that the remaining chip only has the\n97\nwaveguide layers present. The goal of this is to see if the optical losses return to their original out-of-foundry values.\n101\nelectric layers, we conclude that the additional losses (˜4dBm−1) result from a combination of metal induced propagation loss\n102\nand processing loss. As this value is higher than simulated values for metal induced propagation loss, we believe that the piezo-\n103\nelectric deposition actually degrades the quality of the cladding above the waveguide. We view the most likely mechanism for\n104\nthis as ultraviolet light (from plasma-based processing steps) exciting long-lived excited states [4].\n105\n107\n1. Mentioned processing induced loss at rMT Page 2 Lines 85-90.\n108\n2. Edited rSI Note 1 to clearly describe the origin of optical loss as metal and processing induced (rSI Page 2 Lines 28-52).\n109\n110\nDensity\nMaterial velocity\n[kgm−3]\n[ms−1]\nAluminum 2700 6300\nAlN 3300 11050\nMo 10200 6636\nRR Table 2: Properties molybdenum (Mo), aluminum nitride (AlN), and aluminum (Al). These numbers are reproduced from\nthe Supplementary Information of [5].\nReviewer: 5. Could the authors provide more information regarding the material properties and method for AlN and Mo?\n111\n113\nthe values here in RR Table 2 for convenience.\n115\nducers are defined via liftoff using 1.8µm thick AZ5209 photoresist. For the dual metal layer transducers, the 60nm Al fingers\n116\nare patterned first. The same liftoff procedure is carried out a second time to pattern the 500nm bus bars.\n117\n119\n6].\n120\n122\n124\ngeneral technique applicable to any low loss optical platform that utilizes an acoustic traveling wave capable of being launched\n125\nacrossachip. WehaveaddedaSIsectiontodiscussthistradeoffindetail(seerSINote3.5). However,thereareafewapproaches\n126\nto improving the interaction that may be appropriate depending on the application.\n127\n1. Increasetheapertureofthepiezoelectrictransducers. Ourelectricalmodelspredicttransducerswithaperture>2mmcan\n128\nincrease modulation index by about 25%.\n129\n2. Bonding of Lithium Niobate (LN) for use as a piezoelectric transducer. Previously, LN has been explored to bring the\n130\nelectro-opticeffecttothickSiNwaveguides[7,8]. However,thissuggestedimprovementwouldseektoleavethemodefully\n131\nin the SiN and utilize a LN-based interdigited transducer to launch acoustic waves in a similar manner to this manuscript\n132\nto preserve ultra-low-loss properties of the SiN process. This has been explored to a degree in [9], but the optical mode\n133\npartially resides in the LN. This suggestion is for using LN purely as a piezoelectric.\n134\n3. Reduce the modulation frequency and utilize PZT as the piezoelectric material [10]. This suggestion is in a similar vein\n135\nto the previous. In lower frequency applications, piezoelectric materials with high dielectric constants become possible to\n136\nuse. As PZT exhibits a stronger piezoelectric coefficient than AlN in this regime, it would likely lead to improvement in\n137\ndevice performance.\n138\n4. Use AlScN as the piezoelectric material [11].\n139\n5. Design the spirals to be phase-matched for the higher order acoustic modes. These modes have been experimentally\n140\nmeasured to have more favorable acousto-optic overlap.\n142\nifabenefitcanbefound. AlthoughAlScN,PZT,andLNhavestrongerpiezoelectriccouplingsthanAlN,theacousticimpedance\n143\nmismatch between the piezoelectric film and silica also need to be favorable for meaningful modulation. This requires detailed\n144\nfinite element simulations.\n145\n147\n1. Mentioned methods to improve acousto-optic interaction in the rMT Discussion section (rMT Page 7 Lines 354-365).\n148\n2. Added a new section discussing improvements to this modulator architecture to the Supplementary Information (rSI\n150\n5\n3. Moved discussion of larger aperture transducers from rSI Note 6 to rSI Note 3.7. rSI Note 3.7 is referenced in rSI Note 6\n151\n(rSI Page 25 Lines 515-516).\n152\n153\n6\n155\nutilize ultra-low loss thin silicon nitride (<100nm) to realize the modulators. The modulator design is optimized by maximizing\n156\nthe optical and acoustic interaction through the use of a long spiral. This device avails modulators to the SiN photonics toolkit.\n158\n160\n162\nmodulator described in this work uses the acousto-optic effect. A table which allows a comparison of modulator merics such as\n163\nhalf wave voltage / bandwidth / loss/ foot print etc. should be added to the paper.\n164\nModulation V L V V Lα\nReference thickness broad- Released Wavelength π π π Size\nfrequency [V·cm] [V] [V·dB]\n[nm] band\nHosseini\n[12]\nFreedman\n[13]\n1.2mm×\nJin [14] 175 No DC-300kHz Yes 1550nm 3.6 8 1.1\n1.2mmc\n1.2mm×\nWang [15] 175 No DC-20MHz No 1550nm 43 - 1.3\n1.2mm\n200µm×\nTian [5] 810 No ˜3GHz Yes 1550nm - - -\n200µm\n1.3mm×\nDong [16] 300 Yes DC-120MHz Yes 780nm 100d 100d 39e\n0.6mm\nThis work 96.5 Yes 704MHz No 1550nm 54.7 9 10.17 23mm2\nRR Table 3: A comparison of technologies for modulating SiN waveguides. V L for our multi-pass devices is defined using\nπ\nthe length of waveguide modulated by the acoustic wave (38×1.6mm = 6.08cm). Thus, our V L reflects a property of the\nπ\nwaveguide cross section and can be used to compare various waveguide platforms. V Lα uses the total spiral length of 26cm as\nπ\nall 26cm of the spiral contribute to insertion loss. See rSI Note 5 for further comments. The green highlights indicate favorable\nproperties for our applications and red highlights unfavorable properties. Orange represents an intermediate case, as released\ndevices provide the means to greatly reduce power consumption and V , but result in process and foundry dependent devices.\nπ\nDevice size is estimated based on information available in the associated reference. Some devices [12, 13] have negligible width.\nIn this case, size is reported as a length. aCalculated using an active length of 10mm. bCalculated from modulation length and\nV L. cEstimated based on the ring resonator radius using single stripe waveguides. dPer phase shifter (i.e., it is not configured\nπ\nas push-pull) at room temperature. eCalculated using V L and a waveguide propagation loss of 0.39dBcm−1.\nπ\nWe have generated two tables that compare state-of-the-art modulators. The first, copied into this document as RR Table 3,\n167\ncompares acousto-optic modulators on SiN platforms and has been added as rMT Table 1 and referenced during the Discussion\n168\nsection of the rMT (rMT Page 6 Lines 341-344). Since our devices are pure phase modulators, optical bandwidths are usually\n169\n100’sofnmorcommensuratewiththelinewidthofaphotonicringresonator(ifthedevicesareopticallyresonant). Todistinguish\n170\nthese two binary cases, we denote devices as “Yes” or “No” for the optically broadband criteria.