Vertical chiral emission from an intrinsically achiral metasurface enabled with anisotropic continuum

Domain: neuroscience
Published: 2026-01-31
Editorial outcome: minor_revision

Abstract
Manipulating emission polarization is crucial for advanced applications such as polarized fluorescence and lasing, thermal radiation control, stereochemistry and spintronics. Existing approaches for generating circularly polarized emission primarily rely on nanostructures with true chirality, where the far-field polarization at the Γ point is believed to require out-of-plane symmetry breaking. This raises a question: can an intrinsically achiral metasurface that preserves out-of-plane symmetry generate chiral emission? Here, we introduce the concept of anisotropic continuum, defined as a continuum state exhibiting distinct responses for orthogonal polarizations of incidence, as a new degree of freedom for intrinsically achiral metasurfaces. In such metasurfaces, chiral emission arises from manipulating the anisotropic continuum together with the metasurface’s in-plane perturbations. Degrees of circular polarization of 0.83 for upward emission and −0.9 for downward emission are achieved experimentally by integrating the fabricated silicon metasurface with fluorescent organic dyes. Our findings not only address a long-standing gap in the understanding of structural chirality, but also open new opportunities for high-performance applications in polarized fluorescence and thermal emission.

Introduction
Electromagnetic chirality refers to the phenomenon in which an object interacts differently with right and left circularly polarized (RCP/LCP) light1–4, a property commonly observed in natural materials with three-dimensional asymmetric structures. This chiral behavior gives rise to a distinct chiroptical response, which can be characterized by circular dichroism (CD) or optical rotation5. While natural materials have been used to generate chiral emission, their low chirality and limited tunability constrain practical applications6,7. Metasurfaces, however, offer a powerful platform to enhance and control chiral emission, enabling new opportunities in polarized emission8–13, chirality tuning14,15, chiral sensing16,17, and photodetection18,19.

Recent advances in chiral metasurfaces and their ability to generate chiral emission have been driven by the incorporation of non-local resonances, especially bound states in the continuum (BIC)20–29 and guided modes30. In such systems, light remains confined within the metasurface while coexisting with a continuum of electromagnetic waves. Typically, intrinsic chirality in metasurfaces, characterized by chiroptical responses at the Γ point, is achieved in geometrically chiral structures through symmetry breaking across all mirror planes6,31–34. To break the out-of-plane mirror symmetry (σz symmetry) and achieve chiral quasi-BIC, various methods have been employed, including slant-etching9,24, grayscale lithography10,25 and bi-layer design35. In these structures, chiral emission arises when the quasi-BIC aligns with a high-transmission background. With mirror symmetry breaking in all planes, chiral emission occurs when near-unity CD is observed (indicated in the left panel of Fig. 1a)24,28. Here, chiral emission refers to a radiative process in which the far-field degree of circular polarization (DCP=(IR − IL)/(IR + IL)) approaches unity. Planar chiral metasurfaces represent another route, where near-unity CD29,36,37 at normal incidence has also been reported. However, these designs primarily focus on transmission properties, and their potential for controlling emission remains largely unexplored (see Supplementary Section 1). Moreover, recent studies have revealed that a large CD in transmission does not necessarily correspond to chiral emission24, highlighting a gap in understanding the emission mechanism of planar chiral systems. In our earlier work, chiral emission was observed in the presence of a dielectric substrate that perturbed σz symmetry12. Conventionally, σz-symmetric metasurfaces are believed to support only extrinsic chiral emission away from the Γ point, typically enabled by breaking in-plane inversion symmetry38–41. The far-field polarization at the Γ point, by contrast, is generally considered nearly linear due to the absence of geometric chirality21,24,28,42. An interesting question arises: can a metasurface with σz symmetry, which is intrinsically achiral, generate circular or even arbitrary polarization at the Γ point? Our answer is yes.

Here, we demonstrate theoretically and experimentally that breaking σz symmetry is not required to generate chiral emission at the Γ point, using a vertically etched silicon metasurface embedded in a uniform environment (right panel of Fig. 1a). An additional degree of freedom is introduced by leveraging anisotropic continuum, characterized by distinct responses for orthogonal polarizations in the continuum, e.g., x-polarized and y-polarized light. The term continuum refers to a range of states that are closely connected and form a smooth, uninterrupted spectrum43. In metasurfaces, the continuum is characterized by a slowly-varying reflection/transmission spectrum, induced by Fabry-Perot resonances44, Mie resonances45, high-contrast grating effects46, and other mechanisms. We show that when a bound mode is embedded within an anisotropic continuum, in-plane perturbations can induce radiative coupling. This leads to chiral emission within a specific continuum, where the radiated polarization exhibits opposite chirality in the upward and downward directions. While ultrahigh-Q modes in metasurfaces, such as quasi-BIC47,48 and leaky guided modes30,49,50, have been extensively studied and widely applied in photonics, the specific influence of the continuum on emission polarization remains largely unexplored. Related work has examined its effect on linearly polarized emission51, whereas its contribution to chiral emission remains an open and critical question. Understanding the role of these states could open new avenues for designing metasurfaces with customized polarization properties.

Results
To show the importance of anisotropic continuum in realizing chiral emission in σz-symmetric metasurfaces, we decompose the far-field polarization of a resonant mode in the σz-symmetric metasurface into Cartesian components |Ex|eiθx and |Ey|eiθy. It is determined by two critical parameters: (i) the phase difference between the x- and y-components Ex and Ey, expressed as φ=θy − θx=arg(Ey/Ex) and (ii) the magnitude ratio of Ex and Ey, denoted as η=|Ey|/|Ex|. We start with a structure that exhibits no polarization conversion in either transmission or reflection between the x- and y-polarized channels to simplify the analysis. For a discrete localized state, the phase difference φ can be expressed in terms of background reflection and transmission coefficients (rx, ry, tx, ty) as follows (Supplementary Section 2)44,52

φ = arg(ry + αz ty) − arg(rx + αz tx) + nπ, (1)

where n is an integer and αz=±1 is a parity number. This equation establishes a connection between the eigenstate far-field polarization and the scattering coefficients of the continuum.

The relation between the eigenstate phase difference φ and the continuum transmission spectra in a σz-symmetric structure is conceptually demonstrated in Fig. 1b. For metasurfaces with a transmissive background or anisotropic continuum (left panels of Fig. 1b), φ is always zero and the vertically radiated polarization remains linearly polarized. For instance, metasurfaces with the unit cell composed of cylinders or circular apertures are unable to generate an arbitrary phase difference φ as they inherently satisfy arg(ry + αz ty)=arg(rx + αz tx). In contrast, a nonzero phase difference between the x- and y-components of the radiated electric field can be generated with the assistance of the anisotropic continuum (right panels of Fig. 1b). To achieve chiral emission, φ=π/2 should be satisfied first. This requires that the metasurface should generally be geometrically anisotropic in a certain direction.

Due to the presence of anisotropic continuum, the transmission and reflection spectra of σz-symmetric metasurfaces exhibit unique features compared with σz-asymmetric ones. As shown in Fig. 1c, under the condition of DCP=1, RCP incidence excites a strong resonance; however, its transmission remains identical to the non-resonant direct transmission under LCP incidence, due to destructive interference with the background (Supplementary Section 3). Consequently, the transmission CD at the Γ point ideally vanishes when the resonant and background scatterings are exactly out of phase.

We consider a σz-symmetric dielectric metasurface, schematically shown in Fig. 1d. The unit cell consists of a silicon dimer embedded in a silica environment, preserving σz symmetry regardless of in-plane variations. This adopted structure follows our earlier work to isolate and emphasize the role of out-of-plane mirror symmetry12. The phase difference φ of the structure is governed by anisotropic continuum modulation, while the ratio η=|Ey|/|Ex| is influenced by in-plane perturbations. Initially, with α=0 and δt=0, no symmetry breaking occurs, and the introduction of the continuum results in φ=π/2. In this condition, the bound mode is embedded in the continuum, allowing coupling to x-polarized waves. Further introducing nonzero α induces simultaneous non-zero |Ex| and |Ey|, producing circular polarization. In this step, breaking the in-plane mirror symmetry to make the structure “2D-chiral” is essential for generating both |Ex| and |Ey|, as the in-plane mirror symmetry guarantees linear polarization. Figure 1e provides a clearer illustration of the role of the anisotropic continuum. The polarization of the far-field radiation can be fully described by a set of Stokes parameters: S1=(|Ex|2−|Ey|2)/(|Ex|2+|Ey|2), S2=2|Ex||Ey|cosφ/(|Ex|2+|Ey|2), S3=2|Ex||Ey|sinφ/(|Ex|2+|Ey|2). Once φ is fixed, the Stokes parameters trace an arc on the Poincare sphere connecting two opposite points on the S1 axis as |Ex| and |Ey| vary. In this case, the phase difference φ is the angle between the arc and the equator, while |Ey|/|Ex| controls the distance between the observed point and the pole along the S1 axis. Without the contribution of anisotropic continuum, radiative modes induced by in-plane symmetry breaking trace a line along the equator of the Poincare sphere (gray line in Fig. 1e). When anisotropic continuum is introduced, this line is lifted toward either the northern or southern hemisphere. Under specific structural parameters, the trajectory intersects the pole, marked by a red star. This evolution is further depicted in the right panel of Fig. 1e, highlighting the changes in the radiated polarization as the structural parameters vary.

To demonstrate control over the phase difference φ, we select an unperturbed metasurface with α=0 and δt=0, and then vary the pillar length L. This variation induces anisotropy of the background response, which results in nontrivial values of φ according to Eq. (1). Note also that the phase difference φ depends on the relative positions between the bound mode and the broad transmission dip of Ty. The variation of φ with L is shown in Fig. 2a, where φ decreases with increasing L and reaches φ=π/2 when L=190 nm. The corresponding transmission spectra Tx and Ty for L=190 nm are shown in the inset of Fig. 2a, with the position of the bound mode marked as a red star. Under this condition, further modulation of the asymmetric parameters α and δt transforms the bound mode into a bright mode that radiates into the far-field. The far-field polarization distribution in k-space is shown on the right side of Fig. 2b, revealing a C point at the Γ point.

A silicon metasurface with α=0.09 and δt=11 nm is fabricated on a silica substrate to experimentally verify our theoretical predictions. The metasurface is subsequently covered with a 50 μm layer of PMMA to achieve refractive index matching with the silica substrate24 (so that the silicon metasurface is symmetrical along the vertical direction) and to minimize the impact of Fabry-Perot resonance on the spectrum. Figure 2c presents the overall scanning electron microscope (SEM) images of the silicon metasurface together with a schematic illustration in the x-z plane, revealing vertically etched structures that preserve the out-of-plane mirror symmetry. Angle-resolved transmission spectra for transverse electric (TE) and transverse magnetic (TM) polarized incident light, denoted by TTE and TTM, respectively, are confirmed by simulations and experiments in Fig. 2d. Under TM-polarized incidence, only the TM mode is excited, whereas TE-polarized incidence excites TM1, TE1, and TM2 modes (note that TE/TM incidence refers to the incident polarization, while TE/TM modes refer to the eigenmodes). The TM1 mode couples to TE and TM components, residing within the broad transmission dip observed under TE incidence. The experimental results closely align with the simulations, confirming the coupling of the TM1 mode to both the x- and y-polarization components and its modulation by the continuum. While the primary discussion in the main text focuses on the TM1 mode, the TE mode also holds potential for chiral emission, as elaborated in the Supplementary Section 4.

To investigate the evolution of radiated polarization, we fabricated a series of metasurfaces with varying configurations: zero α and δt, nonzero δt only, and both nonzero α and δt. Transmission spectra of these metasurfaces were simulated (solid lines in Fig. 3), theoretically derived with TCMT (indicated by “×” in Fig. 3), and experimentally measured (indicated by “Δ” in Fig. 3) to provide insight into the continuum and bound modes. For α=0 and δt=0, the transmission spectrum Ty exhibits a broad dip between 700 nm and 900 nm, while Tx maintains high transmission (Fig. 3a). In this configuration, no bound mode is excited due to symmetry protection. The phase difference φ is calculated through Eq. (1) with αz=−1, and is depicted as a dotted gray line in the upper panel of Fig. 3a. Although a nonzero φ is generated across the wavelength range, we have |Ex|=|Ey|=0. For α=0 and δt=11 nm, the bound TM1 mode becomes leaky, experimentally resulting in a sharp transmission dip at λ=778 nm for Tx, while the line shape of Ty remains nearly unchanged (Fig. 3b). This leakage, independent of C2 symmetry breaking, indicates that the mode is a quasi-guided mode arising from band-doubling rather than a symmetry-protected BIC. For α=0.09 and δt=11 nm, the transmission spectra exhibit resonant features under both x-polarized and y-polarized light illumination. At λ=775 nm, a transmission dip appears for Tx while a transmission peak emerges for Ty, located near the broad dip of Ty (Fig. 3c). The simultaneous presence of the dip and peak signifies coupling to both x- and y-polarizations. The TCMT-fitted spectra show excellent agreement with numerical simulations, validating that the model accurately describes the key features of vertical chiral emission.

In terms of the resonant mode field distribution, the coupling behavior can be directly understood from the overlap integral between the incident field and the resonant mode: symmetry enforces zero overlap, δt alone allows coupling only to x-polarization, and the combination of δt and α yields finite overlap for both x- and y-polarizations with a phase difference close to π/2. Full derivations and supporting figures are provided in Supplementary Section 5.

The chiral emission capabilities of metasurfaces play a significant role in modulating fluorescence, laser emission and thermal radiation. Here, we further examine the fluorescence properties enabled by the σz-symmetric dielectric metasurface, with the absorption characteristics shown in Supplementary Section 6. As shown in Fig. 4a, in the case where L=190 nm, the long and short axes of the radiated polarization consistently align with the x or y axis, with only the ellipticity changing as α and δt vary. Thus, the phase difference φ remains nearly π/2 for small values of α and δt. This variation demonstrates that the phase difference φ induced by continuum scattering coefficients is robust against in-plane perturbations. Since δt and α control |Ex| and |Ey| independently, there are multiple instances where |Ey|/|Ex|=1, resulting in C points (Fig. 4b). Larger values of α and δt introduce greater symmetry breaking, which leads to lower Q-factors. In the experiment, a thin layer of IR140 organic dye is first spin-coated onto the fabricated metasurface, followed by a 50 μm PMMA coating. The sample is then excited with a 532 nm laser, and its photoluminescence (PL) characteristics are analyzed (Supplementary Section 7). The PL from the dye is strongly modulated by the TM1 mode supported by the metasurface, with its polarization determined by the eigenstate. Figure 4c displays the polarization-resolved upward PL spectra for three cases with different α values at a fixed δt of 11 nm. For α=0, the RCP and LCP components of the PL spectrum are nearly equal, indicating linearly polarized emission. As α increases, the proportion of the LCP component decreases, resulting in an increased DCP.

Figure 4d demonstrates the x-z cross sections of Ex±iEy of the eigenstate in the case of α=0.09 and δt=11 nm. The upward and downward leaky waves are RCP (red circular line) and LCP (blue circular line), both represented by Ex − iEy due to the change in direction21. The reversal of radiated circular polarization is expected, given that the structure exhibits opposite chirality when viewed from above and below. Experimentally, a prominent RCP peak is detected in the upward emission, with negligible LCP contribution, resulting in a DCP of 0.83 (upper half of Fig. 4e). Conversely, for downward emission, the LCP component dominates, yielding a DCP of −0.9 (lower half of Fig. 4e). This reversal in circular polarization confirms the absence of net chiral flux in the far field, consistent with the preserved σz symmetry. The small difference in absolute DCP between the upward and downward emissions may be attributed to the coated thin dye layer, which degrades the out-of-plane symmetry to some extent.

Methods
Numerical simulation
All simulations are performed using COMSOL Multiphysics 5.6 “Electromagnetic Waves Frequency Domain” module. The refractive indices of silicon and surrounding materials are taken as nSi=3.9 (Supplementary Section 10) and nPMMA=nSiO2=1.45, respectively. Periodic conditions are applied in the x and y directions of the simulated unit cell, and perfectly matched layers are employed along the z direction. The far-field eigen-polarization is calculated through COMSOL Multiphysics 5.6 with MATLAB. In the calculation of continuum transmission, the incidence port is set as x/y polarization by setting the electric mode field to (1, 0, 0) or (0, 1, 0). Equation (1) is calculated through the polarization-resolved scattering coefficients obtained from ports.

