Mid-infrared chirality and chiral thermal emission from twisted α-MoO_3

Domain: physics
Published: 2025-12-12
Editorial outcome: major_revision

Abstract
Chirality in the mid-infrared spectral range plays a crucial role across physical, chemical, and biological sciences, yet sources of chiral infrared light are currently difficult to obtain. Their development, using principles from the mature field of metamaterials, requires complex three-dimensional architectures that call for high-resolution lithography. Here, we leverage the natural optical anisotropy found in several van der Waals crystals, for example α-MoO3, to demonstrate experimentally that its twisted bilayers break inversion-rotation symmetry and are thereby intrinsically chiral. Via direct thermal emission measurements of microscopic twisted bilayers, we demonstrate that these heterostructures generate chiral light through incandescence. Twisted configurations of van der Waals materials do not require any lithography and offer a platform for large-scale chiral filters and thermal sources beyond conventional meta-architectures.

Introduction
Chirality is the geometric property that makes an object not superimposable onto its mirror image through neither rotation nor translation. It plays a crucial role in the development of life as we know it1,2 and becomes relevant across various disciplines in applied science and technology. For example, the fundamental vibrational modes of various molecules, occurring primarily in the mid-infrared (mid-IR) region of the electromagnetic spectrum, are highly sensitive to chiral configurations3. This sensitivity is often leveraged in organic chemistry and pharmaceuticals, where distinguishing between enantiomers – molecules that are mirror images of each other—is essential, since these can exhibit distinct biological activity and therapeutic effects4,5. Nonetheless, the degree of chiral response of naturally occurring molecular systems, quantified as the differential absorption between left- and right-circularly polarized light is five orders of magnitude smaller than the absorption of unpolarized light3,6,7. Techniques like vibrational circular dichroism spectroscopy utilize mid-IR light to differentiate enantiomers, offering vital insight into their intrinsic configurations and purity8,9.

Since sensing and detection of biological substances operate in the mid-IR region, the role of IR light sources is critical in chiral analysis. However, mid-IR lighting technology is primarily limited to the established–but lithographically complex—quantum-cascade laser, or globars and Nernst glowers that yield incoherent light. Both approaches lack the functionality to control the polarization state of light in a compact device platform at mid-IR frequencies. At the same time, in this spectral range, naturally available chiral systems such as molecular ones do not interact strongly with circularly polarized light3,6,7, highlighting the promise of materials engineering for mid-IR chirality and sources. Conveniently, however, at near-room temperatures, the spectrum of blackbody radiation emitted through incandescence peaks near 10 μm, thereby overlapping spectrally with the vibrational and phonon modes relevant in chiral spectroscopy. Therefore, incandescence presents a promising avenue for cost-effective mid-IR thermal sources10. Although light generated from incandescence is by nature achiral, thermal emitters with tailorable polarization characteristics have been reported in recent years, leveraging the collective response of three-dimensional metamaterials and metasurfaces10. Most recently, thermal emission with chiral characteristics has also been reported, using metamaterials composed of elementary unit cells that are geometrically asymmetric in the microscale11,12. However, the large-scale development of such meta-architectures requires expensive high-resolution lithography and synthesis.

In Fig. 1a, we illustrate chirality across different scales, starting with the most familiar chiral object in the macro-scale, a human hand, which serves as an example of mirror asymmetry. Beyond the aforementioned principles of conventional three-dimensional metamaterials with geometrically asymmetric unit cells, even achiral objects, such as a geometric cross, can serve as a unit cell of a planarized metamaterial that demonstrates chirality through twisting adjacent unit cells13–15, thereby inducing various effects typically observed in three-dimensional metamaterials with quasi-two-dimensional motifs16–18. As an example, the middle of Fig. 1a shows a twisted combination of such crosses that break inversion-rotation symmetry, representing the meso-scale and the regime of metamaterials. The realization of planarized twisted metamaterials, however, is subject to similar fabrication challenges as their three-dimensional counterparts11,12.

