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[Chih‐Zong Deng](https://orcid.org/0009-0005-2398-5353), Sunhao Shi, Chun‐Hao Chiang, [Mu‐Hsin Chen](https://orcid.org/0000-0002-3885-5720), Shuaicheng Liu, Haruyuki Sakurai, Jui‐Han Fu, [Kuniaki Konishi](https://orcid.org/0000-0003-2389-9787), [Masanobu Iwanaga](https://orcid.org/0000-0002-8930-6940), Vincent Tung, [Ya‐Lun Ho](https://orcid.org/0000-0001-8274-5978)

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[Freestanding Polymer Metasurface Supporting Higher‐Order Optical Resonances for Strong Field Enhancement in TMD Monolayers](https://mdr.nims.go.jp/datasets/cfab3ff5-fdb3-4b5d-b27a-f26f7c7be781)

## Fulltext

Freestanding Polymer Metasurface Supporting Higher‐Order Optical Resonances for Strong Field Enhancement in TMD MonolayersSmallwww.small-journal.comRESEARCH ARTICLEFreestanding Polymer Metasurface SupportingHigher-Order Optical Resonances for Strong FieldEnhancement in TMDMonolayersChih-Zong Deng1 Sunhao Shi2 Chun-Hao Chiang1 Mu-Hsin Chen1 Shuaicheng Liu3 Haruyuki Sakurai4Jui-Han Fu2 Kuniaki Konishi4 Masanobu Iwanaga1 Vincent Tung2 Ya-Lun Ho11Research Center for Electronic and Optical Materials, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, Japan 2Department of ChemicalSystem Engineering, Graduate School of Engineering, The University of Tokyo, Bunkyo, Tokyo, Japan 3Department of Physics, Graduate School of Science,The University of Tokyo, Bunkyo, Tokyo, Japan 4Institute For Photon Science and Technology, Graduate School of Science, The University of Tokyo, Bunkyo,Tokyo, JapanCorrespondence: Ya-Lun Ho (HO.Ya-Lun@nims.go.jp)Received: 28 October 2025 Revised: 14 April 2026 Accepted: 28 April 2026Keywords: light–matter interaction | membrane | suspended metasurface | transition metal dichalcogenide monolayerABSTRACTEnhancing light–matter coupling in two-dimensional (2D) semiconductors, such as transition metal dichalcogenide monolayers,remains a central challenge in nanophotonics due to their atomic thickness, which limits their interaction volume with light.Here, we demonstrate that higher-order optical resonances, including photonic guided modes (GMs) and quasi-bound states inthe continuum (quasi-BICs) supported by a freestanding metasurface, provide exceptionally strong surface field enhancement,enabling efficient coupling with a tungsten disulfide (WS2) monolayer. Triangular-lattice polymer patterns on silicon nitridemembranes are fabricated to realize these higher-order modes. Simulations reveal that second-order modes possess optimalsurface electric-field distributions that strongly overlap with the overlying WS2 monolayer, significantly outperforming theirfirst-order counterparts. Photoluminescence (PL) measurements confirm a remarkable PL enhancement factor of 193 for thesecond-order GM, over an order of magnitude greater than that of the first-order modes. These results establish higher-ordermodes in freestandingmetasurfaces as a promising route to engineer light–matter interactions in 2D semiconductors for advancednanophotonic and quantum photonic applications.1TsptutCTo©ShIntroductionwo-dimensional (2D) transition metal dichalcogenides (TMDs),uch as WS2 and MoS2 monolayers, have emerged as a centrallatform for advancing next-generation optoelectronic and quan-um technologies [1, 2]. Their atomically thin nature providesnique opportunities for extreme miniaturization and integra-ion, while their strong excitonic resonances and valley-selectivehih-Zong Deng and Sunhao Shi contributed equally to this work.his is an open access article under the terms of the Creative Commons Attribution Licenriginal work is properly cited.2026 The Author(s). Small published by Wiley-VCH GmbHmall, 2026; 22:e13320ttps://doi.org/10.1002/smll.202513320optical selection rules open pathways toward exciton-baseddevices. These features have motivated intense research intoTMD-based photodetectors, light-emitting devices, and quantumemitters, positioning them as key building blocks for futureinformation and communication technologies [3–8]. However, amajor bottleneck arises from the intrinsically weak interactionvolume between light and monolayer semiconductors. BecauseTMD monolayers are atomically thin, their absorption andse, which permits use, distribution and reproduction in any medium, provided the1 of 10http://www.small-journal.comhttps://doi.org/10.1002/smll.202513320https://orcid.org/0009-0005-2398-5353https://orcid.org/0000-0003-2389-9787https://orcid.org/0000-0001-8274-5978mailto:HO.Ya-Lun@nims.go.jphttp://creativecommons.org/licenses/by/4.0/https://doi.org/10.1002/smll.202513320http://crossmark.crossref.org/dialog/?doi=10.1002%2Fsmll.202513320&domain=pdf&date_stamp=2026-05-17etdpiNsiovd[AplmIbp1frowBrnawsmAastlstsowcefrsIpsSlsspemu2 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatimission cross-sections are small compared to bulk semiconduc-ors, severely limiting their efficiencywhen integrated into opticalevices. Overcoming this limitation requires carefully engineeredhotonic environments that can amplify and control light–matternteractions at the nanoscale.anophotonic resonators and metasurfaces offer an