Sample fabrication
A layer of 210 nm silicon is deposited on a 4-inch silica substrate through plasma-enhanced chemical vapor deposition and subsequently cleaved into small 1 cm × 1 cm slices. Each sample is cleaned sequentially in acetone, isopropyl alcohol, and deionized water, and then spin-coated with 270 nm electron-beam resist (PMMA 679.04). The pattern is defined by E-beam exposure (Raith 150 EBL) and developed in methyl isobutyl ketone and isopropyl alcohol. A 30 nm Al film is deposited using electron beam evaporation (Denton) as the hard mask onto the patterned resist and is lifted off by ultrasonic cleaning in acetone. The pattern is then transferred to the silicon by dry etching (Multiplex ICP STS) using C4F8 and SF6, and the residual Al is finally removed in the Al etching solution. The fabrication process of the sample is summarized in Supplementary Section 10.

Covering of IR140 and PMMA
The fabricated sample is cleaned first with acetone and isopropyl alcohol, and then baked on a hot plate at 120 °C for 10 min. The clean sample is spin-coated with a drop of 20 μL IR140 dissolved in ethanol in the following steps: starting at 500 rpm for 3 s, followed by 2000 rpm for 30 s, and lastly at 0 rpm for 3 s. The coated sample is left for stand for 5 min to evaporate the ethanol and improve the film uniformity. To form a thick PMMA layer on the metasurface, the PMMA solution is concentrated through solvent evaporation. Then, the PMMA is spin-coated on the metasurface in the following steps: starting at 500 rpm for 3 s, followed by 4000 rpm for 60 s, and lastly at 0 rpm for 3 s. A layer of 50 μm PMMA is formed by repeating this procedure five times.