In this work, we experimentally demonstrate a fundamentally different approach to inducing chirality, leveraging the unique properties of emerging low-dimensional van der Waals crystals. Instead of relying on external lithographic patterning along the in-plane directions as in the case of metamaterials, we harness the natural, intrinsic in-plane optical anisotropy observed recently in several emerging van der Waals materials, such as α-molybdenum trioxide (α-MoO3)19–21 and α-vanadium pentoxide (α-V2O5)22, and twist adjacent layers to induce chirality. The concept of twisted anisotropic bilayers is demonstrated on the right of Fig. 1a, where twisted layers (heterostructures) of an in-plane anisotropic material are shown. This can be understood in direct analogy with the meso-scale and the case of twisted crosses; the blue and red colors in the middle- and right-side of Fig. 1a, represent, respectively, the two branches of a cross and the two dissimilar symmetry axes of an in-plane anisotropic crystalline material. In both cases, inversion-rotation symmetry is evidently broken via twisting. Importantly, however, in the platform introduced here via twisting uniform anisotropic crystals, chiral effects are enabled without the need for any patterned meta-atoms or their coupling. The reported chirality is intrinsic and thereby geometrically robust, as opposed to extrinsic chirality which is only observable for certain orientations of incident light23. The only requirement for inducing chirality in this platform is a pronounced intrinsic in-plane anisotropic material response. While several numerical studies have recently explored twisting anisotropic materials for mid-IR and terahertz chirality24–29, there has been no previous experimental demonstration.

We experimentally realize twisted bilayers composed of exfoliated flakes of α-MoO3, which exhibit strong in-plane anisotropy at mid-IR frequencies21, and show via absorption measurements that left- and right-hand-polarized light interacts differently with twisted layers of α-MoO3, revealing a strong chiral response. We carry out direct thermal emission measurements of van der Waals-based twisted flakes that have small lateral dimensions (tens of micrometers), and report thermally excited chiral light in a lithography-free platform. These results open up simpler ways to create photonic functionalities leveraging the unique properties of low-dimensional materials, eliminating the need for lithography in mid-IR chirality engineering.

Results
Achiral optical response can be described through circular dichroism (CD), which quantifies the difference in absorption or emission between right- and left-circularly polarized light. Based on Kirchhoff’s law of thermal radiation, a chiral response observed in an absorption experiment will manifest itself identically in light emission30. This suggests that a chiral absorber also constitutes a chiral thermal emitter of light that, in contrast to conventional blackbody radiation, has a chiral degree of freedom expressed through CD. For a chiral material onto a reflective substrate with vanishing transmission, we can define CD as:

CD = R↺ - R↻, (1)

where R↺ and R↻ denote the reflectance of left- and right-hand circularly polarized light. In this work, we confirm the chiral characteristics of twisted bilayers via both absorption and thermal emission experiments. In the following section, we identify the intrinsic material properties and underlying physical mechanisms required for engineering a chiral thermal emitter with twisted anisotropic bilayers.

Design rules for circular dichroism in twisted bilayers
Let us start with a heterostructure composed of two in-plane anisotropic materials on a reflective substrate, as shown in Fig. 2a, where the top and bottom layers are indicated, respectively, with indices 1 and 2. In principle, these two materials can be dissimilar with refractive indices ni,1,2 = ηi,1,2 + iκi,1,2, where ηi,1,2 and κi,1,2 denote the real and imaginary parts of the refractive index, respectively, along each axis i=x,y,z. In order for this system to thermally emit chiral light, we consider the thermal emission to occur primarily on the bottom layer, for which this layer must be lossy, based on the fluctuation-dissipation theorem. By contrast, the top layer tailors the polarization of light, for which it should operate as a phase retarder that is, ideally, lossless. Without loss of generality, we assume that ny,1 = ny,2 = 0, and we restrict the analysis to normal incidence, hence the out-of-plane refractive index (nz) of each layer is not relevant.

