Ultrathin Quarter-Waveplates Based on Two-Dimensional Anisotropic NbOCl_2

Domain: biology
Published: 2026-03-18
Editorial outcome: major_revision

Abstract
The development of miniaturized waveplates is foundational to the continued scaling of integrated photonic and polarization-resolved optical systems. However, when commercial waveplates are scaled to reduced dimensions, they become constrained by intrinsically weak optical anisotropy, scattering losses, and surface roughness from mechanical polishing, all of which detrimentally distorts their polarization control. Herein, we demonstrate ultrathin waveplates based on two-dimensional NbOCl₂, which combines strong in-plane optical anisotropy with an atomically smooth, van der Waals surface. Polarization parameters of these waveplates are highly tuneable through thickness-dependent modulation – including ellipticity and polarization plane axis – facilitating the realization of highly compact quarter-waveplates. Notably, the NbOCl₂ quarter-waveplates are endowed with exceptional retardance tolerance (< λ/600 to λ/300) across multiple operating wavelengths, including a record-thin 269 nm device operating at 614 nm. Our results position NbOCl₂ as a compelling platform for subwavelength, high-fidelity polarization optics, offering a scalable route toward chip-integrated polarization control in emerging photonic technologies.

Introduction
As demands for more compact and on-chip integrated optical systems grow, fabricating waveplates that can maintain precise modulation of the polarization state of light at increasingly smaller scales is of critical importance. The development of miniaturized waveplates would further drive advancements in both fundamental research and industrial applications, such as quantum photonics1, fiber-optic communication2 and polarization-sensitive sensors3. However, downscaling of conventional waveplates is hindered by escalating scattering losses4,5, as polishing-induced surface roughness becomes non-trivial in comparison to the reduced thickness. Achieving arcsecond-level parallelism and <λ/10 wavefront precision for effective polarization control, which becomes challenging to maintain at thinner dimensions, resulting in phase distortions and efficiency losses due to surface scattering and interference. Additionally, combined with the inherently weak and non-uniform birefringence6,7 of many conventional materials, the manufacturing of commercial waveplates typically involves costly operations, with devices limited to sub-millimetre thickness. In the production of conventional crystalline waveplates, bulk single crystals (quartz, calcite, sapphire) are typically screened to exclude domains with optical distortions arising from internal stress-strain, before shaping and thinning down optically pristine domains to the desired dimensions. The millimetre scale waveplates are then polished to a laser-quality finish, typically within sub-micron thickness tolerance. In contrast, polymer waveplates are constructed from micrometre thick polymer sheets that are laminated within polished glass plates. In both instances, the polishing step and weak birefringence poses significant challenges in preserving tight specifications when the waveplate is scaled to sub-micrometre thickness and thinner.

In this regard, ultrathin layered van der Waals 2D crystals stand out due to their atomically flat van der Waals surface and high compatibility with state-of-the-art silicon photonic technology8, presenting scalable birefringent on-chip nanophotonic devices without the need for mechanical processing. Representative 2D materials such as hexagonal boron nitride9,10 and transition metal dichalcogenides11-13 were found to exhibit impressive out-of-plane birefringence owing to the contrast between the intralayer covalent and interlayer van der Waals interactions. However, the daunting challenge to confine light within the sub-nanometre cross-section parallel to the out-of-plane axis discourages practical utility in various applications11,14. Consequentially, 2D systems with in-plane or biaxial anisotropy stemming from crystallographic asymmetries, including rhenium dichalcogenides15,16, germanium selenide17,18, α-phase molybdenum trioxide19-22 and black phosphorus15,23,24 were evaluated. For example, black phosphorus have been extensively investigated for polarization control devices, including waveplates and electro-optic modulators25, leveraging their in-plane anisotropy or by integrating it onto cavity structure. However, these materials only presented moderate birefringence, where reported birefringence values typically remain below 0.1, particularly in the ultraviolet-visible-infrared spectral regions.

With recent investigations involving niobium oxychloride (NbOCl₂) crystals, it was revealed that the 2D material possessed a unique in-plane biaxial crystal structure, with highly anisotropic in-plane optical properties26-30, including outstanding birefringence (0.26-0.46) across a wide visible-NIR transparency window29. Furthermore, the crystal structure of NbOCl₂ features a vanishing interlayer electronic coupling26,27, much weaker than the typical van der Waals interaction in other 2D materials, allowing ease of exfoliating a cleaner surface with uniform material thickness and polarization uniformity. The suitability of NbOCl₂ for miniaturized polarization optics prompted our evaluation of its performance as ultrathin quarter-waveplates (QWPs) in this work. The extent of optical anisotropy and polarization-plane rotation were assessed in correlation to a variety of sample thicknesses, generating ellipticity values and dichroic ratios as metrices for the selection of waveplate thickness for various operating wavelengths. Across a few devices of differing NbOCl₂ crystal thicknesses, we demonstrate excellent polarization modulation across a range of wavelengths, with profiles that corroborated against the mathematical model for quarter-wave characteristics. These QWPs presented outstanding retardance tolerance benchmarked against commercial QWPs, with substantially reduced dimensions including a thinnest 269 nm QWP functional at operating wavelength of 614 nm.

Results
Material Characterization and determination of crystallographic orientation

NbOCl₂ crystallizes in a monoclinic structure belonging to the C2/m space group26. The unit cell contains two Nb, two O, and four Cl atoms, forming a hexacoordinated octahedral unit around each Nb centre. Two distinct Nb displacements in the distorted octahedra contribute to the weak interlayer coupling26. The exfoliated flakes often exhibit well-defined orthorhombic edges, which not only reflect the material's strong anisotropic in-plane bonding characteristics but also enable direct identification of the b-axis and c-axis (Supplementary Fig. 2a). Attributed to the anisotropic optical properties of NbOCl₂, axis determination can also be accomplished from cross-polarization optical microscopy. Under a crossed-polarization setup, the optical image turns completely dark when the sample’s edge is aligned with either of the polarizers, while misalignment induces birefringence, producing colours in the image (Fig. 1a). Correspondingly, the variation in light intensity as a function of sample angle is consistent with the observed changes in the optical images (Fig. 1b). As the analyser rotates from 0° to 360°, four intensity peaks are observed, further affirming the biaxial optical nature of NbOCl₂. The associated surface uniformity of the NbOCl₂ nanoflakes were also assessed by AFM measurements made across samples spanning a broad range of thickness (Fig. 1c, Supplementary Fig. 1), with average root-mean-square (RMS) surface roughness (Rq) on the sub-nanometre scale, reaching less than 0.1% of the sample thickness. This extremely low surface roughness arising from the interlayer van der Waals interaction assures high quality surface with uniform polarization purity and reduced distortion.

Beyond, the vibrational modes and crystalline orientation of NbOCl₂ was also characterized by angle-resolved polarized Raman spectroscopy (ARPRS)31-33. The Raman spectrum obtained under a non-polarized setting (Supplementary Fig. 2b) displayed five prominent peaks at 156 cm⁻¹, 177 cm⁻¹, 296 cm⁻¹, 342 cm⁻¹, and 670 cm⁻¹, consistent with previously reported results34. Unsurprisingly, the spectrum adopts an increasing trend in signal intensity with increasing sample layer-number for both fresh and aged samples (Supplementary Fig. 3). Subsequently, ARPRS under cross and parallel polarizer configurations (Supplementary Fig. 4) were adopted, whereby the polarized Raman measurements were taken for sample rotation in steps of 10°. The angular dependence of the Raman intensity mapped under cross and parallel polarization is distinctly apparent. Under the cross (perpendicular) polarizer configuration, a four-pleated symmetry of π/2 periodicity was acquired with the nodes aligned along the crystallographic axes (Fig. 1d, Fig. 1f, Supplementary Fig. 5a-e; b-axis and c-axis referenced against optical image in Supplementary Fig. 2a). In contrast, the signals under parallel polarizer alignment adopted dual-pleated two-fold symmetries of π periodicity, that are aligned along either of the crystallographic axes (Fig. 1e, Fig. 1g-h, Supplementary Fig. 5f-j), allowing direct identification of the corresponding axis directions.