\n172\nacousto-optics (electro-optics, free-carrier, and bulk devices). Many of these devices have substantially different use cases than\n173\nour own (e.g., electro-optics are often used in telecom and require modulation up to 100GHz).\n174\n176\n1. Added RR Table 3 to the rMT (rMT Table 1) and comment on it in the Discussion section (rMT Page 6 Lines 341-344).\n177\n2. Added RR Table 4 to the rSI (rSI Page 14 Table 2).\n178\nRF Modu-\nV L V Lα chip Modulated Loss, α\nReference Mechanism Platform lation V π π\nπ [V·cm] [V·dB] IL length [cm] [dBcm−1]\nbandwidth\n[dB]\nElectro-\nXu [17] TFLN DC-48GHz 1.9 2.47a 3.42b 1.8 1.3 -\noptic\nRenaud Electro- DC to\nTFLN <1 <1 <0.7c 0.7d 1 0.7\n[18] optic >35GHz\nHybrid\neRahman Electro-\nLN-thick DC-110GHz 6.4 3.8 - 3.8 0.6f -\n[8] optic\nSiN\nElectro-\ngWang [19] LT DC-40GHz 7.6 1.9 0.11h - 0.25 0.056\noptic\niRahim Plasma 0.058\nSi ˜50GHzj - - - 0.01 to > 0.1 10 to 80\n[20] dispersion to 2\nAcousto- AlN on\nThis work See captionk 9 54.7l 10.17l 1.12 6.08 0.0431\noptic thin SiN\nRR Table 4: A comparison of modulator technologies across a variety of integrated platforms. aCalculated from V = 1.9V\nπ\nand a modulated length of 1.3cm. bCalculated from V and on chip insertion loss of 1.8dB. cCalculated from propagation loss\nπ\nand V L. dCalculated from on propagation loss and modulated length. eThe numbers in this row correspond to Device 3 in [8].\nπ\nfCalculatedfromV LandV . gThenumbersinthisrowcorrespondtothemeasurementscarriedoutatanopticalwavelengthof\nπ π\n1550nmin[19]. hComputedfromV Landpropagationloss. iThisrowsummarizesresultsnotedinTable2of[20]. Complicated\nπ\ntradeoffs exist between the listed parameters based on the exact design, so only ranges are noted. jOnly data rates are cited\nin Table 2 of [20]. 50GHz is a common modulation bandwidth found in [20]. k0.57MHz at a modulation frequency of several\nhundred megahertz. lV L for our multi-pass devices is defined using the length of waveguide modulated by the acoustic wave\nπ\n(38×1.6mm=6.08cm). Thus, our V L reflects a property of the waveguide cross section and can be used to compare various\nπ\nwaveguide platforms. V Lα uses the total spiral length of 26cm as all 26cm of the spiral contribute to insertion loss. See rSI\nπ\nNote 5 for further comments.\n180\ncan be done to reduce it? The interaction length through ultra-low loss silicon nitride requires a 26cm length. There should be\n181\na fundamental limit to how long the waveguide can be that is loss limited. Can the authors comment on whether increasing the\n182\nlength is a feasible approach to reduce Vpi\n183\n184\n3) Within the context of comment (2), there should be a trade off with the modulator footprint which may be useful to\n185\ndiscuss as well.\n186\n188\naddressing these questions as a new section as rSI Note 3.5. This section contains a new figure, rSI Page 16 Figure 6, that\n189\nsupports the discussion. It is copied into this document as RR Figure 1 for convenience.\n191\nmodulation index and the sidebands maintain their Bessel-like character. Therefore, half-wave voltage can actually be contin-\n192\nually decreased with increased spiral size at the expense of insertion loss. It is therefore useful to adopt a figure-of-merit that\n193\nestablishes a limit on insertion loss, such as V (the V of a modulator with 3dB of insertion loss). In RR Figure 1f, a spiral\n194 π,3dB π\nwith 3dB of insertion loss comprises of approximately 90 modulated segments. As the 502.1MHz mode exhibits minimal rolloff\n195\ndue to phase-mismatch (compared to e.g., the 704.3MHz mode), we can estimate a V ≈ 5V for the 502.1MHz mode. If\n196 π,3dB\nour spirals were specifically optimized for the higher frequency 704.3MHz mode, further improvements are possible.\n197\n199\n1. Addedanewfigure(rSIPage16Figure6)thatshowsscalingrulesandprojectedperformanceofourdevicesandfootprint.\n200\n2. Added a new section (rSI Note 3.5) that provided details discussion of the trade-offs of scaling modulation index, V ,\n201 π\nwidth, height, area, waveguide length, and insertion loss.\n202\n203\n204\nin the article? If so, how did they decide on the number of measurements used for the averaging?\n205\n207\n1. oMT-Figure 5f, top panel: The transfer function of the optical accelerometer is estimated using long averaging times (1Hz\n208\nintegration bandwidth) for each measured frequency point via our lock-in amplifier. Transfer function estimates improve\n209\nwith longer integration times, especially since this device operates in a frequency range susceptible to acoustic noise and\n210\nenvironmental disturbances. Our selected integration time balances quality of the transfer function estimate with exper-\n211\niment runtime. This estimate of the transfer function can then be used with the characterization of the noise PSD (e.g.,\n212\nrSI Page 27 Figure 12) to produce accurate noise-equivalent acceleration (NEA).\n213\n2. rSIPage27Figure12(pointedoutbythereviewer): Wehaveautomatedourexperimentsuchthatatime-domaincapture\n214\nof noise is collected immediately before shaking the accelerometer at a given frequency (this occurs hundreds of times\n215\nthrough the course of the experiment — the shaker table is disabled, PSD measured, and then re-enabled). This was\n216\noriginally intended to assist in debugging the experimental setup and ensuring there were no disturbances in lab. For each\n217\nof these time-domain measurements of noise, the Welch method is used to estimate the noise PSD — providing a tradeoff\n218\nbetween the estimator variance and frequency resolution of the estimated PSD. Our choice of Welch window length results\n219\ninafrequencyresolutionof25Hz—approximatelyhalfofthelinewidthofthemechanicalresonance.Wehavehundredsof\n220\nestimates of the noise throughout the experiment and they ultimately reveal a similar noise PSD throughout the duration\n221\noftheexperiment. Simplybecausewehavethisdataonhand,weaverageallthesePSDestimates(199total,corresponding\n222\nto the number of shake frequencies present in the experiment) to produce the manuscript plots. This is not necessary and\n223\na single estimate of the noise would suffice.\n224\n3. The reported mode frequencies in rMT Figure 3f,g and rSI Page 25 Figure 11c,d. This is mentioned in rMT Figure 3’s\n225\ncaption. As these plots comprise of measurements of several devices that widely vary in pass count, the fringing pattern\n226\nas a function of f will be slightly different. For each device, it is driven at the optimal f for a given mode. This value\nRF RF 227\nis logged and the average among all spirals is simply used for labeling purposes to distinguish the four acoustic modes in\n228\nthe mentioned figures. The number of points used for averaging therefore corresponds to the number of spirals measured\n229\nfor one of the aforementioned plots.