When the bottom layer exhibits in-plane dichroism (κx,2 ≠ κy,2), it emits preferentially linearly polarized light either along the x or y direction, for which it can also be viewed as an absorbing polarizer operating in emission mode. Since ky,2 = 0, the emitted electric field emitted by the bottom layer is primarily x-polarized. Upon appropriate selection of the thickness of the top layer, d1, it can operate as a quarter-wave plate introducing a phase shift of π/2 between the two orthogonal linear polarization components and converting the emitted light from layer 2 into circularly polarized light. For quarter-wave plate operation, the top layer must exhibit in-plane birefringence (ηx,1 ≠ ηy,1). In this configuration, henceforth, we refer to the bottom layer as the lossy dichroic emitter and the top layer as the lossless quarter-wave plate of the bilayer. In this idealized system, since κy,2 = ny,1 = 0, by misaligning the in-plane crystal axes of the layers by an in-plane rotation of angle α (Fig. 2a), the thermally emitted light can become circularly polarized. The refractive index of the quarter-wave plate (layer 1) along the x-direction is taken as purely real, nx,1 = ηx,1, while the refractive index of the dichroic emitter along the x-direction is complex, nx,2 = ηx,2 + iκx,2.

Figure 2b shows transfer matrix simulations of the circular dichroism as a function of the layer thicknesses d1 and d2, capturing the main features of our idealized model. Tuning d1 yields a periodic change of sign of CD, originating from the quarter-wave plate condition,

dQWP = (2(l+1)λ) / (4Δη1), (2)

where λ is the operational wavelength, Δη1 = ηx,1 − ηy,1 = ηx,1 is the birefringence of the top layer, and l is the integer that indicates the order of the wave plate31. Even orders of l yield a phase difference of π/2 mod 2π, for which the resulting CD is positive, (blue-colored features in Fig. 2b), whereas odd orders give a phase difference of 3π/2 mod 2π, for which CD is negative (orange-colored features in Fig. 2b). Thereby, light that is emitted from the dichroic emitter (layer 2) is converted into either left- or right-circularly polarized light depending on the thickness of the quarter-wave plate (layer 1).

From Fig. 2b, tuning d2 also yields a resonant behavior of CD. In order for the bottom layer to maximally emit, it should maximally absorb. Maximizing this absorption is dictated by Fabry–Pérot resonances that arise at particular thicknesses d2, and it is straightforward to show that the spacing of these resonances is λ/2ηx,2 (see Supplementary Note 1). By combining these two effects – quarter-wave conversion in the top layer and resonant emission in the bottom layer – the considered idealized system can produce perfectly circularly polarized emission, achieving maximal CD values of ±1.

Figure 2c shows the circular dichroism as a function of the twist angle α for two different thickness combinations. The blue curve corresponds to d1 = 3.1 μm, d2 = 2.3 μm (blue dot in Fig. 2b), and the red curve to d1 = 4.5 μm, d2 = 2.3 μm (red dot in Fig. 2b), corresponding to the second (l=2) and third (l=3) order of the quarter-wave plate. In both cases, CD reaches its maximal values of ±1 at the twist angle α = 45°, as expected in quarter-wave plate operation. Importantly, maximal CD can also be achieved at other twist angles by adjusting the layer thicknesses.

In Fig. 2d, we demonstrate the role of the optical loss in each layer – κx,1 and κx,2. Maximal CD is achieved when the top layer is lossless (κx,1 = 0), as expected for ideal wave-plate operation, while the bottom layer exhibits an optimal finite value of κx,2. Physically, this is expected since some losses in the dichroic emitter layer are necessary to yield thermal emission, but excessive losses suppress the resonant (Fabry–Pérot) effect that enhances CD. The white curves are contour plots for which CD reaches the value of 0.4, 0.6, 0.8, while the dashed white line marks the case where both layers are made from the same material (κx,1 = κx,2 = κx). It is thereby demonstrated that high CD values, above 0.6, can be achieved over a broad range of κx. The black circle indicates the value of κx for α-MoO3 at λ = 12.8 μm, demonstrating that realistic material parameters are well within the high-CD regime.