The efficiency of Raman scattering31,32 depends on the Raman tensor 𝐑 and the specific polarization configuration:
S = A|𝐞_𝐬 ⋅𝐑⋅𝐞_𝐢 |² (1)
where the 𝐞_𝐬 and 𝐞_𝐢 denote the Jones vectors of the scattered and incident light, respectively. For NbOCl₂, the layers are stacked along the a-axis, which is defined here as the X-axis. The b-axis and c-axis are defined as the Y-axis and Z-axis respectively, which means that the 𝐞_𝐬 and 𝐞_𝐢 lies in the Y-Z plane. Setting the angle between the incident light polarization and Y-axis as θ, the Jones vectors can be expressed as: 𝐞_𝐢 = (0, cos θ, sin θ)ᵀ, 𝐞_𝐬 = (0, cos θ, sin θ) for parallel polarization and 𝐞_𝐬 = (0, -sin θ, cos θ) for cross polarization. Since NbOCl₂ crystallizes in the C2/m space group, the corresponding Raman tensors are:35-37
𝐑(Ag) = (a d 0; d b 0; 0 0 c) (2)
𝐑(Bg) = (0 0 ⅇ; 0 0 f; ⅇ f 0) (3)
where the c-axis is chosen as the C2 rotation axis, and the nonzero elements represent components that contribute to Raman scattering. By substituting the Raman tensors and Jones vectors to equation (1), we can obtain the observed scattered light intensity:
S(Ag,⊥) ∝ (sin²𝜃)² (4)
S(Ag,∥)∝ (bcos²𝜃+csin²𝜃)² (5)
S(Bg,⊥) ∝(cos²2𝜃)² (6)
S(Bg,∥)∝ (sin²2𝜃)² (7)
The Raman scattering efficiency of the Ag and Bg modes under parallel polarization thus manifests as two-lobed and four-lobed symmetrical patterns, respectively. As a result, P1-P5 Raman modes are all associated with Ag-like phonon modes. However, the P1, P2 and P3 modes under parallel polarization were observed to exhibit minor lobed components orthogonal to its main two-lobed feature. This pseudo-four-lobed behaviour can be attributed to the Raman tensor elements with both real and non-negligible imaginary components38, arising from the anisotropic optical absorption of NbOCl₂29. Nonetheless, the maximum intensity (main lobe direction) remains identifiable for P1 and P5 along the b-axis, while P2, P3 and P4 demonstrates the main intensity lobe along the c-axis. This allows the crystallographic orientation to be well-defined through analysis of these intensity changes of these Raman peaks.

Optical anisotropy characterization of NbOCl₂ waveplates

To evaluate the differences in optical anisotropy between the thin and thick NbOCl₂ flakes, samples with differing layers were mechanically exfoliated onto Si/SiO₂ substrates, before their thicknesses were measured using an Atomic Force Microscope (AFM) (Supplementary Fig. 6). The corresponding images of the samples under a polarized optical microscope demonstrate symmetric trends in optical colour evolution under varying analyser angles (Supplementary Fig. 7). The reflectance spectra of two representative NbOCl₂ nanosheets (60 layers (60 L) versus 246 layers (246 L)) were measured across a range of analyser rotation for effective comparison. The 60 L sample displays a stable reflectance spectrum profile (Fig. 2a) with no discernible peak shifts across the analyser rotation angles, while the 246 L sample exhibits angle-dependent variations (Fig. 2d), reflecting changes in spectrum shape and noticeable redshifts in peak positions. To better represent the axial anisotropies, reflective dichroic ratios defined as r_c / r_b and r_b / r_c were introduced, whereby r_b and r_c represent the reflectance intensities when the analyser angles are aligned along the b-axis and c-axis, respectively. The dichroic ratio for the 60 L sample demonstrates spectrum mirrored across y = 1.0, with no observable intersections within the visible light window (Fig. 2b), whereas the 246 L sample displays two intersections at 517 nm and 695 nm (Fig. 2e), along with points of maximal difference between r_c / r_b and r_b / r_c occurring at 460 nm and 625 nm. These results corroborate well with the normalized polar plots, whereby the thinner sample (Fig. 2c) possess aligned polarization planes (defined as direction of maximum intensity) for different wavelengths, while the thicker sample (Fig. 2f) exhibits polarization planes with wavelength-dependent orientations. The interesting phenomena of wavelength-dependent polarization plane orientation was found reproducible from the reflectance spectra and polar plots across a broad range of NbOCl₂ nanosheets with varying thicknesses (Supplementary Fig. 8 and Fig. 9). Similar phenomena were also observed in various other systems and were attributed to non-orthogonal exciton resonances39, which typically occur in low-symmetry crystals with triclinic and monoclinic crystal structures. These results implied that thick samples exhibit more pronounced and richer optical anisotropy suitable for waveplate considerations.

Alongside polarization-plane angle, the metric of ellipticity serves as another polarization parameter used to characterize the appropriateness of multilayer NbOCl₂ as waveplates. Ellipticity quantifies the strength of polarization and is defined as e = I_min / I_max, where I_max and I_min represent the maximum and minimum light intensities measured with the rotating analyser, respectively. As the value of ellipticity approaches 1, the polarization of the reflected light increasingly approaches circular polarization (with the incident light being linearly polarized), indicating light-polarization behaviour closer to an ideal QWP. Evaluated across samples with varying layer numbers (Fig. 3a), the ellipticity spectra facilitated the selection of NbOCl₂ thicknesses suitable for waveplate functionality at specific operating wavelengths. Across the trending change in ellipticity spectrum, samples with similar layer numbers exhibit resembling spectral profiles with minor peak shifts. For instance, the ellipticity-λ spectra for 414 L and 433 L adopted analogous peak features, except for a distinct blueshift for 433 L spectrum. Likewise, the spectra for 575 L and 601 L are similar as well, with a redshifted 601 L spectrum. These results demonstrate the layer sensitivity of the optical response, which is further corroborated by the analogous layer-dependent evolution of the polarization plane angle (at 550 nm and 650 nm) in the polar plots of NbOCl₂ flakes with varying layer thicknesses (Figs. 3b and 3c). Together, these results assure that key polarization parameters such as ellipticity and polarization plane angle can be modulated through NbOCl₂ flake thickness, prompting the optimization of wavelength-specific NbOCl₂ QWPs through layer-engineering. Herein, it is worth noting that NbOCl₂ flakes of varying thicknesses can be readily obtained via mechanical exfoliation, often yielding series of samples with similar thicknesses within a single run, typically with lateral dimensions of 50 μm× 50 μm.

NbOCl₂ Quarter-Waveplate performance

Since the associated band structure of NbOCl₂ was known to induce weak linear dichroism (i.e. weak in-plane anisotropic absorption) at the sub-bandgap regime29, the wavelength operating window for potential NbOCl₂ QWPs can be narrowed by identifying pronounced ellipticity points beyond 500 nm. For instance, the 414 L nanoflake was evaluated at a specific wavelength above 500 nm that possesses near-unity ellipticity. The resultant normalized intensity as a function of φ under 45° illumination remains essentially constant (Fig. 3d), affirming that the NbOCl₂ waveplate can effectively convert linearly polarized light into circularly polarized light. Subsequently, a polarization light modulation setup (Fig. 3e) was designed to verify the waveplate performance and determine the phase retardance. Measurements were taken for every 15° analyser rotation, while the sample was rotated in 15° increments. The reflectance intensity as a function of sample angle and analyser angle (Fig. 3f) was analysed at a wavelength of 652 nm for samples with varying layer number. In comparison with a baseline reference comprising the polarization modulation profile of a Si/SiO₂ substrate, a gradual modulation was observed as the sample thickness increases. These results further illustrate the potential for customizable permutations of sample thickness and operating wavelength for a series of tuneable NbOCl₂ waveplate.