\n231\n233\n1. All raw data to reproduce the conclusions and plots of this study has been added to a Zenodo repository. Example codes\n234\nthat are useful in recreating the plots and processing the data in the manner described above have also been uploaded.\n235\n237\nimprovementstoenhancethemodulatorperformanceiswarrantedgiventhatLiNbO3modulatorsarecurrentlyverycompetitive.\n239\ngive better performance etc.\n240\n242\nand discuss these in the Discussion section of the rMT (rMT Page 7 Lines 354-365). This information can also be found at RR\n244\n246\n1. Added a section discussing further improvements, including increasing modulated segment count, alternative transducer\n247\ndesigns, and alternative piezoelectric materials, to the Supplementary Information (rSI Note 3.7).\n248\n2. Mentioned methods to improve acousto-optic interaction in the rMT Discussion section (rMT Page 7 Lines 354-365).\n249\n250\n251\nexcited. Theauthorsshouldclarifythis. Ifthereisadifficultyinexcitingaspecifichigherordermodeandthedesignistypically\n252\noptimized for a specific mode, then is there an inherent tradeoff?\n253\n255\nin initial design considerations. This mode requires stronger control over the silica layer thicknesses to ensure favorable overlap.\n257\nwaveguide could fall in a strain anti-node and hence modulation performance would severely suffer. From a risk management\n258\nperspective,weelectedtodesignthespiralsforthelowerfrequencymodes. Inhindsight,thisconcernwascompletelyunfounded.\n260\npected from finite element modeling. The higher order modes can be predicted by simulation and designed for.\n261\n263\n1. Added a discussion to rSI Note 3.7 that discusses designing for the higher order modes (rSI Page 14 Lines 366-369).\n264\nperformance of spirals on this work’s layer stack can be extrapolated using the theoretical model. Since the spirals were not\noptimized for the higher order acoustic modes, roll-off can be seen in the modulation index for higher order acoustic modes.\nb. V is extrapolated in a similar manner to (a). c.-d. Geometric parameters of the spirals as modulated segment count, C,\nπ\ncontinues to increase. e. Total spiral waveguide length and the associated insertion loss, assuming optical losses of 4.31dBm−1.\n11\n266\nthin-film silicon nitride, using travelling acoustic waves from IDTs on a Mo/AlN top layer. In contrast to prior work on silicon\n267\nnitride, this modulator design does not use optical resonant enhancement, or suspended structures as in other recent work [31].\n269 π\nof ˜9 V is achieved for acousto-optic phase modulation at 704 MHz with 1.1 dB insertion loss.\n271\n273\n275\nin part because the design is primarily based on principles that have already been reported in other recent work,\n276\n278\nconsequence, additional degrees of freedom must be utilized to tractably design phase-controlled spirals. To the best of our\n279\nknowledge, the design, analysis, and experimental results represent the first ever investigation of a non-uniform spacing of\n280\ndozens of waveguides, emphasized in rSI Page 5 Figure 3c, for phase-control. Other spiral designs in literature rely on acoustic-\n281\nwavelengthspacingofthewaveguidesanddedicateddelaylines. Theprimaryinnovationisthatthedelaylinesareimplicitwhen\n282\nthe placement of the waveguides themselves in the acoustic field are taken as degrees of freedom.\n283\n285\n1. Include sentences in the rMT to further highlight the novelty and importance of the waveguide placement (rMT Page 3\n287\n289\nand high RF power for producing phase modulation at a single RF frequency, particularly related to the next point:\n290\n292\nwithin a rectangular footprint of area 20mm2. Combined with the largest transducer of area 2.8mm2, these devices occupy a\n293\ntotalareaofaround23mm2. However, asinglehigh-Qringresonatoronthisplatform(suchasthoseusedfortheaccelerometer,\n294\nwith a 5mm diameter) occupies a circular area of 19.6mm2. If we utilize the same “minimally sized rectangular footprint”\n295\ncriteria we employ for spiral size, this becomes 25mm2. Furthermore, recent work on thin SiN utilizes spiral cavities the size\n296\nof an entire chip to stabilize lasers to [21]. We therefore view the size of the structure quite reasonable as other fundamental\n297\nbuilding block devices on this platform are of similar size or larger. This is a consequence of the large minimum bending radius\n298\non thin SiN platforms.\n301\nan avenue around that. For some of our motivating applications (optical gyroscope), we found watt-scale RF power to be an\n302\nacceptable cost to bring the modulator on chip. Furthermore, for applications such as PDH locking, utilizing far smaller powers\n303\nis acceptable as a nearly π/2 phase shift is no longer necessary. Our accelerometer demo utilized 0.25W, for example, and this\n304\ncan be reduced even further.\n305\n307\n1. WehaveaddedanewSupplementaryInformationsectiondiscussingreductionofV andconsequentlypower(rSINote3.7).\n308 π\n310\nbroadband in the RF/acoustic sense,\n311\n312\n313\nasrMTFigure2d(oMTFigure2d)quicklydispelsthisnotion. WewilladdalineexplicitlystatingourRFbandwidthtoensure\n314\nthis is clear to readers (rMT Page 3 Lines 183-190).\n315\n317\n1. Explicitly call out our RF bandwidth of 0.57MHz in the main text (rMT Page 3 Lines 183-190).\n318\n320\nfrequency are placed in series, there can be constructive or destructive interference of the modulation index depending on the\n321\nphase delay. The authors explore this in the supplement, and use this to design specific delay lengths between each segment.\n323\naroundacertaintheoreticaldesignwavelength,butIdonotseehowthiscanproducebroadbandoperationover100+nm. Inany\n324\ncase,muchmorenarrowband/continuouswavelengthdatawouldbeneededtobeprovidedtojustifyanyclaimaboutbandwidth.\n325\nof wavelength for the four acoustic modes presented throughout this work. These plots correspond to spiral S2 (largest spiral).\nThere are 1000 equally spaced data points in each subfigure. The RF drive frequency, f , is fixed at the f value denoted\nRF RF\non the plot for the collection of these 1000 data points. The variability on the order of 0.2dB is due to resolution limits of the\nmeasurement setup. e. This plot is analogous to (d) for spiral S6 (second largest spiral). f.-h. The modulation efficiency as a\nfunctionofRFdrivefrequencyforafewopticalwavelengths, λ, forspiralS6. Thefringingpatternremainsvirtuallyunchanged,\nexcept for a slight shift downwards in accordance with (e) with increased wavelength, allowing for a fixed frequency RF drive\ntone to modulate all wavelengths simultaneously.