Optical characterization
In the transmission measurement, the sample is fixed on a rotating sample stage (Supplementary Section 6). A white light source is turned on and the light passes through a polarizer and an aperture before being focused onto the sample by an objective lens of a low numerical aperture, in which case the incident wave can be treated as an approximate plane wave. The incident polarization is switched between x and y by rotating the polarizer. The transmission spectra for different incident angles are collected by rotating the sample stage. In the PL measurement, a 532 nm continuous-wave laser is used to stimulate IR140 organic dyes. The PL is collected by a 20× objective lens, and analyzed by a zero-order quarter-wave plate, a half-wave plate and a linear polarizer. The fast axis of the quarter-wave plate is fixed to 45° with respect to the polarizer. When the fast axis of the half-wave plate is rotated to 0°/45°, RCP/LCP light is selected.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the submitted manuscript, the authors studied vertical chiral emission from dielectric metasurfaces that preserve out-of-plane (sigma_z) symmetry. They conducted very detailed theoretical studies on how the polarization state of radiation from an out-of-plane symmetric dielectric metasurface is influenced by anisotropic non-resonant background scattering (called scattering by 'anisotropic continuum' in the current manuscript). The authors also verified their theoretical studies by measuring chiral emission from the emitter-coated dielectric metasurface and reported very good experimental results for vertical chiral emission. The current study surely enhances a fundamental understanding of planar chiral structures and provides novel insights into chiral metasurface design. The manuscript is well written, and I think that the current study could be of great interest to the relevant research communities.\nHowever, I see several important issues in the current manuscript. There have been several relevant studies in literature. And the merits of the out-of-plane symmetric metasurfaces for chiral emission are still not clear. Specifically, I'd like to ask the authors to clarify the following issues:\n1) It was previously noted that the polarization state of radiation from a dielectric metasurface (or photonic crystal slab) is strongly constrained by the direct non-resonant scattering (or continuum scattering) process. For example, see\n- arXiv:1708.02197 (2017), \"Polarization state of radiation from a photonic crystal slab\"\nThe discussions in the current manuscript seem closely related to this previous study. This article also commented that, when the direct-scattering (or continuum-scattering) coefficients are the same for the two orthogonal polarization components, the radiation from the dielectric slab should be linearly polarized.\nAs another example, the following paper studied how to achieve maximal planar chirality using dielectric metasurfaces. This article also noted that no chiral response can be obtained if the effective background only has an isotropic response (Section II in Supporting Information).\n- Nat. Comm. (2022) 13:4111, \"Planar chiral metasurfaces with maximal and tunable chiroptical response driven by bound states in the continuum\"\nTherefore, I think the authors should clarify the advancement and difference of the current manuscript compared to the previous studies in literature.\n2) Terminology issue: The title includes the term 'non-chiral'. I suppose the authors wanted to stress that the current study considered a more ideal case for planar chiral metasurfaces that preserved out-of-plane symmetry while previous studies mostly considered structures that still involved out-of-plane symmetry breaking. However, the current study also used a chiral geometry (non-zero alpha in Figure 1a) that breaks in-plane mirror symmetry, and this type of structure has been commonly called planar 'chiral' structure in literature. Therefore, the use of the term 'non-chiral' could be very confusing. It would be great if the authors could come up with a different term.\n3) In the current manuscript, the authors demonstrated vertical chiral emission from dielectric metasurfaces that preserve out-of-plane symmetry. However, similar chiral emission in the vertical direction is also expected from planar chiral metasurfaces on a substrate that break the out-plane-symmetry [e.g., when emitters are coated on the planar dielectric structures in the article above, Nat. Comm. (2022) 13:4111]. Do out-of-plane symmetric metasurfaces have 'practical merits' for chiral emission compared to other planar chiral structures?\n4) In Figure 4, the authors considered asymmetric parameter ‘alpha’ up to 0.09. The chiral response (degree of circular polarization, DCP) gradually increased up to this point. Then, what happens when the alpha increases further beyond 0.09? And what is the optimal value of alpha in the current design?\n5) Effect of absorption losses: In the current manuscript, I think lossless dielectric structures are assumed. But light emission from emitters (either from dye molecules or from semiconductor materials) implies that absorption should also exist at the same wavelength. Therefore, emitter-integrated dielectric metasurfaces should have some absorption losses at the emission wavelength. How do the absorption losses affect the theoretical description of vertical chiral emission in the current manuscript? Is anisotropic continuum still required for vertical chiral emission? For example, according to the current study, gammadion structures made of lossless dielectric materials cannot be used for vertical chiral emission because they are rotationally symmetric and do not support anisotropic continuum scattering. However, when emitters are integrated with such lossless dielectric metasurfaces, the entire system becomes lossy. I am wondering whether vertical chiral emission is still suppressed in this case (or it can be now achieved without anisotropic continuum).\nIn a similar way, I suppose that plasmonic chiral metasurfaces may behave differently for vertical chiral emission due to their intrinsic absorption losses (in addition to the absorption losses of emitters). I would be thankful if the authors clarify these issues.", "reviewer_2": "The authors report on the design and experimental demonstration of a planar metasurface of broken in-plane symmetry, which hosts specific high quality factor photonic eigenstates emitting circularly polarized waves of opposite handedness in the vertical up and down directions. They study how such a state arises in arrays of silicon nanobar dimers subjected to weak symmetry breaking perturbations and attempt to relate the emission chirality with a birefringent background scattering (here called anisotropic continuum). Such metasurfaces are then fabricated and demonstrate that indeed, upon cladding with luminescent organic dye, the properly designed samples emit light with the degree of circular polarization (DCP) up to 0.9 in magnitude and of the opposite handedness in the opposite directions. The paper is accompanied by the Supplementary Information (SI) elaborating proposed theoretical explanations formulated in terms of the temporal coupled-mode theory (TCMT), describing the details of fabrication and optical experiments. Additional modeling clarifies the role of material parameters as well as suggests how the proposed approach can be realized using differently shaped meta-atoms.\nThe subject of the paper is very timely: high-purity sources of chiral light are desired for many emerging chiroptical applications. The main simulations and experimental results look solid and support the conclusion that a planar metasurface can emit circularly polarized light. However, this has already been shown in recent works published by essentially the same group!\nI cannot recommend publishing in NatComm as I seriously doubt the qualitative novelty of this work.\nMy doubts are further strengthened by the fact that the authors avoid citing their own papers, and only briefly mention one in the SI.\nAs a matter of fact, practically identically designed metasurface was used in [R1] to perform exactly the same task and has reached DNC up to 0.74 of emission of a quantum dot cladding. The particular size parameters are different now to ensure a somewhat different emission wavelength. However, the metasurface design is identical to that in [R1]. Compared to [R1], the manuscript contains only more elaborate (and not always well justified) theoretical explanations and additional simulations. Note also that in another recent Ref. [R2] the authors present a similarly designed trimer metasurface performing chiral thermal emission. Therefore, I strongly doubt the novelty of the current findings.\nHaving stated this, I must recognize the potential importance of the theoretical framework developed in order to explain the simulated and repeatedly measured properties. As the authors will definitely look for opportunities to publish their work elsewhere, I formulate a couple of related suggestions and critical remarks:\n1. Simulated (Fig 1b) and measured (Fig. 3) transmission spectra clearly resemble those generally predicted 20 years ago in Ref. [52] for a pair of non-orthogonal modes of an open lossless resonator. More recently, such modes are termed “coupled via-the-continuum” [48]. It seems much more reasonable to start with postulating the existence of two modes of the same parity rather than to presume the existence of strongly birefringent background of unknown origin. Note that I am unaware of a justified procedure of rewriting TCMT equations in order to include a state into the background. From the general viewpoint, this may severely violate the energy conservation. Presumably, Section S3 of the SI attempts to describe such a procedure, but it is hard to comprehend this section due to many undefined notations and possible typos. Please provide a detailed explanation how a state can be phenomenologically included into the background. Otherwise, one can directly follow the strategy of Ref. [52] and start with a pair of states.\n2. To clarify the peculiar eigenstate interplay, it might be useful to analyze them in metasurfaces subjected to different symmetry perturbations as those used to produce Fig. 3. In particular, this could elucidate how the shape perturbations open the state coupling via the continuum. Note also that the field distributions of the states are now given only on a single tiny inset in Fig 2a. These can also clarify the states origin, their coupling and the role of symmetry breaking perturbations.\n3, Finally, to prove the TCMT applicability, one usually derives the model expressions for the transmission and reflection amplitudes and shows how well they fit the simulated transmission and reflection spectra. Otherwise, the usefulness of TCMT remains elusive. Successful fitting will definitely demonstrate that all essential phenomena are adequately understood and captured by the phenomenology.\n[R1] Sun, Y. et al. Enhancing Circularly Polarized Emission by a Planar Chiral Dielectric Metasurface. Advanced Optical Materials 2300197 (2023) doi:10.1002/adom.202300197.\n[R2] Sun, Y., Shi, K., Hu, Z., Jin, Y. & He, S. Highly circularly polarized and coherent thermal emission based on chiral quasi bound states in the continuum. Opt. Lett. 49, 6329 (2024)."}, "author_response": "Response to the Reviewers’ Comments on the manuscript NCOMMS-25-33719\nsubmitted to Nature Communications\nWe would like to sincerely thank the Editor and Reviewers for their careful\nevaluation of our manuscript and their constructive comments, which have helped us\nsubstantially improve the clarity, completeness, and scientific rigor of our work.\nConsidering these critical comments, we have further stated the novelty and related\nadvantages of our work in the areas of chiral emission, while the changes in the revised\nmanuscripts are marked in red. In the following, we provide a point-to-point response\n(in blue) to all reviewers’ questions and comments (in black). We do hope that the\neditor and reviewers may appreciate our extended efforts to improve the paper\nfollowing their suggestions, and we also hope our efforts and clarifications may\nconvince the reviewers of the significant advances of our proposed strategies in\nproviding the paradigm of chiral emission in out-of-plane mirror symmetric\nmetasurfaces.\nIn the response letter and revised manuscript, we have addressed problems mainly\nin following aspects:\n1. Title: Clarified the terminology by replacing “non-chiral” with “intrinsically\nachiral metasurface” to avoid ambiguity.\n2. Novelty: Performed a targeted comparison with representative prior works and our\ngroup’s earlier studies across structural design, symmetry conditions, optical\nresponse, and underlying mechanisms, thereby highlighting the distinct\ncontributions of this work.\n3. New figure: Incorporated both simulated spectra and temporal coupled-mode\ntheory (TCMT) fitting curves into Figure 3, highlighting the strong agreement\nbetween analytical TCMT predictions and numerical results. In Figure 4b,\nextended the x- and y-axis ranges to better reveal the trends under larger asymmetry\nparameters ( and t).\n4. Supplementary information: Revised Section 3 to enhance readability and ensure\nrigor in the derivation. Added Section 5 to explicitly reveal the role of symmetry\nbreaking perturbations via the overlap-integral formulation, supported by\nadditional figures.\nWe believe these revisions fully address the concerns regarding novelty and\nprovide a clearer distinction from previous works. We thank the Reviewers again for\ntheir constructive and insightful feedback.\nIn the submitted manuscript, the authors studied vertical chiral emission from dielectric\nmetasurfaces that preserve out-of-plane ( ) symmetry. They conducted very detailed\nz\ntheoretical studies on how the polarization state of radiation from an out-of-plane\nsymmetric dielectric metasurface is influenced by anisotropic non-resonant background\nscattering (called scattering by 'anisotropic continuum' in the current manuscript). The\nauthors also verified their theoretical studies by measuring chiral emission from the\nemitter-coated dielectric metasurface and reported very good experimental results for\nvertical chiral emission. The current study surely enhances a fundamental\nunderstanding of planar chiral structures and provides novel insights into chiral\nmetasurface design. The manuscript is well written, and I think that the current study\ncould be of great interest to the relevant research communities.\nReply:\nWe sincerely thank the reviewer for their positive and encouraging comments on\nour work! We are pleased that the reviewer recognizes the novelty and significance of\nour study, particularly the detailed theoretical analysis of vertical chiral emission from\nout-of-plane symmetric dielectric metasurfaces and the experimental validation.\nHowever, I see several important issues in the current manuscript. There have been\nseveral relevant studies in literature. And the merits of the out-of-plane symmetric\nmetasurfaces for chiral emission are still not clear. Specifically, I'd like to ask the\nauthors to clarify the following issues:\n1) It was previously noted that the polarization state of radiation from a dielectric\nmetasurface (or photonic crystal slab) is strongly constrained by the direct non-resonant\nscattering (or continuum scattering) process. For example, see - arXiv:1708.02197\n(2017), \"Polarization state of radiation from a photonic crystal slab\" The discussions in\nthe current manuscript seem closely related to this previous study. This article also\ncommented that, when the direct-scattering (or continuum-scattering) coefficients are\nthe same for the two orthogonal polarization components, the radiation from the\ndielectric slab should be linearly polarized.\nAs another example, the following paper studied how to achieve maximal planar\nchirality using dielectric metasurfaces. This article also noted that no chiral response\n2\ncan be obtained if the effective background only has an isotropic response (Section II\nin Supporting Information). - Nat. Comm. (2022) 13:4111, \"Planar chiral metasurfaces\nwith maximal and tunable chiroptical response driven by bound states in the\ncontinuum\"\nTherefore, I think the authors should clarify the advancement and difference of the\ncurrent manuscript compared to the previous studies in literature.\nReply:\nWe thank the reviewer for pointing out these relevant works. In the development\nof optical chirality, many studies have pursued two major directions: achieving strong\ncircular dichroism (CD)1–6, with or without  -symmetry breaking, and realizing highly\nz\ncircularly polarized emission (high DCP) in structures where  -symmetry is broken7–\nz\n9. A key open question, however, is whether high DCP can be obtained while preserving\n symmetry. Among the two references mentioned by the reviewer, Ref. [10]\nz\nmaintained  -symmetry but focused on linearly polarized emission, and Ref. [11]\nz\nexplored high CD in planar chiral metasurfaces.\nOur study builds upon these works but extends them in multiple important ways.\nIn terms of scientific contribution, we clarify the physical conditions under which  -\nz\nsymmetric metasurfaces can generate highly chiral emission, thereby resolve a long-\nstanding misconception and provide a general theoretical framework for future planar\nchiral designs. In terms of significance, this framework is robust and extendable:\nalthough we demonstrate it in  -symmetric systems, it can also be applied when a\nz\nsubstrate of moderate refractive index is present, making it practical for realistic device\nconfigurations. In terms of potential applications, high-purity sources of chiral light\nare increasingly desired for emerging chiroptical applications, such as enantioselective\nsensing, quantum light sources, and polarization-resolved detection, and our results\nprovide a practical pathway toward such applications.\nTable R1 Comparison between our work and two relevant studies from four dimensions:\n symmetry, DCP, CD and the origin of emission polarization.\nz\nCategory Feature Ref. [10] Ref. [11] This work\nStructure\n× (substrate breaks\n symmetry √ (preserved) √ (preserved)\nz\n)\nz\nIn-plane\n× √ √\nchirality\nLinear-polarized High CD in High DCP in\nPrimary goal\nemission transmission vertical emission\nOptical DCP (vertical\nN/A (not studied) small / not the focus 1\nproperties emission)\nCD\nN/A (not studied) high 0\n(transmission)\nYes —\nYes — anisotropic\nmechanism of Partly — CD\nPhysical continuum sets\nlinear emission explained; vertical\nMechanism mechanism phase/amplitude\n(continuum- chiral emission not\nclarified? ratio; TCMT +\nmediated established\nquantitative fits\ninterference)\nTo explain in detail, we provide a comparison table R1 for our work and these two\nstudies from four dimensions:  symmetry, DCP, CD and the origin of emission\nz\npolarization.