Versatile on-chip plasmonic lattices enabled by Kekulé metasurfaces

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

Abstract
Surface plasmon polaritons (SPPs) lattices created by artificial plasmonic metasurfaces, can carry tremendous optical information and have implications for resilient and secure optical communication. However, tailoring the intensity, spectral, and spatial distributions of these SPP lattices intentionally remain challenging. Here, we develop, theoretically and experimentally, a variety of optical SPP lattices in a category of metasurface named as Kekulé metasurface. This plasmonic nanostructure localizes surface plasmonic polaritons into assorted optical lattices at the two-dimensional limit, visualized by noninvasive leakage radiation microscopy. The spatial distribution and relative intensity of the SPP lattice sites are evolved and tailored by superposing an extra wing-shaped nanoslit set. A configurable on-chip light-emitter array and high-security imaging encryption/decryption using such optical lattices are further demonstrated. This work reports a versatile Kekulé metasurface platform and well-defined SPP lattices with multiple degrees of freedoms, featuring rich physic phenomena and potential photonic elements for applications into existing technologies.

Introduction
Analogous to electrons, surface plasmon polaritons (SPPs), recognized as transverse magnetic-polarized optical surface wave at the outset, have been recently casted enormous interest as quasiparticles at their most fundamental levels1–5. The quasiparticle properties of SPPs are defined by the electromagnetic field, material dielectric response function, geometry of light-matter interaction, and multiparticle scattering6. On generation, SPP quasiparticles confines in a two-dimensional (2D) metal surface, is somehow liquid-like7 and decays exponentially or into incoherent particles, varies in intensity, spectral, and spatiotemporal evolution that are otherwise accessible8. The controlled ordering of such SPP quasiparticles into demanded lattices is attractive because not only exotic but elusive multiparticle properties and quantum dynamics are uncovered but potentially it also satisfies Maxwell’s equations6 and applicable boundary conditions as required as the case for developing planar SPP amplifiers, compact radiation sources and integrated (nano) photonics devices. However, a versatile planar platform for probing macroscopic ordering and evolutions of such SPP quasiparticles is lacking, especially in 2D limit.

Herein, we demonstrate a range of highly-tunable SPP lattices based on a category of plasmonic nanostructures at optical frequency, termed as Kekulé metasurface (Fig. 1), in which patterned nanoslits in head-to-tail fashion assemble into regular hexagon nanostructures. This multivariant platform enables us to manifest the lattice type, spatial distributions, and relative intensity of lattice sites, with controllable parameters and symmetry, which has three salient features. First, most SPP lattice possesses distinguished orbital angular momentum, evolving into another SPP lattice under different combinations of helical excitation and detection lights. Secondly, the lattice topography, for example, the relative intensity of in-plane lattice sites, could be selectively cumulatively augmented by chiselling extra open nanoslits along six corner vertices acting as the outer-wings, while the shape of other lattice sites orientationally and radially smoothly evolves into blister-like lattice geometry. Thirdly, high-fidelity SPP lattices from Kekulé metasurfaces are 2D planar and maintain even under white light excitation. Here, SPP localizations are in-plane confined and presumably enable the compact integration of miniaturized plasmonic circuits with modern-day electronic circuits, differentiating from conventional 3D localization or focusing techniques, using nano-tips9–12, Fresnel lenses13, circular lenses14–16, metalenses17–19, or plasmonic Archimedean spirals20,21. As conceptual proofs, we further show that SPP lattices with amplitude-amplified sites can be principally applied as configurable on-chip light-emitting arrays and image encryptions/decryptions, enriching the metasurface family for advanced nanolasers and information security.

Results
Tunable SPP lattices in Kekulé metasurface
Illuminated under circularly polarized laser, the nanoslits milled in gold film interact with the perpendicularly polarized component, and emit out intensive SPPs tailored by the geometric dimensions and orientation angles of nanoslits (please see SI Section S1)22. To be specified, as-generated SPPs stem from the superposition of co-polarized and cross-polarized fields. The extra phase shift in the latter allows the engineering of Pancharatnam-Berry (PB) phase (also termed as geometric-phase factor, expressed as exp(i2\alpha), where \alpha is the in-plane rotation angle of nanoslits)23. Departing from these, we develop a Kekulé metasurface via integrating such individual nanoslit (Fig. 2a) to create SPP lattices. The multiple open nanoslits are head-to-tail arranged into ‘benzene-like’ configuration with the same rotation angle (\alpha), maintaining a fixed gradient, which can convert the 2D incident circularly polarized light into a stable hexagonal lattice in the co-polarized state and customized lattices in cross-polarized state. The in-plane electric field (E||) can be expressed as follows (more detail please see SI Section S1):

E|| \propto \sum_{n=1}^{6} (\eta \sigma jE\sigma i+\eta -\sigma e-i2\sigma\alpha n jE-\sigma i)e-ik spp [xcos\theta n+ysin\theta n] (1)

where \alpha n=(n−1)l\pi/6 represents the rotation angle of n th array; l\pi/6 is the phase gradient, and l is a constant which equals to half of the lattice topology charge (TC); k spp is the wave vector of SPPs; \theta n=(n+0.5)\pi/3 denotes the angle of n th side, determining the propagating phase of SPPs; \sigma refers to different incident spin states (i.e., \sigma equals to 1 and −1, which represent left and right circularly polarized light respectively); \eta \sigma and \eta -\sigma refer to the coefficients of co-polarization order (E \sigma) and cross-polarization order (E -\sigma). Akin to the classic electron transport with a channel, liquid-like SPP propagation along the gold-dielectric interface decays because of free-electron scatterings with the polycrystal gold film. The geometric parameters of the Kekulé metasurface are optimized (see SI Fig. S2).

Equation (1) implies that several degrees of freedom (DOFs) including l, \sigma and \eta \pm\sigma, emerge for manipulating the SPP lattice in real space. For instance, when the phase gradient is zero under right circularly polarized (RCP) incidence (TC=0), we obtain a stable hexagonal SPP lattice with TC equals to 0 in left circularly polarized (LCP) state (Fig. 2b). Meanwhile, by combining with the axial (out-of-plane) electric field (Fig. 2c, see SI Section S3 for more details), meron-antimeron like lattice in normalized 3D electric field (Fig. 2d) affirms the quasiparticle characteristic of SPP lattice24. Figure 2e shows the feasible transformation of hexagonal SPP lattice into hexagonal vortex lattices (TC=1), Kagome lattices (TC=2), and honeycomb lattices (TC=3) in LCP state, at quasi-2D limit, by modulating l to be 0.5, 1, 1.5 (see SI Fig. S4), respectively. From Fig. 2a−e, we conclude that versatile SPP lattices could be manifested by Kekulé metasurfaces, enriching the lattice family and their effective control by metasurface designs (please see SI Table S1 Section S5).

To selectively engineer the SPP lattice site, we coupled the Kekulé metasurface with extra wing-shaped nanoslit sets along three high-symmetric axes passing through six corners (Fig. 2f). Combining with Eq. (1), the in-plane electric field of wing-shaped nanoslit sets in cross-polarization state can be expressed as:

E|| o, t \propto \sum_{n=1}^{6} (E||, -\sigma+ A M e-2(\alpha n+\Delta\alpha)\sigma i e-ik spp (xcos(\theta n+\Delta\theta)+ysin(\theta n+\Delta\theta)))|E-\sigma i (2)

where \Delta\alpha and \Delta\theta (herein, equals to \pi/6) are the relative values of the rotation and azimuth angle of the outer wing-shaped nanoslits to the angle (\alpha n, \theta n). A M is the factor that is affected by the number (M) of the wingsets and distance (|r i|, i=1 to 6) to the enhanced lattice site (O). Therefore, deriving from Eq. (2), the intensity of lattice sites can be selectively engineered by \Delta\alpha, M, and its relative distance (\Delta r, which equals to |r|-Rsin(\pi/3)). Figure 2g presents that the center spot (lattice site A) intensity monotonically increases with M increment and exhibits no sign of saturation for neglected SPP decay. For M=4, the in-plane electric field at hexagonal SPP lattice site A (central image, Fig. 2h) is enhanced up to 390% with respect to that of M=0 metasurface (Fig. 2b), while the intensity of surrounding lattice site B remains barely changed (normalized 3D electric field, see SI Fig. S5). The rigid shift of wing-shaped nanoslit set relative to the nanoslit hexagon along three high-symmetry axis (offsets equal to \lambda spp/sin(\pi/3), Fig. 2f) leads to remarkable intensity enhancement (~320%) of SPP lattice site B. These good correlations clearly show the custom-tailoring of the designed Kekulé metasurface over SPP lattice, which is superior to other hexagonal metasurfaces (see SI Fig. S6).

Realization and control of versatile SPP lattices
We next reproduce the SPP lattice in real space based on M=0, 1, 2, 3, and 4 Kekulé metasurfaces via finite-difference time-domain (FDTD) simulation (Fig. 3a–e, please see Methods for more details). For M=0, lattice sites B located at the vertices of a regular hexagon is surrounding lattice site A with a quite weak secondary maximum. After incorporating wing-shaped nanoslit arrays varying M from 0 to 4, two strikable features arise: (1) the intensity of lattice site A grows linearly and increases by approximate fourfold, accompanied by an increasingly intensified ring emerging between lattice site A and B; (2) the outer lattice site B tend to evolve from regular hexagon into a ring-like pattern composed of multiple bright spots. These salient features are reminiscent of the recently reported electronic crystallization and melting behaviors in two-dimensional van der Waals heterostructures25–31. Interestingly, such evolution phenomena are also visualized for other TC Kekulé metasurfaces by adding wing-shaped nanoslit sets (see SI Fig. S6).

To validate our predictions, we fabricated a series of Kekulé metasurfaces with M varying from 0 to 4 (Fig. 3f–j, bottom panels, please also see Methods). Considering that these SPP lattices dynamically consist in-plane SPPs under strong local-field and are highly susceptible to external fluctuations, in particular a sharp metallic tip based on near-field interactions9–12,32, leakage radiation microscopy (LRM)‒a versatile optical far-field method to direct quantitative imaging and analysis of SPPs in 2D limit is adopted33. Moreover, a mask and a filter were employed for both spatially and spectrally filtering the light directly transmitted through the sample, so that only pure SPPs were collected. The observed SPP ring in Fourier space (see SI Fig. S8) proves that pure SPP modes in real space (upper panels, Fig. 3f–j) were recorded by our home-made leakage radiation microscope. Surprisingly, patterns of measured SPP lattices from M=0, 1, 2, 3, and 4 Kekulé metasurfaces consistently dovetail with experimental and simulated references. The strong regularity between the selection of extra nanoslit positions and the optical lattice field intensity is also validated (see SI Fig. S9). Yet another interesting observation is that SPP localizations at lattice site A near linearly increase with added wing-shaped nanoslit sets, by carefully examining the intensity line profiles from experimental results (Fig. 3k). These features coincide with our simulated results, and suggest the cumulative SPP localizations and instinctive information-carrier nature of SPP lattices. Besides the in-plane SPP modes, our proposed Kekulé metasurface is also suitable for enhancing the scattering field, which is experimentally verified with optical lattice distribution as middle panels in Fig. 3f–j (more experimental details, please see SI section S12). The corresponding intensity profile (Fig. 3k) similarly exhibits optical lattices and tunable intensity. To further verify the universality of our proposed wing-shaped Kekulé metasurfaces, we also demonstrate the feasibility with different sizes and different plasmonic metals (see SI Note S11). Overall, the unique combination of extra wing-shaped nanoslits and basic Kekulé metasurface offers a major boost to the field intensity enhancement both for in-plane SPPs and scattering light.