\nAuthor: We have provided rSI Page 24 Figure 10, copied into this response as RR Figure 2, that includes a finer optical sweep\n327\ndemonstrating broad optical bandwidth in accordance with the criteria outlined by the Reviewer. Additionally, it has been\n328\nincorporated into rMT Figure 4. In this Figure, broadband plots corresponding to multiple modes and the two largest spiral\n329\ndevicescanbefound. Itcanbeseenthatthe3dBbandwidthextendsevenbeyondthe90nmrangewearecapableofmeasuring\n330\nwith our laser. A variation in modulation efficiency with wavelength on the order we observe is typical for broadband phase\n331\nmodulators [18]. Additionally, we provide measurements of the fringing pattern for a few wavelengths to dissuade any notion\n332\nthat these devices need to be tuned to operate at a certain wavelength.\n333\n335\n1. Provided new fine wavelength sweeps to experimentally verify broadband operation (rSI Page 24 Figure 10). New data\n336\nalso included into rMT Figure 4.\n337\n13\n2. Added a new Supplementary Information section, rSI Note 6.1, to accompany rSI Page 24 Figure 10.\n338\n3. Update the figure-of-merit table (rSI Page 22 Table 3) to include the new data taken in response to this review.\n339\n341\nlengths is possible without post-fabrication trimming, due to variations in waveguide width and film stress and thickness across\n342\nthewafer. However, perhapsgiventheweakconfinementofthinsiliconnitridewaveguidesandtheuseofafoundryprocess, this\n343\nis possible in principle.\n344\n346\nofthewaveguidelayersafterleavingfoundry. Tothebestofourknowledge, everyspiralonthe8”waferleavingthefoundrycan\n347\ncorrectly function without modification.\n348\n350\nwavelength bands due to material and waveguide dispersion. This is understood from basic modulator theory. If you have two\n351\nmodulators in series so that there is a phase difference theta between them:\n352\nϕ(t)=βcos(ωt)+βcos(ωt+θ) (1)\nthen this can be rewritten as\n353\nϕ(t)=2βcos(θ/2)cos(ωt+θ/2). (2)\nIf the phase theta is π between the two modulation segments, then the modulation cancels. So, we want to keep theta to a\n354\nmultiple of 2π. This can be achieved, but it cannot be entirely “broadband” unless phi doesn’t vary as a function of wavelength.\n356 g\nover tens of cm.\n357\n359\nΩ n\n∆k = m g (3)\nc\n0\nwhereΩ istheradialmodulationfrequency,n isthegroupindex,andc thespeedoflightinvacuum. Thiscanbecorroborated\n360 m g 0\nby viewing Equation 3 in [22]. We now adopt the notation of Reviewer 3 to argue that our devices result in virtually identical\n361\nϕ(t) across theclaimedbandwidth. The phase difference θ, can beexpressedin terms of the phase-mismatch ∆k per unit length\n362\nand the separation length between the modulated segments, D (we used D here to be consistent with notation in the original\n364\nΩ n\nθ =∆k·D = m g ·D (4)\nc\n365 m\nθ =2.56·n . (5)\ng\nWe can see that a few percentage change in n will lead to a correspondingly small change in θ. rSI Page 9 Figure 4c details\n366 g\nthis result simulated with a coupled amplitude model factoring in all the path lengths in the real spiral geometry for the C =38\n367\nmodulated segment device (spiral S2).\n369\nthe group delay. The device equivalently can be viewed to operate off of a velocity matching principle where the group velocity\n370\nof the light is matched to the phase velocity of the acoustic wave. Utilizing a toy model of two phase modulators in series, as\n371\nproposed by Reviewer 3, the group delay, ∆t(λ), at 1500nm and 1600nm from modulator 1 to modulator 2 over a separation\n372\nlength D only varies by\n∆t(1500nm)−∆t(1600nm)=(n (1500nm)−n (1600nm)) ≈O(10−2)·1ns. (6)\ng g c\n374\nperiod. The group index, n , is the appropriate quantity here as it is the relevant parameter characterizing the phase of the\n375 g\ncarrier to its sidebands.\n376\noptical bandwidth for which all segments in a spiral of length D will constructively contribute.\nWe now provide an estimate of the phase-matched optical bandwidth by considering the wavelength-dependent group index\n377\nof the fundamental TE mode plotted in RR Figure 3a. To do so, we assume we have two modulators separated by a distance D.\n379\nwavelength λ , the spirals are designed such that\n0 380\n∆k(λ )·D =2πn (7)\n0\nwhere n is an integer. Substituting the expression for phase-mismatch,\n381\nΩ D\nm ·n (λ )=2πn. (8)\nc g 0\n± 0 ± 382\nΩ D π\nm |n (λ )−n (λ )|= . (9)\nc g ± g 0 2\n+ − 383\nspirals fabricated in this work, the phase-matched optical bandwidth is so large (>100nm) that other effects will dominate the\n384\noverall optical bandwidth (such as variation in the acousto-optic overlap as a function of wavelength). Even for spirals that are\n385\n40× longer than what is realized in this work, phase-matched optical bandwidth will still be on the order of 100nm.\n386\n388\n1. A new Supplementary Information section (rSI Note 3.4) has been added that captures the theory details based on this\n389\nresponse.\n390\n2. RR Figure 3 has been incorporated into the rSI (rSI Page 11 Figure 5).\n391\n393\nwith random phases between each segment, it should be possible to find “good” wavelengths where most of the interference is\n394\nconstructive. Conversely, there are “bad” wavelengths where most of the interference is destructive. This is already reported\n395\nin detail in many papers, e.g. [33] and [37]. Another way of thinking about it is that, from the standpoint of light waves,\n396\nexperiencing many discrete modulation segments in series is not temporally very different from experiencing modulation at a\n397\ndiscrete point in a resonator that it traverses numerous times, except that phase-matching is more perfectly achieved for the\n398\nlatter via the resonance condition.\n399\n401\ntail bandwidth limitations. However, these concerns arise for interband scattering. Our devices are intraband. This does not\n402\napply for our devices.\n403\n405\n2g, which shows modulation data at a series of coarse, discrete points across 100 nm. The same plot could be constructed from\n406\n15\nmeasurements of modulation in a resonator, as long as the laser was tuned to the resonant frequencies (equivalent to “good\n407\nwavelengths” mentioned above). So in that sense the resonator approach would also seem to meet the authors’ criterion for\n408\n“broadband.”\n410\ncontradicts this assessment, then the results of this paper are all a bit hard to interpret–since V is going to vary as a function\n411 π\nof wavelength, and the result of 9 V may occur only at certain magic wavelengths. I do think that the device may be able to\n412\nachieve “broadband” operation over smaller continuous bands, but I believe that it cannot be continuously broadband over the\n413\n100 nm band shown in Fig. 2e given the design parameters.\n414\n416\nfollowing experimental procedure was followed for their collection:\n417\n1. Scan RF frequency across a ˜10-20MHz range to find the optimal drive frequency for a given mode. This procedure is\n418\nonly carried out once during this experiment. For example, in oMT Figure 2g, this optimal value is was reported as\n419\nf =467.15MHz and used for all points collected in oMT Figure 2g. Drive the device at this f .