Finally, in Fig. 2e, we consider the case where the two layers consist of the same material, and evaluate how CD depends on the real part of its refractive index along each coordinate direction, ηx and ηy. In this panel, d1 = 0.2 μm and d2 = 2 μm, while we set κx = 0.3 and κy = 0, corresponding to realistic values for α-MoO321,32. As expected, along the dashed line where ηx = ηy, CD vanishes as the bilayer does not break mirror symmetry. By contrast, CD is maximized when the refractive index along either coordinate direction vanishes, demonstrating the critical role of strong in-plane birefringence. At the wavelength of λ = 12.8 μm, the optical response of α-MoO3 is indicated with the black circle in Fig. 2e, at which CD = 0.73.

The results demonstrate that a combination of strong in-plane anisotropy, appropriately tuned layer thicknesses to satisfy Fabry–Pérot and quarter-wave plate conditions, and moderate optical loss in the emitting layer can yield a strong chiral response in twisted bilayers. We note that, by reciprocity, the concept discussed in this section in terms of thermal emission applies to optical absorption as well, for which twisted bilayers can also serve as preferential absorbers of either left- or right-circularly polarized light. We verify this in the experiments we carried out as discussed in the following sections.

α-MoO3 for chirality
In the previous section, we identified that creating a chiral emitter out of twisted bilayers requires a bottom layer with considerable in-plane dichroism and a top layer with in-plane birefringence. Its strong in-plane optical anisotropy makes α-MoO3 an ideal material for realizing twisted bilayers that emit chiral light. This anisotropy arises from the orthorhombic crystal structure and interlayer interactions, enabling an intrinsic chiral response when two adjacent α-MoO3 layers are twisted relatively to each other. Exfoliated flakes of α-MoO3 typically possess a rectangular shape, as shown in the microscope image of a twisted bilayer in Fig. 1c, where we define the crystal directions [100], [001] and [010], as the x-, y- and z-axis, respectively. In Fig. 3a, b, we present the real (η) and imaginary parts (κ), respectively, of the refractive index of α-MoO3 along the in-plane crystal axes (x and y). The pronounced resonance along the x-direction at 12.35 μm is associated with the phonon mode of α-MoO3 along that axis.

As shown in panel b of Fig. 3, α-MoO3 possesses a considerable dichroic response (κx − κy), making it a suitable material for the bottom layer of the twisted chiral bilayers discussed in the previous section. At the same time, it also has a birefringence (ηx − ηy) that reaches a value of 9.4 near 12.4 μm, thereby α-MoO3 is also a suitable material for the top component of the twisted bilayer, where polarization conversion occurs (see previous section)33. In fact, due to the extreme value of its birefringence, the top layer can be deeply subwavelength unlike conventional quarter-wave plates33. The suitability of α-MoO3 for creating chiral bilayers is also confirmed with the black circles in Fig. 2d and e, marking the values of κ and η of α-MoO3 for which CD exceeds 0.6.

Figure 3c presents transfer-matrix simulations of CD as a function of wavelength and twist angle for a α-MoO3 bilayer with thicknesses d1 = 0.2 μm and d2 = 2 μm, which are selected upon optimization. The structure exhibits a high CD of 0.61 at a wavelength of 12.8 μm and a twist angle of 58°. Remarkably, at α = 67° (black cross in Fig. 2c), one circular polarization is almost completely suppressed: 97% of the absorbed light is right-hand circularly polarized, while CD remains high at 0.56 (see Supplementary Note 2).