Here, theoretical fitting based on the ideal QWP model was performed for demonstration. The Jones vector of the incident light along the y-axis is set as (0, 1)ᵀ, and the Jones matrix of the rotatable waveplate is derived as follows:
𝐌(𝜃)=𝐑(−𝜃)⋅𝐌⋅𝐑(𝜃) (8)
= (cos²𝜃+ⅇi𝛿sin²𝜃 (1−ⅇi𝛿)cos𝜃sin𝜃; (1−ⅇi𝛿)cos𝜃sin𝜃 sin²𝜃+ⅇi𝛿cos²𝜃)
where θ is the rotation angle of waveplate, R(θ) is the rotation matrix, M(θ) is the waveplate intrinsic matrix40 and δ is phase retardance. Setting δ equals to π/2 (i.e. for a QWP), the intensity of the output light after passing through the rotatable waveplate and analyser can be expressed as (details provided in Supplementary Note 4):
I_QWP = 1/2 (|sin𝜑(−isin(2𝜃−𝜑)+sin𝜑)|²+|cos𝜑(−isin(2𝜃−𝜑)+sin𝜑)|²) (9)
where φ is the analyser angle.

Depicted as a 2D colour map, the theoretical model (Supplementary Fig. S10, Equation (9)) manifests as distinct elliptical patterns that emphasizes the polarization behaviour for the ideal QWP system (Fig. 4a). For the QWPs fabricated from NbOCl₂, similar polarization profiles can be observed from permutations of different sample layer-number and specific operating wavelengths (Fig. 4b-d). Since the mechanical exfoliation method can produce many high-quality NbOCl₂ crystals (regular rectangular shapes with sharp defined edges) of differing thickness each time, it would be easy to generate a glossary of NbOCl₂ waveplates catered for each specific wavelength within a broad window. Furthermore, the excellent agreement between the experimental data and the theoretical fitting substantiates the functionality of these NbOCl₂-based QWP.

Subsequently, the intensity profile from parallel-polarization and cross-polarization can be decoupled from the polarization modulation results, together with determination of the phase retardance and its associated tolerance. Under parallel polarization and cross-polarization, the reflected light intensity at a sample rotation angle θ can be determined by the interference of the p- and s-polarized components, expressed as:
I_sam+sub,parallel = (E_c sin𝜃)²+(E_b cos𝜃)²+2√(E_c sin𝜃)²∙(E_b cos𝜃)²cos𝛿 (10)
I_sam+sub,cross = (E_c² + E_b²)sin𝜃∙cos𝜃+2√(E_c sin𝜃)²∙(E_b cos𝜃)²cos𝛿 (11)
where E_b, E_c are components of the reflected electric field along the b-axis and c-axis, respectively, δ is phase retardance of NbOCl₂ (Supplementary Fig. S11 and detailed discussion). This formula considers the effects of the substrate thin film interference and birefringence on the reflection intensity. The experimental results under both parallel- and cross-polarization conditions (Fig. 4e-g), were in concordance with the sinusoidal fitting derived by the multi-interface model. Meanwhile, the phase retardance can be calculated by setting θ=45°:
1/e = (I_b + I_c)² / (1+√1−4sin²𝛿 I_b I_c) (12)
where e refers to ellipticity, I_b and I_c are intensities when the analyser direction is aligned with the b-axis and c-axis, respectively. Benchmarking the performance of the NbOCl₂ QWPs against commercially available QWPs shows that their retardance tolerance rivals that of conventional commercial QWP (Fig. 4h), highlighting their competitive edge. Operating within a similar wavelength range (500-700 nm), the NbOCl₂ QWP, on average, presents a distinctly narrower retardance tolerance. We also provide a table for comparison of retardance numerical values of NbOCl₂-based QWPs and some commercial QWPs (Supplementary Table 1). Finally, to demonstrate the practicality of the NbOCl₂ waveplate to modulate an optical polarization state, a beam of linearly polarized light (broadband) was directed through a commercial QWP (Thorlabs AQWP05M-600, thickness 0.72 mm, operating wavelength 400-800 nm, retardance accuracy < λ/300) onto the NbOCl₂-based QWP (NbOCl₂ – 414 layers, thickness 269 nm, measurement wavelength 614 nm), with the fast axes of these QWPs aligned orthogonal to each other (Fig. 4j). The fact that the minimum value in the resultant sinusoidal profile approaches zero certifies that the NbOCl₂ waveplate effectively cancels the phase retardation introduced by the QWP, reinstating the linear polarization characteristics (Fig 4i). Collectively, these findings highlight the ideal compatibility for NbOCl₂ as QWPs with exceptional performance that holds great promise for next-generation ultrathin waveplates. The ability to tune the waveplate operating wavelength by selecting samples of corresponding thicknesses further amplifies the potential commercial value of NbOCl₂ waveplates.

Methods
Sample fabrication and reflective spectroscopy

NbOCl₂ nanosheets are prepared using a mechanical exfoliation method. The pristine bulk crystal of NbOCl₂ (2D Semiconductors, 6N purity no electronic impurities) is progressively thinned down to a suitable thickness using Nitto blue tape. The thinned sample is then transferred onto a polydimethylsiloxane (PDMS) substrate, which is subsequently placed over a SiO₂ (285 nm)/Si substrate. Following an annealing process, the PDMS layer is subsequently peeled off, leaving the sample deposited on the SiO₂/Si substrate. Reflection spectra of the prepared NbOCl₂ nanosheets are characterized using an optical microscope (Olympus BX51) coupled with an Ocean Optics Flame Miniature Spectrometer.

Polarized Raman characterization and AFM measurement

Based upon a general Raman spectrometer (Renishaw, inVia Raman microscope) with a 532 nm excitation laser, two linear polarizers were added close to the incident light path and reflective light path respectively, to first calibrate the two polarization axes in parallel. Then the sample on a rotation stage is rotated in steps of 15° to measure the polarized Raman signal. The sample thicknesses were obtained by an Atomic Force Microscope (Dimension Icon, Bruker, tapping mode).