\n2. Tune the laser to the shortest wavelength reported (1510 nm). Measure the modulation efficiency. These wavelengths are\n421\nselectedarbitrarilybyjustlinearlyspacingoutpointswithinthedesiredsweeprange(1000datapointsovera90nmrange,\n422\nwith spacing of 90pm).\n423\n3. Tune the laser to the next point. Measure modulation efficiency. Repeat until all wavelengths have been measured.\n425\ntuned in any way, we view many of the experiments presented in the original manuscript to be impossible without true optically\n426\nbroadband operation.\n427\n429\n1. Included new experimental data demonstrating optically broadband operation as rMT Figure 4g.\n430\n2. Explicitly discussed the procedure for collecting the optically broadband data in rSI Note 6.1 (rSI Page 24 Lines 482-491)\n431\nto dispel any notion that our devices require tuning.\n432\n434\n1 mm path length will produce a phase difference of 2*pi*(1.4446-1.443)*(1 mm)/(1550 nm) = 6.5 rad over this range. A 25\n435\ncm path length would produce a phase difference of ˜1600rad. Within one operation band, we probably need the phase to vary\n436\nby ˜1rad or less over the bandwidth, so for the 25 cm device that might mean that the actual continuous bandwidth we can\n437\noperate over at once is on the rough order of 1/16 nm. This is certainly more wideband than many resonant devices, but is\n438\nquite narrowband compared to many other AOM demonstrations. The other recent work in [31] does achieve broad bandwidth\n439\nbecause it consists of a single travelling-wave modulator, by comparison.\n440\n442\nin their device of length 2mm is negligible, and therefore they do not need to compensate for it.\n444\n2π(1.4446−1.443)·1mm\n≈6.5rad (10)\n1550nm\ndoes not capture the relevant phase difference required for operation of our devices. The only important optical phase difference\n445\nfor the operation of our devices is between the carrier and sidebands (separated by only a few hundred MHz). Framing this in\n446\nterms of this equation used by Reviewer 3,\n447\n2π(n (ω+Ω )−n (ω)) ω(n (ω+Ω )−n (ω))\neff m eff ·D = eff m eff ·D (11)\nλ c\n0\n=(k(ω+Ω )−k(ω))·D (12)\nm\n=∆k·D (13)\nΩ n\n= m g ·D (14)\nc\n0\n16\nwecanseethisequationreducestotheearlierexpressionforphase-mismatchthatwedescribedasbeingappropriateforintraband\n448\n(Equation 3).\n450\nsatisfy the optically broadband criteria laid out by Reviewer 3. Consider a series modulator setup similar to that proposed by\n452\n[31]), we can separate this continuous length of modulators into three segments of lengths 0.5mm, 1mm, and 0.5mm. We let β\n453\nbe the total phase modulation imparted by the first and last (0.5mm) segments.\n454\nϕ(t)=βcos(Ω t)+2βcos(Ω t+θ )+βcos(Ω t+θ ) (15)\nm m 12 m 13\nHere, θ is the phase difference between the first and second modulated segments, while θ is the phase difference between the\n12 13 455\nfirst and third modulated segments. We will focus on the terms for the first and third modulated segments, whose midpoints\n456\nare separated by 1.5mm. Therefore if we use (the incorrect) Equation 10 to calculate phase-mismatch θ between the first and\n13 457\nlast segments across a 100nm bandwidth centered at the 730nm operation wavelength of [13], we would find\n458\n(wrong) 2π(2.0341−2.0255)·1.5mm\nθ = ≈111rad. (16)\n13 730nm\nSince [13] utilizes thick SiN waveguides, we have used the refractive index of SiN in the equation immediately above. Therefore,\n459\nϕ(t) can be re-written as\n460\nϕ(t)=2βcos(θ /2)cos(Ω t+θ /2)+2βcos(Ω t+θ ). (17)\n13 m 13 m 12\nThus, if Equation 10 was used to calculate the phase difference, the devices cited as optically broadband would also fail to meet\n461\nthe definition of Reviewer 3 when examining the series modulator model. In our case and in [13], Equation 3 must be used.\n462\n464\nwork, but in any case, the characterization of device performance as a function of wavelength is currently inadequate to support\n465\nany claims of bandwidth at all.\n467\nbeen fully thought through. It does not mean that the results are not interesting, but if it is difficult to produce a device for\n468\noperation at a specific wavelength without extensive trial and error, then the results may not be too practical.\n469\n471\nviewer3mirrortheauthors’owninternaldiscussionswhenconsideringwhetherornotthesedeviceswouldwarrantaverycostly\n472\nand time consuming fabrication run at a commercial foundry.\n474\nand rSI Page 9 Figure 4. That is, the devices from the first foundry run produced all data found in this manuscript, and we\n475\nobserved no evidence indicating deviation from expected performance.\n477\nintheeventthatthisfactoredintothispointintheReviewer’scomment. Thisissimplyanartifactofourchip-scaleprototyping\n478\nof transducers. As the aluminum layer is defined through a liftoff process, chip scale processing can often lead to deposition\n479\nor re-deposition of metal that by chance damages/blocks the edge couplers we use on our spirals. This has nothing to do with\n480\nprocess variations in the actual spirals themselves. This would be wholly eliminated by wafer level processing of the transducers\n481\n— but naturally this is inefficient for iterating to optimize the transducers.\n482\n484\native sentences, without relationships or connections explained between them. Numerous sentences in a row start with ”The”\n485\nat several points in the paper, and some statements seem like non sequiturs.\n486\n488\nditionally, we have combed the text for sentences that are not closely linked to the experimental data that supports their claim\n489\nand revised them.\n490\n492\n1. Revisit all text in the manuscript, factoring in the language and clarity considerations discussed by the reviewer (this\n493\nmotivated some restructuring of some portions of the manuscript, see RR Section 5).\n494\n17\n2. Revisit all claims made in the manuscript, checking for non-sequiturs.\n495\n3. Checked the text for multiple sentences in a row starting with “the”, and revised. Some cases are listed here: rMT Page\n496\n497\nbandwidth — it now avoids multiple “the“’s (rMT Page 3 Lines 208-211).\n498\n4. Linked the multiplicative increase in modulation index to underlying theoretical calculations (rMT Page 3 Lines 126-131).\n499\n501\nhard work went into it. I just do not think the experimental data presented justify all of the claims made, particularly based\n502\non prior literature, and that a more detailed experimental investigation is warranted. I would love to be proven wrong, but I’m\n503\nworried that the data presented do not tell the full story.\n504\n506\nof our modulator within the Main Text and Supplementary Information.