Multiplexed back focal plane imaging with on-chip integrated microlens array

Domain: biology
Published: 2026-04-04
Editorial outcome: minor_revision

Abstract
On-chip optical architectures that enable angle-resolved spectroscopy are essential for advancing photonic platforms towards low-volume, scalable, and cryo-compatible devices. Here, we introduce spatially resolved momentum-space imaging using arrays of 3D-printed microlenses directly integrated onto semiconductor optical microcavities. Each microlens functions as an independent optical element with a high numerical aperture (approx.0.95),enablingparallelbackfocalplaneimagingacross,inourimplementation,64distinctlocations.Thisapproach eliminates the need for bulky microscope objectives while maintaining broad wavevector access, even undercryogenicconditions. Wedemonstrateitsversatilityacrossvariouscavitysystems,includingdielectricplanarresonators,GaAs-basedpolaritonmicrocavities,andCdTeplatformssupportingnonequilibriumBose-Einsteincondensationofexciton-polaritons. ThemicrolensesnotonlyenhancEecollectionefficiencybutalsoenabletightlyfocusedexcitation,yieldinganorderofmagnitudereductionincondensationthresholdscomparedwithconventional setups. Our results establish 3D-printed microlens arrays as a compact, versatile, integrated platform for next-generationangle-resolvedspectroscopyinnanophotonicsPandquantummaterials.

Introduction
Back focal plane (BFP) imaging, also referred to as reciprocalspace,k-space,orFourierplaneimaging,isa widelyusedexperimentaltechniquethatmLapstheangular distribution of light emitted or transmitted by a sample.Inmanyopticalandphotonicsystems,thisangle is directly linked to the in-planewavevector (momentum)oflightorquasiparticleTexcitations.

As such, momentum-resolved spectroscopy offers direct insights in all subfields of photonics1,2. Yet, accessing momentum-space typically relies on bulky microscope objectives that limit experimental flexibility, especially under cryogenic conditions or in scalable device geometries. On-chip optical elements offer a pathway toward compact and integrable solutions,wherelightcanbecollected,focused,andmanipulateddirectlyatthedevicelevel. Inparticular,three-dimensionalprintingofmicroopticalcomponentsprovides remarkable freedom to design monolithic architectureswithsite-specificfunctionality.

In nanophotonics and plasmonics, the directionalityoflightpropagationplaysanessentialrole. There, BFP imaging has been adapted to investigate various devicessuchasplasmonicnanowires3,4 ornanoantennas5–7, as well as diverse optical phenomena such as surface-enhancedRamanscattering8,secondandthird harmonicgeneration9,10,cathodoluminescence11,12,and up-conversion13. Thetechniquehasalsoprovenvaluableinthequantumregime14–16, whereitprovidesaccesstotheangularemissioncharacteristicsofquantum emitters.

On the fundamental level, BFP imaging allows to determine the direction of a dipole transition, such as identifying the orientation of single molecules17,18 or carbonnanotubes19.Thesamemethodhasbeenusedto distinguishthein-planeorout-of-planecharacterofexcitonsinlayeredmaterials20,21, theirheterostructures22 andthinorganicfilmsinOLEDs23.Italsoallowstodifferentiate from the most common electric-dipole transitions scarce magnetic-dipole ones, occurring in rare earthscomplexes24orin2Dperovskites25.

In systems such as photonic crystals, nanostructures, metasurfaces, or optical cavities, the wavelength and wavevector of photons are connected, forming intricate energy-momentum dispersion relations. There, momentum-resolved spectroscopy enables the experimental study of a wide range of physical phenomena originating from the specific structure in momentum-space. Thisincludestopologicalstates,suchasbound states in the continuum26,27, topologically protected edgemodes28–30, andphotonicanaloguesofelectronic topological insulators31,32. It also allows exploration of solid-state analogies, including photonic lattices33, Dirac cones34, and Berry curvature-related phenomena35–37. Furthermore, this approach provides access tonon-Hermitianphysics,suchasmanipulationofexceptional points38,39, or optical simulations of exotic physics far from classical optics, such as analogues of blackholehorizons40,41andnewphasesofmatter42.

Conventional approaches to reciprocal space imaging rely on high-magnification, high-numerical-aperture(NA)microscopeobjectivestoaccessabroad angle range, often spanning several tens of degrees. These same objectives are typically used for excitation, as their large NA enables the tight focusing requiredtoachievethehighpowerdensitiesnecessary for reaching nonlinear phenomena. However, these optical elements come with significant limitations. Their short working distances make integration with cryogenicsystemsparticularlychallenging. Moreover, they inherently restrict measurements to a single spatial location at a time, since they integrate angular informationovertheentirecollectionarea. Asaresult, conventionalexcitationanddetectionschemeslackthe capability for spatially multiplexed momentum-space imaging,limitingexperimentalaccesstonon-localphenomena.Thisprecludesstudiesofspatiallydistributed momentum-space dynamics and related phenomena suchasJosephsonoscillations,site-to-sitecouplings,or momentum-dependent particle population, flow, and thermalization.

Here,wepresentaphotonicapproachbasedonellipsoidalmicrolensesdirectlyprintedontopofopticalmicrocavities, replacingtheconventionalmicroscopeobjectiveinboththeexcitationanddetectionpaths. This allows for simultaneous momentum-space imaging of multiple (up to 64) spatial positions, each with access to large emission angles (up to 72 degrees in air, NA = 0.95), all while eliminating the need for bulky microscope objectives. The high NA of microlenses also provides tight focusing of the excitation beam, which significantly reduces the threshold of polariton Bose-Einsteincondensationbynearlyanorderofmagnitude compared to conventional microscope objective excitation. The versatility and robustness of printed microlensesisdemonstratedinbothpurelyphotonicand exciton-polaritonopticalmicrocavities.

Results
The light ray paths in the traditional configuration with an optical microscope and presented here microlenses are shown in Figs. 1a,b, respectively. In the microscopic configuration (Fig. 1a), the collection of a highemissionanglesislimitedbythegeometryofthe objective, its NA and working distance. On the other hand,amicrolens(Fig.1b)locateddirectlyonthesurfaceofthesample,thankstoitssolidimmersionproperties,allowsformoreeffectivelightharvesting,especially at high emission angles, which correspond to a higherNA.