Polarization Modulation characterization

The schematic diagram illustrating the setup for analysing wave plate characteristics is included in Figure 3e. In this setup, the incident light traverses through a linear polarizer before being reflected by the sample mounted on a rotatable stage, allowing for adjustable orientation. The reflected light then travels through an analyser and is ultimately captured by a spectrometer. To determine the phase retardance and ellipticity, the sample orientation angle, θ, was set at 45° relative to the perpendicular direction and measurements were taken at 15° increments of the analyser rotation. In addition, to assess the tunability of the waveplate, the sample was rotated by 15° concurrently with each 15° increment of the analyser, generating a contour-colour map by recording the variations in reflective intensity as both the sample and analyser angles are altered.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper mainly researched the potential of the ultrathin NbOCl2 quarter-waveplates (QWPs), from the perspective of key polarization parameters such as ellipticity and polarization plane angle. The reflectance spectra and ellipticity are layer-sensitive, showing rich properties in thicker materials. Moreover, the authors benchmarked the performance of the NbOCl2 QWPs against commercially available QWPs. I recommend that the manuscript be considered for publication after revisions.\n1. Based on the literature (Nature 613, 53–59 (2023)), the b-axis was defined as C2 rotation axis. In this paper, the c-axis is set as the C2 rotation axis according to Raman tensors (equation 2). For clarity, it would be beneficial to explicitly label the crystal axes.\n2. In equations (4)-(7), the Jones vectors related to the cross polarization are (e_s ) ⃗=(0,-sinθ,cosθ). The consideration was neglected.\n3. The paper emphasizes the importance of layer numbers. Polarization planes show wavelength-dependent orientations in a thicker sample (Figure 2f). Polar plots for reflection intensity are layer-number, as well as ellipticity (Figure 3a-c). However, for samples of different thicknesses, the polarization parameters seem irregular and unpredictable. Could the phenomenon be reproducible in the samples with identical layers? In other words, for a sample with a fixed layer number, are its operating wavelengths always the same?\n4. In line 226, the imaginary number should be written as i to keep consistent with equation (9) and supplementary information. The specific expression of M_polarizer (φ) is missed in the derivation.\n5. Some panels in Figure 3f deviate from the ideal QWP. What does this indicate/suggest? In part of the theoretical fitting based on the ideal QWP model, the key parameter is the waveplate intrinsic matrix. What is the relationship between the matrix and specific materials?\n6. The caption of Figure 4e-g is unclear: “Experimental data and fitting results” of what? Additionally, providing the analytical expression for the cross-polarized reflected light intensity would be useful, where the fitting result has already been exhibited in Figure 4e-g.\n7. It’s inspiring that the performance of the ultrathin NbOCl2-based QWPs is as good as commercially available QWPs. Moreover, the authors could further summarize and compare the performance of NbOCl2-based QWPs and other 2D materials to highlight the advances. For example, plot a figure to show the effective wavelength range, phase retardance, and other parameters of 2D materials.", "reviewer_2": "In this manuscript, Jia et. al. investigated quarter-waveplate behavior from ultrathin NbOCl2 nanosheets, leveraging its large in-plane optical anisotropy and atomically flat surfaces. The authors have performed polarization-resolved reflectance, angle-resolved polarized Raman spectroscopy (ARPRS), and ellipticity experiments to identify the optical anisotropy and demonstrated polarization modulation experiment to quantify the optimum QWP behavior across several visible wavelengths, with a device thickness as low as 269 nm. The manuscript demonstrates promising experimental evidence for using NbOCl2 nanosheet as an ultrathin QWP, however, several aspects of this manuscript need clarification:\n1. The manuscript claims strong in-plane anisotropy. Although the author has provided angle-resolved Polarization Raman spectroscopy to support the anisotropy, they do not talk about birefringence, Δn(λ) values for the NbOCl2 ultrathin crystal. Can the authors verify, using their cited Δn values, that the measured flake thickness yields quarter-wave retardance at the studied wavelengths?\n2. In most real cases, QWP is used in transmission, but the device is exclusively characterized in reflection mode. Did the authors perform the analogous polarization modulation experiment in transmission mode? Has any difference been observed?\n3. Can the authors explain whether the phase-retardance mechanism in their system is fundamentally equivalent to that of standard waveplates, as commercial QWPs typically operate in transmission geometry, while for NbOCl2, it operates in reflection geometry?\n4. The schematic in Supplementary Fig. 7 shows the analyzer but does not include the incident polarizer, which is essential for polarized optical microscopy. Could the author re-verify or clarify this schematic?\n5. In Fig. 3f the samples are labeled by layer number, whereas in Fig. 4a–d, they are labeled by thickness. For clarity and consistency, I recommend using a single nomenclature throughout the manuscript. Could the authors revise the labeling accordingly?\n6. Can the authors provide a physical explanation for wavelength-dependent polarization plane orientation?\n7. The samples are prepared using a simple exfoliation method, which is not reliable for producing uniform thickness at a commercial scale. Do the authors have suggestions for overcoming this limitation, or can they comment on alternative fabrication methods that would enable thickness-controlled and scalable production?\n8. Can the authors provide information regarding the optical damage threshold of the NbOCl₂ nanosheet?", "reviewer_3": "In this work, the authors experimentally reported ultrathin quarter-waveplates based on two-dimensional anisotropic NbOCl2. It is demonstrated that ultrathin waveplates of two-dimensional NbOCl₂ utilize strong in-plane optical anisotropy with an atomically smooth, van der Waals surface. Polarization parameters of these waveplates can be engineered by thickness-dependent modulation. The NbOCl₂ quarter-waveplates exhibit retardance tolerance (< λ/600 to λ/300). The work is interesting. I recommend this work for consideration for publication in Nature Communications, provided that the following issues are addressed:\n1. The introduction is not sufficient. As two-dimensional material, black phosphorus with strong anisotropy has also been to achieve polarization devices including waveplates. In addition, MoS₂, WS₂, ReS₂, ReSe₂ are also utilized in this field. The authors should discuss the relevant concepts and compare them. Please refer to the following literatures, 10.1021/acsphotonics.7b00507, 10.1126/science.abj7053.\n2. The authors may enhance the underlying physics explanations. For instance, the results in Fig. 1, how do the intensity depend on the anisotropy? Have the authors measured the refractive index difference?\n3. To better represent the axial anisotropies, reflective dichroic ratios defined as rc / rb and rb / rc were introduced. Why do the authors use this method to represent the anisotropy?\n4. The authors should enhance the novelty descriptions in this work.\n5. In Fig. 3(a), the ellipticity-λ spectra for 414 L and 433 L adopted analogous peak features, except for a distinct blueshift for 433 L spectrum. However, the ellipticity spectra exhibit a clear difference compared with other layers. The authors may discuss and explain the layer-dependent modulation according to the results.\n6. Does Figure 4(a) show fitting results showing polarization modulation for an ideal QWP? What is an ideal QWP? Its phase shift is 90deg?\n7. In Fig. 4h, the “retardance tolerances” of the NbOCl₂-based QWPs and the commercial QWPs appear almost identical. This seems inconsistent with the statement in the text that the NbOCl₂ devices present a “distinctly narrower retardance tolerance”. The authors should: (i) clearly define how “retardance tolerance” is quantified; (ii) provide numerical values (e.g. as a table) rather than only a visual comparison; and (iii) discuss whether the experimental accuracy is sufficient to resolve the claimed λ/600 versus λ/300 performance. As it stands, Fig. 4h does not convincingly support the claimed superiority."}, "author_response": "Responses to the reviewers’ comments (Manuscript number NCOMMS-25-89837-T)\nChanges in the revised manuscript as a response to the reviewers’ comments are highlighted in red color and clarifications regarding the reviewer’s comments are provided in blue color.