\nThe work in Ref. [10] derives the relationship between radiation phase difference\nand direct-scattering coefficients. It gives us a sense that the coupling constants cannot\nbe arbitrary but are instead related to the scattering matrix of the direct process, as\npointed out by Shanhui Fan, et al in Ref. [12]. This work focuses on the linear\npolarization constraints in photonic crystal slabs and emphasizes that C -symmetric\n2\nstructures yield only linearly polarized emission. Metasurfaces without C symmetry,\n2\nsuch as metasurface with planar chirality, are not involved. Chirality is an emerging\nfield in nanophotonics, and the understanding of the emission properties is of great\nsignificance. Our study extends the theory into the chirality field, demonstrating that\ncircularly polarized emission emerging at Γ or non-Γ points is relevant to anisotropic\ncontinuum.\nThe work in Ref. [11] explores high circular dichroism in transmission and assumes\nan anisotropic background is required for planar chirality. Our work advances and\n4\ndiffers from this article in many aspects:\n1. Symmetry condition difference: The conclusion of the study is based on a\nmetasurface with a substrate, which breaks the out-of-plane mirror symmetry.\nBreaking this symmetry via a substrate is a widely accepted approach in the\nliterature and is often considered a necessary condition for achieving strong optical\nchirality. For example, Ref. [13] pointed out the substrate can play an important role\nin inducing maximum intrinsic optical chirality. In contrast, our work demonstrates\nthat high chiral emission can be realized even when this symmetry is preserved,\nthereby challenging this conventional view.\n2. Chiral emission mechanism gap: This paper does not clarify the conditions for\nachieving high DCP in vertical emission. Later in 2023, an article published in\nNature3 refers to this paper and said “Although false chirality may yield similar CD\nsignals as its counterpart of true chirality, its applications in a range of important\nfields such as chiral emission and polarized photodetection are notably limited”. In\nthe Supplementary Section 13 of the paper, they proved that large CD in planar\nchiral metasurface doesn’t ensure chiral emission. Thus, the chiral emission ability\nof planar chiral metasurface was doubted, and should be further clarified. Our work\ndirectly addresses this gap by developing a TCMT-based framework and\nsystematically analyzing the role of anisotropic continuum.\n3. Quantitative analysis of continuum scattering: Regarding to anisotropic\nbackground, they pointed out “The maximal linear CD is not necessarily related to\nthe circular eigen-polarization state due to the existence of background scattering”.\nThis is a qualitative description. The role of background plays in generating chiral\nresponse is unclear and there lacks a quantitative description. In contrast, we\nprovide the relationship between radiation phase difference and direct-\nscattering coefficients, which has never been systematically investigated and is\na great advancement compared to the literature.\nOverall, our work provides a comprehensive and quantitative theoretical\nframework for realizing high DCP in emission. The related revisions in the manuscript\nare as follows:\n(Page 2, lines 56-59)\n“Planar chiral metasurfaces represent another route, where near-unity circular\ndichroism at normal incidence has also been reported6,11,14. However, these designs\nmainly address transmission responses, leaving their potential for controlling emission\nlargely unexplored. By contrast,”\n5\n(Page 3, lines 75-79)\n“While ultrahigh-Q modes in metasurfaces, such as quasi-BIC15,16 and leaky guided\nmode17–19, have been extensively studied and applied in photonics, the specific\ninfluence of the continuum on emission polarization remains largely unexplored.\nRelated work has examined its effect on linearly polarized emission10, whereas its\ncontribution to chiral emission remains an open and critical question.”\n2) Terminology issue: The title includes the term 'non-chiral'. I suppose the authors\nwanted to stress that the current study considered a more ideal case for planar chiral\nmetasurfaces that preserved out-of-plane symmetry while previous studies mostly\nconsidered structures that still involved out-of-plane symmetry breaking. However, the\ncurrent study also used a chiral geometry (non-zero alpha in Figure 1a) that breaks in-\nplane mirror symmetry, and this type of structure has been commonly called planar\n'chiral' structure in literature. Therefore, the use of the term 'non-chiral' could be very\nconfusing. It would be great if the authors could come up with a different term.\nReply:\nWe thank the reviewer for pointing out the potential ambiguity of the term non-\nchiral in the title. We intended to emphasize that the current study focuses on\nmetasurfaces that preserve out-of-plane mirror symmetry, in contrast to most previous\nworks where such symmetry was broken. We agree, however, that because the present\ndesign breaks in-plane mirror symmetry, the term “non-chiral” could be misleading, as\nsimilar geometries are often referred to as planar chiral structures in the literature.\nTo avoid any misunderstanding, we have replaced “non-chiral” with “intrinsically\nachiral metasurface” in the title, which more accurately reflects the physical structure\nwhile aligning with the common terminology used in the literature.\n3) In the current manuscript, the authors demonstrated vertical chiral emission from\ndielectric metasurfaces that preserve out-of-plane symmetry. However, similar chiral\nemission in the vertical direction is also expected from planar chiral metasurfaces on a\nsubstrate that break the out-plane-symmetry [e.g., when emitters are coated on the\nplanar dielectric structures in the article above, Nat. Comm. (2022) 13:4111]. Do out-\nof-plane symmetric metasurfaces have 'practical merits' for chiral emission compared\nto other planar chiral structures?\nReply:\nWe thank the reviewer for pointing out the relevant work. As we have explained\n6\nin the response to question 1, the structure in Ref. [11] primarily achieved high circular\ndichroism (CD = (T  T )/(T + T )) in transmission, not high DCP in vertical emission,\nR L R L\nas they stressed in the abstract “demonstrate experimentally chiroptical responses with\nultra-high Q-factors and near-perfect circular dichroism (CD = 0.93) at optical\nfrequencies”. Although coating emitters on such a substrate-based structure was not\ndemonstrated in that work, a paper published thereafter3 compared the emission\nproperties between intrinsic chiral BIC (the structure in the Ref. [3]) and quasi-BIC with\nfalse chirality (the structure in Ref. [11]) in Supplementary Section 13. By putting an\nelectric dipole inside the structure, they obtained the degree of circular polarization\n(DCP) of only 0.097 (Figure R1a) and noted that such a weak DCP is generated by\nthe different refractive indices above and below the silicon structure, but not\nattributed to the structural asymmetry of the silicon nanostructure. What’s more,\nthey used the same structure to simulate the absorption under RCP and LCP normal\nincidence, as chirality-dependent absorption is another basic feature of high-Q chiral\nresonances. Although this structure can exhibit large CD in transmission, the chirality\nof the quasi-BIC is limited, exhibiting small CD in absorption, with a retrieved CD of\nonly 0.28 (Figure R1b).\nIn contrast, our study focuses on the condition of generating high DCP, and shows\nthat even metasurfaces with strict out-of-plane symmetry can support high DCP through\nanisotropic continuum coupling, verified from both emission property and absorption\nproperty (Figure R1c and R1d).\nelectric dipole (Excerpted from Ref. [3]). b, Simulated absorption spectra of the\nanisotropic silicon metasurface showing a limited difference between RCP and LCP\nincidence (Excerpted from Ref. [3]). c, Experimental upward and downward\nfluorescence spectra for the metasurfaces covered by organic dyes in our work. d,\nSimulated absorption spectra for RCP and LCP incident waves in our work with\ndifferent symmetry breaking parameters and losses.\nAs for the merits raised by the reviewer, our work has “practical merits” compared\nwith earlier works in two important aspects:\nFirst, our work establishes a general theoretical framework that connects mode\nsymmetry, continuum scattering, and polarization control through TCMT. Unlike many\nprevious studies that relied on case-specific structural perturbations or purely numerical\ndemonstrations14,20, our framework reveals the underlying physical constraints and\nprovides a systematic way to predict and design the polarization state of emission. This\nnot only clarifies why certain existing structures exhibit or fail to exhibit chiral\nresponses, but also offers a design principle applicable across a wide class of\nmetasurfaces. In this sense, the contribution is not limited to a single design but rather\nlays a theoretical foundation for the design of future planar chiral metasurfaces with\n8\ntailored emission properties.\nSecond, our design is highly extensible — it can be adapted to photonic crystal\nslabs and even tolerate minor symmetry breaking. If a substrate is introduced, as long\nas the refractive index contrast between the substrate and superstrate is moderate, the\nphysical principles remain valid. This demonstrates that our approach is robust and\nextendable, and thus practical for realistic experimental conditions where\nsubstrates are unavoidable. As we pointed out in page 10 of main text: “The present\ntheory is applicable to metasurfaces with arbitrary refractive index (Supplementary\nInformation section 8) and metasurfaces with a substrate, provided that the substrate\nrefractive index is close to that of the superstrate medium, thereby enhancing its\nsuitability for practical applications”.\n4) In Figure 4, the authors considered asymmetric parameter ‘alpha’ up to 0.09. The\nchiral response (degree of circular polarization, DCP) gradually increased up to this\npoint. Then, what happens when the alpha increases further beyond 0.09? And what is\nthe optimal value of alpha in the current design?\nReply:\nWe thank the reviewer for this question. In the revised manuscript, we have\nextended the analysis in Figure 4 to clarify the effect of further increasing the\nasymmetry parameter 𝛼. In our current design, DCP depends jointly on 𝛼 and the in-\nplane offset 𝛥𝑡, as shown in Figure R2a. By varying both parameters simultaneously\n(e.g., increasing 𝛼 from 0 to 0.12 while adjusting 𝛥𝑡 from 0 nm to 14 nm), the DCP\ncan be continuously tuned and can reach unity (DCP = 1). If 𝛥𝑡 is adjusted accordingly\nwith 𝛼 , there is always a combination of (𝛼,𝛥𝑡 ) that can restore DCP to 1. This\nindicates that there is not a single “optimal” value of 𝛼, but rather a set of (𝛼,𝛥𝑡) pairs\nthat yield perfect circular polarization. Therefore, in the current design, 𝛼 and 𝛥𝑡\nshould be viewed as two coupled parameters. The “optimal” condition for DCP = 1 can\nalways be achieved by jointly optimizing both parameters, even when 𝛼 is larger than\n0.09.\nand  (left axis), and quality factor and  (right axis), with t fixed at 11 nm.\nIn our original Figure 4, the maximum value of 𝛼 is set to 0.09, and we use 𝛼 =\n0.09 and 𝛥𝑡 = 11 𝑛𝑚 for experimental demonstration. When 𝛼 is increased\nbeyond 0.09 while 𝛥𝑡 is kept fixed, as indicated by the dotted line in Figure R2a and\nthe curves in Figure R2b, DCP begins to decrease due to the imbalance between the\ntwo orthogonal polarization channels. Also, different  not only means different DCP,\nbut also influences quality factor. The quality factor decreases with , as larger  means\nlarger symmetry breaking.\n5) Effect of absorption losses: In the current manuscript, I think lossless dielectric structures are assumed. But light emission from emitters (either from dye molecules or from semiconductor materials) implies that absorption should also exist at the same wavelength. Therefore, emitter-integrated dielectric metasurfaces should have some absorption losses at the emission wavelength. How do the absorption losses affect the theoretical description of vertical chiral emission in the current manuscript?\nReply:\nWe thank the reviewer for this important question regarding the role of absorption\nlosses. The integration of emitters (organic dye in our case) will indeed introduce small\nabsorption to the system. To illustrate the influence of absorption to the chiral emission\nproperty, we introduce a nonzero imaginary part  in the silicon we used and simulate\nthe relationship between the DCP of our aimed mode and the imaginary part of silicon.\nAs shown in Figure R3, the DCP is stable with increasing . It’s slowly decreasing but\nmaintains a very high level (larger than 0.98) when  is smaller than 0.1. Although the\nabsorption loss doesn’t affect DCP, it affects quality factor a lot. This is why we should\ncontrol the absorption to a small degree in the experiment. With  increasing, the quality\n10\nfactor decreases severely. In addition, the maximum intensity of the emission drops at\nhigher losses, which is also accompanied by the resonance broadening.\nFigure R3 a, Relation between DCP and  (left axis), and quality factor and  (right\naxis). b, RCP emission intensity at different imaginary part .\nIs anisotropic continuum still required for vertical chiral emission?\nReply:\nThank you for the thoughtful question. We clarify that in our temporal coupled-\nmode theory (TCMT) model, the emergence of vertical chiral emission fundamentally\nrelies on the interference between the x- and y-polarized radiation channels with a\nnontrivial phase difference. This phase difference originates from the structural\nasymmetry that induces anisotropic coupling to the continuum, not from absorption.\nIn the standard TCMT formalism12,21, the total decay rate of a resonance is given\nby:\n𝛾 = 𝛾 +𝛾 , (𝑅1)\n𝑟 𝑛𝑟\nwhere 𝛾 is the radiative decay rate and 𝛾 represents non-radiative decay\n𝑟 𝑛𝑟\n(absorption). Specifically, the emission into the x- and y-polarized channels is governed\nby:\n𝑑 𝑑\n𝑥 𝑦\n𝑞 (𝜔) = ,𝑞 (𝜔) = , (R2)\n𝑥 𝑖(𝜔−𝜔 )+𝛾 𝑦 𝑖(𝜔−𝜔 )+𝛾\n0 0\nwhere d and d are coupling coefficients determined by the mode profile and symmetry\nx y\nselection rules, q (ω) and q (ω) denote the complex radiation amplitudes of the resonant\nx y\nmode into the x- and y-polarized far-field channels, respectively. Introducing material\nabsorption (e.g., from integrated emitters or plasmonic materials) increases the total\ndecay rate γ, thereby broadening the resonance and reducing overall emission amplitude,\nbut does not create or enhance the phase difference between q and q , which are\nx y\ndetermined solely by the spatial symmetry and polarization overlap of the resonant\nmode. Therefore, in the absence of anisotropic continuum (i.e., without symmetry-\n11\nbreaking perturbations that allow for asymmetric coupling), vertical chiral emission\nremains suppressed even in lossy structures.\nThe far-field polarization state is determined by the relative amplitude and phase\nof d and d . In particular, the chirality (Stokes parameter S ) is proportional to the\nx y 3\nimaginary part of their cross term:\n𝑆 ∝ 2𝐼𝑚(𝑑∗𝑑 ), (𝑅3)\n3 𝑥 𝑦\nThus, a finite S requires that both d and d be nonzero and possess a nonzero phase\n3 x y\ndifference, which typically arises due to anisotropic structural perturbations that break\nin-plane mirror symmetry.\nFor example, according to the current study, gammadion structures made of lossless dielectric materials cannot be used for vertical chiral emission because they are rotationally symmetric and do not support anisotropic continuum scattering. However, when emitters are integrated with such lossless dielectric metasurfaces, the entire system becomes lossy. I am wondering whether vertical chiral emission is still suppressed in this case (or it can be now achieved without anisotropic continuum).\nReply:\nFigure R4 a, The case from Ref. [22], including a gammadion structure lying on a thick\nsubstrate, and the electric field distribution of the emitter plane under LCP and RCP\nincidence. b, The case of gammadion structure without substrate, and the eigenmode\nelectric field distribution. c, The case of gammadion structure with loss, and the\nrelationship between DCP (left axis), quality factor (right axis) and .\nGammadion shapes are well-known for their chiral response while also exhibiting\n4\neven though the geometry is in-plane chiral, the isotropic continuum scattering means\nthat vertical chiral emission cannot be achieved unless the up–down (out-of-plane)\nsymmetry is broken. Our work targets a different regime—an intrinsically achiral\nmetasurface that preserves out-of-plane mirror symmetry—and introduces a\nmechanism for achieving maximum optical chirality through anisotropic continuum\nscattering.\nTo clarify the role of anisotropic continuum scattering and loss, we provide three\nrepresentative cases in Figure R4:\n1. Gammadion with substrate and embedded emitters (adapted from Ref. [22]): In\nthis configuration, the substrate breaks the out-of-plane mirror symmetry. The\ninteraction between the substrate-induced mode and the resonant mode leads to\npolarization-dependent interference in the near field, creating spatial regions where\nleft- and right-handed circularly polarized components are unequally enhanced.\nAccording to reciprocity principle, vertical emission with DCP = 0.26 can be\nobserved.\n2. Gammadion without substrate (out-of-plane mirror symmetry restored):\nRemoving the substrate eliminates the vertical asymmetry, restoring up–down\nsymmetry. Simulations show that the far-field polarization of the intrinsic mode\nbecomes purely linear (DCP = 0), indicating that without anisotropic continuum\nscattering, no vertical chiral emission is possible regardless of the in-plane chiral\nshape.\n3. Lossy gammadion without substrate: Starting from case 2, we gradually increase\nthe imaginary part  of the refractive index from 0 to 0.02 to introduce absorption.\nAs expected, the resonance Q-factor decreases due to non-radiative losses, but the\nfar-field polarization remains linear (DCP = 0) over the entire range. This confirms\nthat adding loss does not alter the isotropy of the continuum channels. The ratio d\ny\n/d remains fixed by the C symmetry, and vertical chiral emission cannot be\nx 4\ngenerated without anisotropic continuum scattering.\nIn summary, for rotationally symmetric metasurfaces such as gammadions, adding\nemitters or material loss does not by itself break the symmetry constraints on the\nradiation channels. Anisotropic continuum scattering remains essential for achieving\nvertical chiral emission in these systems.\nIn a similar way, I suppose that plasmonic chiral metasurfaces may behave differently\n13\nfor vertical chiral emission due to their intrinsic absorption losses (in addition to the\nabsorption losses of emitters). I would be thankful if the authors clarify these issues.\nReply:\nThank you for raising this interesting point. We agree that plasmonic chiral\nmetasurfacesnmay exhibit different behavior compared to lossless dielectric designs\ndue to their intrinsic absorption losses. However, whether such losses can enable\nvertical chiral emission without requiring an anisotropic continuum depends critically\non the underlying resonant modes and symmetry properties of the structure.\nIn our current work, the mechanism for vertical chiral emission relies on\ninterference between two orthogonally polarized radiation channels, with a phase\nrelationship governed by symmetry-breaking-induced anisotropy in the background\ncontinuum. If one were to directly convert our dielectric structure into a plasmonic one\nby replacing the high-index dielectric with metal (e.g., gold or silver), the supported\nresonant modes would change significantly. In particular, the modes would no longer\nbe the same quasi bound mode with out-of-plane mirror symmetry and weak leakage\ninto free space. As a result, the symmetry-protected mechanism that we exploit for\nchiral emission would no longer be present.