Reconfiguring on-chip light-emitting array
The achievement of high-tunable SPP lattices by an extra wing-shaped nanoslit set in our Kekulé structure is promising in various applications. For example, reconfigurable light-emitting array uses SPP lattices with different lattice sites A intensity to enable on-chip patterned light sources, to the best of our knowledge, which has barely been reported before34,35. Kekulé metasurfaces with M=0 and M=4 were configured into array on a single chip, as sketched in Fig. 4a. Multiple M=4 Kekulé structures were assembled into ‘N-U-A-A’ letters while the rest sites were occupied by M=0 Kekulé structures. The ‘N’ and ‘U’ letters consist of ten M=4 structures while ‘A’ letter is composed of twelve M=4 structures. By collecting spatial coordinates and localized SPPs at the lattice site A, the real-space pattern of ‘N-U-A-A’ array (Fig. 4b) appears, and there exist no obvious SPP crosstalk between adjacent Kekulé structures. We further compared the normalized optical field intensity distribution data (see SI Fig. S13 for details), where the intensity of central lattice site A collected from M=4 structure is four times than that for M=0 one, consistent with the measured intensity ratio from two independent structures. Noted that scattering mechanism may occur and emit light out from the basal gold plane, once the thickness of gold film surpasses 70 nm due to limited leakage transmission. The conceptual validation of out-of-plane light-emitting arrays is displayed in SI Fig. S12. In addition, the on-chip planar Kekulé arrays exhibit similar optical lattices and ‘N-U-A-A’ emission pattern even under broad white light irradiation (please see SI Fig. S16), indicating their appropriateness as broadband nano-lenser arrays, at a wafer-scale levels.

In-plane SPP lattices for imaging encryption/decryption
The variable SPP lattices with multiple DOFs are potentially detached channels for in-plane imaging encryption36. We propose an encryption/decryption scheme by employing an in-plane Kekulé metasurface under RCP incident light (Fig. 5a), and the image information stored in different encryption channels of co-polarized (RCP) and cross-polarized (LCP) analyzers, which behaved as the keys. When the LCP analyzer is the key, a binary Cameraman cover image is constructed (Fig. 5b), which can be recognized as a matrix A a×b (a=b=256) with values of 0 and 1, corresponding to black and white in the targeted cameraman binary image, respectively. Here, we encrypted two stable in-plane hexagonal and honeycomb lattices (Fig. 5c) as 1 and 0, respectively.

With the RCP analyzer as the other key, a Couple gray cover image is encrypted and each pixel intensity value is fitted for a gray scale ranging from 0 to 255 (Fig. 5d). Different from aforementioned LCP channel, we employed the widely continuously tunable amplitude of lattice site A as another matrix A R a×b (a=b=512) with 0 to 255 different values according to its brightness. Afterwards, this Couple image could be decoded into a series of binary images based on the conversion between decimal and binary (Fig. 5e), and in our scheme, two cipher binary images of the logo of Chinese characters of ‘南京航空航天大学‘ (360 pixels×360 pixels, Fig. 5f) and letters of ‘NUAA’ (181 pixels×70 pixels, Fig. 5g) are stored in the 0th and 1st of the least significant bit (LSB) of upper left corner of Couple cover image (details see SI section S17). Such anti-counterfeiting process by encrypting and decrypting is based on in-plane optical SPP lattices rather than reflected or transmitted light in conventional optical encryption with metasurfaces36.

Methods
Sample fabrication
Using an electron-beam evaporation system (Syskey E-Beam Evaporation system), 5nm thick Ti (serving as an adhesion layer, deposition rate of 0.5Å/s) and 50nm (200nm) thick Au layers (deposition rate of 2Å/s) were sequentially deposited on a quartz substrate or a PET film. Afterward, Kekulé structures were precisely milled within Ti/Au film using a FEI Helios G4 UX focused ion beam (FIB) system. The FIB milling parameters were set to: voltage of 30 kV and current of 7 pA. Under a scanning electron microscope, the uniform geometry of nanoslits-the building block of Kekulé structure-is confirmed to be ~230 nm in length and ~118 nm in width. The processing field for the array is 50 μm, with a processing time of approximately 2 minutes. When processing a small field (such as 7 μm), the processing time for a single Kekulé metasurface structure is approximately 10 seconds.

Optical characterization
Using an inverted optical microscope (NanoWizard Sense) with an oil immersion objective lens (100× magnification, NA=1.30), the leakage radiation from the underside of the sample was collected. The collected radiation was then directed through a custom-built optical path (the signal was further processed via a filter and mask), and finally imaged using a CCD camera (Princeton Instrument PIXIS 1024) for real-space and Fourier-plane imaging. The detailed design optical path is shown in SI Fig. S8.

Numerical simulations
Full-wave numerical simulations were performed using the finite-different time-domain (FDTD) technique. A single nanoslit unit cell in 50nm-thick gold film was adopted. The incident wave was polarized along x- or y-axes and illuminated the nanoslits from the substrate side. Along x- and y-axes, periodic boundary conditions were applied, and a perfectly matched layer (PML) boundary condition was used along the z direction. The polarization conversion efficiency (PCE) is obtained as a function of nanoslit length L and width W at a wavelength of 633 nm (see Supplementary Fig. S2) by sweeping these values between 50 nm and 250 nm with an interval of 5 nm.