\nReviewer #1 (Remarks to the Author):\nThe paper mainly researched the potential of the ultrathin NbOCl quarter-waveplates 2 (QWPs), from the perspective of key polarization parameters such as ellipticity and polarization plane angle. The reflectance spectra and ellipticity are layer-sensitive, showing rich properties in thicker materials. Moreover, the authors benchmarked the performance of the NbOCl QWPs against commercially available QWPs. I 2 recommend that the manuscript be considered for publication after revisions.\n1. Based on the literature (Nature 613, 53–59 (2023)), the b-axis was defined as C 2 rotation axis. In this paper, the c-axis is set as the C rotation axis according to Raman 2 tensors (equation 2). For clarity, it would be beneficial to explicitly label the crystal axes.\nResponse: We thank the reviewer for pointing out this important clarification. We agree with the reviewer’s suggestion that explicitly labelling the axes would improve the clarity of the manuscript. Accordingly, we changed one sentence of the first paragraph in Page 5: “where the c-axis is chosen as the C rotation axis, and the nonzero elements 2 represent components that contribute to Raman scattering”.\n2. In equations (4)-(7), the Jones vectors related to the cross polarization are (e_s ) ⃗=(0,-sinθ,cosθ). The consideration was neglected.\nResponse: We appreciate the reviewer’s comment and fully agree that the Jones vector for cross polarization should be explicitly defined in the manuscript. We would like to clarify that this vector, 𝑒⃗⃗⃗⃗ = (0, -sin θ, cos θ), was indeed used in the calculations 𝑠 underlying equations (4)-(7). The following provides a brief overview of the calculation process for A : g 𝑎 𝑑 0 2 𝑆(𝐴 ,∥) ∝ [(0,cos⁡𝜃,sin⁡𝜃)(𝑑 𝑏 0)(0,cos⁡𝜃,sin⁡𝜃)𝑇] = [(𝑑 ∗cos⁡𝜃,𝑏∗ 𝑔 0 0 𝑐 𝑐𝑜𝑠⁡𝜃,𝑐 ∗sin⁡𝜃)(0,cos⁡𝜃,sin⁡𝜃)𝑇]2 = (𝑏𝑐𝑜𝑠2𝜃 +𝑐𝑠𝑖𝑛2𝜃)2 , 𝑆(𝐴 ,⊥) ∝ 𝑔 𝑎 𝑑 0 2 [(0,−sin⁡𝜃,cos⁡𝜃)(𝑑 𝑏 0)(0,cos⁡𝜃,sin⁡𝜃)𝑇] = [(−𝑑 ∗𝑠𝑖𝑛⁡𝜃,−𝑏∗𝑠𝑖𝑛⁡𝜃,𝑐 ∗ 0 0 𝑐 2 cos⁡𝜃)(0,cos⁡𝜃,sin⁡𝜃)𝑇]2 = [( 𝑐 − 𝑏 )∗𝑠𝑖𝑛⁡2𝜃] ∝ (𝑠𝑖𝑛2𝜃)2 . However, its explicit 2 2 statement was inadvertently omitted, which may have affected the clarity of the derivation. In response, we have now revised the content in Page 5 accordingly, ensuring the presentation is both complete and clear: “Setting the angle between the incident light polarization and Y-axis as θ, the Jones vectors can be expressed as: ⃗𝑒⃗⃗ = 𝑖 (0, cos θ, sin θ) T, 𝑒⃗⃗⃗⃗ = (0, cos θ, sin θ) for parallel polarization and 𝑒⃗⃗⃗⃗ = (0, -sin θ, 𝑠 𝑠 cos θ) for cross polarization”.\n3. The paper emphasizes the importance of layer numbers. Polarization planes show wavelength-dependent orientations in a thicker sample (Figure 2f). Polar plots for reflection intensity are layer-number, as well as ellipticity (Figure 3a-c). However, for samples of different thicknesses, the polarization parameters seem irregular and unpredictable. Could the phenomenon be reproducible in the samples with identical layers? In other words, for a sample with a fixed layer number, are its operating wavelengths always the same?\nResponse: We understand the reviewer’s concern and have addressed it as follows:\nBoth the ellipticity and the polarization plane axis exhibit a gradual variation with increasing layer numbers. Specifically, the ellipticity shows a peak shift, while the polarization plane axis undergoes quasi-continuous rotation as the layer number increases. To provide further clarity, we have plotted the ellipticity spectra for three nanoflakes with similar layer numbers, as shown in Figure RL 1a. These spectra demonstrate a minor but gradual shift in ellipticity, confirming the trend observed in thicker samples. This tunability of NbOCl waveplates can be attributed to their 2 exceptionally weak interlayer electronic coupling (Nature, 2023, 613, 53-59). Additionally, we confirm that the phenomenon is reproducible in samples with identical layer numbers. As shown in Figure RL 1b, two independent measurements on a sample with the same number of layers reveal consistent operating wavelengths (~500 nm). This consistency underscores the reliability of the observed behaviour.\nFigure RL 1. a, Ellipticity spectra of nanoflakes with layer numbers of 349 L, 361 L and 367 L. b, Ellipticity spectra from two independent measurements of a sample with a fixed layer number.\n4. In line 226, the imaginary number should be written as i to keep consistent with equation (9) and supplementary information. The specific expression of M (φ) is polarizer missed in the derivation.\nResponse: We acknowledge the reviewer’s notice and have revised the manuscript to address it. The Equation (8) in Page 9 has been changed as follows:\n𝑀 (𝜃) = 𝑅(−𝜃)⋅𝑀⋅𝑅(𝜃) (8)\n𝑤𝑎𝑣𝑒𝑝𝑙𝑎𝑡𝑒\n𝑐𝑜𝑠2𝜃 +𝑒𝑖𝛿𝑠𝑖𝑛2𝜃 (1−𝑒𝑖𝛿)𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜃\n= ( )\n(1−𝑒𝑖𝛿)𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜃 𝑠𝑖𝑛2𝜃 +𝑒𝑖𝛿𝑐𝑜𝑠2𝜃\nThe specific expression of M (φ) has been added and can be found on Page 12 of polarizer the supporting information:\n𝑐𝑜𝑠2𝜑 𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝜑\n𝑀 (𝜑) = ( )\n𝑝𝑜𝑙𝑎𝑟𝑖𝑧𝑒𝑟 𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝜑 𝑠𝑖𝑛2𝜑\n5. Some panels in Figure 3f deviate from the ideal QWP. What does this indicate/suggest? In part of the theoretical fitting based on the ideal QWP model, the key parameter is the waveplate intrinsic matrix. What is the relationship between the matrix and specific materials?\nResponse: Thank you for the insightful observation. Figure 3f is intended to demonstrate the broad tunability of our NbOCl -based general waveplates by 2 showcasing the continuous polarization modulation achieved through varying thickness. Its primary purpose is to illustrate the principle of phase retardance control via thickness, rather than to depict the performance of a fixed QWP. The characterization for a targeted QWP is the focus of Figure 4.\nRegarding the relationship between the waveplate intrinsic matrix and specific material properties, your point is well-taken. The connection is fundamentally established through the phase retardance. This key parameter, which defines the action of the matrix, is directly determined by the intrinsic birefringence (Δn) of specific materials and the fabricated device thickness (d) at the operating wavelength (λ), governed by the equation δ =2π·Δn·d/λ and the multi-interface model\n𝐼 = (𝐸 𝑠𝑖𝑛𝜃)2 +(𝐸 𝑐𝑜𝑠𝜃)2 +2√(𝐸 𝑠𝑖𝑛𝜃)2 ∙(𝐸 𝑐𝑜𝑠𝜃)2𝑐𝑜𝑠𝛿\n𝑠𝑎𝑚+𝑠𝑢𝑏,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑐 𝑏 𝑐 𝑏\n𝐼 = (𝐸 2 +𝐸 2)𝑠𝑖𝑛𝜃 ∙𝑐𝑜𝑠𝜃+2√(𝐸 𝑠𝑖𝑛𝜃)2 ∙(𝐸 𝑐𝑜𝑠𝜃)2𝑐𝑜𝑠𝛿\n𝑠𝑎𝑚+𝑠𝑢𝑏,𝑐𝑟𝑜𝑠𝑠 𝑐 𝑏 𝑐 𝑏\n6. The caption of Figure 4e-g is unclear: “Experimental data and fitting results” of what? Additionally, providing the analytical expression for the cross-polarized reflected light intensity would be useful, where the fitting result has already been exhibited in Figure 4e-g.\nResponse: We fully agree the reviewer’s suggestion.\nAccordingly, we changed the caption of Figure 4 in Page 10 as follows: “Figure 4. QWP based on NbOCl . a, Fitting results showing polarization modulation for an ideal 2 QWP. b-d, Experimental results for polarization modulation in NbOCl QWPs, for 2 NbOCl flakes of 269 nm (414 L), 282 nm (433 L) and 374 nm (575 L), respectively. 2 e-g, Experimental data and fitting results of the normalized intensity under parallel- polarization (polarizer and analyzer aligned) and cross-polarization (polarizer and analyzer perpendicular) conditions, plotted as a function of the sample rotation angle. h, Performance comparison of NbOCl QWPs against commercially available QWPs, 2 inclusive of Thorlabs WPQSM05-514 (514 nm), WPQSM05-588 (588 nm), WPQ05ME-633 (633 nm) and Edmund Optics #49-221 (670 nm). i, j, Experimental result and schematic illustration of the modulation measurement for linearly polarized light passing through a QWP and NbOCl₂, whereby the fast axes of the QWP and NbOCl are perpendicular to each other”. 2\nWe also supplemented the analytical expression (11) in Page 11 as follows:\n𝐼 = (𝐸 2 +𝐸 2)𝑠𝑖𝑛𝜃 ∙𝑐𝑜𝑠𝜃 +2√(𝐸 𝑠𝑖𝑛𝜃)2 ∙(𝐸 𝑐𝑜𝑠𝜃)2𝑐𝑜𝑠𝛿 (11)\n𝑠𝑎𝑚+𝑠𝑢𝑏,𝑐𝑟𝑜𝑠𝑠 𝑐 𝑏 𝑐 𝑏\n7. It’s inspiring that the performance of the ultrathin NbOCl -based QWPs is as good 2 as commercially available QWPs. Moreover, the authors could further summarize and compare the performance of NbOCl -based QWPs and other 2D materials to highlight 2 the advances. For example, plot a figure to show the effective wavelength range, phase retardance, and other parameters of 2D materials.\nResponse: We thank the reviewer for the valuable suggestion. While there are reports on the use of other 2D materials, such as black phosphorus (BP), ReS , ReSe (ACS 2 2 Photonics 2017, 4, 12, 3023-3030) and α-MoO (Commun. Mater. 2024, 5, 16), for 3 waveplate applications, they often lack sufficient direct data on some parameters, including the effective wavelength range and precise phase retardance, so we are currently unable to provide a detailed benchmark figure comparing the performance of different 2D materials. Thank you again for your valuable feedback.