attractiveolution to this challenge. By confining electromagnetic fieldsnto subwavelength regions and enhancing their intensity, res-nant photonic structures can compensate for the low opticalolume of TMD monolayers. This strategy has already beenemonstrated in various contexts, including photonic crystals4], plasmonic nanoantennas [6], and dielectric metasurfaces [9].mong these approaches, dielectricmetasurfaces are particularlyromising due to their compatibility with large-area active areas,ow optical losses, and ability to sustain a rich set of resonantodes with tailored spectral and spatial characteristics.n this context, bound states in the continuum (BICs) supportedy dielectric metasurfaces have recently emerged as an especiallyowerful concept for enhancing light–matter interactions [10,1]. BICs are non-radiating states that remain perfectly con-ined within photonic systems, despite being embedded in theadiation continuum. When perturbed by symmetry breakingr fabrication imperfections, they transform into quasi-BICsith extremely high but finite quality (Q) factors. These quasi-IC metasurfaces produce strong field confinement and narrowesonances, enabling applications in lasing [12–14], sensing [15],onlinear optics [16], and quantum light generation [17]. Thebility of quasi-BIC metasurfaces to concentrate light into sub-avelength regions with minimal radiative loss makes themuited for coupling with atomically thin materials such as TMDonolayers [18–27].critical design consideration in enhancing light–matter inter-ction is whether the metasurface is supported on a substrate oruspended as a freestanding structure. Substrate-supported struc-ures are easier to fabricate and integrate but suffer from severalimitations: the lower refractive index contrast between the sub-trate and the nanostructure often leads to radiation leakage intohe substrate, reducing the achievable Q-factors; furthermore, theubstrate can perturb the field distribution, reducing the overlapf resonant modes with surface-bound emitters [28, 29]. Recentorks have demonstrated that membrane-based metasurfacesan effectively suppress substrate-induced leakage [30, 31] andnable access to higher-order resonances [32] with improved con-inement and symmetry. In particular, these studies highlight theole of vertical symmetry restoration and high index contrast intabilizing guided-mode (GM) resonances and quasi-BIC states.n contrast, freestanding membranes eliminate substrate leakageathways and allow for symmetric light confinement on bothides of the structure [18–20, 33].ilicon nitride (SiN) membranes with comparable thickness andateral dimensions are known to exhibit high intrinsic tensiletress, whichmechanically stabilizes the suspended structure anduppresses buckling or wrinkling after release. The tensile stressromotes global planarity and minimizes membrane curvature,ven for relatively large, suspended areas. As a result, suchembranes typically maintain excellent structural flatness andniform stress distribution, which is essential for preservingof 10optical symmetry and high-Q resonances [34, 35]. Furthermore,substrate removal restores vertical symmetry and suppressesadditional radiation channels, enabling higher Q-factors in pho-tonic crystal slabs [18–20]. The freestanding configuration alsomaximizes refractive index contrast and enhances near-surfacefield confinement, which is particularly advantageous for cou-pling to monolayer 2D materials. Within this mechanically andoptically robust freestanding platform, the choice of patternedmaterial becomes a key factor in determining device function-ality and fabrication practicality. The utilization of polymeras photonic device material provides significant advantages interms of fabrication efficiency, structural quality [31, 36–38],and sustainability. Unlike traditional dielectric metasurfaces thatrequire complex multi-step procedures including material depo-sition, hard-masking, and reactive ion etching, the polymer-basedapproach collapses the workflow into three primary steps: spin-coating, exposure, and development. By repurposing the resist asthe final device material, etching-related defects such as mate-rial redeposition and geometric perturbations are eliminated,ensuring high-fidelity nanopatterns whose precision is limitedonly by the initial lithography step. Although polymers possessa lower refractive index compared to traditional semiconductorslike silicon, the implementation of a freestanding architecturemaximizes the index contrast with the surrounding air.Most prior studies have focused on exploiting first-order modes.These fundamental modes, which typically concentrate fieldsinside the photonic slab, have been used to enhance spon-taneous emission, exciton–polariton formation, and nonlinearoptics in TMDs [18, 21–27]. However, reports on higher-ordermodes remain limited [13, 14, 39]. Because of their distinctfield distributions, second-order modes exhibit stronger fieldlocalization near the surface region, thereby improving couplingefficiency with material placed on the surface. Such surface-localized resonances, which exhibit strong field enhancement onthe top surface, are