\n507\n509\nthe data in Fig. 2f, instead of a random linear fit. In addition, the phrase “Indeed, the linear trend does continue with the\n510\nexperimentally collected data in Figure 2f” does not really mean anything. A linear increase does not “validate” the design\n511\nmethodology. A linear fit can have a slope of zero. Basically any curve is linear if you zoom in enough. A linear fit where 10\n512\nsegments has 10x the modulation index of 1 segment, and where 30 segments have 30x the modulation index of 1 segment and\n513\n3x the modulation index of 10 segments, would validate the design methodology. Anything else is a false conclusion.\n514\n516\nmodulation index multiplicatively increases with modulated segment count” is more appropriate. “Multiplicatively” is intended\n517\nto convey behavior obeying β =β C, while “increase“ conveys that the modulation index of a single segment, β , is nonzero.\n518 0 0\n520\n1. Updated rMT Figure 2g to utilize the theory model as a fit, rather than a linear model.\n521\n2. Updated the caption of rMT Figure 2g to use this more accurate language.\n522\n3. Updated sentences in the main text that fall under this comment (rMT Page 3 Line 129, rMT Page 3 Lines 194-205, rMT\n524\n526\ntheory or the text, or cited with references to the supplement or whatever, besides the reference for “coherence length” which is\n527\na bit of an interesting definition and might merit a bit more description to the reader in terms of what it actually means for this\n528\nstudy.\n529\n531\ndescribesthespiraloperationwithananalogytoquasi-phase-matching, motivatingthecoherencelengthdefinition. IntherMT,\n532\nwenowusethisanalogyastheprimarywaytoexplainthedeviceoperationaswell(rMTPage3Lines134-164). rMTFigure1f,g\n533\nhave also been changed to plots that draw this analogy. We have removed Equations 5 and 6 — definitions such as this can still\n534\nbe found in the Supplementary Information, however.\n535\n537\n1. Motivated the coherence length discussion (rMT Page 3 Lines 134-164) with a new Supplementary Information section\n538\n(rSI Note 3.6) drawing analogy to quasi-phase-matching.\n539\n2. Replaced oMT Figure 1f,g with rMT Figure 1f,g which better communicate the spiral function.\n540\n18\n3. Removed Equations 5 and 6 (definition of modulation index, modulation efficiency, relationship to the Bessel functions).\n541\n544\n546\nmatching by driving down parasitic resistance and capacitance, in turn allowing for larger aperture transducers.”\n547\n549\n1. Revised the sentence pointed out by the reviewer (rMT Page 4 Lines 255-258).\n550\n553\nin great detail. The arc length calculation for the bends is neat, but depending on fabrication tolerances it may not be required\n554\nat that precision.\n555\n557\ntionofacousticallymediatedRabioscillations[24](oSIreference[5])asaworkthatcanberegardedasthe“closest”toourown.\n559\n1. The spirals do not “spiral out” — light must be accessed using grating couplers and leaves vertically from the chip in the\n560\ncenter of the spiral. This is impractical for mass produced PICs as one port of the spiral is only accessible from the top\n561\nof the chip. However, this may be acceptable for some applications, particularly within AMO physics where atoms can be\n562\naddressed via vertical couplers [25, 26].\n563\n2. The structure is released and part of a phononic crystal. This is perfectly fine for highly confining Si waveguides, but\n564\nobviously cannot be translated to thin SiN.\n565\n3. TheSIdetailsdesignofdelaylinesanddiscussesthetransfermatrixmethodbeingusedtomodelthedevice. Itultimately\n566\nis not clear the structure of their delay lines or how they are designed, but we view our own geometry as a substantial\n567\nadvance over current literature. All methods we are aware of to design spiral-multi-pass AOMs in literature prior to our\n568\nmanuscript become intractable when more than a few passes are required. Our SI details design of multi-pass AOMs with\n569\neffectivelyanarbitrarymodulatedsegmentcount—afirstthatenablesustodirectlytradeoffinsertionlossandareawith\n570\nmodulation strength to bring optically broadband AOMs to thin SiN.\n571\n4. Previous devices do not explore waveguide placement in a traveling acoustic field as the primary degree of freedom used\n572\nto design spiral multi-pass AOMs — they are typically spaced at integer multiples of acoustic wavelength. To the best of\n573\nour knowledge, we are the first manuscript that has explored this as our devices are sufficiently long to warrant it.\n574\n5. Previous devices use multiple (sometimes several) transducers to drive the spirals.\n576\nof the coherence length in the main text to help gauge when our methods are necessary. In rSI Page 5 Figure 3c, we provide\n577\nmeasurements of the separation between adjacent waveguides in a laid-out device (spiral S2) to illustrate this. The numbers\n578\nmeasuredinthisfigurefollownoclearpatternandcannotbeguessed—theymustbecalculatedusingthemethodologyoutlined\n579\nin rSI Note 3. Improperly designed devices were explored in rSI Note 3.3 and rSI Page 9 Figure 4b.\n580\n582\nrecovering the foundry loss [56],” what does recovering mean? I thought losses were dominated by the Mo metal layer? Do you\n583\nmean that the Mo and AlN could be deposited only in specific areas via a mask or liftoff, and that would make the insertion\n584\nlosses lower, similar to the best foundry values? I wonder if that might be a bit more feasible than removing it if it’s already on\n585\ntop of the oxide clad.\n586\n19\n588\nbe removed above the waveguide — not just the AlN.\n591\noriginate from ultraviolet exposure from plasma etch processes leading to long-lived excited states [4]. In future studies, one\n592\ncould attempt to revert the losses back to their foundry values, possibly through an anneal step following the removal. In doing\n593\nso, the AlN and Mo can be removed above the waveguides via alternative transducer designs (e.g., [27]). Improved devices may\n594\nthen have insertion losses that are improved by a factor of ˜16 as optical propagation losses could return to 0.25dBm−1 from\n595\n4.31dBm−1.\n597\nand optimization, this may in principle be possible. However, our commercial vendor cannot guarantee quality of the AlN film\n598\nwhen the deposition surface is not of uniform height.\n599\n601\n1. Corrected the sentence noted by the reviewer to refer to both AlN and Mo. Further revised to clarify the proposed\n602\nimprovement (rMT Page 7 Lines 347-354).\n603\n605\nexamining the slope of modulation efficiency for the 1st and 2nd order sidebands in response to an RF power sweep, shown in\n607\ndo not say anything at all about the interaction being acousto-optic. Those power laws are the same for all linear sinusoidal\n608\nmodulation in all systems. It suggests that you are seeing phase modulation as expected. Saying the sidebands scale with 1x\n609\nand 2x the power in dBm is true, but it’s probably more correct to say that the first and second sideband powers scale linearly\n610\nand quadratically with the applied RF power, in accordance with the expected trend (from the Jacobi–Anger Bessel expansion).