\nReviewer #2 (Remarks to the Author):\nIn this manuscript, Jia et. al. investigated quarter-waveplate behavior from ultrathin NbOCl nanosheets, leveraging its large in-plane optical anisotropy and atomically flat 2 surfaces. The authors have performed polarization-resolved reflectance, angle-resolved polarized Raman spectroscopy (ARPRS), and ellipticity experiments to identify the optical anisotropy and demonstrated polarization modulation experiment to quantify the optimum QWP behavior across several visible wavelengths, with a device thickness as low as 269 nm. The manuscript demonstrates promising experimental evidence for using NbOCl nanosheet as an ultrathin QWP, however, several aspects of this 2 manuscript need clarification:\n1. The manuscript claims strong in-plane anisotropy. Although the author has provided angle-resolved Polarization Raman spectroscopy to support the anisotropy, they do not talk about birefringence, Δn(λ) values for the NbOCl ultrathin crystal. Can the authors 2 verify, using their cited Δn values, that the measured flake thickness yields quarter- wave retardance at the studied wavelengths?\nResponse: We sincerely thank the reviewer for this insightful comment. The reviewer is correct that under standard transmission conditions, the retardance condition is primarily governed by the equation #1: δ =2π·Δn·d/λ, and we acknowledge that directly citing Δn values for NbOCl would provide a useful reference point. The core of our 2 work relies on a reflection-based, asymmetric cavity configuration. This case introduces a fundamental deviation from the standard model, making the simple application of equation #1 insufficient to describe or predict the achieved retardance. The key mechanism is the cavity-modulated effective phase accumulation. Our primary focus lies in the functional verification of the device as a QWP. That is, we experimentally validate whether the achieved phase retardance satisfies the condition for QWP operation (Table RL 1).\nTable RL 1. Comparison of numerical value.\nMaterial Thickness Wavelength Phase Retardance\n(nm) (nm) retardance tolerance (nm)\n(rad)\n239 523.90 1.5708±0.0272 ~λ/250\n269 613.79 1.5708±0.0097 ~λ/650\nNbOCl 2 282 605.00 1.5708±0.0120 ~λ/600\n374 500.60 1.5708±0.0043 ~λ/1450\n391 561.94 1.5708±0.0072 ~λ/850\nCrystalline 1920000 514 1.5708±0.0209 ~λ/300\nQuartz\n(Thorlabs)\nCrystalline 1580000 588 1.5708±0.0209 ~λ/300\nQuartz\n(Thorlabs)\nLiquid Crystal 2000000 633 1.5708±0.0628 ~λ/100\nPolymer\n(Thorlabs)\nPolymer Film 6350000 670 1.5708±0.0179 ~λ/350\n(Edmund\nOptics)\nAs a reference point following the reviewer’s suggestion, here we have calculated the theoretical optical path required for standard zero-order and first-order transmission- type QWPs at our central wavelengths for comparison, where Δn are adapted from “Nat. Photon. 2024, 18, 1170–1175”.\nOperation wavelength (zero-order path, first-order path, reflection-based double path):\nλ=500.6 nm (250.3 nm, 750.9 nm, 748 nm),\nλ=523.9 nm (291.1 nm, 873.2 nm, 478 nm),\nλ=561.9 nm (326.7 nm, 980.1 nm, 782 nm),\nλ=605.0 nm (387.8 nm, 1163.46 nm, 564 nm),\nλ=613.8 nm (414.7nm, 1244.2 nm, 538 nm).\nAs shown in the comparison, the optical path (748 nm) of our reflection-based device at λ=500.6 nm aligns closely with the theoretical value for a first-order QWP (750.9 nm), while for other wavelengths, the measured values fall between the theoretical zero- order and first-order benchmarks. For the specific case at λ=500.6 nm, the cavity effect compensates for the deviation from the transmission-only path.\n2. In most real cases, QWP is used in transmission, but the device is exclusively characterized in reflection mode. Did the authors perform the analogous polarization modulation experiment in transmission mode? Has any difference been observed?\nResponse: We fully agree with the reviewer that commercial QWPs are typically used in transmission, and complementary transmission-mode data would strengthen our study. During the experimental phase, we did attempt to prepare samples on quartz and glass, respectively. However, the exfoliated flakes were much smaller than the 50 μm aperture of our measurement system and often exhibited non-uniform thickness and occasional wrinkles imparted during the transfer process. Given these constraints, we strategically pivoted to the reflection-based geometry using the NbOCl /SiO /Si 2 2 structure. Our current approach is performance oriented. However, if the aforementioned limitation for transmission mode measurement were resolved, the research focus would naturally shift from this empirical optimization to the engineering of specific thickness based on intrinsic birefringence.\n3. Can the authors explain whether the phase-retardance mechanism in their system is fundamentally equivalent to that of standard waveplates, as commercial QWPs typically operate in transmission geometry, while for NbOCl , it operates in reflection 2 geometry?\nResponse: We thank the reviewer for raising this critical question. The phase-retardance mechanism in our NbOCl /SiO /Si reflection structure is not fundamentally equivalent 2 2 to that of a standard transmission-geometry waveplate.\nA commercial QWPs operating in transmission relies on the propagation phase difference accumulated as light passes once through a slab of birefringent crystal. The retardance is governed by the well-known equation: δ =2π·Δn·d/λ. The design transmission is straightforward: for a target λ, one chooses a crystal and precisely machines its thickness d to satisfy δ = π/2 or an odd multiple thereof.\nIn our configuration, the total phase difference between orthogonal polarization components in the reflected beam is not simply double pass. In essence, the phase retardance mechanism in our system can be understood as a hybrid that combines the foundational principle of birefringent phase accumulation with a multi-interface interference model (Supplementary Figure S11 at Section 5).\n4. The schematic in Supplementary Fig. 7 shows the analyzer but does not include the incident polarizer, which is essential for polarized optical microscopy. Could the author re-verify or clarify this schematic?\nResponse: We thank the reviewer’s careful observation regarding the optical setup. The absence of an incident polarizer in Supplementary Fig. 7 is intended by design. In Fig. 2 and Supplementary Fig. 7, we aim to quantify the variation in optical contrast of the microscopy images taken from the same sample flake under different analyzer angles, to provide a preliminary comparison of the optical anisotropy between thin and thick flakes.\nIn contrast, the waveplate characterization requires full control over both the input and output polarization states to measure the phase retardance. Therefore, an incident polarizer is essential and was indeed included in those experiments (as shown in the schematic of Fig. 3e).\n5. In Fig. 3f the samples are labeled by layer number, whereas in Fig. 4a–d, they are labeled by thickness. For clarity and consistency, I recommend using a single nomenclature throughout the manuscript. Could the authors revise the labeling accordingly?\nResponse: Thank you for this careful observation regarding our labelling consistency. To maintain a consistent labelling throughout the manuscript, we have revised Figure 4a-d captions in Page 10 accordingly: “a, Fitting results showing polarization modulation for an ideal QWP. b-d, Experimental results for polarization modulation in NbOCl QWPs, for NbOCl flakes of 269 nm (414 L), 282 nm (433 L) and 374 nm 2 2 (575 L), respectively”.\n6. Can the authors provide a physical explanation for wavelength-dependent polarization plane orientation?\nResponse: We thank the reviewer for this excellent question regarding the physical origin of the wavelength-dependent polarization plane orientation observed in our NbOCl waveplates. Notably, similar phenomenon has been previously reported in 2 other systems (ACS Photonics, 2017, 4, 12, 3023–3030, Nat. Commun., 2024, 15, 1552). Here we provide a physical explanation based on the concept of non-orthogonal exciton resonances as follows:\nIn conventional materials with high symmetry, the principle optical axes are fixed in the crystal frame. However, in some low-symmetry triclinic or monoclinic crystals, these principal axes are not fixed. Their orientation within the crystal plane can depend on the light’s wavelength. This occurs because the effective dielectric tensor of the material, which defines these axes, is a superposition of contributions from multiple electronic or excitonic transitions. When these transitions have non-orthogonal transition dipole moments, their relative strength and phase vary wavelength. This leads to a wavelength-dependent rotation of the eigenvectors of the dielectric tensor, resulting in the observed rotation of the output polarization plane.