especially advantageous for TMDmonolayers,enabling efficient coupling where the material is placed. Despitethis compelling potential, systematic investigations into the roleof higher-order modes for enhancing TMD emission remainscarce.Here, we experimentally demonstrate that second-order modessupported by a freestanding metasurface—comprising a poly-mer hole-array slab on a SiN membrane—enable dramaticallystronger photoluminescence (PL) enhancement in WS2 mono-layers on top of the metasurface. Through field enhancementsimulations and PL measurements, we identify the field distribu-tions of second-order modes and confirm their decisive role inenhancing the field on the top surface. Our results demonstratesecond-order modes in freestanding metasurfaces as a powerfulnew design principle for boosting light–matter interaction in2D materials. This approach can offer a general platform forengineering strong excitonic effects, nonlinear responses, andquantum optical functionalities, opening new directions forhybrid photonic–2D material systems.2 Results and DiscussionFigure 1 illustrates the freestanding metasurface designed tostrongly enhance the field near the top surface, therebySmall, 2026ve Commons LicenseFIGURE 1 Photoluminescence (PL) from a tungsten disulfide(WS2) monolayer strongly enhanced by a freestanding metasurface sup-porting second-order guided mode (GM), which provide intense surfacefield confinement and efficient exciton–photon coupling. (a) Schematicillustration of the concept: A WS2 monolayer is placed on a freestandingmetasurface, which is a hole-array polymer slab on a silicon nitride (SiN)membrane. Simulated electric energy density Eden distribution at (b) first-order GM and (c) second-order GM in yz-plane. (d) PL spectra of the WS2monolayer under first-order GM (light red curve), second-order GM (redcurve), and on an unstructured membrane (black curve).ssooSfemfetaaotsoPtmuProcFipdtiimFIGURE 2 Freestanding metasurface engineered to supportsecond-order GMs and quasi-BICs with strong field enhancement atthe top surface. (a) Schematic diagram of the membrane metasurface,consisting of a triangular-lattice air-hole array patterned in polymerresist with a lattice period P = 560 nm, a hole diameter D = 280 nm, anda thickness T = 400 nm on a 50 -nm-thick SiN membrane. (b) Simulatedangle-resolved transmittance spectra under x-polarized illuminationalong the y-direction, showing GMs and quasi-BICs. Electric energydensity Eden distributions for the (c) first-order and (d) second-ordermodes, the incident angle θ = 2.5◦.S 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatiignificantly enhancing the PL of a TMD monolayer at theurface. This enhancement is achieved by leveraging the second-rder modes. As shown in Figure 1a, the proposed device consistsf a freestanding metasurface—a polymer hole-array slab on aiN freestanding membrane. This specific geometry is criticalor supporting the desired second-order modes. The simulatedlectric energy density Eden profiles of the proposed freestandingetasurface, as shown in Figure 1b,c, visually confirm the strongield confinement. The second-order mode shows a strong fieldnhancement near the top surface of the metasurface, wherehe monolayer is located. This strong overlap between the fieldnd the exciton-rich region of the monolayer is essential forchieving efficient exciton-photon coupling. In contrast, the first-rder mode exhibits a weaker and more delocalized field athe top surface, leading to a less effective interaction. Figure 1dhows the PL spectrum of the WS2 monolayer on the second-rder modes metasurface (red curve), which shows a remarkableL enhancement—a dramatic increase in intensity compared tohe PL from the same WS2 monolayer on the first-order modesetasurface (light red curve) or the WS2 monolayer on thenstructured membrane (black curve). The strongly enhancedL confirms that the second-order modes significantly boost theadiative efficiency of the WS2 monolayer, a direct consequencef the strongly enhanced field and efficient exciton-photonoupling.igure 2a shows a schematic diagram of the proposed freestand-ng metasurface, consisting of a triangular-lattice air-hole arrayatterned in polymer resist with a lattice periodP= 560 nm, a holeiameter D = 280 nm, and a thickness T = 400 nm on a 50-nm-hick SiN freestandingmembrane. This freestandingmetasurfaces designed to support GMs and BICs, with second-order modesn particular providing a strong field enhancement for the light–atter interactions with a WS2 monolayer. The simulated angle-mall, 2026resolved transmittance spectra of the freestanding metasurfaceare shown in Figure 2b. The light is x-polarized illuminationalong the y-direction, calculated using rigorous coupled-waveanalysis (RCWA) to characterize the structure. The incident angleθy is varied between 0◦ and 2.5◦ to resolve symmetry-protectedBICs expected at the Γ point. At normal incidence, the spectrumexhibits vanishing linewidths for BIC modes, allowing a cleardistinction from GMs. In the longer wavelength range, the fourfirst-order modes are identified, including one GM (GM1st) andthree BICs (BIC1st,1, BIC1st,3, BIC1st,4). In