Polymer,micrometer-sizedlenseshavCealreadybeen usedforefficientobjective-freelightcollection43. However, thatdesignoptimizedforemittedbeamcollimation results in a highly distorted Fourier plane, hinderingmomentum-resolvedimaging. Here,wedevelopedray-tracingsimulations[seeSupplementaryInformation(SI),sectionRayTracing]todesignamicrolens withoptimizedshapesofthebackfocalplane.Thegoal wastomaximizetheangleoflightcollection(targeting anumericalapertureofuptoNA ≈0.95)whilemaintaininghighfidelityoftheFourierplanebyminimizing opticalaberrationsanddistortions. Inaddition,thegeometry of the microlenses was optimized to precisely matchthestructureofeachsample.

Theellipsoidalmicrolenseswerefabricatedbytwo-photon polymerization lithography (for more details, seeMethods,sectionTwo-photonLithography). Their final dimensions, namely the vertical half-axis a, the horizontalhalf-axisb,andthecuttingpositiondalong the z-axis, are provided for each structure in Supplementary Table I of the SI. The Fourier plane corresponding to each microlens is located approximately 10–15 µm above the top of the microlens. An optical setupallowingimagingofthisFourierplaneprojected bythemicrolensandperformingmomentum-resolved measurementsispresentedinFig.1aanddescribedin moredetailinFig.S5binSI.Thisconfigurationisanalogoustoaconventionalmicroscope,whereamicroscope objective and an imaging (tube) lens project a magnifiedimageoftheFourierplaneofthemicrolensontoa cameraortheentranceslitofaspectrometer.

However, the use of microlenses provides an additional advantage. In a conventional k-space imaging setup,accesstotheFourierplaneislimitedtoasingle spatialpositionatatimeandtolightraysthathavenot diverged significantly before entering the microscope objective. Incontrast,ourapproachreplacestheobjectivewithmicrolensesdirectlyfabricatedonthesample surface,whichlocallycollimatetheemittedlight.Thus, each microlens acts as an independent miniature opticalsystem, enablingparallelmomentum-spacemapping across a spatially multiplexed array of emission sites,asshowninFig.1c.

To demonstrate this use case, we fabricated a latticeofellipsoidalmicrolensesarrangedinaregular8×8 squarearraywithacenter-to-centerspacingof20µm, providingsufficientspatialseparationtopreventopticalcross-talkbetweenneighboringelements,whileallowing simultaneous acquisition of k-space information from all microlens positions. A representative scanning electron microscope image of the fabricated arrayisshowninFig.1d.

Asanillustrationoftheversatilityofourapproach, we applied those structures to three distinct types of opticalmicrocavitysystems: (SampleA)apurelyphotonicSiO /TiO microcavityoperatingatroomtemperature; (SamplSe B) a GaAs-based microcavity, operatingatcryogenictemperaturesinthestronglight-matter couplingregimeandcharacterizedwithhomogeneous photonic potential; and (Sample C) a CdTe-based microcavityexhibitingnonequilibriumBose-Einsteincondensationwithinintrinsicphotonicpotentialtraps. As a consequence of strong coupling, exciton polaritons, mixed light–matter quasiparticles, are formed. They are characterized by two distinct dispersion branches (upper and lower polaritons), whose curvature dependsontherdetuningbetweenthephotonicmodeand the exciton in the quantum well. Under strong and tightly focused excitation, these quasiparticles enable thestudyofnonlinearinteractionsabovethethreshold foraphasetransitiontoaBose-Einsteincondensate.

We first characterized the optical signal collected throughasinglemicrolensatroomtemperatureusing SampleA,whichconsistsofasimpleandwell-defined dielectric stack supporting a single photonic cavity mode(seeMethods,sectionSamples,forstructuraldetails).Todemonstratethebroadangle(wavevector)collection capability of our approach, Figs. 1e–g present acomparisonbetweenmomentum-resolvedreflectivity spectraobtainedbysimulationandexperiment.Specif- ically,Fig.1eshowsthetheoreticallycalculateddispersion using the Berreman method44,45, while Figs. 1f,g show experimental spectra measured using a planar cavityinsetupshowninFig.1aandwithasinglemicrolensandmicroscopeobjective50×asaBertrandlens in setup Fig. 1b, respectively. Although the illuminationspotislargerthantheprintedarea,onlylightcollected and collimated by the microlens forms a well-definedlocalFourierimage,withangularfilteringprovidedbytheBertrandlens. ThisFourierimageisspatially separated from light originating outside the microlens,whichiscollectedonlyasareal-spacesignalby themicroscopeobjective.Forclarity,thedatainFig.1g arecroppedtodisplaythesignaloriginatingfromasin- glemicrolensonly.

Inallthreecases,theparabolicdispersionofthecavity mode is clearly observed. In Fig. 1e, dashed lines markthewavevectorrangescorrespondingtothenumericalaperturesofNA=0.55andNA=0.95,which correspondwelltothewavevectorrangesobservedexperimentallyinFigs.1f,g,respectively. Toavoidspectralstitching,thedatainFig.1gwerecollectedusinga lower-resolutiongrating,which,togetherwiththephotonic response of the cavity to the printed microlens, resultsinasmallincreaseofphotonicmodelinewidth. A comparison of linewidths for the two experimental configurationsmeasuredwithcomparablespectralresolutionisprovidedinSectionVI(MicrolensesOptical Performance),subsectionVI.DoftheSI.

Tovalidatethewavevectorrangeintheexperimental data, the cavity mode dispersion was extracted by Lorentzian fitting to the resonance energies and compared to the simulated dispersion (see Fig. 1h). Theseresultsconfirmthatthemicrolensnotonlyserves as a light collection element but also provides access to a significantly broader wavevector range, reaching NA ≈ 0.95. Additional discussion of the polarization performanceofthemicrolensescanbefoundintheSI, SubsectionVI.E.

Although under ambient conditions, high-NA microscope objectives offer similar performance to microlens, they become impractical for use in cryogenic experiments. This limitation is particularly relevant for studies of semiconductor-based polaritonic microcavities,whereexperimentsaretypicallyperformedat low temperatures using closed-cycle or liquid helium cryostats. In contrast, microlenses can be directly integrated into the cryogenic environment and cooled along with the sample. This approach enables broad wavevector-range momentum-space imaging at cryogenic temperatures,withoutrelyingonbulky,high-NA microscopeobjectivesinthedetectionpath.

Figure 2 presents a comparison of momentum-resolved photoluminescence spectra acquired from strongly-coupled semiconductor cavity, Sample B, usingsetupfromFig.1b(i.e.,withasinglemicrolens)in combination with various Bertrand lenses. Microcavityexhibitsclearlyresolvedupperandlowerpolariton branches.Theobservedpolaritondispersion wasfitted usingacoupledoscillatormodelandsuperimposedon the experimental spectra for reference (for details, see SI,sectionAdditionalExperimentalResults).