\nNbOCl hosts strong, anisotropic in-plane excitonic resonances. According to the 2 framework established for triclinic or monoclinic van der Waals materials, the interference between these non-orthogonal excitonic resonances is the primary driver for the wandering axes. At a given wavelength, the optical response manifests as a specific superposition of these excitonic contributions, which defines a unique set of principal axes correspondingly.\n7. The samples are prepared using a simple exfoliation method, which is not reliable for producing uniform thickness at a commercial scale. Do the authors have suggestions for overcoming this limitation, or can they comment on alternative fabrication methods that would enable thickness-controlled and scalable production?\nResponse: We agree with the reviewer’s comment regarding the limitations of mechanical exfoliation for scalable production. In this foundational study, we employ mechanical exfoliation method to obtain NbOCl crystals. AFM measurements 2 revealed sub-nanometer surface roughness, with the RMS value being less than 0.1% of the flake thickness. For this foundational study, the sample dimensions are adequate for our intended use. However, transitioning to scalable, thickness-controlled fabrication is essential. We envision two primary pathways:\n Firstly, the development of controlled vapor-phase growth, particularly chemical vapor deposition (CVD), represents a fundamental pathway toward wafer-scale integrated photonics. By designing suitable precursors (e.g. Nb O , NbCl , Cl ) in 2 5 5 2 a right stoichiometric ratio, using a substrate with quasi-lattice matching and compatible symmetry, it would enable wafer-scale, direct growth of films with precise thickness control.\n Secondly, building upon wafer-scale NbOCl films, the precisely controlled 2 construction of homo-junctions can be achieved using the direct bonding and debonding technique (Nat. Electron., 2025, 8, 1038–1045). As recently demonstrated for other 2D semiconductors, this innovative method allows for the layer-by-layer assembly of wafer-scale films. This process enables the creation of ultra-clean interfaces and allows for precise control over both the layer numbers and the interlayer twist angle. Applied to NbOCl , this technique could facilitate 2 the scalable fabrication of custom-designed homo-structures with specific optical phase retardance.\n8. Can the authors provide information regarding the optical damage threshold of the NbOCl₂ nanosheet?\nResponse: Thank you for raising this point regarding the optical damage threshold of the NbOCl flake. In response, we performed laser damage tests using a 532 nm laser 2 on samples with varying thicknesses. The incident laser was focused via an objective lens upon the sample surfaces with a beam diameter of approximately 2 μm, and processed to raster at increasing laser powers. The threshold was determined at the instance when distinct optical changes (either from damage or sample thinning) were observed under the microscope. The results are presented in Figure RL 2, which shows that for thick NbOCl flakes, the optical damage threshold is about 200 kW/cm2. While 2 we do expect discrepancies for samples of differing thicknesses due to their different absorption (and reflective) spectrum profiles (i.e. they absorb 532 nm light to differing extents), their consistently high threshold (in comparison against designed commercial standards of 500 W/cm2 (e.g. Ultra-Thin NIR Achromatic Polymer Retarder; Edmund Optics, and λ/4 Precision Zero Order Retarder; Edmund Optics)) ensures suitability of these samples for conventional waveplate optics.\nFigure RL2. Optical damage threshold of NbOCl flakes.\nIn this work, the authors experimentally reported ultrathin quarter-waveplates based on two-dimensional anisotropic NbOCl . It is demonstrated that ultrathin waveplates of 2 two-dimensional NbOCl₂ utilize strong in-plane optical anisotropy with an atomically smooth, van der Waals surface. Polarization parameters of these waveplates can be engineered by thickness-dependent modulation. The NbOCl₂ quarter-waveplates exhibit retardance tolerance (< λ/600 to λ/300). The work is interesting. I recommend this work for consideration for publication in Nature Communications, provided that the following issues are addressed:\n1. The introduction is not sufficient. As two-dimensional material, black phosphorus with strong anisotropy has also been to achieve polarization devices including waveplates. In addition, MoS₂, WS₂, ReS₂, ReSe₂ are also utilized in this field. The authors should discuss the relevant concepts and compare them. Please refer to the following literatures, 10.1021/acsphotonics.7b00507, 10.1126/science.abj7053.\nResponse: We thank the reviewer for the insightful suggestion and fully agree to discuss relevant works on anisotropic 2D materials in this field. We have changed the contents in Page 2 as follows: “Consequentially, 2D systems with in-plane or biaxial anisotropy stemming from crystallographic asymmetries, including rhenium dichalcogenides15,16, germanium selenide17,18, α-phase molybdenum trioxide19-22 and black phosphorus15,23,24 were evaluated. For example, black phosphorus have been extensively investigated for polarization control devices, including waveplates and electro-optic modulators25, leveraging their in-plane anisotropy or by integrating it onto cavity structure. However, these materials only presented moderate birefringence, where reported birefringence values typically remain below 0.1, particularly in the ultraviolet-visible-infrared spectral regions.\nWith recent investigations involving niobium oxychloride (NbOCl ) crystals, it was 2 revealed that the 2D material possessed a unique in-plane biaxial crystal structure, with highly anisotropic in-plane optical properties26-30, including outstanding birefringence (0.26-0.46) across a wide visible–NIR transparency window29. Furthermore, the crystal structure of NbOCl features a vanishing interlayer electronic coupling26,27, 2 much weaker than the typical van der Waals interaction in other 2D materials, allowing ease of exfoliating a cleaner surface with uniform material thickness and polarization uniformity. The suitability of NbOCl for miniaturized polarization optics prompted our 2 evaluation of its performance as ultrathin quarter waveplates (QWPs) in this work”.\n2. The authors may enhance the underlying physics explanations. For instance, the results in Fig. 1, how do the intensity depend on the anisotropy? Have the authors measured the refractive index difference?\nResponse: We thank the reviewer for the suggestions to clarify upon the underlying physics. For the polarized Raman results in Fig. 1, the observed angle-dependent intensity patterns are the direct experimental manifestation of NbOCl ’s anisotropic 2 Raman tensor, which is rigidly fixed to its crystal frame. The tensor’s form is dictated by the crystal’s C point group symmetry, and its element values encode the distinct 2 optical polarizabilities along b- and c- axes. When linearly polarized light interacts with the rotating crystal, the scattering intensity S∝∣e ⋅R⋅e∣2 projects this intrinsic material s i tensor into a measurable angular output. This results in the characteristic two-lobed or four-lobed polar plots. Fitting these patterns to the symmetry-derived formulas allows us to determine the crystal orientation. Additionally, since a holistic evaluation of the refractive index difference for NbOCl has been reported in a previous paper (Nat. 2 Photon. 2024, 18, 1170–1175), we relied upon these report values for the analyses. Should the reviewer feel that these measurements may be crucial to reiterate reliability, we can process further measurements.\n3. To better represent the axial anisotropies, reflective dichroic ratios defined as r / r c b and r / r were introduced. Why do the authors use this method to represent the b c anisotropy?\nResponse: We thank the reviewer for raising this point. We plot both r /r and r /r ratios c b b c to enhance chart readability and make the trends visually apparent. Through this way, we can directly and more precisely identify the intersection at which the polarization plane orientation undergoes a significant change.\n4. The authors should enhance the novelty descriptions in this work.\nResponse: We thank the reviewer for the suggestion to enhance the novelty descriptions in our work. To address this, we have further clarified the significance of our study as follows:\n We emphasize that NbOCl , as an emerging anisotropic van der Waals material, 2 offers unique advantages over traditional waveplate materials like quartz and calcite. Its strong in-plane optical anisotropy and weak interlayer electronic coupling enable ultrathin waveplate fabrication, breaking the sub-micron thickness barrier for quarter-waveplates which has not been reported before. This represents a significant breakthrough, as it combines the benefits of ultrathin thickness with precise optical performance.