\n611\n613\n615\n1. Updated the caption of rMT Figure 2h to “...following the expected trend for phase-modulation.”\n616\n2. Updated the manuscript text in accordance with the suggestion made by the reviewer (rMT Page 3 Lines 205-211).\n617\n619\nit’s specifically interference between the modulation in the different segments that creates the peaks and nulls, I believe?\n620\n622\n624\n1. One instance of “coherent modulation” was removed as a result of other edits.\n625\n2. Rephrased rMT Page 3 Lines 183-189.\n626\n3. rMT Figure 1e was rephrased.\n627\n630\npassive waveguides. In any case, subject-verb agreement would dictate “photonics are.” The phrase “They are cored down” I\n631\nassume is of course referring to the processed wafers, but based on the sentence structure it would be referring to the photonics\n632\n20\nthemselves, not the wafers, when the wafers are what are being cut down. It would also be helpful to readers to mention which\n633\nfoundry process if that’s not proprietary.\n634\n636\nis now located at rMT Page 2 Lines 81-85 and revised in accordance with this comment. Unfortunately, we cannot disclose the\n637\nfoundry process used.\n638\n640\n1. Revised the manuscript in accordance with this comment (rMT Page 2 Lines 81-85, rMT Page 2 Line 65, rMT Page 5\n642\n644\narea.” Interjecting the foundry process here again makes it sound like that is the part that increases the interaction length. We\n645\nalready know it is from a foundry process since that was mentioned in the prior paragraph. If it is to be included, that phrase\n646\nshould be between commas here. Later in this paragraph you refer to this approach as “novel,” which I am not sure is so true\n647\nany there are several works that have introduced similar multi-pass designs.\n648\n650\non novelty, please see our response to earlier comments.\n651\n653\n1. Removed the text that is pointed out by the reviewer.\n654\n21\n656\nclarity and conciseness. For example, Reviewer 3 requested general edits to the manuscript to revise stiff language and improve\n657\nlogical flow (RR Page 17 Line 484). In doing this, certain structural changes have been made to the manuscript. Additionally,\n659\nto develop an analogy to quasi-phase-matching that is far superior to what was originally present in the oMT. Edits like these\n660\nare difficult to track using line numbers alone, as they either involve structural changes to the manuscript or subtle phrasing\n661\nimprovements that do not alter the ideas or results presented in the oMT.\n663\nwith numbers, while sub-ideas/results within that paragraph are labeled with letters. Note that no subtractive changes in\n664\nregard to the results or claims of the manuscript have been made. New material has, however, been added in\n665\nresponse to the Reviewers. The changes made are explained and referenced back to a reviewer question via Roman numeral\n666\nsuperscripts.\n667\nIntroduction Introduction\n1. Motivating SiN modulators 1. Motivating SiN modulators\na. Current applications of SiN a. Current applications of SiN\nb. No general purpose modulators on thin SiN b. No general purpose modulators on thin SiN\nc. New applications enabled by thin SiN modulators c. New applications enabled by thin SiN modulators\n2. Published acousto-optic modulation strategies in inte- 2. Published acousto-optic modulation strategies in SiNI\ngrated photonics integrated photonics\na. Optically and/or mechanically resonant devices a. Optically and/or mechanically resonant devices\nb. Brief mention of techniques used on SOI waveguides b. Current techniques do not transfer to thin SiN\nc. Current techniques do not transfer to thin SiN I\n3. Surveyofastrategycommonlyfoundonotherplatforms\n(e.g., Si waveguides with moving boundary)\n4. Difficulties with modulating thin SiN waveguidesII,\n3. Overview of our solution and preview the results overview of our solution and preview of the results\nII\nResult (Device design and theory) Result (Spiral design)\n1. Challenges arising in modulating thin SiNII\na. Weak acousto-optic interactions 668\nb. Current solutions\n2. Basic device layout and fabrication 1. Basic device layout and fabrication\n2. Introduce the basic idea of the spiral design, discuss its\n3. Introduce the basic idea of the spiral design noveltyIII\n2. Draw an analogy to quasi-phase-matching (QPM) to\n4. Discuss the necessity of phase-matching explainIV the necessity of phase-matching\na. Coherence length a. Better motivate theV coherence length\nb. Definition of modulation index and efficiencyVI\nb. Spiral design details framed in terms of the QPM\nanalogyVII\nc. Limitations of other transducer designs and the spe-\nVII\ncific need for traveling acoustic waves, framed in terms of\nthe discussion of coherence length and QPMVII\n5. Spiral design details\n6. Long spirals on low loss platforms overcome challenges\non our thin SiN platformVIII.\n7. Limitations of other transducer designs and the specific VII\nneed for traveling acoustic wavesVII\n673\nto the Introduction.\n677\nsteps in the design (RR Page 3 Line 64).\n679\nalso links in with the revision discussed in IV motivated by a question by Reviewer 1 (RR Page 3 Line 64).\n684\nResult (Validation of sprial design) Result (Acousto-optic modulator)\n1. Description of single metal layer transducer results 1. Description of single metal layer transducer results\na. Explanation of chip layout and rationale behind de- a. Explanation of chip layout and rationale behind de-\nvice splits vice splits\nb. Measure the electrical response of the transducer b. Measure the electrical response of the transducer\nc. Measure optical modulation efficiency, explain mea- IX 2. Measureopticalmodulationefficiency,explainmeasured\nsured fringes fringes\ni. RF bandwidth a. RF bandwidth\nii. Low acoustic losses b. Low acoustic losses\nd. Measure several spirals and verify linear relationship X 3. Measure several spirals and verify a multiplicative in-\nbetween modulation index and segment count crease between modulation index and segment count\n2. MeasureandconfirmadditionalmodulationpropertiesX a. Sidebands indicate phase modulation\nX\na. Devices are optically broadbandX\nb. Sidebands indicate phase modulationX\nResult (Examination of higher-order acoustic\nmodes) Result (Higher order acoustic modes)\n685\n1. Confirm the presence of higher order acoustic modes 1. Confirm the presence of higher order acoustic modes\nand note the strongest performing mode and note the strongest performing mode\n2. Examine the phase-matching physics via the higher or- 2. Examine the phase-matching physics via the higher or-\nX\nder modes der modes\nResult (Optimization of electromechanical Result (Optimization of electromechanical\nimpedance match) impedance match)\n1. Motivate and explain mm-scale MEMS transducers for 1. Motivate and explain mm-scale MEMS transducers for\nacousto-optics acousto-optics\n2. Measure the new transducers 2. Measure the new transducers\n3. Reach a modulation index of π/2 3. Reach a modulation index of π/2\n4. Devices are optically broadband\nResult (Use of modulators in an optomechanical Result (Use of modulators in an optomechanical\nsensing system) sensing system)\n1. Experimental details and results, future\nwork/motivation for a fully integrated optomechani- XI\ncal accelerometer 1. Experimental details and results\n2. Future work/motivation for a fully integrated optome-\nchanical accelerometer\n687\n(RR Page 12 Line 310).