It is important to clarify that, unlike other recently reported phenomena in α-MoO3 that rely on its hyperbolic response in the mid-IR – such as directional and topological polaritons34,35, negative reflection36, and reversed Cherenkov radiation37 – the intrinsic chirality discussed here does not require this hyperbolicity. Thereby, other materials that are strongly in-plane anisotropic but not hyperbolic could also serve as constituents of chiral bilayers, as derived in the previous section.

Absorption spectroscopy
Following the methodology outlined above, we experimentally realized twisted bilayers of α-MoO3 through exfoliation and stacking (see Methods). Upon exfoliation, we have a variety of thicknesses of flakes to select. We use numerical predictions to select the most appropriate thicknesses of flakes that yield pronounced CD, while having control over the twist angle which we use as a degree of freedom. The lateral dimensions of the fabricated bilayers range from 10 μm to 40 μm. The two devices discussed henceforth are termed Device 1 and 2 and consist of a 0.6 μm-thick flake on top of a 1.1 μm-thick flake twisted at an angle of 33° and a 0.8 μm-thick flake on top of a 0.85 μm-thick flake, twisted at an angle of 42° (Fig. 1c–e), respectively. An atomic force microscopy (AFM) scan of the Device 2 is presented in Fig. 1d, while the corresponding height profile is shown in Fig. 1e. Both devices were transferred onto a gold-coated glass substrate to perform CD measurements in reflection. We employed a Fourier transform infrared (FTIR) microscope (36× magnification, Bruker, Hyperion II) for these measurements. The measured area of the devices was restricted to that containing twisted flakes using the knife-edge aperture of the FTIR microscope.

With respect to Eq. (1), determining the spectrum of CD requires a broadband quarter-wave plate to circularly polarize the incident beam onto the sample (red beam path in Fig. 4). Nonetheless, ideal broadband quarter-wave plates are not commercially available at mid-IR wavelengths33. To circumvent this, we utilized a narrow-band wave plate designed for operation near the wavelength of 13 μm (CdSe from VM-TIM GmbH), and characterized the phase shift that it introduces between the x- and y-component of the electromagnetic field (δ(λ)), for the whole spectral range of interest (see diagram in Fig. 4) using the technique outlined in38. The combination of this wave plate and polarizer, which initially polarizes the IR light of the FTIR spectrometer source (Bruker, Vertex 80), are shown in the beam path of Fig. 4. Consistent with Eq. (1), it can be shown that, for a reflective substrate with vanishing transmission, CD can also be expressed as (see Supplementary Note 1):

CD = (R45° - R-45°) / sin(δ), (3)

where R45° and R-45° are the intensities of the reflected electric field when the wave plate’s fast axis is rotated by 45° and −45°, respectively, with respect to the linearly polarized light exiting the polarizer. Within the spectral range of interest, the phase shift of the waveplate (δ) presents values near 90°, ensuring that the factors in sin(δ) remains near-unity, thereby avoiding singularities in Eq. (3) and minimizing measurement errors.

These FTIR measurements are shown in Fig. 5a, yielding nearly 20% CD, confirming the predictions from the previous section as well as previous theoretical estimations24–27. The theoretical predictions for the experimentally measured devices are shown in panel Fig. 5b, demonstrating the same spectral position where CD is maximized, but larger values of CD as compared to the experimental measurements are observed. This discrepancy arises from the small lateral dimensions of the fabricated twisted areas of α-MoO3, which are on the scale of the measured wavelength. In particular, transfer matrix calculations assume infinitely extended surfaces, thereby they do not account for edge effects that arise in small-area exfoliated samples. The slight difference between the resonant position of CD in the two devices is expected due to thicknesses variations of the two adjacent layers differ.

The results of Fig. 5 confirm that twisting of anisotropic bilayers induces a strong chiral response. According to Kirchhoff’s law of thermal radiation30, the preferential circular polarization observed in absorption measurements (red beam path in Fig. 4) should also manifest in thermal emission measurements (blue beam path in Fig. 4), which is confirmed in the following section.