The measurements shown in Figs. 2a–e were obtained at 4.5 K using Bertrand lenses of varying focal lengths: microscopeobjectiveswithf = 4mm(50×), f = 10mm(20×),f = 20mm(10×),andf = 40mm (5×),aswellasaf = 25.4mmbiconvexlens,respectively, for both excitation and collection of light. For clarity, allpanelsarecroppedtoshowthesignalfrom a single microlens. All spectra exhibit a qualitatively consistentcavitypolaritondispersion,withtypicalanticrossing behavior of the upper and lower polariton branches. The variation of Bertrand lenses affects the beam spot size on the microlens under fixed excitationpower,therebyinfluencingthelocalexcitationdensity,whichleadstoamodifiedpopulationdistribution withinthelowerpolaritonbranch.

Figure S10 in the SI section Additional ExperimentalResultspresentsacomparisonofmeasurementson Sample B taken without and with a single microlens. Thisrevealsanincreasedobservablewavevectorrange upto7.13µm−1,inexcellentagreementwiththetarget NA=0.95.

Thecombinedeffectofthephotonicresponsetothe additional polymer structure and the local strain inducedbythemicrolensresultsinanenergyshiftofthe lowerpolaritonbranch. Thiseffectcanbeseen,forexample, in Fig. 2d, where the signal at 1.457 eV correspondstotheminimumofthelowerpolaritonbranch intheregionoutsidetheareacoveredbythemicrolens andwastakenintoaccountinthemodeling(Additional ExperimentalResultssectioninSI).Additionally,residual real-space emission from beneath the microlens, collected using a Bertrand lens with a short working distance (Fig. 2a at energies around 1.461 eV), reveals the spatial profile of the resulting modification of the lower polariton energy. A detailed discussion of the modification of the photonic potential by the printed structuresisprovidedinSI,subsectionsVI.AandVI.B.

Asthemagnificationoftheopticsinthedetectiondecreases, a broadening of the polariton branches is observed. This is attributed to the reduced wavevector resolution per pixel, caused by the smaller size of the Fourier plane image projected onto the detector. Although this loss of resolution can be compensated by introducinganadditionaltelescopicmagnificationelementinthedetectionpath,thiswasomittedtomaintain consistent experimental conditions. In the case of the simplebiconvexlens, theadditionalspectralbroadeningisduetothelackofsphericalaberrationcorrection, whichisotherwiseprovidedbyhigh-resolutionmicroscope objectives. For comparison, Fig. 2f shows the cross-sections at normal incidence of the spectra from Figs.2a–e. Amoredetaileddiscussionofthetrade-offs between different Bertrand lenses can be found in the SIsectionMicrolensesopticalperformance,subsection VI.C.

Nevertheless, these results clearly demonstrate that momentum-resolvedpolaritonspectroscopycanbeeffectively performed using only the microlens in combination with low-NA optics, thereby eliminating the needforconventionalmicroscopeobjectivesinthedetectionpath,evenundercryogenicconditions.

The additional advantage of a microlens approach isabilitytomultiplexmomentum-spacemeasurements fromamicrolensarray.Fig.3demonstratesthesimultaneous momentum-space imaging of exciton-polariton photoluminescence from multiple spatially separated positions on Sample B. This is made possible by the use of multiple independent microlenses, each acting asanindependentopticalsystem. Theentire8×8microlensarraywasilluminatedwithanexpandedlaser beam, using a 10× microscope objective (f = 20 mm) astheBertrandlens.Equivalentmeasurementsusinga 25.4 mm focal length lens are provided in the SI (seesectionAdditionalExperimentalResults,Fig.S11).

Figure 3a shows the multiple momentum-resolved photoluminescence spectra acquired in a single measurement by projecting Fourier planes from a row of eightmicrolensesontotheentranceslitofthespectrometer. Each microlens provides a well-resolved polaritondispersion,withclearlyseparatedupperandlower branches. Toachievespatiallyvaryingpopulationdistributions within the lower polariton branch, we employed an excitation beam with a Gaussian intensity profileratherthanaflat-topdistribution. Thisresulted inanon-uniformexcitationpowerdensityacrosstheil- luminatedmicrolensarray. Consequently,microlenses locatednearthecenteroftheexcitationspotexhibitenhanced emission at the minimum of the lower polaritonbranch,whereasthosepositionedtowardtheedges showamoreuniformlypopulateddispersion.

Furthermore, momentum-space maps spectrally filtered at selected photoluminescence energies and collected on the CCD camera, as shown in Figs. 3b–d, provide isoenergetic momentum-space cross-sections simultaneously captured from all 64 microlens positions. Theseenergyslicescorrespondtodifferentparts ofthelowerpolaritonbranch,namely,thehighin-planemomentumregion,themid-dispersionregion,andthe branch minimum. The specific energies at which the sliceswerecollectedareindicatedwithcoloreddashed linesinFig.3aforreference.

Theseresultsdemonstratethatevenwitharelatively simpleopticalexperiment,theprintedmicrolensarray enables parallel, spatially resolved momentum-space spectroscopy, allowing simultaneous investigation of polaritondispersionandpopulationdynamicsatmultipledistinctpositionsacrossthesample.

Thenextstepofourstudyaimedtodemonstratethe influence of microlens-assisted excitation on nonequilibrium Bose-Einstein condensation and associated thresholdpulseenergies. Toachievethis,arraysofmicrolenses were printed on Sample C, which consisted ofaCdTe/CdMgTemicrocavityembedding6quantum wells. Thisstructurefeaturesintrinsicphotonicdisorder that forms natural photonic traps where spatially localizedpolaritoncondensationtypicallyoccurs46. In thiscase,themicrolensshape,originallyderivedfrom detectionoptimizationcriteria,wasmodifiedtoachieve a higher numerical aperture (NA = 1), at the cost of a slightlydistorteddispersionimage(seeFig.S2a),withoutexplicitoptimizationofexcitation-specificparameterssuchasfielduniformityorpumpintensityprofile.

Figures 4a,b show momentum-resolved photoluminescence spectra acquired in the setup presented in Fig. 1b, collected below and above the condensation threshold,respectively. Belowthethreshold,thespontaneous emission is uniformly distributed along the lowerpolaritonbranch. Abovethethreshold, asharp and intense signal emerges, indicating that the condensate predominantly occupies localized trap states formedbyintrinsicphotonicdisorder,behaviorthatis typicalforCdTe-basedmicrocavities47.