Data availability
All data needed to evaluate the conclusions in the paper are present in the paper or the Supplementary Materials. The materials that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this work, the authors studied the interference of surface plasmon polaritons (SPPs) into periodic patterns in a metal film by arranging nanoslits into a Kekulé pattern. By adding additional nanoslits in a wing-shaped configuration, the authors observed transformations in the patterns, particularly a brighter central spot. They further utilized this design for various applications, such as configurable optical arrays and optical encryption.\nHowever, my main concern with this work is the appropriateness of using the term “Wigner crystal” to describe the optical phenomenon observed. A Wigner crystal typically refers to periodic patterns formed by electron-electron interactions, such as Coulomb repulsive forces. In this study, the pattern is formed purely by interference, and the system is linear, with no interactions between photons. Therefore, the analogy of the photonic system to a Wigner crystal does not seem valid. Indeed, the use of terminologies such as “melt into” and “SPP crystallization” in the abstract and throughout the main text appears to be an overreach.\nIn my opinion, the concept of an optical Wigner crystal presented in this work is fundamentally flawed. Moreover, there is already a substantial body of research on using geometric phases to manipulate the interference patterns of SPP waves on 2D metallic platforms. Based on these considerations, I do not recommend the publication of this manuscript in Nature Communications.", "reviewer_2": "The paper presents an innovative contribution to the field of plasmonics and nanophotonics by introducing a novel Kekulé metasurface platform for creating optical Wigner crystal (WC) lattices. The concept of extending Wigner crystals from electrons to photons is very interesting. It opens new avenues for exploring quantum phenomena in photonic systems. The design of the Kekulé metasurface, with its head-to-tail arrangement of nanoslits, is well-conceived and allows for precise control over the spatial distribution and relative intensity of WC lattice sites. The ability to tailor these properties by superposing extra wing-shaped nanoslits is particularly impressive, offering a high degree of tunability. The experimental validation of the theoretical predictions is robust, with leakage radiation microscopy (LRM) providing clear visualization of the optical WC lattices. The alignment between experimental results and finite-difference time-domain (FDTD) simulations further underscores the reliability of the proposed platform.\nThe paper could benefit from addressing several limitations and providing more detailed analyses.\nOne notable omission is a thorough discussion of surface plasmon polariton (SPP) decay and losses. SPPs are known to suffer from significant propagation losses due to Ohmic damping in metals, which could limit the practical applications of the proposed platform. A more in-depth exploration of how the Kekulé metasurface mitigates these losses, or how they impact the performance of the optical WC lattices, would strengthen the paper. For instance, the authors could investigate the use of low-loss materials like silver or alternative plasmonic materials to enhance performance.\nAdditionally, the paper does not mention the scalability of the Kekulé metasurface for large-scale integration. The fabrication of such precise nanostructures, particularly with the addition of wing-shaped nanoslits, could pose significant challenges and may limit practical implementation. Providing more details on the fabrication process, including potential challenges and strategies for scaling up production, would be valuable.\nOn the other hand, it would be useful to see the quantitative metrics for evaluating the performance of the demonstrated applications. For example, the quantification of the efficiency of the light-emitting arrays and the security level of the image encryption scheme. Understanding this is the early stage of the technology, maybe an analysis of the potential would be sufficient. This would be helpful to assess their practical viability compared to existing technologies.\nFinally, it would be good to see more details on the theoretical framework for the formation of optical WC lattices, the mathematical treatment could be more rigorous. Expanding the derivation of the in-plane electric field (Equation 1) to include more detailed explanations of the underlying assumptions and approximations, as well as a deeper discussion of the physical mechanisms governing the formation and melting of the optical WC lattices, would enhance the theoretical depth of the study."}, "author_response": "List of changes made in this revision\nDuring this revision, we have conducted additional experiments and analyses to\nclarify the claims and potential of our work. The new results have been incorporated\ninto the revised manuscript and Supplementary Information as outlined in the\nfollowing.\n(a) Regarding the questions of Reviewer #1 about the appropriateness of using ''Wigner\ncrystal lattice'' to describe SPP localization phenomena in linear plasma systems,\nwe have carefully reconsidered the terminology and revised ''optical Wigner crystal\nlattice'' to ''optical Wigner-type lattice''. This modification, along with its\njustifications and the fundamental distinctions from conventional electronic Wigner\ncrystals in terms of formation mechanisms and physical principles, have been\ndetailed in SI Note1.\n(b) Regarding the comment of Reviewer #1 about the overuse of specialized\nterminology, we have revised the term 'melt into' from both the main text and\nsupplementary materials. Additionally, we have replaced 'SPP Crystallization' with\nthe more accurate description 'SPP Localization' throughout the manuscript. Similar\nterminology adjustments have been made where appropriate to ensure conceptual\nclarity while maintaining scientific precision.\n(c) Regarding the suggestion of Reviewer #2 about detailed discussion of surface\nplasmon polaritons' decay and loss issues, we provided the comparison of Ag\nKekulé metasurfaces in Figures S11 and discussed on Page S15 Section 11 of SI.\n(d) Regarding the suggestion of Reviewer #2 about discussing the scalability of Kekulé\nmetasurfaces for large-scale integration and the details/challenges of sample\nfabrication, we have supplemented relevant experiments, designed and fabricated\ntwo Kekulé metasurface structures with diameters of R=1μm and 1.5μm, and two\ntypes of closely integrated Kekulé metasurface array structures, apparently\nverifying the feasibility of large-scale integration of Kekulé metasurfaces. These\ncontents have been supplemented in SI Note 11 and SI Note14 respectively.\nMeanwhile, we have also incorporated additional details and challenges regarding\nthe structural fabrication in both the Methods section (Page 12) and SI Note 14.\n(e) Regarding the suggestion of Reviewer #2 about quantifying the efficiency of\nluminescent array and evaluating the security level of image encryption, we have\nadded the evaluation of efficiency in Section 16 in SI. Besides, we also\nsystematically analyzed the existed and achievable multi-level encryption\nprotection measured in this encryption scheme in SI Note 18. Additionally, we have\nconducted a quantitative evaluation of the attack resistance capability of least\nsignificant bit (LSB) steganography and performed a comprehensive analysis of\nstructural integrity protection for masked images.\n(f) Regarding the suggestion of Reviewer #2 about providing details on the theoretical\nframework, we have complemented more details of the derivation of Equation 1\nincluding assumption and approximation, which is added in Section 2 in SI.\nMinor revisions have been made through the manuscript. The revised text and\ndiscussions are highlighted in red in the revised manuscript.\nPoint-by-point response to referee’s comments for manuscript No. NCOMMS-\n24-72188A to Nature Communications.\nGeneral response.\nWe sincerely appreciate two reviewers for their time and efforts in evaluating our manuscript\nand providing valuable comments. Reviewer #2 made positive assessments and recommended\nthis work for publication after revision. In response to these comments, we conducted further\ntheoretical and experimental analyses, which verify Reviewer’s speculation and strengthen the\nuniversality and potential of Kekulé metasurfaces and SSP lattices. The Reviewer #1's decision\nto reject our manuscript seems to be largely based on the usage of “optical Wigner crystal”,\nalthough which should come from a misunderstanding in accordance to our extensive literature\nreview and fundamental analysis. We have revised this term in the title, main text, and\nSupplementary Information to enhance conceptual clarity and explicitly delineate the physical\nmechanisms underlying concept transfer. With all these efforts and revisions, we hope the\nclarity and accuracy of the manuscript can now be suitable to be accepted for publication in\nNature Communications.\nComments to the Author\nReviewer #1:\nIn this work, the authors studied the interference of surface plasmon polaritons (SPPs) into\nperiodic patterns in a metal film by arranging nanoslits into a Kekulé pattern. By adding\nadditional nanoslits in a wing-shaped configuration, the authors observed transformations in\nthe patterns, particularly a brighter central spot. They further utilized this design for various\napplications, such as configurable optical arrays and optical encryption.\nResponse:\nThank you for these constructive comments and recognitions of our manuscript. The referee is\ncorrect that the design of Kekulé patterned nanoslits is one of the key findings in this work,\nwhich could be overlayed with extra wing-shaped nanoslits to tailor as-generated optical lattices,\nin terms of lattice categories and intensities. More importantly, the customized optical lattices\nenable us to demonstrate their potential together in configurable optical arrays and optical\nencryption, to the best of our knowledge, which is relatively lagged behind yet.\nIn view of your’s concerns and comments, we concentrated our focus upon 2D optical lattices\nand corresponding modulations in the revised manuscript. We hope that you may find the\nupdated version appropriate and publishable in Nature Communications.\nComment 1: However, my main concern with this work is the appropriateness of using the\nterm “Wigner crystal” to describe the optical phenomenon observed. A Wigner crystal typically\nrefers to periodic patterns formed by electron-electron interactions, such as Coulomb repulsive\nforces. In this study, the pattern is formed purely by interference, and the system is linear, with\nno interactions between photons. Therefore, the analogy of the photonic system to a Wigner\ncrystal does not seem valid. Indeed, the use of terminologies such as “melt into” and “SPP\ncrystallization” in the abstract and throughout the main text appears to be an overreach. In my\nopinion, the concept of an optical Wigner crystal presented in this work is fundamentally flawed.\nMoreover, there is already a substantial body of research on using geometric phases to\nmanipulate the interference patterns of SPP waves on 2D metallic platforms. Based on these\nconsiderations, I do not recommend the publication of this manuscript in Nature\nCommunications.\nReply #1: We sincerely thank you and understand your concern. Surface plasmon polaritons\n(SPPs) exhibit both wave and particle properties[ Nat. Phys. 5, 470-474, (2009)], therefore,\nnumerous envisions emerge attempting to elucidate the formation and evolution SPPs from the\nview of quasiparticles[ Nat. Rev. Phys. 2, 538-561, (2020)], exactly as what we try in this study.