\nThat said, we do not exclude the possibility that a different plasmonic chiral\nmetasurface, specifically designed to support the appropriate mode symmetry and\ninterference conditions, could achieve vertical chiral emission. However, that would\ninvolve a different design principle and lies beyond the scope of the present work. Our\ncurrent theory and experiments are specifically constructed around symmetry-\ncompatible modes in low-loss dielectric metasurfaces.\nThe authors report on the design and experimental demonstration of a planar\nmetasurface of broken in-plane symmetry, which hosts specific high quality factor\nphotonic eigenstates emitting circularly polarized waves of opposite handedness in the\nvertical up and down directions. They study how such a state arises in arrays of silicon\nnanobar dimers subjected to weak symmetry breaking perturbations and attempt to\nrelate the emission chirality with a birefringent background scattering (here called\nanisotropic continuum). Such metasurfaces are then fabricated and demonstrate that\nindeed, upon cladding with luminescent organic dye, the properly designed samples\nemit light with the degree of circular polarization (DCP) up to 0.9 in magnitude and of\nthe opposite handedness in the opposite directions. The paper is accompanied by the\nSupplementary Information (SI) elaborating proposed theoretical explanations\nformulated in terms of the temporal coupled-mode theory (TCMT), describing the\ndetails of fabrication and optical experiments. Additional modeling clarifies the role of\nmaterial parameters as well as suggests how the proposed approach can be realized\nusing differently shaped meta-atoms.\nThe subject of the paper is very timely: high-purity sources of chiral light are desired\nfor many emerging chiroptical applications. The main simulations and experimental\nresults look solid and support the conclusion that a planar metasurface can emit\ncircularly polarized light. However, this has already been shown in recent works\npublished by essentially the same group!\nI cannot recommend publishing in NatComm as I seriously doubt the qualitative\nnovelty of this work.\nMy doubts are further strengthened by the fact that the authors avoid citing their own papers, and only briefly mention one in the SI.\nAs a matter of fact, practically identically designed metasurface was used in [R1] to\nperform exactly the same task and has reached DNC up to 0.74 of emission of a\nquantum dot cladding. The particular size parameters are different now to ensure a\nsomewhat different emission wavelength. However, the metasurface design is identical\nto that in [R1]. Compared to [R1], the manuscript contains only more elaborate (and\nnot always well justified) theoretical explanations and additional simulations. Note also\nthat in another recent Ref. [R2] the authors present a similarly designed trimer\nmetasurface performing chiral thermal emission. Therefore, I strongly doubt the\n15\nnovelty of the current findings.\nReply:\nThanks for the reviewer’s comments. But as for some comments like: “The\nmetasurface design is identical to that in [R1]. the manuscript contains only more\nelaborate (and not always well justified) theoretical explanations and additional\nsimulations”, we respectfully disagree for several reasons:\n1. The reason for employing similar structure\nThe apparent similarity in metasurface geometry is intentional and crucial to\nthe purpose of this study. In our previous work26, the metasurface was placed on a\ndielectric substrate that breaks out-of-plane mirror symmetry and belongs to different\nclassifications as our current work. To isolate the impact of out-of-plane symmetry, we\nintentionally retained the same in-plane geometry used in Ref. [26]. Importantly, we\nemphasize that the observed phenomenon is not limited to this specific design: in other\ncommon configurations we have also seen similar phenomena (Supplementary\nInformation Fig. S2), confirming that the role of anisotropic continuum is a general\nfeature rather than a structure-specific effect. This is precisely why we chose an\nidentical in-plane geometry as Ref. [26], so that the effect of  symmetry could be\nz\nclearly isolated and assessed.\nWe also note that our another previous work Ref. [27] focuses on chiral thermal\nemission using metallic metasurfaces and does not involve photoluminescence. The\nunderlying physics and application contexts are thus entirely distinct from the current\nall-dielectric work. Ref. [27] is deliberately not cited because its focus (chiral thermal\nemission via metallic metasurfaces) differs significantly from the current study.\n2. Unclear origin of chiral emission in previous works\nIn 2023, an article published in Nature3 referred to planar structures with out-of-\nplane mirror symmetry and said “Although false chirality may yield similar CD signals\nas its counterpart of true chirality, its applications in a range of important fields such\nas chiral emission and polarized photodetection are notably limited”. The cognition\nindicated that there still existed a fundamental question in the chiral research field: can\na metasurface with  symmetry, which is geometrically non-chiral, generate circular\nz\nor even arbitrary polarization at the  point? There is an urgent requirement to answer\nthis question and fill the long-existing gap in chiral research field. We are the first to\ninvestigate whether chiral emission can emerge from a metasurface that strictly\npreserves out-of-plane mirror symmetry. This is a fundamental question that, to the best\n16\nof our knowledge, has never been theoretically modeled or experimentally verified. Our\ntheory provides a general and extensible theoretical framework applicable to a broad\nrange of metasurfaces.\n3. Uncovering a unique counterintuitive phenomenon in  symmetric\nz\nmetasurfaces\nWithin  -symmetric metasurfaces, we identify a striking phenomenon where the\nz\ntransmission circular dichroism reduces to zero, yet the emitted light maintains a\ndegree of circular polarization of unity, happening when background scattering\nand resonant scattering happen out of phase, while the amplitude of resonant\nscattering is twice larger than the amplitude of the background scattering. With the\ninterference of anisotropic continuum, the transmission circular dichroism is largely\nmodulated, decoupling resonance from circular dichroism in transmission. The related\nrevisions in the manuscript are as follows:\n(Page 5, lines 120-127)\n“Due to the presence of anisotropic continuum, the transmission and reflection\nspectra of  -symmetric metasurfaces exhibit unique features compared with  -\nz z\nasymmetric ones. As shown in Fig. 1c, the cross-polarization transmission is governed\nby a strong resonant term (t ), yet its resonant nature can be hidden in intensity\nRL\nmeasurements, leading to an ideally vanishing transmission CD (derived in\nSupplementary Section 4). Consequently, the transmission CD at the C point does not\nreach unity. Instead, the C point is characterized by only a slight imbalance between\nT and T (typically < 0.1), indicating that the CD can be very small, and in some\nRL LR\ncases even vanish.”\nWe have no intention of repeating prior work. On the contrary, our aim is to\nhighlight the conceptual contrast by keeping geometry constant and varying only\nthe symmetry condition — an approach we believe provides clarity rather than\nredundancy. We believe these elements collectively establish clear novelty, as also\nrecognized by Reviewer #1: “The current study surely enhances a fundamental\nunderstanding of planar chiral structures and provides novel insights into chiral\nmetasurface design”, our work originates from a fundamental question and will\ndefinitely enhance the development of chiral research field.\nIn summary, far from being repetitive, our study offers a conceptual and\nmechanistic breakthrough by showing that chiral emission can be achieved without\nbreaking out-of-plane symmetry, solely via anisotropic continuum coupling. We hope\n17\nthese clarifications address the reviewer’s concerns and we sincerely thank them again\nfor the thoughtful critique.\nHaving stated this, I must recognize the potential importance of the theoretical\nframework developed in order to explain the simulated and repeatedly measured\nproperties. As the authors will definitely look for opportunities to publish their work\nelsewhere, I formulate a couple of related suggestions and critical remarks:\nReply:\nWe thank the reviewer for “recognize the potential importance of the theoretical\nframework”. However, we respectfully clarify that our experimental approach is not a\nrepetition of previous measurements. In our work, fluorescence detection is employed\nas a well-established but highly effective method to directly probe the intrinsic\npolarization state of the mode. This technique is widely recognized in the field and has\nbeen used in numerous high-impact studies3,7,8, precisely because it can reveal far-field\npolarization characteristics without affected by other scattering channels.\nIn our case, fluorescence measurements are not the primary novelty in themselves,\nbut are essential for validating our theoretical predictions and confirming the chiral\nnature of the radiated fields, which cannot be unambiguously inferred from reflection\nor transmission spectra alone. Thus, while fluorescence is an established technique,\nits use here in combination with our theoretical mechanism constitutes a novel\ncontribution that goes beyond earlier experimental demonstrations.\n1. Simulated (Fig 1b) and measured (Fig. 3) transmission spectra clearly resemble those\ngenerally predicted 20 years ago in Ref. [52] for a pair of non-orthogonal modes of an\nopen lossless resonator. More recently, such modes are termed “coupled via-the-\ncontinuum” [48].\nReply:\nWe thank the reviewer for pointing out Ref. [21], which is one of the foundations\nfor TCMT. While our observed transmission spectra bear resemblance to the lineshapes\ndescribed in Ref. [21], we emphasize that the underlying physical mechanisms and\nmodeling strategies differ significantly.\nshow the evolution of transmission lineshapes with Δ𝜔 for Ref. [21] and our work,\nrespectively.\nRef. [21] discusses the interference of two non-orthogonal resonant modes of the\nsame parity within a lossless open cavity. Assume these two modes possess the same\nlinewidth 𝛾 and different central frequency: 𝜔 = 𝜔 +Δ𝜔/2 , 𝜔 = 𝜔 −Δ𝜔/2 .\n1 0 1 0\nWhen the separation between two modes gets closer, which means decreasing Δ𝜔, a\nnarrow transmission peak appears. The width of such transmission peak is dependent\nupon the frequency spacing of the two modes and can be infinitesimal when the two\nfrequencies are close to each other. Especially, when two modes overlap, the\ntransmission peak vanishes. The evolution process is illustrated in Figure R5a, with\nΔ𝜔 decreases from 𝜔 /3 to 𝜔 /6 then to 0, the transmission peak becomes\n0 0\nnarrower and then vanishes.\nIn contrast, our system involves a sharp high-Q resonance coupled to a broadband\nlow-Q response that originates from the anisotropic continuum states, which we\nphenomenologically refer to as the “background”. Figure R5b shows the transmission\nspectra of T and T when the high-Q resonance exhibits same coupling constant to x-\nx y\nand y-polarization. In this case, Δ𝜔 is the center frequency distance of the high-Q\n19\nresonance and the broadband low-Q response. T exhibits a transmission dip and T\nx y\nexhibits Fano resonance lineshape at the resonant frequency. The quality factor of the\nFano resonance depends on the high-Q mode and keeps constant regardless of the center\nfrequency distance Δ𝜔.\nThese two cases resemble in some aspects: (1) the lineshape is a result of multiple\nmode interference, (2) the case of Ref. [21] presents a sharp transmission peak inside a\nbroad transmission dip when Δ𝜔 is close to 0, and our work presents a T transmission\ny\npeak when Δ𝜔 is 0. However, the formation process and behavior of these two cases\nare significantly different. Especially, our work focuses on different responses for an\northogonal polarized incidence, which is the reason why T forms a sharp dip in a\nx\ntransmissive background and T forms a sharp peak in a broadband reflective\ny\nbackground.\nIt seems much more reasonable to start with postulating the existence of two modes of\nthe same parity rather than to presume the existence of strongly birefringent background\nof unknown origin.\nReply:\nWe appreciate the reviewer’s suggestion. Our intention is not to presume the\npresence of a physical birefringent background of unknown origin. Rather, we\nintroduce the background channel as a phenomenological construct to describe the\nbroadband anisotropic response, which plays a crucial role in shaping the polarization\nstate of the far-field radiation.\nFig. S2 Different types of continuum states in chiral metasurfaces for generating chiral\nradiation.\nThe formation of the continuum channel is generally complicated and cannot be\nreduced to a single eigenmode. As illustrated in Supplementary Figure S2, this\n20\nbackground response originates from a continuum of radiation channels with\nanisotropic scattering strengths. We emphasize that the background is not a physical\neigenmode, but an effective representation of broadband scattering channels that share\nthe same parity as the resonant mode. The transmission spectrum further confirms that\nthis effect cannot be attributed to a single resonance.\nIn Supplementary Section 3, for intuitive understanding and modeling simplicity,\nwe approximate this broadband anisotropic response as an effective background mode.\nThis approximation allows us to analytically derive the condition for achieving\ncircularly polarized radiation. In this way, our treatment eliminates the need to invoke\nan unknown birefringent background and provides a straightforward framework to\npredict the polarization-dependent phase difference that governs the chirality of\nradiation.\nNote that I am unaware of a justified procedure of rewriting TCMT equations in order\nto include a state into the background. From the general viewpoint, this may severely\nviolate the energy conservation. Please provide a detailed explanation how a state can\nbe phenomenologically included into the background. Otherwise, one can directly\nfollow the strategy of Ref. [52] and start with a pair of states.\nReply:\nWe appreciate the reviewer’s concern regarding the energy conservation in our use\nof a broadband background response. We have rigorously verified that treating a\nbroadband contribution as a “background mode” in the TCMT framework does not\nviolate energy conservation.\nTo clarify this, we introduce a background matrix C that describes the scattering\namplitude from the broadband response. When a mode is included in the background\nand contributes to both 𝑥- and 𝑦-polarized channels, the matrix C takes the form:\n𝑖𝛼|𝑑𝑐|2 𝑖|𝑑𝑐|2\n−\n𝑥\n𝑖−\n𝑥\n0 0\n𝛾 −𝑖(𝜔−𝜔 ) 𝛾 −𝑖(𝜔−𝜔 )\n𝑐 𝑐 𝑐 𝑐\n𝑖|𝑑𝑐|2 𝑖𝛼|𝑑𝑐|2\n𝑥 𝑥\n𝑖− − 0 0\n𝛾 −𝑖(𝜔−𝜔 ) 𝛾 −𝑖(𝜔−𝜔 )\n𝑐 𝑐 𝑐 𝑐\n𝐶 = 2 2 ,(𝑅4)\n𝑖𝛼|𝑑\n𝑦\n𝑐| 𝑖|𝑑\n𝑦\n𝑐|\n0 0 − 𝑖−\n𝛾 −𝑖(𝜔−𝜔 ) 𝛾 −𝑖(𝜔−𝜔 )\n𝑐 𝑐 𝑐 𝑐\n2 2\n𝑖|𝑑𝑐| 𝑖𝛼|𝑑𝑐|\n𝑦 𝑦\n0 0 𝑖− −\n[ 𝛾 −𝑖(𝜔−𝜔 ) 𝛾 −𝑖(𝜔−𝜔 ) ]\n𝑐 𝑐 𝑐 𝑐\nHere, 𝜔 is the central frequency of the broadband response, 𝛾 is its linewidth, and\n𝑐\n𝛼 is a symmetry factor. For lossless systems, energy conservation requires that the\noverall scattering matrix is unitary, i.e.,\n21\n𝐶+𝐶 = 𝐼, (𝑅5)\nThis condition leads to two constraints:\n1. Diagonal terms of 𝐶+𝐶 must equal 1:\n2 2\n2|𝑑𝑐| (|𝑑𝑐| −𝛾)\n1+\n𝑗 𝑗\n= 1 → |𝑑𝑐|\n2\n= 0 or |𝑑𝑐|\n2\n= 𝛾 , (𝑅6)\n𝛾2 +(𝜔−𝜔 )2 𝑗 𝑗 𝑐\n𝑐 𝑐\n2. Off-diagonal terms of 𝐶+𝐶 must vanish:\n2 2\n2𝛼|𝑑𝑐| (|𝑑𝑐| −𝛾)\n𝑗 𝑗\n= 0 → |𝑑𝑐|\n2\n= 0 or |𝑑𝑐|\n2\n= 𝛾 , (𝑅7)\n𝛾2 +(𝜔−𝜔 )2 𝑗 𝑗 𝑐\n𝑐 𝑐\nThus, the condition 𝐶+𝐶 = 𝐼 can only be satisfied if each polarization channel is\n2 2\neither fully coupled (with |𝑑𝑐| = 𝛾 ) or not coupled at all (with |𝑑𝑐| = 0 ). The\n𝑗 𝑐 𝑗\n2\nintermediate case 0 < |𝑑𝑐| < 𝛾 violates unitarity and is therefore unphysical in a\n𝑗 𝑐\nlossless background model.\nIn our manuscript, the anisotropic background response was deliberately\n2\nconstructed to obey this constraint: we use |𝑑𝑐|2 = 0 , |𝑑𝑐| = 𝛾 , ensuring that\n𝑥 𝑦 𝑐\nenergy conservation is strictly satisfied. This formulation corresponds to embedding a\nstrongly radiative eigenmode with broadband spectral characteristics into the\nbackground, such that it modifies the scattering matrix without introducing additional\nresonance into the TCMT.\nRegarding Ref. [21] (Ref. [52] in the question), their strategy is to directly start\nwith two resonant modes of the same parity. This approach is indeed powerful for\ndescribing systems where such modes naturally coexist. However, in our case the\nphysical situation is different: we observe the interference between a high-Q resonance\nand a broad continuum, which in general cannot be reduced to two well-defined discrete\nmodes (such as the cases shown in Fig. S2). Our treatment with an effective anisotropic\ncontinuum provides a simpler and more transparent way to reveal the polarization-\nrelated phase difference, while still remaining fully consistent with energy conservation.\nIn summary, our model respects unitarity and reciprocity, and the background-\nmode treatment is both mathematically consistent and physically justified. In the\nrevised version, we have added the derivation of energy conservation in Supplementary\nInformation section 3.\nPresumably, Section S3 of the SI attempts to describe such a procedure, but it is hard\nto comprehend this section due to many undefined notations and possible typos.\nWe acknowledge that Section S3 in the previous version of the Supplementary\nInformation was insufficiently clear and may contain ambiguous notations. On the one\nhand, we have completely revised this section to clarify our formalism, carefully\ndefining all quantities and illustrating how the background term emerges from a\nbroadband continuum channel. On the other hand, the updated Section S3 now derives\nand summarizes the key constraints of the continuum states, which clarify their role in\nthe analytical model and ensure consistency with energy conservation.\nThe related revisions in the manuscript are as follows:\n(Supplementary Information, Section 3)\n“Constraint 1:\nConstraint 1 directly arises from the requirement that the phase difference between\nthe x-polarized and y-polarized radiation supported by the continuum. t t r r\nxx yy xx yy\nshould satisfy equation (10), which can be written as follows:\n2 2 2 2\n𝑖𝑡|𝑑𝑐| +𝛼𝑐𝑟|𝑑𝑐| 𝑟|𝑑𝑐| +𝑖𝛼𝑐𝑡|𝑑𝑐|\n𝑦 𝑧 𝑦 𝑦 𝑧 𝑦\n𝑖𝛼 𝑡−𝛼 +𝑟− =\n𝑧 𝑧 𝛾 −𝑖(𝜔−𝜔 ) 𝛾 −𝑖(𝜔−𝜔 )\n𝑐 𝑐 𝑐 𝑐\n𝑖𝑡|𝑑𝑐|2 +𝛼𝑐𝑟|𝑑𝑐|2 𝑟|𝑑 |2 +𝑖𝛼𝑐𝑡|𝑑𝑐|2\n𝑒𝑖∗2(𝜃𝑦−𝜃𝑥)(𝑖𝛼 𝑡−𝛼 𝑥 𝑧 𝑥 +𝑟− 𝑥 𝑧 𝑥 ), (20)\n𝑧 𝑧 𝛾 −𝑖(𝜔−𝜔 ) 𝛾 −𝑖(𝜔−𝜔 )\n𝑐 𝑐 𝑐 𝑐\nThis equation can be simplified as:\n2\n(1−𝑒𝑖∗2(𝜃𝑦−𝜃𝑥))(𝛾 −𝑖(𝜔−𝜔 )) = (1+𝛼 𝛼𝑐)(|𝑑𝑐| −𝑒𝑖∗2(𝜃𝑦−𝜃𝑥)|𝑑𝑐|2), (21)\n𝑐 𝑐 𝑧 𝑧 𝑦 𝑥\nIf  =  –  = /2, one can get:\ny x\n2\n2𝛾 −2𝑖(𝜔−𝜔 ) = (1+𝛼 𝛼𝑐)(|𝑑𝑐| +|𝑑𝑐|2). (22)\n𝑐 𝑐 𝑧 𝑧 𝑦 𝑥\nThe equation (22) means:\n2\n𝛼𝑐 = 𝛼 ,𝜔 = 𝜔 ,|𝑑𝑐| +|𝑑𝑐|2 = 𝛾 . (23)\n𝑧 𝑧 𝑐 𝑦 𝑥 𝑐\nConstraint 2:\nSince the broadband contribution is treated as an effective background mode in\nTCMT, it is necessary to ensure that such treatment does not lead to unphysical\namplification or loss in a lossless system. Therefore, the background scattering matrix\nC must be unitary, i.e.,\n𝐶+𝐶 = 𝐼, (24)\nThis condition leads to two constraints:\n3. Diagonal terms of 𝐶+𝐶 must equal 1:\n23\n2 2\n2|𝑑𝑐| (|𝑑𝑐| −𝛾 )\n1+\n𝑗 𝑗 𝑐\n= 1 → |𝑑𝑐|\n2\n= 0 or |𝑑𝑐|\n2\n= 𝛾 , (25)\n𝛾 2 +(𝜔−𝜔 )2 𝑗 𝑗 𝑐\n𝑐 𝑐\n4. Off-diagonal terms of 𝐶+𝐶 must vanish:\n2 2\n2𝛼𝑐|𝑑𝑐| (|𝑑𝑐| −𝛾 )\n𝑧 𝑗 𝑗 𝑐\n= 0 → |𝑑𝑐|\n2\n= 0 or |𝑑𝑐|\n2\n= 𝛾 , (26)\n𝛾 2 +(𝜔−𝜔 )2 𝑗 𝑗 𝑐\n𝑐 𝑐\nThus, the condition 𝐶+𝐶 = 𝐼 can only be satisfied if each polarization channel is\n2 2\neither fully coupled (with |𝑑𝑐| = 𝛾 ) or not coupled at all (with |𝑑𝑐| = 0 ). The\n𝑗 𝑐 𝑗\n2\nintermediate case 0 < |𝑑𝑐| < 𝛾 violates unitarity and is therefore unphysical in a\n𝑗 𝑐\nlossless background model.