Figures 4c,d present the emission intensity, spectral linewidth,andenergyblueshiftasafunctionofexcitationpulseenergy,measuredunderthemicrolensesusing setupfromFig.1b,andinanearbyunpatternedregion usingtypicalimagingsetupfromFig.1awitha50×objective(NA=0.55),respectively.Inbothcases,thedata exhibit signatures of polariton condensation in semiconductormicrocavities: anonlinearincreaseinemissionintensity,apronouncednarrowingofthespectral linewidth,andablueshiftoftheemissionenergyatthe condensationthreshold.

However,anotabledifferenceisobservedintheexcitationpulseenergyrequiredtoreachthecondensation threshold. Withthemicrolensexcitation,thethreshold isnearlyanorderofmagnitudelowercomparedtothat inneighboringunpatternedregions. Tosystematically confirmthis,twomeasurementserieswereperformed fortwodifferentexciton-photondetuning(seeSI,sectionAdditionalExperimentalResults,Fig.S12fordata corresponding to the second detuning). Each series included measurements from 13 identical microlenses and 13 neighboring unpatterned areas. The resulting condensation threshold values are summarized in the histograms shown in Fig. 4e. Here, orange bars representthresholdsobtainedundermicrolensexcitation, whileroyalbluebarscorrespondtothosemeasuredusing a microscope objective. The data clearly demonstrate that microlens excitation consistently decreases the energy needed to reach the condensation thresholds.

We attribute the reduced condensation threshold to the more efficient focusing provided by the microlens. Themicrolensexhibitsahighnumericalaperture (NA ≈ 1), offering a significantly smaller excitationspotcomparedtothatproducedbythemicroscope objectiveusedinthismeasurements(NA=0.55). Underdiffraction-limitedconditions,themicrolensyields aspotareaapproximatelythreetimessmaller(2.1µm2 versus 0.6 µm2). These results highlight that microlenses can serve not only as light-collection optics butalsoasefficientexcitationelements,enhancingthe localpowerdensity.

Methods
Forconvenience,allcriticalsample,fabrication,and experimental parameters are summarized in SupplementaryTablesinSectionVIIIoftheSI.

Two-photonlithography
Microlenses were fabricated using a “Photonic Professional” (Nanoscribe, GmbH) system based on the two-photon absorption process. This technique involves using a photosensitive resin that polymerizes onlyatthefocalpointofatightlyfocusedlaserbeam. Theresinisappliedonthesamplesurface,andthenan immersionmicroscopeobjectivewithanumericalaperture(NA)greaterthan1isimmerseddirectlyintothe resin. In our case, the refractive index of the IP-Dip resinwasn = 1.52,andtheimmersionobjectiveused hadanumericalapertureofNA=1.3.

ThefabricationprocessutilizedaCalmarLaserMendocino fiber-coupled femtosecond laser with a wavelength of λ = 785 nm, a repetition rate of 50 MHz, andapulsedurationofapproximately100fs. Afterselectively polymerizing the desired structures with the laser,theunpolymerizedresinwasremovedbywashing with solvents: di(propylene glycol) methyl ether and isopropanol. The structures were first rinsed in di(propylene glycol) methyl ether for 20 minutes and theninisopropanolforanother20minutes,bothtimes under magnetic stirring. Following the washing process,thestructureswereallowedtodryunderambient conditionstoenableevaporationofresidualsolvent.

InSupplementaryInformation,sectionImagesofthe Printed Structures, SEM images of representative microlenseswithdifferentsizesfabricatedusingthetwo-photonpolymerizationprocessareshowninFigs.S3a–d, and an optical microscope image of white light reflection from an 8×8 microlens array is presented in Fig.S3e.

Samples
Sample A consisted of two Bragg reflectors (DBRs) wascomposedoffivepairsofSiO 2 /TiO 2 layersanda centralcavitylayermadeofSiO 2 .Thestructurewasdesignedforacentralwavelengthofλ 0 =732.77nm,operatingatroomtemperaturewithouttheneedforplacinginacryostat.

SampleBisamicrocavitymadeoftwoBraggmirrors madeofGaAs/AlAs.Alowermirrorwascomposedof 15.5pairsofGaAs/AlAslayersandanupperonecomposedof12pairs.BetweenDBRs,insidethecavityfour stacks of In 0.05 Ga 0.95 As quantum wells were placed. Eachstackcontainedthree8nmthickwellsseparated by 12 nm thick GaAs barriers. The structure was designedforawavelengthofλ 0 =860nm.

SampleCconsistedofaCdTe-basedmicrocavitycontaining six CdTe quantum wells, doped with manganese (each 20 nm thick) arranged in three stacks of two quantum wells, separated by 5 nm barriers. The Bragg mirrors were made of alternating layers ofCd 0.88 Zn 0.04 Mg 0.08 TeandCd 0.40 Mg 0.60 Te,withthe uppermirrorcontaining16pairsandthelowermirror containing20pairs,andthedesignedwavelengthwas λ 0 =750nm.

Formoredetailsonallthreesamplesandacompari- sonbetweenexperimentandsimulation,seetheSI,sectionSamplesandBerremanSimulations.

Experimentalsetups
Intheexperiment,reciprocalspacereflectancemaps acquired for Sample A and Sample B were carried out using a halogen lamp. Photoluminescence measured for Samples B and C were performed using a Ti:sapphire Mira-900 laser operating in picosecond mode, with a pulse duration of approx. 4 ps, a repetition rate of 76 MHz, and horizontally polarized excitation. The excitation wavelength was adjusted dependingonthesamplebeingmeasured(forSampleB,it was785nm,correspondingtoanenergyof1.58eV,and for Sample C, 730 nm, corresponding to 1.70 eV), but excitationalwaysoccurrednon-resonantly,atanenergy correspondingtothefirstBraggminima.SampleAwas measured at room temperature, while the Samples B andCwereplacedinacryostat. Unlikeastandardreciprocal space imagingsetup,withthemicroscopeobjective located outside the cryostat, in our setup this functionwasperformedbyamicrolensprinteddirectly onthesamplesurface,operatingundercryogenicconditions. The variable element in our setup was a socalledBertrandlens-themiddlelensinthereciprocal space imaging system, which could be realized either withaconventionallensoramicroscopeobjective.For moredetails,seetheSIsectionExperimentalSetups.