\nBy patterning polygonal metasurface with hexagonal symmetry, several plasmonic lattices are\nreported, such as optical skyrmion lattice[ Science 361, 993-996, (2018)] and hexagonal\nlattice[ Sci. Adv. 11, eadv3938, (2025)]. However, tuning the 2D topography and relative\nintensity of these plasmonic lattices remains challenging. To tackle these limitations, we\ndeveloped a Kekulé metasurface featured with (1) nanoslits in head-to-tail fashion assembled\ninto regular hexagon nanostructures, (2) benzene-type hexagon with alternatively neighboring\nstructures and (3) extra wing-shaped nanoslit sets, and elegantly realize the spatial control of\nSPPs with numerous degrees of freedom (DOFs), analogous to kaleidoscopic electron\nlocalization behaviors in 2D electron systems. As you pointed out, however, the expression of\n“Optical Wigner Crystal” is inappropriate and immature at present stages. In this concern, the\n“Optical Wigner Crystal lattices” has been carefully revised to “Optical Wigner-type lattices”,\nand some misleading expression including “melt into” and “SPP crystallization” was removed,\nfor the sake of appropriateness. The usage of “Wigner-type” is to visually describe the lattice\npattern with tunable topography, and hopefully attempt to inspire more investigations of 2D\nSPPs as (quasi-)particles. Below is our detailed interpretation from five essential aspects:\n1) Generalized Wigner lattice beyond traditional electron landscape: The classical\n“Wigner crystal”, first predicted by Eugene Wigner in 1934, describes the periodic patterns of\nelectrons under certain electron-electron interactions. More recently, however, a variety of\ngeneralized Wigner crystals were reported and categorized in the following Table R1. As a\nsupplement to the classical electron system, generalized Wigner crystals (WCs) have been\nsuccessionally demonstrated in Moiré superlattice systems (for holes) and even molecular\nensembles. These generalized WCs typically arises from the synergistic interplay between\nthe Moiré potential confinement and long-range Coulomb interactions among\nquasiparticles. In addition, WCs were also reported in cold atomic/ionic systems through\nengineered approaches such as Feshbach resonance, optical lattice confinement, dipolar\ninteraction modulation, and ion trap potentials. It is noteworthy that, particularly in cold atomic\nsystems, the intrinsic interatomic interactions (dominated by van der Waals forces) are\nextremely weak and only become significant at ultralow interatomic distances. These\nnatural interactions are far insufficient to overcome quantum or thermal fluctuations to induce\nspontaneous spatial ordering. Without engineered strategies to (i) enhance repulsive\ninteractions, (ii) suppress kinetic energy, and (iii) tailor geometric configurations, Wigner\ncrystallization cannot emerge spontaneously. These studies stand in stark contrast to\nconventional electron systems, where WCs form spontaneously due to the naturally dominant\nlong-range Coulomb interactions. In our work, we utilize Kekulé design to \"customize\" the\nboundary conditions of surface plasmon polaritons (SPPs), achieving periodic modulation of\nSPP fields. This approach shares conceptual similarities with engineered potential design in\ncold atomic systems: both relying on artificially designed potentials (e.g., optical lattices or\nnanostructures) to break natural symmetry and establish functional periodicity.\nTable R1. Generalized Wigner crystals reported in literatures.\n2) SPPs as quasiparticles. Numerous theoretical and experimental studies have confirmed the\nquasiparticle behavior of SPPs[ Nat. Phys. 5, 470-474, (2009); Nat. Nanotechnol. 8, 719-722,\n(2013); Nature 450, 402-406, (2007); Phys. Rev. Appl. 2, 014004, (2014)]. Among these, Dheur\nM C et al. pioneerly demonstrated the wave-particle duality for a single SPP freely propagating\nalong a planar metal-air interface[ Sci. Adv. 2, e1501574, (2016)]. Stimulated by these, we re-\nconsider 2D SPPs more from the quasiparticle perspective, which involves designing Kekulé\nnanostructures to regulate the momentum of SPPs, thereby achieving efficient quasiparticle\nwavefunction superposition. Given the absence of many-body interactions among SPP\nquasiparticles here, we replaced \"Wigner crystal lattice\" by \"Wigner-type lattice\" to\nemphasize structural WCs analogy while distinguishing it from traditional systems\ndominated by Coulomb interactions.\n3) Theoretical Commonalities between electronic Wigner Crystals and plasmonic system.\nSchulz H J et al. provided a unified theoretical framework for Wigner Crystal in one\ndimension[ Phys. Rev. Lett. 71, 1864, (1993)]. In such framework, plasmon and spin excitations\nin one-dimensional structures is somehow consistent and the electron arrangement rules may\nalso suitable for collective oscillation of electrons (e.g. SPPs). This suggests the feasibility\nof extending the WC lattice over SPPs but in a broader way. Thus, \"Wigner-type lattice\" is\nadopted here to capture and present SPPs behavior as plasmonic quasiparticles, similar to what\nWigner Crystals lattice to electron and its analogs.\n4) Electronic-to-photonic conceptual migration. The cross-disciplinary migration of\nscientific concepts is exemplified by the cases such as the extension of \"optical skyrmions\"\nconcept from non-linear nuclear physics, spintronics to photonics via several studies upon\nlinear plasmonics[Phys. Rev. Lett. 87, 037203, (2001); Science 341, 636-639, (2013); Science\n361, 993-996, (2018)]. To be specified, the concept of Skyrmions was initially proposed by\nTony Skyrme[Series A. Mathematical and Physical Sciences 260, 127-138, (1961)]and\nrepresents topological manifestations of strongly interacting matter in nuclear physics,\nfundamentally relying on non-perturbative QCD effects. Later in emerging spintronic\ntechnologies, two-dimensional magnetic Skyrmions, as topological spin textures, emerge from\nthe synergistic interplay of multiple magnetic exchange interactions (e.g., Heisenberg\nexchange, Dzyaloshinskii-Moriya interaction, etc.). In contrast, optical Skyrmions were first\ntheoretically proposed and experimentally realized by Tsesses S et al. in 2018[ Science 361,\n993-996, (2018)]. The formation of optical Skyrmions relies entirely on evanescent field\nmanipulation within linear plasmonic systems, without requiring SPPs interactions.\nAlthough their formation mechanisms and physical origins differ significantly from those in\nnuclear physics and spintronic systems (non-linear to linear evolution), the extension of\nSkyrmions into photonic systems opens up diverse possibilities in photonics, including optical\ninformation processing, transmissions, and storages.\nAnother familiar example is the concept of \"photonic crystals\", which is borrowed\nfrom semiconductor band theory in solid-state physics. Unlike the periodic Coulomb potentials\nin atomic lattices, photonic crystals utilize designed periodic dielectric constant distributions as\neffective potentials. In addition, electronic bandgaps arise from destructive interference of\nelectron wavefunctions in periodic potentials, whereas photonic bandgaps result from Bragg\nscattering-induced destructive interference of light in dielectric structures[ Phys. Rev. Lett. 58,\n2059, (1987)]. This seemingly unrelated concept between its electronic and photonic\ncounterpart triggers many impressive progresses and promotes the adoption of \"Wigner-type\nlattice\" to describe the periodic photonic pattern in this study.\n5) Research highlights of our work. Linear plasmonic systems holds significant scientific\ninterests. For instance, Tsesses S et al. recently employed geometric phase to design plasmonic\nquasi-crystalline structures, and established the intrinsic connection between global symmetry\nand topological properties in two-dimensional plasmonic quasicrystals[ Science 387, 644-648,\n(2025)]. In another study, Schwab J et al. utilized geometric phase to engineer Morse soliton\nsuperlattice structures and explored dual electronic paradigms in plasmonic systems with non-\ntrivial topology[ Nat. Phys., 1-7, (2025)]. These works collectively underscore the broad\nresearch and application potential of linear plasmonic systems.\nIn the scope of linear plasmonic systems, we proposed and demonstrated how the Kekulé-type\nmetasurfaces become new controllable and abundant degrees of freedom for engineering\npotential fields toward configurable optical arrays and optical encryption. The key message in\nthis work lies in four aspects:\na) The plasmonic lattice based on Kekulé structures exhibits unique orbital angular\nmomentum, under different combination of polarization states of incident and detected\nlights, leading to the topographic evolution of distinct Wigner-type lattices.\nb) Adjusting the number and positions of extra wing-shaped nanoslits over the Kekulé\nstructure cumulatively alters the intensity and morphology of in-plane lattice sites, in a\nprecisely controlled way.\nc) The high-fidelity Wigner-type lattice demonstrates broadband characteristics,\nmaintaining its properties even under white light excitation. In addition, this Wigner-\ntype lattices well retains although the Kekulé metasurface is scaled down to 2 µm. This\nbroadband feature without crosstalk showcasing the potential of Kekulé metasurface\nfor miniaturized plasmonic integrated circuits.\nd) We demonstrate that optical Wigner-type lattices with amplitude-amplified lattice sites\ncan be applied as configurable on-chip light-emitting arrays and image\nencryption/decryption systems, thereby enriching the family of metasurfaces for\nadvanced nanolasers and information security applications.\nIn conclusion, the novelty of our work lies in the designed Kekulé metasurfaces, extra wing-\nshaped nanoslits and their corresponding modulations over plasmonic lattices, accompanied by\ntheir use in configurable light-emitting arrays and image encryption/decryption. To avoid any\ninappropriateness or misleading caused upon as-manifested SPPs pattern, the expression of\n\"Wigner Crystal lattice\" was replaced by “Wiger-type lattice” to describe these periodic\nplasmonic lattice pattern akin to conventional and generalized electronic ones.\nAction: In both the main text and supplementary materials, we have revised the\nterminology from \"optical Wigner crystal lattice\" to \"optical Wigner-type lattice\" to avoid\nany misleading or inappropriateness. We have also replaced potentially ambiguous terms\nsuch as \"melt into\" and \"SPP crystallization\" with proper expression of \"SPP localization\".\nFor instance, on page 2 of the main text, we now re-state: \"Motivated by electronic Wigner\ncrystallization lattices, we identify such SPP lattices as optical Wigner-type lattices here (see\nSI 1), which exhibit three salient features.\" The text continues: \"Here, SPP localizations are\nin-plane confined, potentially enabling compact integration of miniaturized plasmonic circuits\nwith modern electronic circuits.\" In SI Note S1 (Interpretation of the definition \"Optical\nWigner-type lattice\"), we explicitly clarified the details of this nomenclature by overviewing\nthe fundamental similarities and differences in formation mechanisms and physical\nprinciples between Optical Wigner-type lattice and conventional electronic Wigner\ncrystals: \"The original \"Wigner crystal\" concept, formulated by Eugene Wigner in 1934,\ncharacterizes the ordered spatial arrangement of electrons governed by specific interelectronic\ninteractions. More recently, numerous studies have demonstrated that (generalized) Wigner\ncrystals can form from electrons, holes, and molecules in moiré superlattice systems, typically\nresulting from the synergistic interplay between moiré potential confinement and long-range\nCoulomb interactions among (quasi)particles. Concurrently, Wigner crystals have also been\nrealized in cold atomic/ionic systems through engineered interactions such as Feshbach\nresonance, optical lattices, dipole modulation, and ion trap confinement. It is particularly\nnoteworthy that in cold atomic systems, the naturally occurring interatomic interactions (van\nder Waals forces) are extremely weak and only become significant at ultralow interatomic\ndistances—far too feeble to overcome quantum or thermal fluctuations and induce spatial\nordering. Without engineered methods to enhance repulsion, suppress kinetic energy, and\ndesign geometric configurations, Wigner crystallization cannot occur spontaneously. This\nstands in contrast to traditional electronic systems, where WCs form naturally due to intrinsic\nlong-range Coulomb forces. In our work, we utilize Kekulé nanostructure design to \"customize\"\nthe boundary conditions of SPPs, achieving periodic modulation of SPP fields. This approach\nshares conceptual similarities with engineered potential design in cold atomic systems: both\nrelying on artificially designed potentials (optical lattices or nanostructures) to break natural\nsymmetry and establish functional periodicity. Under conceptual analogy, we re-consider 2D\nSPPs more from the quasiparticle perspective, which involves designing Kekulé nanostructures\nto regulate the momentum of SPPs, thereby achieving efficient quasiparticle wavefunction\nsuperposition. Since SPP quasiparticles in our system lack significant many-body interactions,\nwe employ the term \"Wigner-type lattice\" instead of \"Wigner crystal lattice\" - preserving the\nstructural analogy to conventional Wigner crystals while clearly differentiating our system\nfrom those governed by Coulomb-dominated physics.