\nConstraints 1 and 2 together yield the conditions for achieving a /2 phase\ndifference in the case where the continuum is reduced to a single resonant mode: (1)\nThe parity of the continuum state should be same with the bound eigenstate; (2) The\nfrequency of the bound eigenstate should coincide with the continuum state; (3) Among\nthe polarization channels, one is maximally coupled (|𝑑𝑐|2 = 𝛾 ,𝑖 = 𝑥 or 𝑦), whereas\n𝑖 𝑐\n2\nthe orthogonal one is entirely decoupled (|𝑑𝑐| = 0,𝑗 = 𝑦 or 𝑥).”\n𝑗\n2. To clarify the peculiar eigenstate interplay, it might be useful to analyze them in\nmetasurfaces subjected to different symmetry perturbations as those used to produce\nFig. 3. In particular, this could elucidate how the shape perturbations open the state\ncoupling via the continuum. Note also that the field distributions of the states are now\ngiven only on a single tiny inset in Fig 2a. These can also clarify the states origin,\ntheir coupling and the role of symmetry breaking perturbations.\nReply:\nThank you for the valuable suggestion. We have now expanded our discussion to\nclarify the origin and coupling mechanism of the resonance modes under different\nsymmetry perturbations, with reference to Fig. 3. Since direct interpretation from\neigenmode field profiles can be unintuitive, we provide a simplified yet insightful\nexplanation based on dipole equivalence and overlap integrals.\nintegration of E and E over each xy plane at different z positions. (c) Cumulative\nx y\nvolume integration of E(x,y,z)eikz for E and E , obtained by integrating from z = 0 to a\nx y\ngiven z value.\nIn the fully symmetric structure (α = 0, Δt = 0), the metasurface preserves out-of-\nplane mirror symmetry (σ ) and multiple in-plane mirror symmetries. Each unit cell can\nz\nbe effectively represented by two z-oriented electric dipoles of opposite phase and equal\nspacing. Their far-field radiation cancels out due to symmetry, resulting in vanishing\ncoupling to the radiation continuum. In general, the coupling strength to normally\nincident plane waves with x- or y-polarization is determined by the overlap integral12,28:\n𝑎 ∝ ∫𝑬 (𝑟)𝑬 (𝑟)𝥿𝜀(𝑟)𝑑3𝒓. (𝑅8)\n𝑟𝑒𝑠 𝑖𝑛𝑐\nHere, 𝑬 denotes the electric field distribution of the resonant mode, 𝑬 denotes\n𝑟𝑒𝑠 𝑖𝑛𝑐\nthe incident electric field, and 𝥿𝜀 represents the permittivity difference between the\nstructure and background material. Figure R6 provides a step-by-step visualization of\nhow the coupling coefficient a in Eq. (R8) is evaluated. We first show the electric field\ndistribution of the resonant mode, then the cross-sectional integration of E and E\nx y\nacross different xy planes along z, and finally the cumulative volume integration of\nE(x,y,z)eikz for both components. This sequence connects the field distribution to the\noverlap integral that determines the coupling strength. Due to mirror symmetries\n(notably xz and yz planes), the spatial average of the mode profile projected along x or\ny vanishes at every z-plane, leading to zero overlap and hence zero radiative coupling\na. This corresponds to a bound mode.\nof the resonant mode. (b) Cross-sectional integration of E and E over each xy plane at\nx y\ndifferent z positions. (c) Cumulative volume integration of E(x,y,z)eikz for E and E ,\nx y\nobtained by integrating from z = 0 to a given z value.\nWhen dimerization is introduced by shifting the two pillars in a unit cell closer\n(Δt ≠ 0), the spacing between neighboring pillars becomes asymmetric, and the\nstructure can now be equivalently described as an effective magnetic dipole oriented\nalong the y-direction. This magnetic dipole couples efficiently to x-polarized light. The\ncoupling strength to normally incident x-polarized plane wave by the overlap integral\nis represented by:\n𝑎 ∝ ∫𝑬 (𝑟)𝑒𝑖𝑘𝑧𝥿𝜀(𝑟)𝑑3𝒓 ≠ 0. (𝑅9)\n𝑥 𝑟𝑒𝑠,𝑥\nFigure R7 illustrates that, while the direct integration of E (x,y,z) over the structure is\nx\nzero (black square in Fig. R7c), the overlap integral E (x,y,z)eikz yields a finite value\nx\n(blue dot in Fig. R7c), since the accumulated phase along the z-direction breaks the\nperfect cancellation of the field components. Due to the remaining xz mirror symmetry,\ncoupling to y-polarized light remains forbidden. This explains the emergence of linearly\npolarized emission along the x-direction in Fig. 3 when only Δt is varied.\n(a) Electric field distribution of the resonant mode. (b) Cross-sectional integration of E\nx\nand E over each xy plane at different z positions. (c) Cumulative volume integration of\ny\nE(x,y,z)eikz for E and E , obtained by integrating from z = 0 to a given z value.\nx y\nFinally, when both perturbations are applied simultaneously (α ≠ 0, Δt ≠ 0), the\neffective magnetic dipole becomes oblique, with both x and y components.\nConsequently, the resonance couples to both polarization channels with a controlled\nrelative phase difference, which we find to be close to π/2. This leads to a chiral\nradiation state, i.e., elliptically or circularly polarized emission. Mathematically, both\ncoupling constants are now finite (Figure R8):\n𝑎 ∝ ∫𝑬 (𝑟)𝑒𝑖𝑘𝑧𝥿𝜀(𝑟)𝑑3𝒓 ≠ 0,𝑎 ∝ ∫𝑬 (𝑟)𝑒𝑖𝑘𝑧𝥿𝜀(𝑟)𝑑3𝒓 ≠ 0. (𝑅10)\n𝑥 𝑟𝑒𝑠,𝑥 𝑦 𝑟𝑒𝑠,𝑦\nBy jointly tuning α and Δt, these two coupling amplitudes can be balanced in both\nmagnitude and phase, maximizing the degree of circular polarization (DCP ≈ 1), as\ndemonstrated in Fig. 3 of the manuscript.\nWe have added this comprehensive discussion to the revised supplementary\ninformation and expanded the description about Fig. 3 accordingly to better convey\nhow the symmetry perturbations give rise to mode coupling via the continuum. The\nrelated revisions in the manuscript are as follows:\n(Page 8, lines 206-211)\n“In terms of the resonant mode field distribution, the coupling behavior can be directly\nunderstood from the overlap integral between the incident field and the resonant mode:\nsymmetry enforces vanishing overlap, t alone allows coupling only to x-polarization,\nand the combination of t and  yields finite overlap for both x- and y-polarizations\nwith a phase difference close to /2. Full derivations and supporting figures are\n27\nprovided in Supplementary Section S3.”\n3, Finally, to prove the TCMT applicability, one usually derives the model expressions\nfor the transmission and reflection amplitudes and shows how well they fit the\nsimulated transmission and reflection spectra. Otherwise, the usefulness of TCMT\nremains elusive. Successful fitting will definitely demonstrate that all essential\nphenomena are adequately understood and captured by the phenomenology.\nReply:\nWe appreciate the reviewer’s valuable suggestion regarding the verification of\nTCMT applicability. We fully agree that explicitly demonstrating the agreement\nbetween TCMT-based analytical expressions and numerical spectra is an important step\ntoward confirming the universality of the model and its relevance to broader situations.\nFollowing this advice, we have derived explicit analytical expressions for the\ntransmission and reflection amplitudes based on our TCMT formalism, as given in the\nrevised supplementary information. The derivation incorporates both the background\nresponse and the resonant contributions, ensuring that interference effects are faithfully\ndescribed.\nFigure R9 (New Figure 3 in manuscript) The evolution of the transmission spectra,\ncorresponding to the process of Figure 1d. Transmission spectra T and T of the\nx y\nmetasurface with the following structural parameters: a,  = 0 and t = 0, b,  = 0 and\nt = 11 nm, and c,  = 0.09 and t = 11 nm. Upper panels show simulated (solid lines)\nand TCMT fitted curves (marked by ), and lower panels show experimentally\nmeasured curves.\nCase 1 – Background-dominated spectrum\nx y\nexhibits a broadband reflection dominated by a low-Q mode with center frequency 𝜔\n1\nand damping rate 𝜾 :\n1\n𝜾 𝜾\n𝑟 ≈0,𝑡 ≈1,𝑟 = 1 ,𝑡 =1− 1 . (𝑅11)\n𝑥 𝑥 𝑦 𝜾 −𝑖(𝜔−𝜔 ) 𝑦 𝜾 −𝑖(𝜔−𝜔 )\n1 1 1 1\nFitting yields: 𝜔 = 783𝑛𝑚 𝜾 = 74.2𝑛𝑚, confirming that this background channel\n1 1\nis well described by a single low-Q resonance.\nCase 2 – High-Q mode coupling to a single polarization\nIn Fig. 3(b), a high-Q resonance couples exclusively to the x-polarized channel,\ncausing a sharp dip in T while leaving T almost unchanged. We denote the center\nx y\nfrequency and damping rate of this high-Q resonance as 𝜔 and 𝜾 :\n2 2\n(𝑡 −𝑟 )𝜾\nt =t − 𝑥 𝑥 2 ,t =t . (𝑅12)\n𝑥𝑥 𝑥 𝜾 −𝑖(𝜔−𝜔 ) 𝑦𝑦 𝑦\n2 2\nFitting yields: 𝜔 = 783𝑛𝑚, 𝜾 = 74.2𝑛𝑚, 𝜔 = 772.5𝑛𝑚, 𝜾 = 0.5𝑛𝑚, showing\n1 1 2 2\nthat the high-Q mode selectively modifies the x-polarization spectrum without affecting\nthe orthogonal channel, in agreement with the modal symmetry.\nCase 3 – High-Q mode coupling to both polarizations\nIn Fig. 3(c), the high-Q mode couples to both x- and y-polarized channels\nsimultaneously. This produces a sharp dip in T and a corresponding sharp peak in T ,\nx y\na signature of polarization conversion. We define the center frequency and damping\nrate of the high-Q resonance to be 𝜔 and 𝜾 .\n3 3\nThe transmission amplitudes are\nexpressed as:\n1 (𝑡 −𝑟 )𝜾 1 (𝑡 −𝑟 )𝜾\n𝑥 𝑥 3 𝑦 𝑦 3\nt =t − ,t =t − ,\n𝑥𝑥 𝑥 2𝜾 −𝑖(𝜔−𝜔 ) 𝑦𝑦 𝑦 2𝜾 −𝑖(𝜔−𝜔 )\n3 3 3 3\n1 𝑖(𝑡 −𝑟 )𝜾 1 (𝑡 −𝑟 )𝜾\n𝑥 𝑥 3 𝑦 𝑦 3\nt =− 𝑦 𝑦 3 ,t = 𝑥 𝑥 3 , (𝑅13)\n𝑥𝑦 2𝜾 −𝑖(𝜔−𝜔 ) 𝑦𝑥 2𝜾 −𝑖(𝜔−𝜔 )\n3 3 3 3\nHere, t and t are both nonzero, confirming the presence of polarization conversion.\nxy yx\nThe total transmittances are given by:\n2 2 2\n𝑇 =|𝑡 |2+|𝑡 | ,𝑇 =|𝑡 | +|𝑡 | , (𝑅14)\n𝑥 𝑥𝑥 𝑥𝑦 𝑦 𝑦𝑦 𝑦𝑥\nFitted yields: 𝜔 = 768𝑛𝑚, 𝜾 = 72𝑛𝑚, 𝜔 = 768.4𝑛𝑚, 𝜾 = 0.75𝑛𝑚, matching\n1 1 3 3\nthe numerical spectra with high accuracy.\nThe above fittings confirm that our TCMT-based model quantitatively reproduces\nall key spectral features, including background transparency, single-channel coupling,\nand polarization conversion. This level of agreement demonstrates that the model fully\ncaptures the underlying physical processes and validates its applicability to the present\nstructure. Moreover, the extracted parameters provide direct physical insight into the\n29\ncoupling strengths, quality factors, and modal symmetries of the system.\nTo demonstrate the validity of the model, we have added simulated transmission\nspectra together with the analytical curves obtained by fitting Eqs. (R11)-(R14) to the\nsimulation data in Fig. 3 of the revised manuscript. Using these parameters, the\ntheoretical spectra (indicated by  in Figure 3) agree well with the numerical spectra\n(solid lines in Figure 3), confirming that our phenomenological model captures all\nessential features of vertical chiral emission. Furthermore, the extracted fitting\nparameters are consistent with the resonance positions and linewidths obtained from\neigenmode analysis, further validating the robustness of our approach.\nThe related revisions in the manuscript are as follows:\n(Page 8, lines 188-190)\n“Transmission spectra of these metasurfaces were simulated (solid lines in Figure 3),\ntheoretically derived with TCMT (indicated by ‘’ in Figure 3), and experimentally\nmeasured (indicated by ‘’ in Figure 3) to provide insight into the continuum and bound\nmodes.”\n(Page 8, lines 203-205)\n“The theoretical spectra agree well with the numerical spectra, confirming that our\nphenomenological model captures all essential features of vertical chiral emission.”\nReference\n1. Gorkunov, M. V., Antonov, A. A. & Kivshar, Y. S. Metasurfaces with Maximum\nChirality Empowered by Bound States in the Continuum. Phys. Rev. Lett. 125,\n093903 (2020).\n2. Overvig, A., Yu, N. & Alu, A. Chiral Quasi-Bound States in the Continuum. Phys.\nRev. Lett. 126, 073001 (2021).\n3. Chen, Y. et al. Observation of Intrinsic Chiral Bound States in the Continuum. Nature\n613, 474–478 (2023).\n4. Kühner, L. et al. Unlocking the Out-of-Plane Dimension for Photonic Bound States\nin the Continuum to Achieve Maximum Optical Chirality. Light Sci. Appl. 12, 250\n(2023).\n5. Dixon, J., Lawrence, M., Barton, D. R. & Dionne, J. Self-Isolated Raman Lasing\nwith a Chiral Dielectric Metasurface. Phys. Rev. Lett. 126, 123201 (2021).\n6. Semnani, B., Flannery, J., Al Maruf, R. & Bajcsy, M. Spin-Preserving Chiral\nPhotonic Crystal Mirror. Light-Sci. Appl. 9, 23 (2020).\n7. Zhang, X., Liu, Y., Han, J., Kivshar, Y. & Song, Q. Chiral Emission from Resonant\n8. Lim, Y. et al. Maximally Chiral Emission Via Chiral Quasibound States in the\nContinuum. Laser Photonics Rev. 17, 2200611 (2023).\n9. Gromyko, D. et al. Unidirectional Chiral Emission Via Twisted Bi-Layer\nMetasurfaces. Nat. Commun. 15, 9804 (2024).\n10. Hsu, C. W., Zhen, B., Soljačić, M. & Stone, A. D. Polarization state of radiation\nfrom a photonic crystal slab. Preprint at https://doi.org/10.48550/arXiv.1708.02197\n(2017).\n11. Shi, T. et al. Planar Chiral Metasurfaces with Maximal and Tunable Chiroptical\nResponse Driven by Bound States in the Continuum. Nat. Commun. 13, 4111 (2022).\n12. Fan, S., Suh, W. & Joannopoulos, J. D. Temporal Coupled-Mode Theory for the\nFano Resonance in Optical Resonators. J. Opt. Soc. Am. A 20, 569 (2003).\n13. Gorkunov, M. V., Antonov, A. A., Mamonova, A. V., Muljarov, E. A. & Kivshar, Y.\nSubstrate-Induced Maximum Optical Chirality of Planar Dielectric Structures. Adv.\nOpt. Mater. n/a, 2402133 (2024).\n14. Duan, Q. et al. Photonic Crystal Slabs with Maximal Chiroptical Response\nEmpowered by Bound States in the Continuum. Photonics Res. 11, 1919–1933\n(2023).\n15. Hsu, C. W. et al. Observation of Trapped Light Within the Radiation Continuum.\nNature 499, 188–191 (2013).\n16. Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound\nStates in the Continuum. Nat. Rev. Mater. 1, 1–13 (2016).\n17. Johnson, S. G., Fan, S. H., Villeneuve, P. R., Joannopoulos, J. D. & Kolodziejski,\nL. A. Guided Modes in Photonic Crystal Slabs. Phys. Rev. B 60, 5751–5758 (1999).\n18. Fan, S. H. & Joannopoulos, J. D. Analysis of Guided Resonances in Photonic\nCrystal Slabs. Phys. Rev. B 65, 235112 (2002).\n19. Sun, K. et al. Infinite-Q Guided Modes Radiate in the Continuum. Phys. Rev. B\n107, 115415 (2023).\n20. Kim, K.-H. & Kim, J.-R. High-Q Chiroptical Resonances by Quasi-Bound States\nin the Continuum in Dielectric Metasurfaces with Simultaneously Broken In-Plane\nInversion and Mirror Symmetries. Adv. Opt. Mater. 9, 2101162 (2021).\n21. Suh, W., Wang, Z. & Fan, S. H. Temporal Coupled-Mode Theory and the Presence\nof Non-Orthogonal Modes in Lossless Multimode Cavities. Ieee J. Quantum\nElectron. 40, 1511–1518 (2004).\n22. Konishi, K. et al. Circularly Polarized Light Emission from Semiconductor Planar\nChiral Nanostructures. Phys. Rev. Lett. 106, 057402 (2011).\n23. Maksimov, A. A. et al. Circularly Polarized Light Emission from Chiral Spatially-\nStructured Planar Semiconductor Microcavities. Phys. Rev. B 89, 045316 (2014).\n24. Lobanov, S. V. et al. Controlling Circular Polarization of Light Emitted by\nQuantum Dots Using Chiral Photonic Crystal Slabs. Phys. Rev. B 92, 205309 (2015).\n25. Zhu, A. Y. et al. Giant Intrinsic Chiro-Optical Activity in Planar Dielectric\nNanostructures. Light Sci. Appl. 7, 17158–17158 (2018).\n26. Sun, Y. et al. Enhancing Circularly Polarized Emission by a Planar Chiral\nDielectric Metasurface. Adv. Opt. Mater. 11, 2300197 (2023).\n27. Sun, Y., Shi, K., Hu, Z., Jin, Y. & He, S. Highly Circularly Polarized and Coherent\nThermal Emission Based on Chiral Quasi Bound States in the Continuum. Opt. Lett.\n49, 6329–6332 (2024).\n28. Lalanne, P., Yan, W., Vynck, K., Sauvan, C. & Hugonin, J. P. Light Interaction with\nPhotonic and Plasmonic Resonances. Laser Photonics Rev. 12, 38 (2018).\n32"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all of my comments and resolved the issues I previously raised. While relevant works exist in the literature, the current manuscript explored distinct aspects and reported interesting new features, particularly clarifying the role of the anisotropic continuum in vertical chiral emission. As explained in the response letter, the current manuscript presents a design principle that is broadly applicable across a wide class of chiral metasurfaces. Therefore, I believe this work will be of broad interest and is well-suited for the diverse readership of Nature Communications.", "reviewer_2": "In my first report, I recognized the timeliness of the topic addressed in the paper but expressed serious doubts regarding the fundamental novelty of the reported results. My major concern was that the authors have already presented the very same effect – chiral emission of light – performed by practically identically designed silicon metasurface in their recent paper. In the original manuscript they managed to fully avoid mentioning this paper. Now it is cited as [12]. In addition, I formulated a couple of suggestions regarding the theoretical background and presentation in case the authors decide to publish the paper elsewhere.\nIn response, the authors write: “The apparent similarity in metasurface geometry is intentional and crucial to the purpose of this study. In our previous work, the metasurface was placed on a dielectric substrate that breaks out-of-plane mirror symmetry and belongs to different classifications as our current work. To isolate the impact of out-of-plane symmetry, we intentionally retained the same in-plane geometry” and also “We have no intention of repeating prior work. On the contrary, our aim is to highlight the conceptual contrast by keeping geometry constant and varying only the symmetry condition”\nThese rather strong statements, however, are not backed in the paper. Instead of resolving the issue, they raise even more serious concerns:\n1. If the similarity to the previous work was intentional, why was it not stated anywhere in the text, and why was the relevant paper not mentioned and cited? Where in the latest version can we read about the physical consequences of the “conceptual contrast” between the previous and current metasurfaces?\n2. If the presence of dielectric substrate was so crucial in the previous work, why did the authors write there that “The out-of-plane symmetry is nearly preserved in the current structure since the side wall of the silicon pillars is vertical and the symmetry breaking induced by the silica substrate is weak.” (see page 2 in Ref. 12). Note that this is a very reasonable statement. Typically, weakly refracting substrates marginally affect optical properties of silicon metasurfaces: one should really search for very specific situations, when a substrate plays a noticeable role.\n3. Is there any scientific evidence of a qualitative difference in the performance of metasurfaces from the present and previous works?\n4. If the out-of-plane symmetry is so crucial, to which extent should one preserve it for the reported effects to take place? Note that the latest metasurface is neither fully symmetrically fabricated. This is seen in Supplementary Fig. S9 subplot 9, as well as it is manifested by different emission spectra from both sides given in Fig. 4e).