\n Although two-dimensional materials such as h-BN and TMDs exhibit considerable out-of-plane birefringence, their utility in polarization optics is hindered by the difficulty of probing their anisotropic response. This requires stringent incidence conditions (normal or oblique to the optical axis), a criterion that is particularly challenging to meet with ultrathin layers. On the other hand, in-plane anisotropic materials, such as BP and ReS , are more practical for controlling polarization 2 states. However, their birefringence is relatively limited. In contrast, NbOCl 2 combines strong in-plane birefringence with a highly tunable layer-dependent thickness, making it uniquely suited for ultrathin polarization optics.\n For NbOCl , because of the relatively large interlayer distance, the saturation of 2 Cl-atom p-orbitals, and the highly localized charge density around Nb atoms at the valence band maximum and conduction band minimum, the electronic coupling between NbOCl layers is very weak. This results in minimal variation in electronic 2 structure and the dominant excitonic optical response from monolayer to bulk, exhibiting a near “layer-independent” character. Precisely because of this weak coupling, the optical response is nearly independent and identical. Therefore, the cumulative phase retardance, which is the key parameter determining polarization conversion, as light passes through a multilayer NbOCl flake scales in an 2 approximately linear relationship with the total thickness. This stands in sharp contrast to most common 2D materials, such as TMDs, whose optical properties undergo drastic changes with layer number.\n5. In Fig. 3(a), the ellipticity-λ spectra for 414 L and 433 L adopted analogous peak features, except for a distinct blueshift for 433 L spectrum. However, the ellipticity spectra exhibits a clear difference compared with other layers. The authors may discuss and explain the layer-dependent modulation according to the results.\nResponse: Our sincere appreciation to the reviewer for raising this point. The observed phenomena that present analogous line shapes with a spectral shift between layers is a feature observed across a certain range of flake layer numbers (e.g. for 349 L, 361 L and 367 L). As shown in Figure RL 3, the direction of this shift is not solely a blueshift or redshift with increasing layer numbers. This is a consequence of the cavity modulation in our structure. The total phase retardance determining the ellipticity spectrum is governed by round-trip phase accumulation within the cavity, which would be influenced by the resonance. This cavity resonance condition ties the flake thickness directly to a discrete set of resonant wavelengths. The observed non-monotonic spectral shift captures this discrete hopping between adjacent resonance orders as the thickness is tuned.\nFigure RL 3. Ellipticity spectra of NbOCl with different layer numbers.\n2\n6. Does Figure 4(a) show fitting results showing polarization modulation for an ideal QWP? What is an ideal QWP? Its phase shift is 90deg?\nResponse: Thank you for the question regarding Figure 4a. Figure 4a presents polarization modulation results based on theoretical fitting for an ideal QWP. An ideal QWP is defined as a retarder that introduces a precise phase retardance of exactly 90 degrees between two orthogonal polarization components, assuming perfect performance without tolerance, absorption, or scattering loss. This serves as a theoretical benchmark against which the performance of our real fabricated device can be compared. Specifically, when retardance δ is set to 90 degrees, the output state becomes purely circular polarization for a 45 degrees linearly polarized input. Consequently, in the derived Equation (11) in our manuscript, the ellipticity reaches its ideal value of 1, and the intensities of the orthogonal polarization components I and I b c become theoretically equal.\n7. In Fig. 4h, the “retardance tolerances” of the NbOCl₂-based QWPs and the commercial QWPs appear almost identical. This seems inconsistent with the statement in the text that the NbOCl₂ devices present a “distinctly narrower retardance tolerance”. The authors should: (i) clearly define how “retardance tolerance” is quantified; (ii) provide numerical values (e.g. as a table) rather than only a visual comparison; and (iii) discuss whether the experimental accuracy is sufficient to resolve the claimed λ/600 versus λ/300 performance. As it stands, Fig. 4h does not convincingly support the claimed superiority.\nResponse: We highly value the reviewer’s suggestion and have provided additional details as follows:\n(i) The procedure is outlined below: First, we conducted polarization modulation experiments on the waveplate, as described in the manuscript, to map the relationship between the output light intensity and the variations in the sample rotation angle and analyzer angle. From this mapping, we focused on the intensity variation with respect to the analyzer angle when the crystal axis of the sample was oriented at 45 degrees to the polarization direction of the incident light. The maximum and minimum intensities were extracted to calculate ellipticity. Next, we also obtained the output intensities I b and I when the analyzer was aligned with the b-axis and c-axis, respectively. These c values were substituted into Equation (11) to calculate the phase retardance. Due to the sine function in the equation, two numerical solutions are typically obtained. Finally, the accuracy was determined by subtracting these solutions from the theoretical retardance of a quarter-waveplate.\n(ii, iii) The table below provides numerical values for the phase retardance of NbOCl - 2 based QWPs and some commercial QWPs. The claimed superiority of λ/600 over λ/300 in the manuscript is an approximation, here to further support the evidence presented in Figure 4h, we have conducted additional analysis on tolerance, which is also included in Table RL 1, and this table has been added to the Supporting Information. Additionally, it is worth noting that Figure 4h illustrates the corresponding mean values and standard deviations.\nIf the reviewer feels additional clarification or further experimental data is necessary, we are happy to provide more detailed explanations or additional measurements.\nTable RL 1. Comparison of numerical value.\nMaterial Thickness Wavelength Phase Retardance\n(nm) (nm) retardance tolerance (nm)\n(rad)\n239 523.90 1.5708±0.0272 ~λ/250\n269 613.79 1.5708±0.0097 ~λ/650\nNbOCl 2 282 605.00 1.5708±0.0120 ~λ/600\n374 500.60 1.5708±0.0043 ~λ/1450\n391 561.94 1.5708±0.0072 ~λ/850\nCrystalline 1920000 514 1.5708±0.0209 ~λ/300\nQuartz\n(Thorlabs)\nCrystalline 1580000 588 1.5708±0.0209 ~λ/300\nQuartz\n(Thorlabs)\nLiquid Crystal 2000000 633 1.5708±0.0628 ~λ/100\nPolymer\n(Thorlabs)\nPolymer Film 6350000 670 1.5708±0.0179 ~λ/350\n(Edmund\nOptics)"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have read the authors' response letter. I think the authors have successfully addressed most of my questions. Now, I recommend the acceptance of this revision.", "reviewer_2": "The authors address all of my previous questions, thus I do agree to publish this work.", "reviewer_3": "The authors almost addressed my concerns. I recommend its publication."}, "author_response": "Responses to the reviewers’ comments (Manuscript number NCOMMS-25- 89837A)\nChanges in the revised manuscript as a response to the reviewers’ comments are highlighted in red color and clarifications regarding the reviewer’s comments are provided in blue color.\nReviewer #1 (Remarks to the Author):\nI have read the authors' response letter. I think the authors have successfully addressed most of my questions. Now, I recommend the acceptance of this revision.\nResponse: We express our sincere appreciation to the reviewer for the various technical questions raised previously that have helped improved the quality of our manuscript. We are glad that our responses were satisfactory in addressing these questions and we thank the reviewer for the recommendation of acceptance for our revised manuscript.\nReviewer #2 (Remarks to the Author):\nThe authors address all of my previous questions, thus I do agree to publish this work.\nResponse: We thank the reviewer for the opportunity to improve our manuscript quality through the specific questions raised previously, and truly appreciate the recommendation to publish our revised manuscript.\nReviewer #3 (Remarks to the Author):\nThe authors almost addressed my concerns. I recommend its publication.\nResponse: We are truly thankful to the reviewer for positive assessment of our work and the critical questions raised previously that allowed us to improve the quality of our manuscript. We are happy to have promptly addressed these questions to your satisfaction, and we thank the reviewer for the recommendation for publication."}]

Decision letter