the shorter wavelengthrange, four second-order modes are identified, including one GM(GM2nd) and three BICs (BIC2nd,1, BIC2nd,3, BIC2nd,4). In addition,BIC1st,2 andBIC2nd,2 are accessible under x-tilted illumination (θx),as shown in Figure S1. In practice, perfect BICs transform intoquasi-BICs due to inevitable radiation leakage arising from fab-rication imperfections, finite-size effects, and nonzero incidentangles. Nevertheless, they maintain exceptionally high Q-factors,enabling strong light confinement. The spatial distributions ofthe Eden for the first-order and second-order modes at θy = 2.5◦are shown in Figure 2c,d, respectively. The top panels showthe in-plane (xy-plane) field profiles at the middle of the SiNmembrane, while the bottom panels show the out-of-plane (yz-plane) cross-sections through the unit cell. The xy-plane fieldprofiles confirm that the first- and second-order modes sharesimilar in-plane symmetries, consistent with their transverseelectric nature (Figure S2). In contrast, the yz-plane field dis-tributions highlight a distinct difference in vertical mode order:the first-order mode exhibits a single antinode confined within3 of 10ve Commons LicenseFIGURE 3 Strong field enhancement on the top surface of the freestanding metasurface via second-order modes. Simulated transmittance spectraas a function of lattice period for (a) substrate-based metasurface and (b) freestanding metasurface. Electric energy density Eden distributions in thexy-plane at the top surface and xz-plane for (c) GM, (d) BIC1, and (e) BIC3 in both the substrate-based metasurface and freestanding metasurface. Theincident light is x-polarized with an incident angle of 2.5◦ along the y-direction.ttpsieTamaetθsarcrratcmcrlc4 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatihe SiN membrane, whereas the second-order mode featureswo antinodes—one within the membrane and another near theolymer–air interface. This strong field enhancement on the topurface highlights the potential of second-order modes as andeal environment for coupling with TMD monolayers, enablingfficient PL enhancement and exciton–photon interactions.o highlight the importance of the freestanding architecture forccessing second-order modes with strong surface field confine-ent, Figure 3 compares the substrate-supported metasurfacend the freestanding metasurface, further contrasting the fieldnhancement of first- and second-ordermodes. Figure 3a,b showshe simulated transmittance spectra, both at an incident angley = 2.5◦, under varying lattice period for polymer hole-arraylabs on a silicon dioxide (SiO2) substrate and the same slab onSiN freestanding membrane, respectively. In both cases, theesonance wavelengths redshift with increasing lattice period,onsistent with the enlarged effective optical path. Notably, theesonant wavelength can be readily tuned across the visibleange by adjusting the lattice period, allowing precise spectrallignment with the excitonic transition of TMD monolayerso maximize light–matter interaction through exciton–photonoupling. As shown in Figure 3b, both first- and second-orderodes are clearly observed in the freestanding metasurface. Inontrast, in the substrate-supported metasurface (Figure 3a), theeduced vertical refractive index contrast between the polymerayer and the supporting substrate introduces additional radiationhannels, which suppress the formation of second-order GMsof 10and quasi-BICs. Moreover, significant field leakage into thesubstrate leads to resonance attenuation, resulting in reducedtransmittance contrast.Figure 3c–e presents the spatial distribution of the Eden for theGM, BIC1, and BIC3 at θy = 2.5◦. The resonancewavelengths of themodeswere tunednear the excitonic emission peakwavelength ofWS2 (∼620 nm) by setting the lattice periods P to 480 and 560 nmfor the first- and second-ordermodes, respectively. The top panelsdisplay the in-plane (xy-plane) field profiles at the top surface,while the bottom panels show the out-of-plane (xz-plane) cross-sections through the unit cell. For the substrate-supported case(left panel of Figure 3c–e), although the field is strongly confinedwithin the SiN membrane, the enhancement at the top surface isreduced by approximately two orders of magnitude, resulting in aweak field localized at the top surface. All modes in the substrate-supported case exhibit significantly weaker field enhancementcompared to those in the freestanding metasurfaces (middle andright panel), revealing pronounced leakage into the substrate.In contrast, the freestanding metasurfaces enable stronger fieldenhancement near the top surface. The first-order modes showslightly stronger enhanced surface fields compared to thesubstrate-supported metasurface, while the second-order modesexhibit even stronger enhancement. Comparing the surfacefield enhancement among first- and second-order modes, themaximum Eden for GM2nd, BIC2nd,1, and BIC2nd,3, are 113, 166, and95, respectively—much larger than their first-order counterpartsSmall, 2026ve Commons LicenseFIGURE 4 Coupling of an WS2 monolayer to a freestanding metasurface. (a) Simulated absorption spectra as a function of lattice