\nThe cross-disciplinary migration of scientific concepts is exemplified by the cases such as the\nextension of \"optical skyrmions\" concept from non-linear nuclear physics, spintronics to\nphotonics via several studies upon linear plasmonics1-3. Originally proposed by Tony Skyrme4,\nskyrmions represented topological phenomena in strongly interacting nuclear matter,\nfundamentally rooted in non-perturbative quantum chromodynamics effects. This concept later\nfound application in spintronics, where two-dimensional magnetic skyrmions emerged as\ntopological spin textures resulting from complex magnetic exchange interactions. A distinct\ndevelopment occurred in 2018 when Tsesses and colleagues first theoretically proposed and\nexperimentally demonstrated optical skyrmions. Unlike their nuclear and magnetic\ncounterparts, these photonic versions form through precise manipulation of evanescent fields\nin linear plasmonic systems, without requiring SPP interactions. Another familiar example is\nthe concept of \"photonic crystals\", which is borrowed from semiconductor band theory in solid-\nstate physics. While traditional semiconductors rely on periodic Coulomb potentials in atomic\nlattices, photonic crystals achieve similar effects through engineered periodic variations in\ndielectric constants. The underlying mechanisms differ significantly-electronic bandgaps arise\nfrom electron wavefunction interference in atomic potentials, whereas photonic bandgaps\nresult from Bragg scattering-induced light interference in dielectric structures5.\nThis seemingly unrelated concept between its electronic and photonic counterpart triggers\nmany impressive progresses. And we adopt the term \"Wigner-type lattice\" in our study to\ndescribe periodic photonic patterns, maintaining conceptual continuity while acknowledging\nkey differences from conventional Wigner crystals.\"\nReviewer #2:\nThe paper presents an innovative contribution to the field of plasmonics and nanophotonics by\nintroducing a novel Kekulé metasurface platform for creating optical Wigner crystal (WC)\nlattices. The concept of extending Wigner crystals from electrons to photons is very interesting.\nIt opens new avenues for exploring quantum phenomena in photonic systems. The design of\nthe Kekulé metasurface, with its head-to-tail arrangement of nanoslits, is well-conceived and\nallows for precise control over the spatial distribution and relative intensity of WC lattice sites.\nThe ability to tailor these properties by superposing extra wing-shaped nanoslits is particularly\nimpressive, offering a high degree of tunability. The experimental validation of the theoretical\npredictions is robust, with leakage radiation microscopy (LRM) providing clear visualization\nof the optical WC lattices. The alignment between experimental results and finite-difference\ntime-domain (FDTD) simulations further underscores the reliability of the proposed platform.\nThe paper could benefit from addressing several limitations and providing more detailed\nanalyses.\nResponse:\nWe thank the referee for carefully reading the manuscript and for these useful and constructive\ncomments. The suggested aspects are clarified and the manuscript is revised following your\ncomments.\nComment 1: One notable omission is a thorough discussion of surface plasmon polariton (SPP)\ndecay and losses. SPPs are known to suffer from significant propagation losses due to Ohmic\ndamping in metals, which could limit the practical applications of the proposed platform. A\nmore in-depth exploration of how the Kekulé metasurface mitigates these losses, or how they\nimpact the performance of the optical WC lattices, would strengthen the paper. For instance,\nthe authors could investigate the use of low-loss materials like silver or alternative plasmonic\nmaterials to enhance performance.\nReply #1: We thank the referee for this constructive suggestion. In our calculation, since the\nsize of Kekulé metasurface (R=2.5 μm) is much smaller than the SPP propagation length at Au\nsurface (~10 μm at 633nm), the plasmon damping can be neglected [ Nat. Photonics 11, 623-\n627, (2017); Nat. Phys., 1-7, (2025)]. To nicely tackle this concern, we compared different\nplasmonic metals accordingly. It is well-known that SPP suffer from significant propagation\nlosses, which is caused by ohmic losses of participating electrons in SPPs and finally results in\na heating of the metal. The propagation length of SPP along the interface is determined by the\nimaginary part γ of the SPP wave vector β (β = k + iγ, 𝛾 =𝑘 𝜀′′𝜀 √𝜀′𝜀 /(𝜀′ +𝜀 )/\nspp spp spp 0 1 2 1 2 1 2\n2(𝜀′2+𝜀′𝜀 ) and it is associated to the dielectric constant𝜀(𝜀 = 𝜀′+𝑖𝜀′′), which is\n1 1 2\nresponsible for an exponential damping of the electric field amplitude. For our Kekulé\nmetasurface, the internal electric field of the metasurface is the superposition of propagating\nSPP generated from six nanoslits arrays, and in the cross-polarization state of the incident beam,\nby ignoring the contribute of the perpendicular component of SPP, the internal field can be\nexpressed as follows (See SI for details):\n𝐸 = ∑𝑛=6 𝐴 𝜂 𝑒−𝑖2𝜎𝛼n𝑒𝑖𝑘spp (𝑥𝑐𝑜𝑠𝜃n+𝑦𝑠𝑖𝑛𝜃n )𝑒−𝜈𝑟 (1)\n||,−σ 𝑛=1 −σ\n√𝑟\nAccording to Equation (1), the SPP propagation loss only influences the light intensity rather\nthan its phase, so the pattern of as-generated lattice is not affected. Next, we focus on the impact\nof SPP propagation loss on light energy. We compared the intensity distribution of different\nplasmonic material for silver (Ag) and gold (Au) in numerical calculations [dielectric constants\nε derived from Jonhnson and Christy database, for silver (ε=-18.3 + 0.5i) and for gold (ε=-\n11.76+ 1.3i) at a wavelength of 633 nm]. For clarifications, the structural parameters were set\nthe same as our designed Kekulé structure in the maintext (Radius R equals to 2.5 μm). As can\nbe seen in Figure R2-1, the intensity and centre lattice increment for Ag sample is slightly\nhigher than Au sample (~1.2 times, Figure R2-1d and R2-1e). To be more quantitatively, for\nAu Kekulé metasurface, the intensity with M=3 (See Figure R2-1d) is around 3.8 times than\nthat of initial structure (M=0, see Figure R2-1a). For Ag Kekulé metasurface, the intensity with\nM=3 (See Figure R2-1e) is simulated to be around 4 times than the basic structure (M=0, see\nFigure R2-1b). Experimentally, by fabricating Ag Kekulé metasurface, we obtained around 3.8\ntimes increment if comparing the intensities from M=3 and M=0 samples (Figure R2-1c and\nR2-1d). These results suggest the universality of Kekulé metasurface and the feasibility of\nneglecting decay and losses.\nFigure R2-1 | Calculated and experimental snapshots of optical WC lattices with different\nplasmonic materials Au and Ag Kekulé structures (R~2.5 μm). a, Calculated intensity\ndistribution with Au Kekulé structures (M=0). b, Calculated intensity distribution with Ag\nKekulé structures (M=0). c, Experimental intensity distribution with Ag Kekulé structures\n(M=0). d, Calculated intensity distribution with Au Kekulé structures (M=3). e, Calculated\nintensity distribution with Ag Kekulé structures (M=3). f, Experimental intensity distribution\nwith Ag Kekulé structures (M=3). The results indicate that when a right-circularly polarized\n(RCP) laser with a wavelength of 633 nm is incident on different Kekulé structures, the\ngenerated light is polarized by a left-circular polarizer (LCP), producing the intensity\ndistribution of the in-plane optical field (each normalized individually). Scale bar: 0.6 m. g,\nThe normalized intensity distributions (dashed line sketched in Fig. R2-1a).\nWe further theoretically compared Au and Ag Kekulé metasurface with a larger size of R=10\nμm since the SPP loss will be more significant at this geometric regime, as shown in Fig. R2-\n2. We found the intensity variations between Au and Ag metasurfaces (Figure R2-2a and R2-\n2b) become larger, with the intensity ratio of 2.2 times for Ag and Au samples. In another word,\nfor larger Kekulé metasurface with radius surpassing the critical values, regardless of silver or\ngold materials, the SPP damping can not be neglected.\nFigure R2-2 | Calculated snapshots of optical WC lattices with different Au and Ag Kekulé\nstructures (R ~10 μm). a, Calculated intensity distribution with Au Kekulé structures (M=0).\nb, Calculated intensity distribution with Ag Kekulé structures (M=0). c, Calculated intensity\ndistribution with Au Kekulé structures (M=3). d, Calculated intensity distribution with Ag\nKekulé structures (M=3). Scale bar: 0.6 m. e, The normalized intensity distributions (dashed\nline represented in Fig. R2-2a).\nBased on the above discussions, the Kekulé metasurface should be controlled within a critical\ndimension, which depends on adopted plasmonic material. In our design, the metasurface radius\nR is selected as 2.5 μm for several reasons. At this scale, the energy retention of one single SPP\nplane wave is about 75% in intensity at the central area. After the SPP superposition generated\nby six nanoslits arrays, the target lattice achieves a high energy utilization rate. For the\nmetasurfaces with outer-wing Kekulé metasurface (M=4), the distance from the center to the\nwing nanoslits ranges from 2.1μm to 4 μm. Although the energy propagation loss of SPP from\nthe innermost to the outermost-wing is reduced from 81% to 61%, the outermost wing structure\nstill enhances the intensity of total light field. Besides, although Ag is considered a better low-\nloss noble metal with respect to Au, its surface becomes spontaneously oxidized upon air\nexposure, such degradation is especially deleterious to its usage for plasmonic.\nAction: As suggested, we have added the sentence “To further verify the universality of our\nproposed wing-shaped Kekulé metasurfaces, we also demonstrated the feasibility with varied\ngeometric sizes and plasmonic metals (see SI Note S11).” into the manuscript at Page 7. In\naddition, we also added the comparison results of Ag Kekulé metasurface into SI Note S11,\nFigure S11, Page S15.\nComment 2: Additionally, the paper does not mention the scalability of the Kekulé metasurface\nfor large-scale integration. The fabrication of such precise nanostructures, particularly with the\naddition of wing-shaped nanoslits, could pose significant challenges and may limit practical\nimplementation. Providing more details on the fabrication process, including potential\nchallenges and strategies for scaling up production, would be valuable.\nReply #2: We thank the referee for this constructive suggestion. The scalability of Kekulé\nmetasurface for large-scale integration is indeed significant for its potential applications. It is\nknown that higher integration density is usually achieved by reducing each individual element,\nwe performed more experiments to validate the feasibility of downscaled Kekulé metasurface\nas integrable plasmonic unit. In addition to the radius of 2.5 μm in the maintext, we here\nexamined the metasurfaces with R=1.5 μm (Figures R2-3a and 3b) and R=1 μm (Figure R2-3c\nand 3d). As can be seen from Figures R2-3e-3h (corresponding to structures a-d, respectively),\nthe lattice morphology barely changes: sublattice sites B at the hexagonal vertices exhibit sub-\nmaximal intensities surrounding site A. More importantly, the intensity at site A for M=4\nsample increases by nearly fourfold compared to the M=0 one (Figures R2-3i-3j),\ndemonstrating a pronounced central convergence trend. Therefore, such reduced dimensions\nallow better scaling of our proposed Kekulé metasurface for large-scale integration.\nFigure R2-3 | Experiments results of optical lattices for reduced dimensions of Kekulé\nmetasurfaces. a-b, SEM images of Kekulé structures (R=1.5 μm) corresponding to M=0 and\n4, respectively. Scale bar: 1 μm. c-d, SEM images of Kekulé structures (R=1 μm) corresponding\nto M=0 and 4, respectively. e-h, Calculation of normalized SPPs-based optical lattices with\ndifferent Kekulé structures corresponding to the upper panel of (a-d), respectively. Scale bar:\n0.6 μm. i-j, Intensity profiles for lattices in e-h (dashed line in e).\nFurthermore, we experimentally verified the feasibility of large-scale integration of Kekulé\nmetasurface structures. Using M=0 and M=4 configurations as integrated units, tightly packed\npatterns were designed (Figures R2-4a and 4b; integration details as illustrated in inset Figure\nR2-4c). Figures R2-4d and 4e shows the measured SPP distributions under global illumination\nof a 633 nm laser. The weak cross-talk between adjacent Kekulé metasurface structures clearly\ndemonstrate themselves ideal repeated unit for large-area integration.