Dataavailability
All data used to generate the figures in the main text are available online on Zenodo at: https://doi.org/10.5281/zenodo.18992306.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Furman et al. present an integration of 3D-printed ellipsoidal microlens arrays directly onto optical microcavities for multiplexed, angle-resolved spectroscopy. The approach successfully replaces bulky microscope objectives with integrated on-chip optics, achieving broad numerical aperture access (up to NA ≈ 0.95) even under cryogenic conditions. The demonstration of 64-site simultaneous k-space imaging represents a genuine breakthrough in experimental methodology. However, a number of conceptual and technical aspects require clarification. These include a fuller quantification of strain-induced effects, explicit comparison of wavevector resolution trade-offs, and a stronger substantiation of the claimed dynamic multiplexing capabilities.\nBelow are some comments for the author’s consideration.\n1. The 3D-printed polymer microlenses introduce localized strain on the semiconductor surface, leading to measurable blueshifts of the exciton and cavity resonances. Given that this strain can affect local mode energies and potentially distort comparisons across the microlens array, its influence requires deeper quantification. The current acknowledgment of this effect in the text is insufficient for reproducibility. The authors should include a supplementary section quantifying both the magnitude and spatial propagation of strain and discuss whether this non-uniformity introduces site-to-site variations, particularly relevant for studies involving inter-site coupling or energy landscapes.\n3. The manuscript notes that reduced wavevector resolution and mild aberrations arise when employing a single low-magnification Bertrand lens, yet the implications are only discussed qualitatively. For a technology that aims to simplify high-NA spectroscopy, a quantitative assessment is essential. The authors should provide a clear comparison of achievable k-space resolution or distortion metrics for different optical configurations. A concise table or figure illustrating trade-offs between magnification, NA, and resolution would make the setup’s performance limits and cost–benefit decisions more transparent to potential users.\n4. The study demonstrates parallel k-space imaging across multiple sites but does not yet showcase the platform’s potential for exploring dynamic or collective effects. The presented data primarily reflect independent site responses without evidence of spatial coupling, relaxation, or cross-talk. Since one of the main claims is enabling multiplexed studies of interacting systems, the inclusion of preliminary results or discussions highlighting site-to-site dynamics or inter-site correlations would substantially strengthen the manuscript’s impact.\n5. The observed reduction in condensation threshold highlights improved excitation efficiency through the microlenses, yet it remains unclear whether the lens shape was optimized specifically for excitation focusing quality or simply derived from detection optimization criteria. The authors should clarify if ray-tracing simulations incorporated parameters such as optical spot size, field uniformity, and intensity profile relevant to excitation. This would establish whether the threshold reduction stems from deliberate excitation design or incidental high-NA performance.\n6. Several essential fabrication and design details are distributed through the Supplementary Information (e.g., Fig. S5, S10, Table I), but the main text references are inconsistent. To ensure reproducibility and clarity, the authors should verify that all critical parameters, including microlens dimensions, array spacing, and refractive index profiles, are clearly compiled and cross-referenced. A single summary table consolidating these parameters would be valuable for readers intending to replicate the fabrication process.\nOverall, the work delivers a methodological advance in cryogenic, angle-resolved spectroscopy. The concept of an integrated microlens array as a miniature optical instrument replacing a conventional high-NA objective is both elegant and impactful. However, to fully establish the approach as a reliable reference for future users, the authors should better quantify fabrication-induced perturbations and performance trade-offs.", "reviewer_2": "The manuscript presented by M. Furman et al. introduces a compact and scalable method for angle-resolved spectroscopy using arrays of 3D-printed microlenses integrated onto semiconductor microcavities. Each microlens enables high-resolution momentum-space imaging without the need for bulky optics, even under cryogenic conditions. The authors demonstrate the capabilities of the technique for both passive microcavities and exciton-polariton studies. They show that the method allows access to larger wavevector values, enables multiplexing of different points in the real-space image, and can reduce exciton-polariton condensation thresholds.\nI have found the reuslts very interesting and creative. The fabrication strategy is well explained, and the characterization is rigorous, including comparisons with theoretical models that support the effectiveness of the technique. I find the paper scientifically sound, with a well-supported hypothesis and appropriate references. The novelty of the work is clearly established in comparison with existing literature even if perhaps the versatilty of th technique in comparison with the literature introduced by the authors can be a bit overrated in the text.\nI believe some clarifications are needed—particularly a clearer explanation of the measurement technique—before the manuscript can be considered for publication.\nBelow, I provide my detailed comments to the authors.\nGeneral comment:\n1. I generally missed a more in-depth discussion on how the presence of the microlens might affect the actual photonic response of the photonic structure under consideration. The authors mention local strain on page 3, paragraph 11, as a source of a blue shift in the exciton energies, but there are no comments on the effect of the microlens on the overall cavity response for samples A, B, or C.\nFor instance, in the case of Sample A, if the top layer is SiO₂ and a microlens layer with a similar refractive index is fabricated on top (as it is the case), one would expect the reflectance of the top mirror—and therefore the cavity response—to change as well. Should the cavity designs be reconsidered to account for this?ç\n2.\nIn the same vein, the authors mention in the conclusions that this system could be suitable for waveguides or 2D material photonics. From the evidence presented, it is clear that the technique works very well for planar samples, but it is difficult for me to foresee how this could be applied to in-plane nanostructured samples without affecting the actual response of the nanostructure itself. It would be helpful if the authors could include a few comments in that direction to clarify the actual effect of the microlens on the photonic response of the sample.