periodfor a freestanding metasurface. (b) Simulated absorption spectra of freestanding metasurface before and after WS2 monolayer transferred. (c) Edendistributions in the xy-plane at themiddle ofWS2 monolayer for GM2nd, BIC2nd,1, GM1st, and BIC1st,1 in a freestandingmetasurface. (d) Eden distributionsalong the z-direction across the entire device and a magnified view of specially within the WS2 layer, highlighting the localized field enhancement. Theincident light is x-polarized with an incident angle of 2.5◦ along the y-direction.GbcsotpttFatvfrrtpePtpoQdfWTtS 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable CreatiM1st (4), BIC1st,1 (5), and BIC1st,3 (7). This enhancement arisesecause the antinodes of the field in second-order modes coin-ides with the near top surface (bottom panel). In summary,ubstrate-induced leakage suppresses the formation of second-rder modes, whereas the freestanding configuration preserveshem. Owing to their field distributions, the second-order modesrovide substantially stronger surface field enhancements thanhe first-order modes, directly benefiting light–matter interac-ions with TMDmonolayers.igure 4 illustrates the coupling between the WS2 monolayernd the proposed freestanding metasurface. Figure 4a showshe simulated absorption spectra for the integrated device underarying lattice periods, confirming that all optical modes persistollowing the transfer of the WS2 monolayer (Figure 4a). Theseesonances exhibit a characteristic redshift due to the highefractive index of the WS2 (Figure 4b). It is noteworthy thathe Q-factor undergoes degradation upon integration with WS2,articularly for the quasi-BICs, which are highly sensitive to localnvironmental changes and damping. For a metasurface with= 580 nm, the Q-factor of the BIC1st,1 decreases from 398 (bare)o 100 (withWS2). In contrast, the first-order guidedmode (GM1st)roves to be significantly more robust, with its Q-factor shiftingnly from 111 (bare) to 92 (with WS2). Note that the simulated-factors were calculated at a fixed incident angle of 2.5◦. Thisemonstrates that while quasi-BICs offer higher theoretical Q-actors, they are heavily dampened by the large absorption of theS2 layer.o compare the field enhancement of different optical modes athe peak absorptionwavelength ofWS2 (620 nm), themetasurfacemall, 2026periods were tuned to align each resonance with this wavelength,as indicated in Figure 4a. The resulting Eden distributions withinthe WS2 layer are presented in Figure 4c. These results indicatethat second-order modes provide greater field enhancementwithin the WS2 layer than first-order modes. Specifically, theGM2nd exhibits a maximum enhancement factor of 227, whichis more than four times the enhancement of 50 observed for theGM1st. This confirms that while theWS2 layer perturbs the opticalresonances, light–matter interaction is nonetheless significantlyamplified, particularly for the GMs, which demonstrate lowersensitivity to environmental perturbations and material loss.One-dimensional Eden profiles (Figure 4d) further confirm thatthe field is strongly confined within the WS2 layer for second-order modes (GM2nd and BIC2nd,1). In contrast, the first-ordermode (GM1st and BIC1st,1) primarily localizes the field withinthe SiN layer rather than the WS2 monolayer, resulting in poorcoupling and lower enhancement factors.The designed freestanding metasurface was fabricated for exper-imental characterization of its optical properties. Figure S1displays the angle-resolved transmission for the fabricated free-standingmetasurface (P= 560 nm). As predicted, the BICs exhibita narrowing linewidth that approaches zero at normal incidence.In contrast, the GMs maintain strong resonances at normalincidence. Since the SiN membrane used in this work exhibitsdefect-related states, a broad-band PL emission is observed underoptical pumping (Figure S4), allowing the investigated GMs andquasi-BICs to be coupled to this PL band. The 488 nm CW laserused for PL excitation is linearly polarized. Prior to the measure-ments, the polarization axis of the laser beam was confirmed byusing a polarizer. To ensure consistency with the simulation, the5 of 10ve Commons LicenseFIGURE 5 Demonstration of both first-order and second-orderGMs and quasi-BICs by freestanding metasurfaces. (a) PL spectra of thefreestanding metasurfaces as a function of lattice period. (b) Scanningelectron microscopy (SEM) images of the freestanding metasurface witha lattice period P = 520 nm. (c,d) PL spectra highlighting the spectralregions corresponding to the first-order (P = 460 nm) and second-order(P = 560 nm) resonances, respectively.mmp4f(PowertafemloW(5Wa6 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatietasurface was mounted on a rotation stage under an opticalicroscope (OM). We aligned the x-axis of the metasurfacearallel to the pre-determined linear polarization direction of the88 nm pump beam. Figure 5a presents experimental PL spectrarom freestanding metasurfaces with varying lattice periods P420 to 600 nm) before the WS2 monolayer was transferred.L spectra reveal multiple emission peaks corresponding toptical resonances. As expected from