\nFigure R 2-4 | Experimental demonstration of large-scale integration of Kekulé\nmetasurfaces. a, SEM images of large-scale metasurface array with M=0 structures. Scale bar:\n5μm. b, SEM images of large-scale metasurface array with M=4 structures. c, Schematic\nillustrations of integration structure. d, Spontaneous light-emitting patterns corresponding to\nintegration in (a). e, Spontaneous light-emitting patterns corresponding to integration in (b).\nFor the fabrication process, the experimental samples were fabricated using focused ion beam\n(FIB) etching, a mature and widely adopted technique in micro/nanofabrication and on-chip\nintegration. The process parameters were set to an acceleration voltage of 30 kV and a beam\ncurrent of 7 pA. For array fabrication with a 50 μm field of view, the total processing time was\napproximately 2 minutes, while a single Kekulé metasurface structure within a smaller field\n(e.g., 5 μm) required only ~10 seconds. These results demonstrate the time-efficient nature of\nthe fabrication process, with SEM characterization and experimental testing further confirming\nexcellent structural fidelity. In addition to the FIB fabrication approach, conventional electron\nbeam lithography (EBL) can also achieve consistent global precision in constructing large-scale\nperiodic metasurfaces. By taking high fabrication efficiency and process scalability of EBL, the\nfabrications of Kekulé metasurfaces and their integration would not be a technological\nchallenge.\nAction: As suggested, we have added the sentence \"To further verify the universality of our\nproposed wing-shaped Kekulé metasurfaces, we also demonstrated the feasibility with varied\ngeometric sizes and plasmonic metals (see SI Note S11).\" into the manuscript at Page 7. In\naddition, we also added the comparison results of Ag Kekulé metasurface into SI note S11,\nFigure S11, Page S15. We have supplemented our discussion on the scalability of Kekulé\nmetasurfaces for large-scale integration in SI Note S14: \"Furthermore, we experimentally\nverified the feasibility of large-scale integration of Kekulé metasurface structures. We\nimplemented densely packed arrays using alternative metasurfaces with M=0 and M=4\nconfigurations (Figures S15a-15b), with detailed integration schematics provided in Figure\nS15c. When illuminated by a 633 nm polarized laser source, the measured surface plasmon\npolariton (SPP) distributions (Figures S15d-15e) reveal minimal interference between\nneighboring structures, confirming the practical viability of high-density integration for these\nmetasurface designs. However, since we employed a divergent laser source in this experiment,\nthe incident beam exhibited weak intensity and non-uniform distribution over large areas,\nresulting in inferior experimental performance compared to individual scanning-mode\nillumination. For practical industrial applications, microlens arrays can be utilized to\nhomogenize and diffuse the incident laser beam, thereby optimizing the experimental\noutcomes.\"\nAdditionally, we have further elaborated on the sample fabrication details in the Methods\nsection (Page 12) of our main text: \"The processing field for the array is 50 μm, with a\nprocessing time of approximately 2 minutes. When processing a smaller field (such as 7 μm),\nthe processing time for a single Kekulé metasurface structure is approximately 10 seconds.\"\nComment 3: On the other hand, it would be useful to see the quantitative metrics for evaluating\nthe performance of the demonstrated applications. For example, (a) the quantification of the\nefficiency of the light-emitting arrays and (b) the security level of the image encryption scheme.\nUnderstanding this is the early stage of the technology, maybe an analysis of the potential would\nbe sufficient. This would be helpful to assess their practical viability compared to existing\ntechnologies.\nReply #3: We thank the referee for these constructive suggestions. For (a), first, we\nquantitatively evaluated the device performance through three aspects: SPP coupling efficiency,\nSPP polarization conversion efficiency and the central lattice coupling efficiency.\ni. SPP coupling efficiency. According to the reference, the SPP coupling efficiency of single\nnanoslit can be defined as the amount of the propagating SPPs coupled in the cross-polarized\nstate (𝐼 ) when an incident beam in the σ polarization state (𝐼 ) is irradiated onto the\nspp,−σ in,σ\nstructures [ Light Sci. Appl. 3, e197-e197, (2014)].\n𝜂 = 𝐼spp,−σ / 𝐼in,σ\nHere, the intensity of propagation SPP (𝐼 ) is related to the acquired leakage radiation\nspp,−σ\nintensity (𝐼 ), which collected by the leakage radiation microscopy (LRM) setup, and it is\nLR,−σ\ndefined as:\n𝐼 = 𝐼spp,−σ / (1+𝛤)\nLR,−σ\nWhereΓ is the loss ratio between absorption in the gold film and the leakage radiation.\nTherefore, the efficiency can be expressed as:\n𝜂 = (1+𝛤)𝐼LR,−σ / 𝐼in,σ\nBy measuring Γ, 𝐼 and 𝐼 , the emission efficiency can be achieved. The simulated SPP\nT,σ LR,−σ\ncoupling efficiency of unit cell is denoted by 𝑇 (details, see in SI section 3). The simulated\n𝑐𝑟𝑜𝑠𝑠\nand measured emitting efficiency of the Kekulé metasurface at 633 nm is about 3.74% and\n1.92%, respectively, which is comparable to the reference [ Nat. Commun. 14, 3915, (2023);\nScience 340, 331-334, (2013)].\nii. SPP polarization conversion efficiency. The polarization conversion efficiency (PCE) is\ndefined as the ratio of the cross-polarized SPP beam in generated SPP beam (𝑃𝐶𝐸 = 𝑇 ⁄(𝑇 +𝑇 )). It is an important parameter of metasurface and is usually used to\ncross co cross\nevaluate the optimized performance of the structural unit. According to the FDTD simulation,\nwe achieve a PCE of ~48% for the Kekulé metasurface. The measured PCE of the Kekulé\nmetasurface is about ~20%, and this reduction may stem from some imperfections or non-\nhomogeneities of as-fabricated nanoslits.\niii. Central lattice coupling efficiency. We employed the extra wing-shaped nanoslit set to tailor\nthe spatial distribution and relative intensities of the lattice sites. For instance, we demonstrated\n“NUAA” display applications based on the degree of light at the central lattice, which can be\nalso defined as the intensity ratio of the central lattice (𝐼 ) to the total amount of SPP\ncentre\ngenerated in the cross-polarized state by the metasurface (𝐼 ).\nspp,−σ\n𝜂 = 𝐼centre / 𝐼spp,−σ\nc\nRetrieved from the simulated and experimental results, we obtained the 𝜂 with different\nc\nnumber of wing-nanoslit set, and results are presented in the following Table R1.\nTable R1. 𝜼 Simulated and Experimental 𝜼 with different number of slits set (M).\n𝒄 𝒄\nKekulé metasurfaces 𝜂 (Simulation) 𝜂 (Experiment)\nc c\nM=0 8% 4.6%\nM=1 19.8% 16.6%\nM=2 20.3% 18.3%\nM=3 21.2% 19.7%\nM=4 21.3% 20.7%\n(b): Our encryption scheme analysis: In our encryption scheme, the hidden information is\nfirst embedded into the least significant bit (LSB) and then second least significant bit of the\ncover image using LSB steganography. The cover image is a 512×512-pixel grayscale image.\nThe speckle information is then encoded into a Kekulé metasurface structure array using optical\nwavelength and polarization state (e.g., RCP) as the key. Our work achieves dual-channel\nmetasurface keys, where the binary image in the LCP channel can serve as a key to interact\nwith the hidden information in the RCP channel. The transformation pattern of cover image\nand interaction rules can also be encoded into the metasurface. For the decryption, authorized\nusers must use the wavelength/polarization key to obtain the LCP-channel key and speckle\ninformation. The cover image is restored and transformed to obtain the hidden image, which is\nthen decrypted using the LCP-channel key[ Nat. Commun. 15, 2607, (2024); Sci. Adv. 7,\neabg0363, (2021)].\nAdditionally, we conducted quantitative evaluations of the LSB steganography employed in\nour encryption scheme. Through discrete Fourier transform (DFT) and histogram distribution\nanalyses comparing the original cover image and the encrypted cover image, we observed that\nboth images exhibit nearly identical global frequency distributions in their magnitude spectra\n(Figure R2-5f-h), with stable low-frequency energy concentration (mean difference <0.5% in\nlogarithmic magnitude values). This confirms that the encryption process preserves the original\nstructural integrity while enhancing resistance against frequency-domain attacks through pixel-\nlevel perturbations—spectral discrepancies cannot be exploited for reverse engineering.\nFurthermore, the histograms of the original and encrypted cover images demonstrate\nstatistically similar distributions (Figure R2-5i-k): the mean intensity remains nearly unchanged\n(original: 123.18 vs. encrypted: 123.31–123.35), the standard deviation stays stable (≈40.06–\n40.07), and overlapping probability density curves validate the unaltered global intensity\ndistribution. These results indicate that the algorithm effectively conceals local pixel\ncorrelations without introducing detectable statistical anomalies, thereby thwarting histogram-\nbased cryptanalysis.\nFigure R2-5 | a-b, Target encrypted images. c, Original cover image. d, Cover image with the\nLSB embedded from target encrypted image (a). e, Cover image with the LSB and second least\nsignificant bit embedded from target encrypted images (a) and (b), respectively. f-h, DFT\nimages corresponding to (c-e), respectively. i-k, Intensity distribution histograms\ncorresponding to (c-e), respectively.\nWe employed three key metrics—Mean Squared Error (MSE), Peak Signal-to-Noise Ratio\n(PSNR), and Structural Similarity Index (SSIM) —to quantitatively evaluate the structural and\nperceptual similarity between images before and after encryption. The obtained values\n(MSE=0.38, PSNR=52.36dB, and SSIM=0.9986) clearly confirm the preservation of structural\nand perceptual characteristics post-encryption.\nFigure R2-6 | a, Original cover image. b, Cover image embedded with two target encrypted\nimages.\nAction: As suggested, we added the efficiency evaluation of the light-emitting arrays in SI\nNote S16. In SI Note S18, we systematically analyzed both existing and achievable multi-\nlevel encryption protections within our cryptographic scheme. Furthermore, we\nconducted quantitative evaluations of the attack resistance capability of Least Significant\nBit (LSB) steganography along with comprehensive assessments of structural integrity\npreservation in cover images: \"We propose an encryption scheme that integrates LSB\nsteganography with Kekulé metasurface optical encryption technology to achieve dual-layer\nsecurity protection:(i) Primary encryption: Information is embedded into the two least\nsignificant bits of a 512×512 grayscale cover image using the LSB algorithm. (ii) Optical\nencryption: The image speckle information is written into the metasurface array using specific\nwavelength-polarization combinations (e.g., RCP). (iii) Dual-channel key (potential): The LCP\nchannel can store interaction keys and transformation rules, while the RCP channel carries\nencrypted information. (iv) In-plane signal protection: Information is stored in surface plasmon\npolariton (SPP) lattices, making traditional scattering field detection ineffective. This scheme\nbreaks through the limitations of traditional optical encryption that relies on scattering fields,\nproviding a new paradigm for high-security-level information hiding20-21. We conducted\nquantitative evaluation of the LSB steganography performance: (i) Spectral analysis: DFT\nshows the magnitude spectrum difference between encrypted and original cover images is less\nthan 0.5% (stable low-frequency energy, Figure S18f-18h), verifying its resistance to\nfrequency-domain attacks. (ii) Statistical characteristics: Histogram distributions remain\nhighly consistent (mean intensity: 123.18→123.33, standard deviation ≈40.06, Figure S18i-\n18k), with overlapping probability density curves. (iii) Quantitative metrics: MSE=0.38,\nPSNR=52.36dB, and SSIM=0.9986 confirm the structural integrity intact after encryption\n(Figure S19).\"\nComment 4: Finally, it would be good to see more details on the theoretical framework for the\nformation of optical WC lattices, the mathematical treatment could be more rigorous. (a)\nExpanding the derivation of the in-plane electric field (Equation 1) to include more detailed\nexplanations of the underlying assumptions and approximations, (b) as well as a deeper\ndiscussion of the physical mechanisms governing the formation and melting of the optical WC\nlattices, would enhance the theoretical depth of the study.