\nIn response to my other comments, the authors extended the discussion of how the birefringent background scattering (they call it anisotropic continuum) can be related to other low-quality-factor resonances. They reasonably note that there can be several resonances contributing here. However, then in SI they attempt to formulate a temporal coupled mode theory (TCMT) describing how the birefringent background can arise due to a single broad resonant mode. I expressed doubts that this is possible, and now would like to warn the authors that their newly added statements are most likely erroneous. Such a procedure expectedly violates the time reversal and energy conservation. This is now explicitly shown by the authors themselves as they arrive at the necessity of Supplementary Eq. (22), which requires the equality of frequency omega to the eigenfrequency omega_c. This particularly means that the time reversal is granted for monochromatic fields of one specific frequency. Of course, the fundamental physical laws must be valid in the whole frequency range where TCMT is considered applicable.\nAlso, in response to my suggestions, the authors have extended the paper by adding TCMT spectra to Fig. 3, and Supplementary Section 5 describing the resonant mode spatial structure and the details of its coupling to plane waves when the structure symmetry is perturbed. I truly appreciate this."}, "author_response": "Response to the Reviewers’ Comments on the manuscript\nNCOMMS-25-33719 submitted to Nature Communications\nWe would like to sincerely thank the Reviewers once again for your careful\nevaluation of our manuscript and for the constructive comments that have helped us\nsignificantly improve the clarity, completeness, and scientific rigor of our work. In\nresponse to the critical points raised by Reviewer 2, particularly regarding the novelty\nrelative to our previous work and the treatment of time-reversal symmetry in the\ntemporal coupled mode theory (TCMT) derivation, we have carefully revised the\nmanuscript and provided detailed clarifications. The changes in the revised manuscripts\nare marked in red. In the following, we provide a point-to-point response\n(in blue) to all reviewers’ questions and comments (in black).\nWe sincerely hope that the editor and reviewers will recognize our extensive efforts\nto address the raised concerns and further strengthen the manuscript. We believe that\nthe revisions clearly establish the novelty of our approach and convincingly\ndemonstrate the significance of our proposed strategy for realizing chiral emission in\nout-of-plane mirror-symmetric metasurfaces.\n********************************\nReviewer #1 (Remarks to the Author)\nComment:\n“The authors have addressed all of my comments and resolved the issues I previously\nraised. While relevant works exist in the literature, the current manuscript explored\ndistinct aspects and reported interesting new features, particularly clarifying the role of\nthe anisotropic continuum in vertical chiral emission. As explained in the response letter,\nthe current manuscript presents a design principle that is broadly applicable across a\nwide class of chiral metasurfaces. Therefore, I believe this work will be of broad interest\nand is well-suited for the diverse readership of Nature Communications.”\nWe sincerely thank the reviewers for their careful evaluation and constructive\nfeedback throughout the review process. We are glad to read the recognition that “the\ncurrent manuscript presents a design principle that is broadly applicable across a wide\nclass of chiral metasurfaces” and that “this work will be of broad interest and is well-\nsuited for the diverse readership of Nature Communications.” Such encouraging\ncomments motivate us and confirm the significance of our work.\n********************************\nReviewer #2 (Remarks to the Author)\nWe are grateful for the reviewer’s help in improving this manuscript’s quality.\nComment 1:\n“In my first report, I recognized the timeliness of the topic addressed in the paper but\nexpressed serious doubts regarding the fundamental novelty of the reported results. My\nmajor concern was that the authors have already presented the very same effect – chiral\nemission of light – performed by practically identically designed silicon metasurface in\ntheir recent paper. In the original manuscript they managed to fully avoid mentioning\nthis paper. Now it is cited as [12]. In addition, I formulated a couple of suggestions\nregarding the theoretical background and presentation in case the authors decide to\npublish the paper elsewhere.\nIn response, the authors write: “The apparent similarity in metasurface geometry is\nintentional and crucial to the purpose of this study. In our previous work, the\nmetasurface was placed on a dielectric substrate that breaks out-of-plane mirror\nsymmetry and belongs to different classifications as our current work. To isolate the\nimpact of out-of-plane symmetry, we intentionally retained the same in-plane geometry”\nand also “We have no intention of repeating prior work. On the contrary, our aim is to\nhighlight the conceptual contrast by keeping geometry constant and varying only the\nsymmetry condition”\nresolving the issue, they raise even more serious concerns:”\n“Is there any scientific evidence of a qualitative difference in the performance of\nmetasurfaces from the present and previous works?” This comment is also put here\nsince it is similar to the above comment.\nReply:\nWe thank the reviewer for highlighting the importance of clarifying the role of the\nsubstrate. The reviewer’s concern mainly pertains to how the present study advances\nbeyond our earlier work. To address this point clearly, we provide a detailed comparison\nbetween the current and previous studies across several key aspects, summarized in\nTable R1.\nTable R1. Comparison between the present work and our previous study.\nAspect This work Previous work1\nTheoretical It provides a general systematic It only presented an original\nframework design principle for  -symmetric numerical case study\nz\nmetasurfaces of chiral eigenmodes, without theoretical\nand establishes a TCMT-based formulation or general\nframework to reveal the physical physical guidance.\norigin.\nPhysical It builds a mode–continuum It reported the phenomenon\ninsight coupling mechanism that enables of chiral emission, but lacked\nchiral emission under  symmetry. explanation of its underlying\nz\nmechanism.\nUnique It discloses a counterintuitive case of This regime was absent.\nregime DCP ≈ 1 and CD ≈ 0, which is\nverified analytically and numerically.\nthis community.\n1) Theoretical generalization and design guidance\nOur previous work presented only a single simulated case demonstrating highly\nchiral emission. Building upon that result, the present study establishes a general\ntheoretical framework for realizing chiral eigenmodes with circularly polarized far-field\nemission in planar  -symmetric metasurfaces. Rigorously, we clarify the physical\nz\norigin of chiral radiation and provide a systematic design principle under  symmetry.\nz\nBy explicitly describing the coupling between a single resonant mode and an\nanisotropic continuum background, the analysis identifies the key parameters\ngoverning the emergence of DCP in far-field emission, thus enabling predictive\ndesign rather than case-specific observation. The resulting physical picture is\nconsistent with the general understanding of circularly polarized waves, while the\nresonant coupling further allows tunable control of the Q factor in chiral emission.\nTherefore, the present work provides both conceptual generalization and practical\ndesign guidance for developing  -symmetric chiral metasurfaces, contributing to the\nz\nbroader exploration of chirality in nanophotonics.\n2) Counterintuitive optical response of DCP ≈ 1 & CD ≈ 0\nAnother major contribution of the present work is the identification of a\ncounterintuitive regime in which DCP ≈ 1 in far-field emission coexists with CD ≈ 0 in\ntransmission. This behavior is fundamentally distinct from conventional chiral-\nemission scenarios, particularly those in three-dimensional chiral metasurfaces2,3,\nwhere DCP ≈ 1 typically appears only when CD ≈ 1 (Figs. R1a,b). The simultaneous\nrealization of DCP ≈ 1 and CD ≈ 0 is significant because it demonstrates a decoupling\nbetween passive (scattering) and active (emission) polarization responses, a\nrelationship that has not been recognized previously.\nIn Supplementary Section 3, we analytically derive this extreme case for a specific\n4\nbackground response. Although the cross-polarization transmission t contains a\nRL\nstrong resonant term, its resonant nature is invisible in intensity measurements, since\n|t |2 exhibits an almost constant profile (Fig. R1c). However, the real and imaginary\nRL\nparts, as well as the phase of t clearly reveal a sharp resonance (Fig. R1d). This hidden\nRL\nresonance becomes apparent only when the scattering phase or the trajectory of t on\nLR\nthe complex plane is examined. In this configuration, t = t and t = t , resulting\nRL LR RR LL\nin CD ≈ 0, while the far-field emission remains perfectly chiral (DCP ≈ 1).\nThis delicate condition depends critically on symmetric radiation channels into the\nupper and lower half-spaces and is therefore realizable only in the  -symmetric\nz\nconfiguration. When a dielectric substrate is introduced, as in our previous work, the\nupward and downward radiation channels become inequivalent, breaking the out-of-\nplane mirror symmetry. Consequently, the interference condition required for the\ncoexistence of unity DCP and vanishing CD can no longer be satisfied.\nFig. R1. Relationship between CD and DCP. a,b Representative LCP and RCP\ntransmission (a) and reflection (b) spectra from previous works. DCP ≈ 1 occurs\ntogether with CD ≈ 1. c,d Cross-polarization transmission spectra T = |t |2 and T\nRL RL LR\n= |t |2 (c) and cross-polarization transmission coefficient t (d) in an illustrating\nLR RL\n5\nexample in this work. There is no resonant signal in the transmission spectra, but the\nreal and imaginary parts and the phase in the transmission coefficient obviously sustain\na resonant signal.\nTaken together, the above discussion confirms that our findings represent a\ngeneral physical principle rather than a geometry-specific effect. The corresponding\nrevisions in the main text have been incorporated into the response to Comment 2.\nMoreover, this  -symmetric system can simultaneously achieve the DCP ≈ 1 and CD\nz\n≈ 0 condition, highlighting its unique polarization behavior. To enhance readability and\nclarity, Supplementary Section 3 has been extensively revised and reorganized as\nfollows:\n“When the background spectrum is approximated by an equivalent broad resonant\nmode, the chiral resonance shows an intriguing effect: the resonant signature can be\ncompletely suppressed in intensity under a specific amplitude-phase matching\ncondition. Fig. S2 shows the analytical results of T and T (T = |t |2, T = |t |2),\nRL LR RL RL LR LR\nalong with the real part, imaginary part, and phase of t . The parameters are set as ω\nRL 0\n= 50,  = 1, and  = 20. Consequently, T exhibits a smooth, nearly constant profile.\nc RL\nIn contrast, t reveals a sharp resonance at  = 50. Due to the combined constraints of\nRL\n -symmetry and electromagnetic reciprocity, the relation T = T always holds for\nz RR LL\nthe present metasurface4, which directly leads to a vanishing transmission circular\ndichroism (CD), whereas the DCP of the emission can still approach unity. Such a\nphenomenon, where the resonance is invisible in intensity but evident in phase,\nrepresents a form of hidden chirality. The underlying mechanism of this hidden chirality\nis that near ω ≈ ω = ω , the background scattering and the scattering from the single\nc 0\nresonant mode happen to be out of phase, while the amplitude of the resonant scattering\nis twice larger than that of the background scattering.\nTransmission spectra T and T with no resonant signal. b, Real and imaginary parts\nRL LR\nand phase of the cross-polarization coefficient t indicating a resonant signal.\nRL\nFrom both simulation and experimental results, the transmission CDs are –0.09\nand –0.093 (Fig. S3), respectively, confirming the validity of the above analysis.\nMeanwhile, the metasurface maintains a near-unity DCP at resonance. The\nsimultaneous realization of DCP ≈ 1 and CD ≈ 0 signifies a decoupling between passive\n(scattering) and active (emission) polarization responses, revealing a fundamental\ndistinction between the chirality of metasurfaces with and without  symmetry3,5.\nz\nFig. S3. Simulated and experimental results showing small CD. a Evolution of the\ntransmission coefficient t on the complex plane. b Simulated transmission spectra\nRL\n(T , T , T and T ) and CD, and c corresponding measured ones.”\n------------------------\nComment 2:\n“If the similarity to the previous work was intentional, why was it not stated anywhere\n7\nin the text, and why was the relevant paper not mentioned and cited? Where in the latest\nversion can we read about the physical consequences of the “conceptual contrast”\nbetween the previous and current metasurfaces?”\nReply:\nWe agree with the reviewer that this point was not made explicit in the last\nsubmission. In the revised manuscript, we have clearly stated at several places that we\nintentionally adopted the same in-plane geometry as that in Ref. [12] in order to isolate\nthe role of out-of-plane mirror symmetry. The related revisions made in the modified\nmanuscript are as follows:\n1) Line 55 at page 2line 68 at page 3\n“Planar chiral metasurfaces represent another route, where near-unity CD6–8 at\nnormal incidence has also been reported. However, these designs primarily focus on\ntransmission properties, and their potential for controlling emission remains largely\nunexplored. Moreover, recent studies have revealed that large CD in transmission does\nnot necessarily correspond to chiral emission3 with the degree of circular polarization\n(DCP) near one in the far field, highlighting a gap in understanding the emission\nmechanism of planar chiral systems. In our earlier work, chiral emission was observed\nin the presence of a dielectric substrate that perturbed  symmetry1. Conventionally,\nz\n -symmetric metasurfaces are believed to support only extrinsic chiral emission away\nz\nfrom the  point, typically enabled by breaking in-plane inversion symmetry9–12. The\nfar-field polarization at the  point, by contrast, is generally considered nearly linear\ndue to the absence of geometric chirality3,5,13,14. An interesting question arises: can a\nmetasurface with  symmetry, which is intrinsically achiral, generate circular or even\nz\narbitrary polarization at the  point? Our answer is definitely yes.”\nWe have also emphasized the unique property in our  -symmetric metasurface:\nz\nour current  -symmetric design can not only realize DCP ≈ 1 as our earlier work did,\nz\nbut also uniquely supports the special phenomenon of DCP ≈ 1 with CD ≈ 0. The related\n8\nrevision in the manuscript is as follows:\n2) Lines 123129 at page 5\n“Due to the presence of anisotropic continuum, the transmission and reflection\nspectra of  -symmetric metasurfaces exhibit unique features compared with  -\nz z\nasymmetric ones. As shown in Fig. 1c, under the condition of DCP ≈ 1, RCP incidence\nexcites a strong resonance; however, its transmission remains identical to the non-\nresonant direct transmission under LCP incidence, due to destructive interference with\nthe background (derived in Supplementary Section 4). Consequently, the transmission\nCD at the C point ideally vanishes when the resonant and background scatterings are\nexactly out of phase.”\n3) Lines 130 at page 5line 133 at page 6\n“We consider a  -symmetric dielectric metasurface, schematically shown in Fig. 1d.\nz\nThe unit cell consists of a silicon dimer embedded in a silica environment, preserving\n symmetry regardless of in-plane variations. This adopted structure follows our\nz\nearlier work to isolate and emphasize the role of out-of-plane mirror symmetry1.”\n4) Line 271 at page 11–line 281 at page 12\n“This is experimentally validated by integrating the metasurface with fluorescent\norganic dyes, achieving photoluminescence with a maximum DCP of 0.83 for upward\nemission and 0.9 for downward emission. The metasurface design follows the same\nin-plane geometry as our earlier work, which involved an unbalanced refractive index\nof substrate and superstrate. In contrast, the present study keeps  symmetry, isolating\nz\nthe role of the anisotropic continuum in generating vertical chiral emission. This\ndistinction clarifies the fundamental difference between substrate-induced and\nsymmetry-preserved chirality. Furthermore, as a general principle and framework, the\npresent theory is applicable to metasurfaces with arbitrary refractive index\n(Supplementary Information Section 9) and metasurfaces with a substrate, provided\nthat the substrate refractive index is close to that of the superstrate medium, thereby\n9\nenhancing its suitability for practical applications.”\n------------------------\nComment 3:\n“If the presence of dielectric substrate was so crucial in the previous work, why did the\nauthors write there that “The out-of-plane symmetry is nearly preserved in the current\nstructure since the side wall of the silicon pillars is vertical and the symmetry breaking\ninduced by the silica substrate is weak.” (see page 2 in Ref. 12). Note that this is a very\nreasonable statement. Typically, weakly refracting substrates marginally affect optical\nproperties of silicon metasurfaces: one should really search for very specific situations,\nwhen a substrate plays a noticeable role.”\nReply:\nWe sincerely appreciate the reviewer’s careful reading and insightful observation\nregarding the statement in our previous work (Ref. [12]). The reviewer is correct that\nthe earlier paper described the substrate effect as weak. That statement was qualitative,\nemphasizing that the vertical sidewalls made the substrate-induced symmetry breaking\nrelatively minor, without involving any quantitative evaluation.\nIn the present work, the requirement of a  -symmetric chiral metasurface allows\nz\nus to establish a rigorous route to chiral eigenmodes. Under  symmetry, the upward\nz\nand downward emissions of the resonant mode are ideally symmetric, which means\ntheir far-field DCP values are equal in magnitude and opposite in sign. In the\nexperiment, to remain consistent with the theoretical model, the fabricated silicon\nmetasurface on a SiO substrate was placed in an almost symmetric environment by\n2\ncoating a PMMA layer on top.\nIn practical situations, a metasurface may be placed in an asymmetric environment.\nWhen the refractive index difference between substrate and superstrate (Δn) increases,\nthe upward and downward DCPs deviate from unity accordingly. However, when Δn is\nmoderate, the geometric parameters of the metasurface can be properly adjusted to\n10\nrestore DCP ≈ 1 on one side (the upper half-space). The operating mechanism can still\nbe approximately interpreted using the physical principle proposed in this work. Our\nprevious study in Ref. [12] falls into this regime, where the environment is weakly\nasymmetric and the substrate effect is conceptually consistent with the present\ntheoretical framework.