\n691\nplaced in a later result subsection. We restructured the resulting sentences to avoid stiff language (Reviewer 3, RR Page 17\n694\n24\n695\n1. Revised the MT and SI for clarity, keeping in mind reviewer comments.\n696\n2. Added discussion of V Lα for our multi-pass devices (rSI Page 23 Lines 469-476). V Lα is a figure of merit given in a\nπ π 697\ncomparison table (rMT Table 1) requested by Reviewer 2 (RR Page 7 Line 162) and warrants definition for multi-pass\n698\ndevices.\n699\n3. Referenced all Supplementary Notes from in the Main Text in accordance with the Nature Communications manuscript\n700\nchecklist. Changed the order of the Supplementary Information sections to appear in the order they are referenced in the\n702\n4. Renamed rSI Note 6 from “Complete characterization of thick bus bar devices” to “Extended experiments on thick trans-\n703\nducerdevices”aswehaveaddednewexperimentaldatainresponsetoReviewerquestions(RRPage13Line320,RRPage\n704\n705\n5. The optically broadband data originally raising concern from Reviewer 3 (RR Page 13 Line 320, RR Page 15 Line 405,\n707\nmain text as part of rMT Figure 4 instead. The original single-metal layer transducers are damaged and cannot be used\n708\nto replace oMT Figure 2g with a finer wavelength sweep. Therefore, we now report the optically broadband data as part\n709\nof rMT Figure 4 (the figure dedicated to the thick bus bar devices).\n710\n6. oMT Figure 2 has further been changed in response to the removal of oMT Figure 2g. The spiral sizes (oMT Figure 2e)\n711\nhas been expanded to two panels (rMT Figure 2e,f). oMT Figure 2f (modulation index vs. modulated segments) has been\n712\nmoved to rMT Figure 2g. Captions have been updated. These changes were made as a result of comments by Reviewer 3\n713\n(RR Page 13 Line 320, RR Page 15 Line 405, RR Page 17 Line 464).\n714\n7. Updated formatting of units in rMT Figure 5f to comply with the Nature Communications manuscript checklist.\n715\n8. The term “modulation depth” was used in some locations (rSI Page 25 Figure 11, rSI Note 6). It has been changed to\n716\n“modulation index”.\n717\n9. Edited the references list to comply with the Nature Communications manuscript checklist. Updated preprint references\n718\nto the corresponding journal article if the cited work has been published.\n719\n720\n1. Boyd, R. W. Nonlinear Optics Fourth edition (2020).\n721\n2. Werner, W. S. M., Glantschnig, K. & Ambrosch-Draxl, C. Optical Constants and Inelastic Electron-Scattering Data for 17\n723\n3. AMS — PVD System https://www.amssb.com/views/products/pvd-prod.html.\n724\n4. Guo, J. et al. Investigation of Q Degradation in Low-Loss Si N from Heterogeneous Laser Integration. Optics Letters 49,\n725 3 4\n4613–4616 (2024).\n726\n5. Tian, H. et al. Hybrid Integrated Photonics Using Bulk Acoustic Resonators. Nature Communications 11, 3073 (2020).\n727\n6. Kamohara, T., Akiyama, M. & Kuwano, N. Influence of Molybdenum Bottom Electrodes on Crystal Growth of Aluminum\n729\n7. Churaev, M. et al. A Heterogeneously Integrated Lithium Niobate-on-Silicon Nitride Photonic Platform. Nature Commu-\n730\nnications 14, 3499 (2023).\n731\n8. Rahman,M.A.et al.High-PerformanceHybridLithiumNiobateElectro-opticModulatorsIntegratedwithLow-lossSilicon\n733\n9. Ghosh,S.,Yegnanarayanan,S.&Ricci,M.Acousto-Optic Modulation in Lithium Niobate on Silicon Nitride Heterogeneous\n735\n10. Lihachev, G. et al. Low-Noise Frequency-Agile Photonic Integrated Lasers for Coherent Ranging. Nature Communications\n736\n13, 3522 (2022).\n737\n11. Erdil, M. et al. Wideband, Efficient AlScN-Si Acousto-Optic Modulator Integrated on a Commercially Available Silicon\n739\n12. Hosseini, N. et al. Stress-Optic Modulator in TriPleX Platform Using a Piezoelectric Lead Zirconate Titanate (PZT) Thin\n741\n13. Freedman, J. M. et al. Gigahertz-Frequency, Acousto-Optic Phase Modulation of Visible Light in a CMOS-Fabricated\n743\n14. Jin, W., Polcawich, R. G., Morton, P. A. & Bowers, J. E. Piezoelectrically Tuned Silicon Nitride Ring Resonator. Optics\n745\n15. Wang, J., Liu, K., Harrington, M. W., Rudy, R. Q. & Blumenthal, D. J. Silicon Nitride Stress-Optic Microresonator\n747\n16. Dong,M.et al.High-SpeedProgrammablePhotonicCircuitsinaCryogenicallyCompatible,Visible–near-Infrared200Mm\n749\n17. Xu, M. et al. High-Performance Coherent Optical Modulators Based on Thin-Film Lithium Niobate Platform. Nature\n751\n18. Renaud, D. et al. Sub-1 Volt and High-Bandwidth Visible to near-Infrared Electro-Optic Modulators. Nature Communica-\n752\ntions 14, 1496 (2023).\n753\n19. Wang, C. et al. Lithium Tantalate Photonic Integrated Circuits for Volume Manufacturing. Nature 629, 784–790 (2024).\n754\n20. Rahim, A. et al. Taking Silicon Photonics Modulators to a Higher Performance Level: State-of-the-Art and a Review of\n756\n21. Heim,D.A.S.,Bose,D.,Liu,K.,Isichenko,A.&Blumenthal,D.J.HybridIntegratedUltra-LowLinewidthCoilStabilized\n758\n22. Kittlaus, E. A. et al. Electrically Driven Acousto-Optics and Broadband Non-Reciprocity in Silicon Photonics. Nature\n760\n23. Cheng, H. et al. A Terahertz-Bandwidth Non-Magnetic Isolator. Nature Photonics 19, 533–539 (2025).\n761\n24. Zhou, Y. et al. Nonreciprocal Dissipation Engineering via Strong Coupling with a Continuum of Modes. Physical Review\n763\n25. Isichenko,A.et al.PhotonicIntegratedBeamDeliveryforaRubidium3DMagneto-OpticalTrap.Nature Communications\n764\n14, 3080 (2023).\n765\n26. Blumenthal, D. J., Isichenko, A. & Chauhan, N. Enabling Photonic Integrated 3D Magneto-Optical Traps for Quantum\n767\n27. Plessky, V., Ballandras, S., Grigorievsky, V. & Yantchev, V. 3rd Type of FBARs? in 2013 IEEE International Ultrasonics\n769\n26"}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have revised the manuscript and addressed my comments. My recommendation is to publish the manuscript.", "reviewer_3": "I appreciate the detailed response and additional experimental and technical analysis. I recommend publication."}, "author_response": ""}]

Decision letter