\nReply #4: We thank the referee for this comment and understand the referee’s concern.\n(a): The detailed derivation of Equation 1 is added as the following (the assumptions and\napproximations are marked by underlines).\nA nanoslit etched in gold-SiO film can be assumed as an electric dipole with two orthogonal\n2\ndipole moments along its horizontal and vertical axes for SPP generation [ Light Sci. Appl. 10,\n67, (2021); Nat. Commun. 6, 8360, (2015)]. The dipole moment can be described by the\nfollowing matrix:\n𝑃 = [𝑃𝑥 0; 0 𝑃𝑦] (6)\nWhere P and P are the complex amplitudes excited by x and y polarized incidences,\nx y\nrespectively. By rotating the nanoslit with an angle , it can be written as the Jones matrix:\n𝑃 = 𝑅(𝛼)𝑃 𝑅(−𝛼) = [ (𝑃𝑥+𝑃𝑦)/2 + (𝑃𝑥−𝑃𝑦)cos2𝛼/2 (𝑃𝑥−𝑃𝑦)sin2𝛼/2; (𝑃𝑥−𝑃𝑦)sin2𝛼/2 (𝑃𝑥+𝑃𝑦)/2 - (𝑃𝑥−𝑃𝑦)cos2𝛼/2 ] (7)\nWhere R() is the rotation matrix.\nWhen illuminated by the circularly polarized light |𝜎⟩, where|𝜎⟩ = 1 (1 𝑖𝜎)𝑇, which\n√2\nrepresents left circularly polarized light (σ=1, LCP) and right circularly polarized light (σ=-1,\nRCP) in linear polarization basis, respectively. Thus, the effective dipole moment of single\nnanoslit unit cell can be expressed as follows:\n𝑃 = (𝑃𝑥+𝑃𝑦)|+𝜎⟩/2 + (𝑃𝑥−𝑃𝑦)𝑒−𝑖2σ𝛼|-𝜎⟩/2 (8)\nSince the propagation distance of SPP in the in-plane significantly exceeds the wavelength,\nthe vectorial Huygens-Fresnel model for SPP is employed to describe the propagation\ndynamics [ Principles of nano-optics. (Cambridge university press, 2012)]. It should be noted\nthat the simplified model neglects multi-slit reflection effects. Therefore, the in-plane\n(transverse plane) SPP field generated by a single nanoslit at point 𝑑 can be expressed as:\n𝐸 ≈ P𝑒−𝑖𝜔𝑡𝑒−𝑖𝑘𝑧𝑧𝑒−𝑖𝛽⃗⃗⃗⃗s⃗⃗⃗p⃗⃗⃗⃗p⃗ ∙⃗𝑟⃗ / √𝑟 (9)\n||,0\nWhere ω=k c is the angular frequency of the electromagnetic wave, with c being the vacuum\n0\nvelocity of light, k being the free-space wavenumber. β is given by the dispersion relation\n0 spp\n𝛽 spp = (𝜔/𝑐)√𝜀𝑑𝜀m/(𝜀𝑑+𝜀m), with dielectric constants ε d for SiO 2 and ε m for metal. For lossy materials,\nβ has a complex component and β = k +iγ, such that k is the SPP wavenumber and 𝜾\nspp spp spp spp\nis the attenuation constant. k refers to the axial wave vector and given by kz=sqrt(k 2-β 2). r is\nz 0 spp\nthe distance between point d and the nanoslits.\nThe time dependence exp(-iωt) and axial dependence exp(-ik z) are omitted, and\nz\nequation (9) can be expressed as:\n𝐸 ≈ (𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼|𝐸 ⟩)𝑒−𝑖𝛽spp (𝑥cos𝜃+𝑦sin𝜃) / √𝑟 (10)\n||,0 𝜎 𝜎 −𝜎 −𝜎\nWhere (x, y) is the coordination of point d, and θ is the azimuth coordination of the point d. η\nσ\nand η refer to the coefficients of co-polarization order (E ) and cross-polarization order (E\n-σ σ -σ\n), respectively. η =(P + P )/2, η =(P + P )/2.\nσ x y -σ x y\nThe SPP field generated by multiple nanoslits is the superposition of wavelets from all sources,\nand therefore, it can be expressed as:\n𝐸 = ∑𝐸 ≈ ∑ (𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼𝑗|𝐸 ⟩)𝑒−𝑖𝛽𝑠𝑝𝑝(𝑥cos𝜃𝑗+𝑦sin𝜃𝑗) / √𝑟𝑗 (11)\n|| ||,0 𝑗 𝜎 𝜎 −𝜎 −𝜎\nSince Kekulé metasurface consists of six channels of slit arrays, each group of arrays has the\nsame rotation angle α and same in-plane angle θ, thus, equation (11) can be simplified as the\nsuperposition of SPP field generated by six groups of slit arrays:\n𝐸 = ∑𝑛=6 𝐴 (𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼𝑛|𝐸 ⟩)𝑒−𝑖𝛽spp (𝑥cos𝜃𝑛+𝑦sin𝜃𝑛 ) / √𝑟𝑛 (12)\n|| 𝑛=1 𝜎 𝜎 −𝜎 −𝜎\nWhere α = (n-1)lπ/6 represents the rotation angle of nth array; lπ/6 is the phase gradient, and l\nn\nis a constant which equals to half of the lattice topology charge (TC); θ =(n+0.5)π/3 denotes\nn\nthe azimuth angle of n side, determining the propagating phase of SPPs; r is the distance from\nth n\nthe study location to n side along the wave vector. A is the effect of the unit cell number in an\nth\narray on the amplitude. Besides, in our work, damping of the plasmon was neglected. By\nomitting the effect of amplitude A/sqrt(r) and the attenuation constant, the in-plane field\ncan be approximate expressed as follows, which is the in-plane electric field in Equation (1):\n𝐸 ∝ ∑𝑛=6(𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼𝑛|𝐸 ⟩)𝑒−𝑖𝑘spp (𝑥cos𝜃𝑛+𝑦sin𝜃𝑛 ) (13)\n|| 𝑛=1 𝜎 𝜎 −𝜎 −𝜎\n(b): The number of SPP sources will determine the number of eigenmodes of the characteristic\nlight field in the system[ Nano Lett. 13, 2558-2563, (2013); Sci. Adv. 11, eadv3938, (2025)],\ntherefore, the symmetry of added SPP field contributes to the evolution of the circular\nsymmetrical lattice, related to the Bessel function [ Phys. Rev. Lett. 101, 043903, (2008)]. For\nthe Kekulé-ordered metasurface with extra wing-type system, the synergy of the wing-type\nelements and Kekulé metasurface integrates a dual hexagonal-symmetric subsystem arranged\nin a concentric counter-rotated geometry (Δθ=30°), exhibiting fundamental consistency with\nthe moiré/skyrmion superlattice system reported by Harald Giessen's team in Nature Physics\n[Nat. Phys., 1-7, (2025)].\nAction: As suggested, a more detailed derivation of the in-plane electric field (Equation 1)\nwith assumptions and approximations is added. In SI Section 2, we have added “According\nto the vectorial Huygens-Fresnel principle for surface plasmonic (SPP)8, the in-plane\n(transverse plane) SPP field generated by a single nanoslit can be expressed as:\n𝐸 ≈ P𝑒−𝑖𝜔𝑡𝑒−𝑖𝑘𝑧𝑧𝑒−𝑖𝛽⃗⃗⃗⃗s⃗⃗⃗p⃗⃗⃗⃗p⃗ ∙⃗𝑟⃗ / √𝑟 (4)\n||,0\nWhere ω=k c is the angular frequency of the electromagnetic wave, with c being the vacuum\n0\nvelocity of light, k being the free-space wavenumber. β is given by the dispersion relation\n0 spp\n𝜽 spp = (𝜔/𝑐)√𝜀𝑑𝜀m/(𝜀𝑑+𝜀m), with dielectric constants ε d for SiO 2 and ε m for metal. For lossy materials,\nβ has a complex component and β = k +iγ, such that k is the SPP wavenumber and 𝜾\nspp spp spp spp\nis the attenuation constant. k refers to the axial wave vector and given by kz=sqrt(k 2-β 2). r\nz 0 spp\nis the distance between point d and the nanoslits.\nThe time dependence exp(-iωt) and axial dependence exp(-ikz) are omitted, and equation\nz\n(9) can be expressed as:\n𝐸 ≈ (𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼|𝐸 ⟩)𝑒−𝑖𝛽spp (𝑥cos𝜃+𝑦sin𝜃) / √𝑟 (5)\n||,0 𝜎 𝜎 −𝜎 −𝜎\nWhere (x, y) is the coordination of point d, and θ is the azimuth coordination of the point d. η\nσ\nand η refer to the coefficients of co-polarization order (E ) and cross-polarization order (E\n-σ σ -σ\n), respectively. η =(P + P )/2, η =(P + P )/2.\nσ x y -σ x y\nThe SPP field generated by multiple nanoslits is the superposition of wavelets from all sources,\nand therefore, it can be expressed as:\n𝐸 = ∑𝐸 ≈ ∑ (𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼𝑗|𝐸 ⟩)𝑒−𝑖𝛽𝑠𝑝𝑝(𝑥cos𝜃𝑗+𝑦sin𝜃𝑗) / √𝑟𝑗 (6)\n|| ||,0 𝑗 𝜎 𝜎 −𝜎 −𝜎\nSince Kekulé metasurface consists of six channels of slit arrays, each group of arrays has the\nsame rotation angle α and same in-plane angle θ, thus, equation (6) can be simplified as the\nsuperposition of SPP field generated by six groups of slit arrays:\n𝐸 = ∑𝑛=6 𝐴 (𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼𝑛|𝐸 ⟩)𝑒−𝑖𝛽spp (𝑥cos𝜃𝑛+𝑦sin𝜃𝑛 ) / √𝑟𝑛 (7)\n|| 𝑛=1 𝜎 𝜎 −𝜎 −𝜎\nWhere α = (n-1)lπ/6 represents the rotation angle of nth array; lπ/6 is the phase gradient, and\nn\nl is a constant which equals to half of the lattice topology charge (TC); θ =(n+0.5)π/3 denotes\nn\nthe azimuth angle of n side, determining the propagating phase of SPPs; r is the distance\nth n\nfrom the study location to n side along the wave vector. A is the effect of the unit cell number\nth\nin an array on the amplitude. Besides, in our work, damping of the plasmon was neglected9-10.\nBy omitting the effect of amplitude A/sqrt(r) and the attenuation constant, the in-plane field can\nbe approximate expressed as follows, which is the in-plane electric field in Equation (1):\n𝐸 ∝ ∑𝑛=6(𝜂 |𝐸 ⟩+𝜂 𝑒−𝑖2𝜎𝛼𝑛|𝐸 ⟩)𝑒−𝑖𝑘𝑠𝑝𝑝 (𝑥cos𝜃𝑛+𝑦sin𝜃𝑛 ) (8)”\n|| 𝑛=1 𝜎 𝜎 −𝜎 −𝜎"}, {"round": 2, "reviewer_comments": {"reviewer_1": "In my initial review, I expressed significant concerns about the use of the term “Wigner crystal” to describe the interference-\nbased SPP patterns, noting that Wigner crystals are defined by nonlinear electron-electron interactions, which are absent in\nthe authors’ linear photonic system. The authors have responded by replacing “Wigner crystal lattice” with “Wigner-type\nlattice” throughout the manuscript and supplementary information, replacing “SPP crystallization” with “SPP localization,”\nand removing ambiguous phrases like “melt into.”\nHowever, I remain concerned that the term “Wigner-type lattice” still implies a stronger analogy to Wigner crystals than is\njustified. Wigner crystals arise from Coulomb-driven, many-body interactions leading to spontaneous lattice formation,\nwhereas the authors’ system relies on engineered nanostructures to produce linear SPP interference patterns. While the\nauthors cite literature on “generalized Wigner crystallization” (Nat. Rev. Phys. 2, 538-561, 2020) to support their terminology,\nthe referenced systems typically involve quasiparticles with some form of interaction, which does not fully align with the\npurely linear optics in this work. The structural periodicity of the SPP patterns is a valid observation, but invoking the Wigner\ncrystal concept risks misleading readers, particularly those from the condensed matter community, about the underlying\nphysics.\nWhile the authors draw parallels to cross-disciplinary terms like optical skyrmions, the analogy here is less robust, as\nskyrmions in photonics retain topological properties akin to their condensed matter counterparts, whereas the “Wigner-type\nlattice” lacks the interaction-driven physics central to Wigner crystals.\nI strongly suggest replacing “Wigner-type lattice” with a more neutral term, such as “SPP lattice” or “Kekulé-patterned lattice,”\nwhich accurately describes the periodic intensity patterns without implying a connection to Wigner crystal physics. If the\nauthors insist on retaining “Wigner-type lattice,” they must include a clear statement in the main text (e.g., in the introduction\nor results section) explicitly clarifying that the term refers solely to structural periodicity and not to\ninteraction-driven phenomena. This would mitigate potential misinterpretation and align the terminology with the physics presented.\nMy initial review questioned the novelty of the work, given the substantial existing research on geometric phase\nmanipulation of SPPs. The authors have responded by emphasizing the unique aspects of their Kekulé metasurface design,\nparticularly the use of wing-shaped nanoslits, and highlighting potential applications such as optical encryption and\nconfigurable arrays. The experimental validations, including leakage radiation microscopy (LRM) results and comparisons\nbetween gold and silver metasurfaces, strengthen the practical relevance of the work. The added discussion on scalability\nand quantitative metrics for efficiency and encryption security (Pages 12-17) further supports the manuscript’s potential\nimpact.\nThe authors have not fully clarified how their work stands out from existing studies on SPP interference patterns. It remains\nuncertain whether the Kekulé metasurface design represents a significant advancement over established geometric phase-\nbased methods or merely introduces another plasmonic interference pattern, sufficient to warrant publication in Nature\nThe authors should provide a clearer comparison with prior work on SPP manipulation, ideally in the form of a table or\ndetailed discussion in the main text, highlighting specific differences in design, control mechanisms, or applications. This\nwould strengthen the case for novelty and help justify the work’s suitability for a high-impact journal.", "reviewer_2": "The authors have satisfactorily addressed the comments raised in the first round of review, and the manuscript has been\nsignificantly improved. I believe the scope and quality of the work are of a high standard and align well with the publication\ncriteria of Nature Communications. I therefore support the acceptance of the manuscript."}, "author_response": "List of changes made in this revision\nDuring this revision, we have modified the relevant terminology according to the\nreviewers' suggestions and supplemented comparative analysis between our work and\nprevious related research to clarify the distinctiveness and potential of our work.