Emission spectroscopy
We used the same experimental setup shown in Fig. 4 for the thermal emission measurements, directly measuring the radiation coming from the sample itself. The sample was placed on a heating stage and its thermal radiation was re-directed towards a mercury cadmium telluride (MCT) detector (see blue beam path). Measuring the polarization state of thermal emission from microscopic samples presents considerable experimental challenges. Most importantly, the signal of the radiation emitted by a microscopic sample is several orders of magnitude smaller than the background radiation from the surrounding and the optical components in the beam path. This makes it difficult to isolate and detect the sample’s thermal signature. To ensure reliable measurements with maximal signal, we focused on Device 2, which had a significantly larger twisted area compared to Device 1, with lateral dimensions of approximately 40 μm (Fig. 1c). Additional challenges in the measurement of thermal emission from microscopic samples include the detector drift, which is on the same order of magnitude as the signal itself, as well as heat-induced mechanical movement of the sample by tens of microns, introducing instabilities. Furthermore, the sublimation temperature of molybdenum oxide is 540°C39, thereby we operated at much lower temperatures to prevent damage of the sample, however this further limited the detectable signal. All aforementioned parameters affected measurement precision and required accurate control of the instrumentation to obtain reliable data. A detailed analysis of these factors is provided in Supplementary Note 3.

The polarization state of the emitted radiation from the twisted bilayer α-MoO3 was characterized using Stokes polarimetry, employing a polarization state analyzer (PSA) – a combination of a linear polarizer and a wave plate – following the method outlined by Nguyen et al.11 and Sabatke et al.40. The emitted radiation from the twisted bilayers is partially polarized and can be fully described by the Stokes vector S=(S0, S1, S2, S3), where S0 represents the total intensity of the emitted light, S1 and S2 quantify the difference in intensity between horizontally and vertically polarized light and diagonally and anti-diagonally polarized light, respectively. S3 characterizes the difference in intensity between right- and left-circularly polarized light, thereby the quantity S3/S0 is the parameter of interest in describing chiral properties of emitted radiation11,12,41–43. Due to the small lateral dimensions of the twisted area of the sample, the measured Stokes parameters contained contributions from the entire microscope field of view that included the twisted area of the sample but also areas of the underlying single flake and that of the bare substrate. Thereby, the component S0 accounts for the total emission from all areas of the sample, while the linear polarization components S1 and S2 had contributions from both the twisted region and the underlying single flake. By contrast, since neither the underlying single α-MoO3 flake nor the substrate exhibit chiral emission, S3, the circular polarization component, arose only from the twisted region which is the only one that breaks inversion-rotation symmetry thereby emitting chiral light.

By using the sample-independent background signal B as a reference in the FTIR emission spectroscopy, we extracted the normalized quantity Se = S/B from measurements with four different PSA configurations (see Supplementary Note 3). From Se, we calculate eS3/eS0 = S3/S0, which is shown in Fig. 6. The quantity S3/S0 must be temperature independent, since it represents an intrinsic property of the emitted light – the difference in emissivity of the two circularly polarized components. To confirm this, we carried out measurements at four different temperatures, namely, 300°C, 350°C, 400°C, and 450°C. As confirmed from Fig. 6, the four measurements overlap, while the small oscillations observed are attributed to the background noise. To reduce the level of noise, we take the average of the four curves, as the bold black curve in Fig. 6.

As expected from Kirchhoff’s law, the spectrum in Fig. 6 is in qualitative agreement with the chiral features in the absorption measurements of Fig. 5a, as well as with the transfer matrix calculations (Fig. 5b). Not being able to use a knife-edge aperture to isolate the twisted region of the sample in emission measurements mean that the measured S0 includes contributions from the entire area of the sample including the un-twisted flakes and the substrate, reducing the magnitude of S3/S0. The inability to focus is a defining difference between thermal emission experiments as discussed in this section compared to the measurements of CD in absorption spectroscopy in the previous section (Fig. 5), where a knife-edge aperture was used. We confirmed this by repeating the absorption measurements while removing the knife-edge aperture (as in emission measurements), and thereby collecting light from the entire region of the sample, which reduced the magnitude of CD, as expected.