\n3. The manuscript relies heavily on the comparison between two illumination/collection strategies: the standard objective lens and the microlens, in both cases combined with a Bertrand lens. However, the diagram that actually illustrates the optical differences between these approaches is only shown in Supplementary Information (SI Fig. S5). This figure needs to be revisited frequently to follow the discussions throughout the manuscript. In my opinion, this figure—or a similar one—should be included in the main text, possibly as part of Fig. 1, due to its importance for understanding the experimental setup and results. Figures 1a and 1b are effective in showing the angular limitations of the objective lens, but they may be misleading regarding the technique, as the Bertrand lens is missing in both cases. Including it would help clarify that the plane analyzed to obtain the dispersion in each scenario is the Fourier plane of the objective lens and the microlens, respectively.\n4. Overall, I have missed any comment or analysis regarding the polarization. Especially considering that the dispersion of optical microcavities like the ones presented here will have a strong dependence on polarization (TE or TM) at large wavevectors. Please include in the text whether the characterization has been performed under polarization-selective conditions and whether this can affect the measurements.\nSpecific comments:\n1. Fig. 1e–f and Related Discussion:\nThe comparison between the standard approach using an objective lens and the proposed microlens approach appears to show that the cavity exhibits a lower Q-factor when measured with the microlens (Fig. 1f and g). While the discussion effectively addresses the dispersion, which fits the experimental data obtained with the microlens quite well, I believe a comment on the noticeable differences in the FWHM of the cavity dip between the two cases would be appropriate here.\nIs the lower Q observed in the microlens measurements due to the reduced momentum-space resolution, as mentioned later in the context of the photoluminescence experiments? Or is it instead related to modifications in the overall photonic system response of the cavity caused by the presence of the microlens?\n2. Fig. 1 – Reflectance Characterization with White Light:\nThe characterization method using incoherent white light in reflectance configuration is not clearly explained for the microlens structure. For instance, how large is the illumination spot in the case of the white light source?\nIt is mentioned on page 3, paragraph 4, that a 50× objective lens is used as a Bertrand lens. Referring to the diagram in Fig. S4, one would expect that areas without microlenses are also illuminated by the white light, and therefore their reflectance could contribute to the measured dispersion—at least at very low angles. Clarifying this aspect would help better understand the spatial selectivity and accuracy of the reflectance measurements in the microlens configuration.\n3. Figure 2 – Momentum Space Resolution vs. Magnification (Page 3, Paragraph 12):\nThe discussion on the trade-off between momentum-space resolution and magnification is very insightful, and the explanation for the reduced resolution at lower magnification is well supported by the contour plots. However, I believe this figure could benefit from an additional panel showing the emission spectra of all cases at a specific wavevector—for example, at normal incidence (k = 0). This would help illustrate the degradation of the emission peak as magnification decreases and provide a more direct comparison of spectral quality across different magnifications.\n4. Page 4, Paragraph 1 – Fig. 3 Discussion:\nThe multiplexing of momentum space is indeed a major advantage of the technique presented, and the plot in Figure 3a clearly illustrates this capability. However, the explanation of how the Fourier plane images from the microlenses are projected onto the slit of the spectrograph is not clearly described.\nAccording to Paragraph 1 on Page 3, the entire line of 8 microspheres’ Fourier planes is projected onto the slit. If that is the case, why do Figures 1g and 2 only show a single dispersion? Is this because spatial filtering was applied to isolate the signal from one microsphere before projection? Or are Figures 1g and 2 simply cropped sections of a larger image that contains the dispersions from all 8 microlenses?\nClarifying this point in the manuscript would greatly improve the reader’s understanding of the optical setup and the interpretation of the data.\n5. Fig. 3b:\nThe isofrequency images in momentum space show some asymmetry, with higher intensity along the Ky direction. If no polarizer was used before the spectrograph, this asymmetry could plausibly be attributed to the polarization profile of the excitation laser. The authors should clarify in the text whether a polarizer was used or if the laser had a specific polarization.\n6. Fig. S8:\nWhat is actually represented in this plot? The caption states that panels a) and b) correspond to different positions above the lens and mentions reflectance, photoluminescence, simulations, and experiments. However, only four plots are shown. Is there a mistake in the description? Based on the caption of Fig. S9, I assume that the measurements in Fig. S8 are only photoluminescence?", "reviewer_3": "Key results\nThe authors have performed a study on the performance of microlens arrays, made via 2-photon lithography, fabricated directly on microcavity structures as a means to produce high-k dispersion plots. These arrays are of particular interest in scenarios where high NA objective lenses, with their low working distance requirements, are not appropriate or feasible to use.\nTo show the breadth and applicability of this approach, three different optical phenomena are analysed via light collected using the microlens array system; a room-temperature bare cavity characterisation, a GaAs cavity that demonstrates strong coupling at cryogenic temperatures and a CdTe microcavity that exhibits Bose Einstein condensation. It is for scenarios akin to the 2nd and 3rd experiment where the microlens technique seems to be particularly effective; for room temperature measurements the system is comparable to traditional optical lenses (as demonstrated by the authors), but in systems requiring the use of a cryostat the physical limitations of temperature and space mean that the high-NA objective lenses required are no longer applicable, offering a real benefit of using the microlens array instead.\nIn addition to this, the array of microlenses also offers a route to parallelising or multiplexing measurements, where the light from each lens in the array can be analysed individually as part of the collective. This also offers advantages over single conventional objective lenses, and the authors present several scenarios where this approach will either improve upon, or even not be possible, Fourier plane objective lens measurement approaches.\nThe paper is more a demonstration of the capabilities of the proposed and demonstrated system than an explanation of the physical phenomena measured. Having said that, the data presented from each of the 3 measurement approaches are clear and well presented, with good correspondence to any modelled data. Where there are small discrepancies, sensible explanations are provided, such as the fabrication induced strain resulting in small blue shifts to the collected data in the strong coupling section. I think the data collected is clear and supports the central message of the paper.