\nThe relevant analyses have been incorporated into the revised manuscript and\nsupplementary information, as detailed below:\n(a) Regarding the questions of Reviewer #1 about the potentially overstated analogy\nbetween the term \"optical Wigner-type lattices\" and \"Wigner crystal\", we have\nremoved the misleading content on conceptual analogy migration throughout the\nmain text and supplementary information. Following the suggestions, we\nsubstituted the original expression \"Wigner-type lattices\" with the more neutral\nterm \"SPP lattice\". Correspondingly, we implemented consistent modifications to\nthe manuscript's title, keywords, and abstract.\n(b) Regarding the suggestion of Reviewer #1 about the incomplete comparison of our\nwork with the prior researches on SPP interference patterns, we have summarized\nseveral milestone literatures on SPP manipulation in Section 5 (Page S8) of the\nsupplementary information. As can be seen, our well-designed Kekulé metasurface,\nespecially coupled with the wing-shaped pattern, combining the geometric phase\nand propagating phase modulations, demonstrates their superiorities in\nmanipulating versatile SPP lattices for advanced applications.\nIn addition, careful revisions have been made through the manuscript and\nsupplementary information. The revised text and discussions are highlighted in red in\nthe revised documents.\nPoint-by-point response to referee’s comments for manuscript No. NCOMMS-\n24-72188B to Nature Communications.\nGeneral response.\nWe sincerely appreciate both reviewers for their time and efforts in evaluating our manuscript\nand providing valuable comments. We thank the Reviewer #2 for highly affirming our work\nand supporting the publication of the revised manuscript as it was, thank the Reviewer #1 for\nsuggesting our work publishable after addressing several technical questions. We have made\nsubstantial improvements and hope that the remaining concerns have been fully addressed with\nfully acceptable clarity and accuracy for publication in Nature Communications.\nComments to the Author\nReviewer #1:\nComment 1-1: In my initial review, I expressed significant concerns about the use of the term\n“Wigner crystal” to describe the interference-based SPP patterns, noting that Wigner crystals\nare defined by nonlinear electron-electron interactions, which are absent in the authors’ linear\nphotonic system. The authors have responded by replacing “Wigner crystal lattice” with\n“Wigner-type lattice” throughout the manuscript and supplementary information, replacing\n“SPP crystallization” with “SPP localization,” and removing ambiguous phrases like “melt into.”\nHowever, I remain concerned that the term “Wigner-type lattice” still implies a stronger analogy\nto Wigner crystals than is justified. Wigner crystals arise from Coulomb-driven, many-body\ninteractions leading to spontaneous lattice formation, whereas the authors’ system relies on\nengineered nanostructures to produce linear SPP interference patterns. While the authors cite\nliterature on “generalized Wigner crystallization” (Nat. Rev. Phys. 2, 538-561, 2020) to support\ntheir terminology, the referenced systems typically involve quasiparticles with some form of\ninteraction, which does not fully align with the purely linear optics in this work. The structural\nperiodicity of the SPP patterns is a valid observation, but invoking the Wigner crystal concept\nrisks misleading readers, particularly those from the condensed matter community, about the\nunderlying physics.\nWhile the authors draw parallels to cross-disciplinary terms like optical skyrmions, the analogy\nhere is less robust, as skyrmions in photonics retain topological properties akin to their\ncondensed matter counterparts, whereas the “Wigner-type lattice” lacks the interaction-driven\nphysics central to Wigner crystals.\nI strongly suggest replacing “Wigner-type lattice” with a more neutral term, such as “SPP lattice”\nor “Kekulé-patterned lattice,” which accurately describes the periodic intensity patterns without\nimplying a connection to Wigner crystal physics. If the authors insist on retaining “Wigner-type\nlattice,” they must include a clear statement in the main text (e.g., in the introduction or results\nsection) explicitly clarifying that the term refers solely to structural periodicity and not to\ninteraction-driven phenomena. This would mitigate potential misinterpretation and align the\nterminology with the physics presented.\nReply 1-1: We sincerely thank you and understand your concern. As you suggested, we\nreplaced “Wigner-type lattice” with a more neutral term of “SPP lattice” throughout the main-\ntext and supplementary information.\nAction: In accordance with the suggestions, we have modified the manuscript title from\n\"Optical Wigner-type lattices enabled by Kekulé metasurfaces\" to \"Versatile on-chip plasmonic\nlattices enabled by Kekulé metasurfaces\". Simultaneously, throughout the main text and\nsupplementary information, we have replaced the term \"Wigner-type lattice\" with the\nmore neutral term \"SPP lattice\" to accurately describe periodic intensity patterns.\nIn the abstract, we have deleted the introductory content regarding optical Wigner\ncrystals: \"Wigner crystal lattice localizes the electrons into a close-packed regular pattern and\nremains one of the most fragile quantum states since its first prediction in 19341. The evidences\nof electronic Wigner crystal lattices were observed in liquid helium2,3, carbon nanotube4,\nextremely clean GaAs/AlGaAs quantum wells5-7, two-dimensional electron gases8,9 and various\nmoiré superlattice10-12.\" and the cited references, and rewritten it as: \"Surface plasmon\npolaritons (SPPs) lattices created by artificial plasmonic metasurfaces, can carry tremendous\noptical information and have implications for resilient and secure optical communication.\nHowever, tailoring the intensity, spectral and spatial distributions of these SPP lattices\nintentionally remain challenging.\"\nMeanwhile, we have deleted all contents and related references in Section 1 (\"The\ninterpretation of the definition 'Optical Wigner-type lattice'\") of the supplementary\ninformation.\nComment 1-2: My initial review questioned the novelty of the work, given the substantial\nexisting research on geometric phase manipulation of SPPs. The authors have responded by\nemphasizing the unique aspects of their Kekulé metasurface design, particularly the use of\nwing-shaped nanoslits, and highlighting potential applications such as optical encryption and\nconfigurable arrays. The experimental validations, including leakage radiation microscopy\n(LRM) results and comparisons between gold and silver metasurfaces, strengthen the practical\nrelevance of the work. The added discussion on scalability and quantitative metrics for\nefficiency and encryption security (Pages 12-17) further supports the manuscript’s potential\nimpact.\nReply 1-2: We sincerely appreciate you for the efforts in evaluating our manuscript again and\nacknowledged our revision and potential of our work.\nComment 1-3: The authors have not fully clarified how their work stands out from existing\nstudies on SPP interference patterns. It remains uncertain whether the Kekulé metasurface\ndesign represents a significant advancement over established geometric phase-based methods\nor merely introduces another plasmonic interference pattern, sufficient to warrant publication\nin Nature\nThe authors should provide a clearer comparison with prior work on SPP manipulation, ideally\nin the form of a table or detailed discussion in the main text, highlighting specific differences\nin design, control mechanisms, or applications. This would strengthen the case for novelty and\nhelp justify the work’s suitability for a high-impact journal.\nReply 1-3: We thank the referee for this constructive suggestion. As you suggested,\ncomparisons with prior works on SPP manipulation were added (see SI Section5 for detail),\nwhich improves the claims and strengthen the novelty of our work.\nAction: As suggested, in Section 5 of the supplementary information, we have presented\na comprehensive comparison in tabular form delineating the specific distinctions between\nour work and prior studies on SPP manipulation: “The superiorities of the Kekulé\nmetasurfaces lie in not only their extra geometric control over SPP lattices, but also the\npotentials in cooperating with extra wing-shaped nanoslits synergistically. Table S1 summaries\nthe designed metasurfaces toward manipulating the SPP interference patterns. As can be seen,\nthe traditional metasurfaces are mainly limited to simple polygonal or circular nanoslit\nstructures. Departing from propagating phase control only, a series of unprecedent SPP\nbehaviors, including optical Skyrmion lattices, moiré Skyrmion superlattices, Meron-like\ntexture and conserved topological charge vectors of SPP lattices in four-dimension were\nrecently discovered in succession. It is anticipated that one extra control mean may push the\nfundamental understanding and device applications of these lattices to a higher level. However,\nintroducing extra nanoslits or geometric control concurrently over these SPP lattices seems\nextremely challenging.\nIn strikingly contrast, the Kekulé metasurface (hexagonal segmented-nanoslits) allows us to\ncontrol the SPP lattices via both propagating phase and geometric phase. Therefore, more\ncategories of SPP lattices with variable topology charges become achieved, with respect to the\nabove-mentioned references. In addition, the controlled intensity of SPP sublattices by another\nwing-shaped nanoslits enables the usage of tunable SPP lattices in practical applications of\noptical encryption and emitter arrays.\nTable S1. Comparison of reported metasurfaces and corresponding SPP patterns.\nIn additional to above important developments on SPP lattices, Table S2 completes some\nmilestone literatures on SPP manipulation especially in the aspect of controlling mechanisms\nand applications. Firstly, the primary control mechanisms for SPP mainly involve geometric\nphase and propagation phase modulations. Compared to the propagation phase, geometric\nphase offers the following distinct advantages: (1) Geometric phase achieves phase modulation\nsolely through the spatial orientation of metasurface unit cells, therefore, significantly\nenhancing the device compactness and integration density; (2) Propagation phase is generally\ninsensitive to polarization state. Geometric phase, however, exhibits its intrinsic polarization\ndependence. Its inherent spin-orbit interaction properties enable efficient spin-selective SPP\nmanipulation, which facilitates the conversion of different circularly polarized light inputs into\nSPP modes with distinct phase distributions, or enables polarization multiplexing\nfunctionalities. Therefore, combining the geometric phase and propagating phase modulations\nfurther enhances the compactness and efficiency of our Kekulé metasurfaces, which is\nadvantageous over the reported metasurfaces in previous literatures.\nSecondly, regarding applications, metasurface modulated SPP have already found widespread\nuse in the areas such as unidirectional propagation, optical information storage, micro/nano-\npatterning, enhanced on chip single photon source. None of these shows the possibility in\nlightening and optical encryption applications. Therefore, our Kekulé metasurfaces, especially\ncoupled with the wing-shaped nanoslits, demonstrate their superiorities in manipulating\nversatile SPP lattices for advanced applications.\nTable S2. Overviews of SPP manipulations toward applications\n\".\nIn the main text, we have supplemented the relevant descriptions, respectively: “From Fig.\n2a-2e, we conclude that versatile SPP lattices could be manifested by Kekulé metasurfaces,\nenriching the lattice family and their effective control by metasurface designs (please see SI\nTable S1 and Section S5).” on Page 5, and \"With respect to reported metasurfaces (please see\nSI Section S5), our well-designed structures, especially coupled with the out-wing pattern,\ncould manifest versatile SPP lattices not only in terms of topology charges but also the intensity,\ndemonstrating themselves greater potentials in modern-day applications.\" on Page 11.\nReviewer #2:\nThe authors have satisfactorily addressed the comments raised in the first round of review, and\nthe manuscript has been significantly improved. I believe the scope and quality of the work are\nof a high standard and align well with the publication criteria of Nature Communications. I\ntherefore support the acceptance of the manuscript.\nResponse:\nWe thank the reviewer for the positive evaluation and recommending publication of our work."}]

Decision letter