simulations, the resonanceavelengths redshift with increasing lattice period due to thenlarged optical path. For the lattice period of 420 nm, a group ofesonances appears near a wavelength of 550 nm, correspondingo first-order modes, and shifts to a wavelength of 750 nm for600-nm lattice period. At 460, 480, and 500-nm periods, theirst-order modes occur around 620 nm, overlapping with thexciton emission wavelength of WS2. In addition, second-orderodes emerge at shorter wavelengths (at 510 nm for a 440-nmattice period). For 560, 580, and 600-nm periods, the second-rder modes overlap with the exciton emission wavelength ofS2. For GMs, the GM1st at 590.2 nm with a Q-factor of 138460 nm lattice period) and GM2nd at 582.6 nm with a Q-factor of5 (560 nm lattice period) near the exciton emission wavelengthS2. The PL spectra with a narrow range to highlight the first-nd second-order quasi-BICs are shown in Figure 5c,d. For aof 10460-nm period (Figure 5c), the multi-peak group is decomposedinto Lorentzian components corresponding to BIC1st,1, BIC1st,2,and BIC1st,3 at 598.7, 601.5, and 605.4 nm with Q-factors of 214,143, and 162, respectively. For a 560-nm lattice period (Figure 5d),the first-order group decomposes into BIC2nd,1, BIC2nd,2, andBIC2nd,3 at 607.7, 613.7, and 616.9 nm with Q-factors of 122, 173,and 251, respectively. These results experimentally demonstratethat the freestanding metasurface architecture can support bothfirst- and second-order optical modes across the visible spectrumby tuning the lattice period, providing a versatile platform forenhancing light–matter interactions with 2D materials such asTMDmonolayers.To verify the PL enhancement arising from the enhanced fieldsof the optical modes, WS2 monolayers were transferred ontothe freestanding metasurfaces (Figure 6). OM images of thefabricated structures before and after the WS2 transfer areshown in Figure 6a,b, respectively. Figure 6c,d presents the PLspectra obtained from the metasurfaces supporting first-orderand second-order modes. In Figure 6c, the metasurfaces withlattice periods P = 460, 480, and 500 nm support first-ordermodes that spectrally overlap with the WS2 exciton emissionband. The emission spectra from bare metasurfaces (dashedcurves) and from WS2 on an unstructured membrane (blacksolid curve) are provided for reference. As shown in Figure 6c,the PL intensities from these periods show no significant differ-ences, indicating that the first-order modes couple only weaklyto the WS2 monolayer. The observed minor PL enhancementprimarily originates from the partially freestanding nature ofthe WS2 over the air holes, which reduces substrate-inducedquenching and nonradiative recombination, rather than fromthe optical resonance effects of the first-order modes. This isfurther confirmed by PL mapping across large areas (FigureS5), which demonstrates consistent enhancement across thepatterned regions that significantly exceeds the fluctuations inthe unstructured regions. Figure 6d displays the PL intensitiesfor metasurfaces with P = 560, 580, and 600 nm, which supportsecond-order modes overlapping with the WS2 emission band.For P = 560 nm, the PL is substantially enhanced as the second-order quasi-BICs spectrally align with the WS2 emission peak,with a secondary contribution from the second-order GM appear-ing around 582 nm. At P = 580 nm, the PL enhancement remainshigh, benefiting from the simultaneous contribution of both thesecond-order GM and quasi-BIC at 605 and 630 nm, respectively.Notably, at P = 600 nm, the PL enhancement is significantlygreater than that observed at other periods. This superior per-formance is attributed to the precise spectral overlap betweenthe second-order GM and the WS2 emission band, alongside thehigh spatial overlap between the second-order mode’s surface-localized field and the WS2 monolayer. This facilitates efficientexciton–photon coupling, resulting in a markedly intensified PLpeak. These experimental findings are in excellent agreementwith our simulations (Figure 4), which predicted that the second-order GM would exhibit high absorption and robustness, leadingto strong PL enhancement. Figure 6e presents the average PLintensity calculated from 16 different locations on the patternedmetasurface (red dashed square) compared to 16 locations onthe unstructured membrane (black dashed square). The insetof Figure 6e shows the corresponding PL intensity mapping,with error bars representing the standard deviation. These resultsconfirm the high quality of the transferred WS2 and validate theSmall, 2026ve Commons LicenseFIGURE 6 Enhanced PL emission fromWS2 monolayers via first-order and second-order resonances in freestanding metasurfaces. (a, b) Opticalmicroscope images of the freestandingmetasurfaces with lattice periods of P= 420, 440, 460, 480, 500, 520, 540, 560, and 580 nm in the top five rows, andP = 300, 400, 500, 600, 700, and 800 nm in the bottom row, shown (a) before and (b) after transfer of the WS2 monolayer. (c, d) PL spectra of WS2monolayers coupled with (c) first-order modes (P = 460, 480, and 500 nm) and (d) second-order modes (P = 560, 580, and 600 nm). The PL spectrumof WS2 on