\nThe related revisions in the manuscript are as follows (the last paragraph in Section\n11 in the Supplementary Information):\n“In the main text, the refractive indices of the substrate and superstrate are\nidentical (n = n ), preserving out-of-plane mirror symmetry and allowing ideal\nsub sup\nupward DCP ≈ 1 in resonant emission. When a finite refractive-index contrast (n =\nn  n ) is introduced, this symmetry is perturbed and the condition for chiral\nsub sup\nemission becomes imperfect. As a result, the upward DCP decrease below unity. For\nthe three metasurface configurations shown in Fig. S15, the DCP is calculated as a\nfunction of n. In all cases, a monotonic decrease in upward DCP is observed as n,\ndemonstrating that the  -symmetry breaking universally degrades the purity of chiral\nz\nemission. When n = 0, the metasurface system is  -symmetric, and the DCPs in the\nz\nupward and downward emissions are equal in magnitude and opposite in sign. As n\nincreases, this balance is lost, and both DCP values gradually approach zero. This\nbehavior is visualized in Fig. S16, where the DCP curves for upward and downward\nemissions progressively converge, clearly revealing how refractive-index mismatch\nbetween the substrate and superstrate introduces polarization asymmetry in resonant\nemission. Nevertheless, when the substrate and superstrate are fixed, geometrical\noptimization of the metasurface can still achieve DCP ≈ 1 in one direction (typically\nthe upper side), following the same physical principle proposed in this work. In\nsummary, while the presence of substrate and superstrate inevitably influences the\nformation of chiral emission to some degree, it does not dominate the mechanism, and\nthe key factor remains the anisotropic continuum coupling governed by \nz\nsymmetry.\nfunction of the refractive-index difference (n = n  n ) for representative\nsub sup\nmetasurface geometries. The insets illustrate the corresponding structures.”\n------------------------\nComment 4:\n“If the out-of-plane symmetry is so crucial, to which extent should one preserve it for\nthe reported effects to take place? Note that the latest metasurface is neither fully\nsymmetrically fabricated. This is seen in Supplementary Fig. S9 subplot 9, as well as it\nis manifested by different emission spectra from both sides given in Fig. 4e).”\nReply:\nWe acknowledge that perfect out-of-plane symmetry can hardly be achieved\nexperimentally. Our analysis shows that the reported effects are robust (|DCP|>0.8) as\nlong as the refractive index difference between substrate and superstrate is small (n <\n0.2) and fabrication asymmetries remain within typical tolerances.\nIn our experiment, although the metasurface is supported by a SiO₂ substrate and\ncovered by a PMMA overlayer, the two materials share the same refractive index (n =\n1.45). Therefore, the structure is effectively out-of-plane symmetric from the optical\nviewpoint. The measured difference between the upward (DCP = 0.83) and downward\n(DCP = −0.90) emissions may arise from two factors. First, the coated thin dye layer\ncould slightly degrade the out-of-plane symmetry, thereby affecting the emission\nbalance. Second, experimental uncertainties, such as alignment and detection errors,\nmay also contribute to the observed deviation. Some words are added in the modified\nmanuscript (lines 25435 at page 10 in the main text):\n“The small difference in absolute DCP between the upward and downward emissions\nmay be attributed to the coated thin dye layer, which degrades the out-of-plane\nsymmetry at some degree.”\nIn addition, if one wants to just put the metasurface on a sustaining substrate (the\nabove superstrate is air), one even has the possibility to make the upward DCP near one\nby appropriately adjust the geometry parameters of the metasurface (please see the\nreply to comment 2). Our raised physical principle is approximately applicable for this\ncase.\n------------------------\nComment 5:\n“In response to my other comments, the authors extended the discussion of how the\nbirefringent background scattering (they call it anisotropic continuum) can be related\nto other low-quality-factor resonances. They reasonably note that there can be several\nresonances contributing here. However, then in SI they attempt to formulate a temporal\ncoupled mode theory (TCMT) describing how the birefringent background can arise\ndue to a single broad resonant mode. I expressed doubts that this is possible, and now\nwould like to warn the authors that their newly added statements are most likely\nerroneous. Such a procedure expectedly violates the time reversal and energy\nconservation. This is now explicitly shown by the authors themselves as they arrive at\nthe necessity of Supplementary Eq. (22), which requires the equality of frequency\nomega to the eigenfrequency omega_c. This particularly means that the time reversal\nis granted for monochromatic fields of one specific frequency. Of course, the\nfundamental physical laws must be valid in the whole frequency range where TCMT is\nconsidered applicable.”\nReply:\nWe thank the reviewer for raising this important point regarding the validity of our\nreversal symmetry must hold over the entire frequency range where TCMT applies, and\nnot only at a specific frequency. We would like to clarify that our intention is not to\nclaim that the birefringent background originates strictly from a single physical\nresonance in microscopic sense. Instead, the broad resonant mode introduced in\nSupplementary Section 3 should be understood as an effective coarse-grained\nrepresentation of multiple overlapping low-Q background resonances, which is\nfully compatible with the TCMT framework and does not violate reciprocity or\nenergy conservation. The condition  = /2 discussed in the revised Supplementary\ninformation is not a requirement for energy conservation or time-reversal symmetry,\nbut merely the specific interference condition under which the degree of circular\npolarization reaches unity. Away from this frequency, both energy conservation and\nreciprocity remain strictly satisfied, while the output polarization continuously evolves\nfrom circular to elliptical. This frequency selectivity is a generic feature of interference\nbetween a narrow discrete resonance and a broadband background and is fully\nconsistent with TCMT.\nFollowing the reviewer’s suggestion, we have carefully re-examined the entire\nderivation in the Supplementary Information and ensured that all fundamental physical\nprinciples are strictly satisfied. We note that our original derivation represents only a\nspecial case of the continuum response rather than the most general scenario, and the\nspecific frequency condition doesn’t apply universally. To avoid possible\nmisunderstanding, we have revised the presentation of this part to remove\nstatements that could be misinterpreted as imposing a restrictive frequency\ncondition. At the same time, the discussion has been reorganized to highlight the\nunderlying physical picture, with support from analytical and numerical results.\nOur case of frequency-related phase difference  in Supplementary Section 3 is\ndirectly analogous to the famous critical coupling condition in perfect absorption15–\n18, in which it is stated that perfect absorption (absorption = 1) is achieved only when\n=  and the material loss () equals the radiative loss (), as shown in the left side\n0 a r\n14\nof Fig. R2. At other frequencies, the absorption is lower than unity, which simply\nreflects the frequency selectivity of the resonance rather than any violation of energy\nconservation. Similarly, in our case, we consider the influence of a broadly resonant\nbackground scattering on the chiral response of a  -symmetric metasurface sustaining\nz\na single resonant mode in Supplementary Section 3. A special scattering response is\nassigned to this assumed continuum, following Supplementary Eq. (15) which is\nderived by the TCMT. The justifiability and energy conservation of including a broad\nstate in the background scattering is proved.\nIn this case, the emergence of chiral emission requires a specific balance\nbetween the resonant mode and the anisotropic background scattering, which is\ninherently frequency-selective. As shown in the right side of Fig. R2, when this\nbalance is achieved at specific frequency, the phase relationship between the orthogonal\nemission channels corresponds to a /2 difference, resulting in circularly polarized\nemission. Away from this condition, the phase deviates from /2, leading to elliptically\npolarized emission. Such frequency dependence is a universal feature of resonant\nsystems and fully consistent with the principles of reciprocity and energy conservation.\nFig. R2. Left: Perfect absorption arises at the critical coupling condition ( = , =\na r\n), where the absorption reaches unity. Right: Chiral emission occurs when the critical\n0\nphase condition ( = /2) is satisfied at = , leading to DCP ≈ 1.\nc\nformulation agree very well with both the numerical simulation and experimental\nmeasurement (see Fig. 3). This close correspondence provides strong evidence for the\nvalidity and completeness of our theoretical model. It confirms that the TCMT-based\nframework not only captures the essential physics of the chiral resonance but also\nquantitatively reproduces the observed spectral features, including the resonance\nposition, linewidth, and polarization response.\nFig. 3. Evolution of the transmission spectra for the disturbed metasurfaces in Fig.\n1d. a  = 0 and t = 0. b  = 0 and t = 11 nm. c  = 0.09 and t = 11 nm. For comparison,\nthree ways are adopted to obtain the transmission spectra T and T , including fitting\nx y\nbased on the TCMT, numerical simulation and experiment measurement. The upper\npanels show simulated (solid) and fitted curves (marked by ‘×’), and the lower panels\nshow experimentally measured curves.\nSupplementary Section 3 in the manuscript has undergone extensive revision to\nmake the reading clearer. The related revisions in the manuscript are as follows:\n“Section 3: Broadly resonant continuum\nBuilding upon the TCMT formulation in Section 2, we now extend the analysis to\nthe case where the background scattering itself exhibits a broad resonance, where 𝛾 ≫\n𝑐\n𝛾 (𝛾 and 𝛾 represent the damping rates of the continuum state and the targeted chiral\n𝑐\n16\neigenmode, respectively). Such a broadly resonant continuum often manifests as a wide\nspectral peak or dip, as in the system discussed in the main text. Under this assumption,\nit is interesting to examine the resulting behavior analytically and experimentally.\nFollowing the discussion above, and by analogy with Eqs. (5) and (6), the\nbackground scattering matrix associated with the broadly resonant continuum can be\nexpressed\nas:\n𝑫𝑫†\n𝑪 = (𝑰− )𝑪 ,\n𝒄\n𝑖(𝜔𝑐−𝜔)+𝛾𝑐\nwhere C denotes the baseline scattering matrix of the continuum and D represents its\nC\ncoupling vector. |𝑑𝑐| and |𝑑𝑐| represent the coupling coefficients of the background\n𝑥 𝑦\ncontinuum state, and 𝛼𝑐 denotes its parity number. This expression is written under\n𝑧\nthe weak-coupling approximation where the background scattering matrix 𝑪\n𝒄\napproximately commutes with the resonant projector 𝑫𝑫† . Eq. (15) itself already\nimplies that if both 𝑑𝑐 and 𝑑𝑐 are nonzero, additional cross-polarization terms of C\n𝑥 𝑦\nwill in general appear. Therefore, to maintain a polarization-diagonal background\nscattering matrix C, the continuum resonance can be chosen to couple predominantly\nto either the x- or y-polarized channel.\nAs a demonstration, Fig. S1 presents analytical results calculated from Eq. (12),\nillustrating a special background continuum state coupled with x-polarized incidence\nbut transparent to y-polarized incidence. For𝛼 = 𝛼𝑐, the phase difference  follows\n𝑧 𝑧\nthe dotted gray line, equaling /2 at a certain wavelength (Fig. S1a). However, for 𝛼 =\n𝑧\n−𝛼𝑐, although the transmission spectra remain identical to those in Fig. S1a, the phase\n𝑧 𝑧 𝑧\ndifference  stays constant at zero (Fig. S1b). The interference between the narrowband\nresonant mode and the broadband background governs the observed degree of circular\npolarization (DCP) in emission. When the phase difference  between the x- and y-\npolarized emission components approaches /2, the output can become circularly\npolarized (DCP ≈ 1). This condition is met in a narrow frequency range around the\ncentral resonance 𝜔 ≈ 𝜔 ≈ 𝜔 . Away from this spectral region,  deviates from /2\n0 𝑐\nand the emission becomes elliptically polarized. Such frequency selectivity is a generic\n17\nfeature of resonance coupling and fully consistent with fundamental physical laws.\nFig. S1. Influence of the background scattering on the phase difference a 𝛼 =\n𝑧\n𝛼𝑐. b 𝛼 = −𝛼𝑐.\n𝑧 𝑧 𝑧\nWhen the background spectrum is approximated by an equivalent broad resonant\nmode, the chiral resonance shows an intriguing effect: the resonant signature can be\ncompletely suppressed in intensity under a specific amplitude-phase matching\ncondition. Fig. S2 shows the analytical results of T and T (T = |t |2, T = |t |2),\nRL LR RL RL LR LR\nalong with the real part, imaginary part, and phase of t . The parameters are set as ω\nRL 0\n= 50,  = 1, and  = 20. Consequently, T exhibits a smooth, nearly constant profile.\nc RL\nIn contrast, t reveals a sharp resonance at  = 50. Due to the combined constraints of\nRL\n -symmetry and electromagnetic reciprocity, the relation T = T always holds for\nz RR LL\nthe present metasurface4, which directly leads to a vanishing transmission circular\ndichroism (CD), whereas the DCP of the emission can still approach unity. Such a\nphenomenon, where the resonance is invisible in intensity but evident in phase,\nrepresents a form of hidden chirality. The underlying mechanism of this hidden chirality\nis that near ω ≈ ω = ω , the background scattering and the scattering from the single\nc 0\nresonant mode happen to be out of phase, while the amplitude of the resonant scattering\nis twice larger than that of the background scattering.\nTransmission spectra T and T with no resonant signal. b, Real and imaginary parts\nRL LR\nand phase of the cross-polarization coefficient t indicating a resonant signal.\nRL\nFrom both simulation and experimental results, the transmission CDs are –0.09\nand –0.093 (Fig. S3), respectively, confirming the validity of the above analysis.\nMeanwhile, the metasurface maintains a near-unity DCP at resonance. The\nsimultaneous realization of DCP ≈ 1 and CD ≈ 0 signifies a decoupling between passive\n(scattering) and active (emission) polarization responses, revealing a fundamental\ndistinction between the chirality of metasurfaces with and without  symmetry3,5.\nz\nFig. S3. Simulated and experimental results showing small CD. a Evolution of the\ntransmission coefficient t on the complex plane. b Simulated transmission spectra\nRL\n(T\nRL\n, T\nRR\n, T\nLL\nand T\nLR\n) and CD, and c corresponding measured ones.”\n------------------\nComment 6:\n“Also, in response to my suggestions, the authors have extended the paper by adding\nspatial structure and the details of its coupling to plane waves when the structure\nsymmetry is perturbed. I truly appreciate this.”\nReply:\nWe sincerely thank the reviewer for the positive feedback and for recognizing our\nadditional TCMT spectra and the expanded Supplementary Section 5.\nFollowing this suggestion, we carefully rechecked the Supplementary Information\nand found several instances in section 2-3 where the definitions of symbols in the\nequations could cause confusion (matrices C, C and S). We have now corrected these\nc\ninconsistencies and refined the notations to ensure full clarity and readability of the\nSupplementary Information. In addition, the Supplementary Information has been\nthoroughly revised to improve its overall readability and presentation quality.\nReferences:\n1. Sun, Y. et al. Enhancing Circularly Polarized Emission by a Planar Chiral Dielectric\nMetasurface. Adv. Opt. Mater. 11, 2300197 (2023).\n2. Zhang, X., Liu, Y., Han, J., Kivshar, Y. & Song, Q. Chiral Emission from Resonant\nMetasurfaces. Science 377, 1215–1218 (2022).\n3. Chen, Y. et al. Observation of Intrinsic Chiral Bound States in the Continuum. Nature\n613, 474–478 (2023).\n4. Menzel, C., Rockstuhl, C. & Lederer, F. Advanced Jones Calculus for the\nClassification of Periodic Metamaterials. Phys. Rev. A 82, 053811 (2010).\n5. Chen, W. et al. Uncovering Maximum Chirality in Resonant Nanostructures. Nano\nLett. 24, 9643–9649 (2024).\n6. Semnani, B., Flannery, J., Al Maruf, R. & Bajcsy, M. Spin-Preserving Chiral\n7. Shi, T. et al. Planar Chiral Metasurfaces with Maximal and Tunable Chiroptical\nResponse Driven by Bound States in the Continuum. Nat. Commun. 13, 4111 (2022).\n8. Duan, Q. et al. Photonic Crystal Slabs with Maximal Chiroptical Response\nEmpowered by Bound States in the Continuum. Photonics Res. 11, 1919–1933\n(2023).\n9. Liu, W. et al. Circularly Polarized States Spawning from Bound States in the\nContinuum. Phys. Rev. Lett. 123, 116104 (2019).\n10. Wang, J. et al. Routing Valley Exciton Emission of a WS 2 Monolayer Via\nDelocalized Bloch Modes of in-Plane Inversion-Symmetry-Broken Photonic Crystal\nSlabs. Light Sci. Appl. 9, 1–8 (2020).\n11. Tian, J. et al. Optical Rashba Effect in a Light-Emitting Perovskite Metasurface.\nAdv. Mater. 34, e2109157 (2022).\n12. Chen, Y. et al. Compact Spin-Valley-Locked Perovskite Emission. Nat. Mater. 22,\n1065–1070 (2023).\n13. Overvig, A., Yu, N. & Alu, A. Chiral Quasi-Bound States in the Continuum. Phys.\nRev. Lett. 126, 073001 (2021).\n14. Qin, H. et al. Arbitrarily Polarized Bound States in the Continuum with Twisted\nPhotonic Crystal Slabs. Light Sci. Appl. 12, 66 (2023).\n15. Qu, C. et al. Tailor the Functionalities of Metasurfaces Based on a Complete Phase\nDiagram. Phys. Rev. Lett. 115, 235503 (2015).\n16. Wang, J. Manipulating bandwidth of light absorption at critical coupling: An\n21\nexample of graphene integrated with dielectric photonic structure. Phys. Rev. B 100,\n(2019).\n17. Tian, J. et al. High-Q All-Dielectric Metasurface: Super and Suppressed Optical\nAbsorption. Acs Photonics 7, 1436–1443 (2020).\n18. Liu, M. et al. Spectral Phase Singularity and Topological Behavior in Perfect\nAbsorption. Phys. Rev. B 107, L241403 (2023).\nMy previous reports were essentially focused on two major issues:\n#1 Inadequate positioning of the results in the context of previous works including a\nrecent one by the authors.\n#2 Insufficient theoretical background with eventually arguable if not even erroneous\nstatements.\nBoth issues seem to be finally resolved in the last third version of the paper.\nRegarding #1, the authors now clearly indicate how and why they follow their earlier\nwork. If previously they approached the problem primarily empirically, now they\nanalyze with much more care the underlying mechanisms, the role of symmetry\nbreaking, etc. This yields general rules which will be potentially interesting for the\nbroader NatComm audience.\nTheoretical flaws #2 are also resolved. Arguable bits of the TCMT phenomenology are\nremoved. The remaining parts are reasonably well formulated and support the main line\nof the discussion.\nOverall, I am pleased that our interaction has led to a gradual improvement of the paper,\nand see no reason to delay its publication."}]

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