\nSignificance\nI think for some specific cases, as given by the authors, this method will offer a real opportunity to make high-k measurements of samples where that would be otherwise very challenging. There are many scenarios I can envision where adding microlenses would not work, or would be actively detrimental to the samples, but there are enough circumstances where this approach would be advantageous that I think it would be of use to the field to publish this work.\nData and methodology\nThe data presented is clear and well explained. Given the nature of this paper, it was very important that the methodology is clear and well explained. Apart for some clarification I think is needed, and outlined below, I think the authors have presented their method well and in a fashion that would allow others to replicate this work or to adapt it for their own research purposes.\nAnalytical approach\nThe analysis of the experimental data, and the comparisons to modelled data, are more than appropriate for the work. The supplementary information provides significant details for the models and simulations used.\nClarity and context\nI have no concerns about the clarity or context of the work, I enjoyed reading the paper and all the language used is clear and appropriate.\nSuggested improvements\nOverall, I think this is an interesting method that opens up a lot of possibilities for otherwise challenging or impossible high-k measurements. I think there are a couple of areas that need slightly clarifying or expanding (see list below) but with those areas covered I would be happy to recommend publishing this work.\n• I appreciate that the quantum well systems are not the purpose of this paper, but if anyone wanted to replicate this work I don’t think they could do as it stands due to the lack of details on their fabrication. Please could you add further details on their fabrication and what substrate the system is fabricated on. Even a reference to a paper detailing their fabrication process would be welcome.\n• From the images of the microlens array, it is clear there is some inhomogeneity to the lens fabrication; some appear slightly different sizes or different shapes. Have you performed any analysis of the structure of the arrays, to give a range of errors on the lens size, for instance?\nGiven the detailed beam propagation work in the SI, it is clear that small deviations from the desired shape can have quite a significant role. Your simultaneous imaging work seems to show that the arrays you have fabricated do not exhibit significant problems from the structural inhomogeneity, but there will be a limit to how far that can be Please could you include some analysis of the inhomogenity of the structures in the methods section or SI.\n•In figure 2, and also in figure 10c, there appears to be an extra mode with a fairly flat dispersion, which isn’t accounted for by the model. Do you have an idea of the origin of this mode, or an account of why it appears experimentally but not in the model? A comment in the paper on its origins would be appropriate, but I don’t think it would in any way negate your interpretation."}, "author_response": "Belowweprovideadetailed,point-by-pointresponsetoeachReviewer’scomment.\nReviewer#1(RemarkstotheAuthor):\nFurman et al. present an integration of 3D-printed ellipsoidal microlens arrays directly onto optical micro-\ncavities for multiplexed, angle-resolved spectroscopy. The approach successfully replaces bulky microscope\nobjectiveswithintegratedon-chipoptics,achievingbroadnumericalapertureaccess(uptoNA≈0.95)even\nundercryogenicconditions. Thedemonstrationof64-sitesimultaneousk-spaceimagingrepresentsagenuine\nbreakthroughinexperimentalmethodology. However,anumberofconceptualandtechnicalaspectsrequire\nclarification. Theseincludeafullerquantificationofstrain-inducedeffects,explicitcomparisonofwavevector\nresolutiontrade-offs,andastrongersubstantiationoftheclaimeddynamicmultiplexingcapabilities.\nBelowaresomecommentsfortheauthor’sconsideration.\nWethanktheReviewerforthevaluablecommentsandforrecognizingoursimultaneousk-spaceimagingmethod\nas a \"genuine breakthrough.\" To improve the quality and clarity of the manuscript, we address the Reviewer’s\nconcernspointbypointbelow.\n1. The 3D-printed polymer microlenses introduce localized strain on the semiconductor surface, leading to\nmeasurableblueshiftsoftheexcitonandcavityresonances. Giventhatthisstraincanaffectlocalmodeenergies\nand potentially distort comparisons across the microlens array, its influence requires deeper quantification.\nThe current acknowledgment of this effect in the text is insufficient for reproducibility. The authors should\nincludeasupplementarysectionquantifyingboththemagnitudeandspatialpropagationofstrainanddiscuss\nwhetherthisnon-uniformityintroducessite-to-sitevariations,particularlyrelevantforstudiesinvolvinginter-\nsitecouplingorenergylandscapes.\nWethanktheReviewerforraisingthispoint. Motivatedbythiscomment,weperformedadditionalmeasurements\nandsimulations,whichimproveourunderstandingofthespectralfeaturesobservedinmicrolens-basedmeasure-\nments. Thisanalysisleadsustoconcludethattheenergyshiftsobservedbeneaththemicrolensesoriginatefroma\ncombinationofstraineffectsandthephotonicresponseofthecavitytotheadditionalpolymerstructuredeposited\nontop.\nTo address the Reviewer’s concern regarding the magnitude of this effect, we performed a systematic statistical\nanalysisoftheenergyshiftsforallthreesamples(SamplesA,B,andC).Foreachsample,arraysofpolymermi-\ncrolenseswerefabricated, with24microlensesprintedperarray. Foreveryindividualmicrolens, thedispersion\nrelationwasmeasuredbothwiththemicrolensandinanearbyplanarreferenceregion,usingamicroscopeobjec-\ntivetocollectthesignal.\nThedispersionswereanalyzedbyfittingLorentzianfunctionstothek = 0crosssections. Inthestrongcoupling\nregime(SamplesBandC),thelowerpolaritonenergywasextracted,whereasintheweakcouplingregime(Sam-\npleA), thephotonic cavitymode energywas analyzed. Theenergy shiftwas definedas thedifferencebetween\nthemodeenergymeasuredwiththemicrolensandthatmeasuredintheplanarreferenceregion.\n[... statistical analysis details ...]\nInsummary,thisanalysisdemonstratesthatmicrolens-inducedenergyshiftsresultfromacombinationofstrain\nand photonic effects, with both the magnitude and spatial extent being sample dependent. Consequently, each\nmaterialplatformorphotonicstructurerequiresindividualcharacterization: forsomesystemstheseeffectsmaybe\nnegligible(especially,whencryogenictemperatureisnotrequired),whereasforothers,theymayplayasignificant\nrole,inparticularwhenaflatphotonicpotentialiscritical. Thespreadobservedinthestatisticaldistributionswe\nprimarilyattributedtocavity-thicknessgradients(notrelatedtothemicrolensesthemselves)andminorvariations\ninmicrolens-substrateadhesion.\nAconcisesummaryofthisdiscussion,togetherwiththecorrespondingfigures,hasbeenincludedintheSupple-\nmentaryInformationinSectionMicrolensesopticalperformance,subsectionPhotonicpotentialresponse. Inthe\nmaintext,weaddedanappropriatereferencetothisdiscussionintheSIandmodifiedthecorrespondingsentences\ntoreflecttherevisedinterpretation:\nThecombinedeffectofthephotonicresponsetotheadditionalpolymerstructureandthelocalstraininducedby\nthemicrolensresultsinanenergyshiftofthelowerpolaritonbranch.