an unstructured freestanding membrane (black solid curve) and the PL spectra of the bare metasurfaces (dashed curves) are provided forreference. (e) Comparison of the peak PL emission intensities for theWS2 monolayer on themetasurfaces versus the unstructuredmembrane. Error barsrepresent the standard deviation calculated across 16measurement points. Inset: PL intensity mapping at the peak emission wavelength and a schematicindicating the sampled areas. The average intensities were calculated from the regions indicated by the red (metasurface) and black (unstructuredmembrane) dashed squares. The scale bar is 20 µm. (f) PL enhancement factor for the metasurface with a 600 nm period, defined as the ratio of the PLintensity on the metasurface to that on the unstructured membrane, demonstrating the superior performance of the second-order guided mode.rauorwt3WbsWsetreemcS 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatieported enhancement factors. The enhancement factor, defineds the ratio of PL intensity on the metasurface to that on thenstructured membrane, reaches a peak of 193 for the second-rder GM at P = 600 nm. Even the second-order quasi-BICesonance yields a substantial enhancement factor of 84, both ofhich far exceed the maximum enhancement of 15 observed forhe first-order modes.Conclusionse have demonstrated that freestanding metasurfaces can hostoth first- and second- order optical modes across the visiblepectrum, enabling efficient coupling with WS2 monolayers.hile first-order modes primarily confine fields inside the free-tanding metasurface, second-order modes provide strong fieldnhancement on the top surface of the freestanding metasurfacehat overlaps with the WS2 monolayer. As a result, second-orderesonances provide significantly stronger PL enhancement—xceeding one order higher than first-order counterparts. Ourxperimental and simulation results demonstrate second-orderodes in freestanding metasurfaces as a powerful design prin-iple for enhancing light–matter interactions in 2D materialsmall, 2026such as TMDmonolayer. The proposed freestanding metasurfaceserves as a versatile photonic platform for enhancing light–matterinteraction in a broad range of 2D materials. The resonancewavelength can be readily tuned across the visible and near-infrared spectrum by adjusting the lattice period, enablingspectral matching to the excitonic transitions of various TMDs(e.g., MoS2, MoSe2, and WSe2). Moreover, the strong field con-finement at the top interfacemakes the structure compatible withother atomically thinmaterials, including graphene for enhancedphotodetection and hBN for quantum emission applications. Thisscalability highlights the generality of the platform for diverse2D material systems. Furthermore, our analysis indicates thatwhile the dispersion behaviors of the first- and second-ordermodes are fundamentally similar (Figure S8), the structured PLin momentum space is dictated by the radiative channels of theseresonant modes. By aligning the excitonic transitions ofWS2 withspecific points in the metasurface dispersion, the optical modesprovide a platform for controlling the radiation directivity [22].Beyond PL enhancement, this approach opens new pathwaysfor engineering strong exciton–photon coupling, nonlinear pro-cesses, and quantum optical functionalities in 2D material–based nanophotonic devices. Notably, the open-system nature7 of 10ve Commons Licenseoensatb[spSps44TawasamtdoiweEV4AmbceuB4W(i1cce3airt8 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creatif these freestanding structures connects our findings to themerging field of non-Hermitian physics. Recent progress inon-Hermitian photonics has shown that radiative loss and dis-ipation can lead to exceptional points (EPs), where eigenvaluesnd eigenstates simultaneously coalesce, enabling unconven-ional wave control and enhanced functionalities. EPs haveeen demonstrated in metasurfaces and open photonic systems40, 41]. While our work focuses on resonances in passivetructures, their open-system nature connects to non-Hermitianhysics and suggests opportunities for future EP engineering.uch developments could further expand the utility of thislatform toward active topological photonics and ultra-sensitiveensing applications.Methods.1 Numerical Simulationshe far-field reflectance spectra of the freestanding metasurfacesnd the near-field electric field profiles of their resonant modesere numerically analyzed using the rigorous coupled-wavenalysis method (DiffractMOD, RSoft Design Group, USA). Theimulations employed periodic boundary conditions along the x-nd y-directions. The complex refractive indices (n, k) for the SiNembrane, polymer resist, and WS2 monolayer were experimen-ally determined via spectroscopic ellipsometry,with the resultingispersion data provided in Figure S6. The wavelength resolutionf the simulation is 10−5 µm. A plane wave was used as thencident source, propagating along the z-axis. The electric field Eas normalized to the amplitude of the incident field. The electricnergy density was calculated as UE = ½∫Re[ε(r′)]|E|2 dV, whereis the electric field, ε is the spatially dependent permittivity, andis