\n[...]\nwherethesignalat1.457eVcorrespondstotheminimumofthelowerpolaritonbranchintheunstrainedregion\noutsidetheareacoveredbythemicrolens[...]\n3. The manuscript notes that reduced wavevector resolution and mild aberrations arise when employing a\nsinglelow-magnificationBertrandlens,yettheimplicationsareonlydiscussedqualitatively. Foratechnology\nthataimstosimplifyhigh-NAspectroscopy,aquantitativeassessmentisessential. Theauthorsshouldprovide\naclearcomparisonofachievablek-spaceresolutionordistortionmetricsfordifferentopticalconfigurations.\nA concise table or figure illustrating trade-offs between magnification, NA, and resolution would make the\nsetup’sperformancelimitsandcost–benefitdecisionsmoretransparenttopotentialusers.\nWehaveaddedanewsubsectionentitled\"Wavevectorresolution\"tothe\"Microlensopticalperformance\"Section\noftheSupplementaryInformation,togetherwithanewFigureS25(Fig.3inthisresponse)andwehaveaddeda\ncorrespondingreferenceinthemaintext. Inthissubsection,wequantitativelyanalyzehowthewavevectorFWHM\ndependsontheBertrandlensused. Wealsoshowhowlowermagnificationaffectstheresolutiononthedetector\nchip.\n4. Thestudydemonstratesparallelk-spaceimagingacrossmultiplesitesbutdoesnotyetshowcasetheplat-\nform’spotentialforexploringdynamicorcollectiveeffects. Thepresenteddataprimarilyreflectindependent\nsiteresponseswithoutevidenceofspatialcoupling,relaxation,orcross-talk. Sinceoneofthemainclaimsis\nenablingmultiplexedstudiesofinteractingsystems,theinclusionofpreliminaryresultsordiscussionshigh-\nlightingsite-to-sitedynamicsorinter-sitecorrelationswouldsubstantiallystrengthenthemanuscript’simpact.\nWethanktheReviewerforthissuggestion. Weagreethatexploringsite-to-sitedynamicsandcollectiveeffectsisan\nexcitingdirectionenabledbyourplatform. However,webelievethatthecurrentmanuscriptisalreadycomplete\nwithinitsintendedscope.\nThisworkfocusesonthetechnologicalrealizationofmicrolensesprinteddirectlyonmicrocavities,theoptimiza-\ntionoftheopticalsetupformomentum-spaceimaging,thedemonstrationthatthisapproachenablessimultaneous\naccesstopolaritondispersionsfrommultiplesites,thereductionoftheenergyrequiredtoreachthecondensation\nthreshold, and, following the revision, a detailed analysis of the optical response performance. Together, these\nresultsformaself-containedcontribution.\nWe believe that a detailed study of spatial coupling, relaxation, and inter-site correlations of exciton polaritons\nBECdeservesaseparatemanuscriptfocusedprimarilyontheunderlyingphysics. Includingpreliminaryresults\nof such effects here would weaken the impact of a planned follow-up study. For this reason, although we have\npreliminarydatainthisdirection,weprefernottoincludetheminthemanuscriptatthisstage,butinsteadshare\nthemhereinourresponse.\n[...]\n5. The observed reduction in condensation threshold highlights improved excitation efficiency through the\nmicrolenses,yetitremainsunclearwhetherthelensshapewasoptimizedspecificallyforexcitationfocusing\nqualityorsimplyderivedfromdetectionoptimizationcriteria. Theauthorsshouldclarifyifray-tracingsim-\nulations incorporated parameters such as optical spot size, field uniformity, and intensity profile relevant to\nexcitation. Thiswouldestablishwhetherthethresholdreductionstemsfromdeliberateexcitationdesignor\nincidentalhigh-NAperformance.\nThe microlens geometry was optimized primarily for momentum-space imaging, with the aim of maximizing\nNAwhilepreservingsufficientdispersionfidelity. Accordingly,theray-tracingsimulationsfocusedoncollection\nperformanceanddidnotexplicitlyincludeexcitation-relatedparameters.\nConsequently,alsointhepartoftheResultsaddressingexcitation,themicrolensshapewasderivedfromdetection\noptimization criteria and only slightly adjusted to further increase the NA while keeping dispersion sufficiently\nwellresolved. Wethereforeattributetheobservedreductionincondensationthresholdtotheincreasedeffective\nexcitationNA,ratherthantoamicrolensdesignexplicitlyoptimizedforexcitation.\nToclarifythispoint,wehaverevisedthecorrespondingsentenceinthemanuscriptasfollows:\nInthiscase,themicrolensshape,originallyderivedfromdetectionoptimizationcriteria,wasmodifiedtoachieve\nahighernumericalaperture(NA=1),atthecostofaslightlydistorteddispersionimage(seeFig.S2a),without\nexplicitoptimizationofexcitation-specificparameterssuchasfielduniformityorpumpintensityprofile.\n6. Several essential fabrication and design details are distributed through the Supplementary Information\n(e.g.,Fig. S5,S10,TableI),butthemaintextreferencesareinconsistent. Toensurereproducibilityandclarity,\ntheauthorsshouldverifythatallcriticalparameters,includingmicrolensdimensions,arrayspacing,andre-\nfractiveindexprofiles,areclearlycompiledandcross-referenced. Asinglesummarytableconsolidatingthese\nparameterswouldbevaluableforreadersintendingtoreplicatethefabricationprocess.\nWe thank the Reviewer for this comment. To improve the clarity of the manuscript, we have consolidated all\nfabricationandexperimentaldetailsintoanewdedicatedsection\"SummaryofSamples,Fabrication,andExperi-\nmentalParameters\"attheendoftheSupplementaryInformation. Thissectioncontainsseveraltablessummarizing\nthecriticalparametersandexperimentaldetails. Thissectionisalsoexplicitlyreferencedatthebeginningofthe\nMethodssection. Thetablesarepresentedbelow(weadditionallyincludeonemoretablewithsampledetailsin\nresponsetoReviewer3,Question1).\n[... tables ...]\nOverall, theworkdeliversamethodologicaladvanceincryogenic, angle-resolvedspectroscopy. Theconcept\nofanintegratedmicrolensarrayasaminiatureopticalinstrumentreplacingaconventionalhigh-NAobjective\nisbothelegantandimpactful. However,tofullyestablishtheapproachasareliablereferenceforfutureusers,\ntheauthorsshouldbetterquantifyfabrication-inducedperturbationsandperformancetrade-offs.\nWethanktheReviewerfortheseconstructivecommentsandhopethattherevisionsimprovethequalityandclarity\nofthemanuscript.\nReviewer#2(RemarkstotheAuthor):\n[... detailed responses to Reviewer 2 ...]\nReviewer#3(RemarkstotheAuthor):\n[... detailed responses to Reviewer 3 ...]"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed my questions satisfactorily, and the manuscript is in an acceptable form.", "reviewer_2": "The authors have provided an extensive and detailed response to my concerns and, from what I can assess, they have also thoroughly addressed the comments of the other two reviewers. Not only have they offered accurate and satisfactory explanations to the issues raised, but they have also performed additional analyses that significantly enrich the manuscript and clarify results that were previously not clearly explained.\nTherefore, I believe that the manuscript could be accepted for publication in Nature Communications.", "reviewer_3": "Following the updates and amendments completed by the authors, I have no further comments to make on this paper, and am happy to endorse publication.\nI would like to say the authors have gone to significant effort to answer the points raised in a comprehensive and detailed manner, including some significant additional experiments, and would like to commend them for doing so. It made for a very compelling case to approve publication."}, "author_response": ""}]

Decision letter