the volume of the simulation domain..2 Fabricationtriangular lattice hole-array pattern was defined in the poly-er resist on the 50 nm-thick SiN membrane using electron-eam lithography. The SiN membranes were provided by Nor-ada, Inc. The nanorod patterns were drawn on a positivelectron-beam resist (AR-P6200 (CSAR 62), Allresist, Germany),sing a high-resolution electron-beam-drawing instrument (ELS-ODEN, ELIONIX, Japan) as shown in Figure S7..3 Preparation for WS2 monolayerS2 films were grown via standard chemical vapor depositionCVD) using a one-zone horizontal quartz tube furnace (2-nch diameter). Tungsten trioxide (WO3, Sigma–Aldrich, 99.9%,00 mg) served as the tungsten source and was placed in theentral heating zone along with c-plane sapphire substrates. Theentral zone was heated to 960◦C and maintained for 15 min tonable film growth. Sulfur powder (S, Sigma–Aldrich, 99.99%,g), pre-solidified prior to use, was positioned upstream inquartz boat and heated to 145◦C using an external heat-ng belt. Sulfur heating began 10 min before the center zoneeached the target temperature. Prior to the growth process,he quartz tube was evacuated to base pressure and purgedof 10with a carrier gas mixture of Ar (200 sccm) and H2 (40 sccm)at a pressure of 20 torr. After growth, the furnace was natu-rally cooled to room temperature while maintaining the Ar/H2flow.Transfer of WS2 films was achieved through a polydimethylsilox-ane (PDMS)-assisted wet-etching technique. A home-preparedPDMS stamp was laminated onto the WS2 surface by naturaladhesion. The sapphire substrate was subsequently etched awayin a KOH solution, releasing the WS2 film onto the PDMS.The PDMS/WS2 assembly was then aligned and brought intocontact with the freestanding metasurface, followed by vacuumtreatment for 1 h to improve adhesion. Finally, gentle heating at60◦C for 10 min facilitated detachment of the PDMS, leaving theWS2 film successfully transferred onto the metasurface.4.4 Optical CharacterizationThe excitation light was focused onto the sample using a 5×objective lens. Photoluminescence (PL) spectra of the freestand-ingmetasurfacesweremeasuredwith a confocal lasermicroscopesystem (alpha300 R,WITec, Germany). A continuous-wave (CW)laser with a wavelength of 488 nm served as the excitation source.The excitation light and the emission light were focused andcollected, respectively, by objective lenses with magnifications of5 × (NA = 0.25, corresponding to an angle within 5.7◦ in air). Theexcited emission was collected and analyzed with a spectrom-eter. The emission intensity distributions were obtained usinga motorized x−y-sample scanning stage for confocal emissionimaging.Author ContributionsThe manuscript was written through the contributions of all authors. Allauthors have given approval to the final version of the manuscript.AcknowledgementsThis work was supported by JSPS KAKENHI under Grant NumbersJP23K26155, JP25KF0083, and JP25H01614. Part of this work was alsosupported by the Ministry of Education, Culture, Sports, Science andTechnology (MEXT) under the MEXT–Quantum Leap Flagship Program(Grant Number JPMXS0118067246) and the Advanced Research Infras-tructure for Materials and Nanotechnology in Japan (ARIM) (ProposalNumber JPMXP1225NM5090).Conflicts of InterestThe authors declare no conflicts of interest.FundingThis studywas supported by JSPSKAKENHIGrantNumbers JP23K26155,JP25KF0083, and JP25H01614. Advanced Research Infrastructure forMaterials and Nanotechnology in Japan (ARIM) Proposal NumberJPMXP1225NM5090. Quantum Leap Flagship Program Grant NumberJPMXS0118067246.Data Availability StatementThe data that support the findings of this study are available in thesupplementary material of this article.Small, 2026ve Commons LicenseRD92Wh3T204Nh5DC6LL7Eh8IMh9nP1“11C(1“(1QCo1uQ11Ru01Wt(1M(1sMo 165307.S 16136829, 2026, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202513320 by National Institute For, Wiley Online Library on [23/06/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creferences1. F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-imensional Material Nanophotonics,” Nature Photonics 8 (2014): 899–07, https://doi.org/10.1038/nphoton.2014.271.. M. Turunen, M. Brotons-Gisbert, Y. Dai, et al., “Quantum Photonicsith Layered 2D Materials,” Nature Reviews Physics 4 (2022): 219–236,ttps://doi.org/10.1038/s42254-021-00408-0.. T. 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See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttps://doi.org/10.1016/j.eurpolymj.2011.07.025https://doi.org/10.1364/OE.26.013148https://doi.org/10.1016/j.mee.2015.02.042https://doi.org/10.1515/nanoph-2023-0672https://doi.org/10.1103/PhysRevLett.134.106901https://doi.org/10.1002/advs.202402615 Freestanding Polymer Metasurface Supporting Higher-Order Optical Resonances for Strong Field Enhancement in TMD Monolayers 1 | Introduction 2 | Results and Discussion 3 | Conclusions 4 | Methods 4.1 | Numerical Simulations 4.2 | Fabrication 4.3 | Preparation for WS2 monolayer 4.4 | Optical Characterization Author Contributions Acknowledgements Conflicts of Interest Funding Data Availability Statement References Supporting Information