Despite experimental restrictions in using an aperture for focusing solely within the active, twisted area of the flakes, we retrieve a maximal value of S3/S0 of approximately 6% (Fig. 6). For reference, recent metasurface-based architectures11,12,42,43 have achieved values of S3/S0 in thermal emission experiments ranging from 25% at wavelengths near 6 μm11 to 83% at wavelengths near 5.3 μm43. Nonetheless, these metasurfaces are composed of geometric shapes that break inversion symmetry, like Z-shapes11,43 or F-shapes42. These approaches require lithographic patterning, whereas the chirality in thermal emission reported here arises from the intrinsic material response of α-MoO3 and does not rely on lithography. Avenues for increasing the measured S3/S0 signal of our twisted bilayers include growth of larger-area flakes, for instance via chemical vapor deposition, as well as careful selection of the thickness of each flake’s thickness and twist angle.

Discussion
In this work, we showed experimentally that unpatterned flakes of van der Waals materials with an in-plane anisotropy can serve as a platform for engineering intrinsic chirality and generating chiral light. Without loss of generality, we demonstrated these properties with α-MoO319–21, however the effect is general and can be observed with other low-dimensional materials as well, for example α-V2O522, as well as their combinations. Both α-MoO3 and α-V2O5 as well as their heterostructures have been recently reported to demonstrate various optical phemomena that originate predominantly from the directional nature of surface phonon polaritons that occur in both materials at mid-IR frequencies34–37,44–47. By contrast, the intrinsic mid-IR chirality and thermally generated chiral light reported here do not rely on polaritonic waves and can be observed in any twisted configuration of in-plane anisotropic materials that have sufficient optical losses.

Despite the unoptimized nature of our flakes, we obtain considerable values of CD reaching 20% in absorption. Although these results already compare with previously reported optimized metamaterial architectures that rely on lithography11,12,42,48–50, they are subject to improvement upon growth of larger-area flakes as well as thickness optimization.

Although thermal emission, in other words incandescence, is by nature unpolarized, unidirectional and incoherent, we demonstrated that twisted, unpatterned bilayers of α-MoO3 can dramatically modify the characteristics of blackbody radiation, emitting chiral thermal radiation. We achieved this by fabricating twisted α-MoO3 bilayers with exfoliation and stacking. Despite challenges related to conducting thermal emissivity measurements of samples with microscopic lateral dimensions and at low-temperatures, we were able to detect and confirm the circular polarization state of the emitted light. This highlights the robustness of twisted bilayer devices and their potential for applications in mid-IR polarization control, mid-IR lighting, chiral sensing and detection. The realization of twisted bilayers does not require any lithography, thereby introducing a simple, planar, and scalable roadmap for chirality engineering beyond the regime of traditional metamaterials and lithography-based meta-devices. The reported values of circular dichroism are primarily limited by the finite lateral dimensions of the flakes rather than intrinsic material constraints; therefore, larger-area fabrication approaches such as chemical vapor deposition can help to achieve even stronger chiral signatures.

Methods
We mechanically exfoliated flakes of α-MoO3 with polydimethylsiloxane-based exfoliation and transfer (X0 retention, DGL type from Gelpak) at 90°C51. Firstly, the bottom flake was transferred onto gold-coated (150 nm) glass and consequently the top flake was transferred onto the bottom flake at the desired twist angle, using an optical microscope which enables rotation and positioning of the flakes. The dielectric permittivity, ϵ, of the batch of α-MoO3 (2D Semiconductors, Bridgman growth technique) used in the devices presented in this article was extracted using FTIR spectroscopy, following the method described in ref. 32. The dielectric permittivity at each frequency is determined by identifying minima in the reflectance spectra near phonon resonances. To recover ϵ(λ) over an extended spectral range, we apply this method to multiple flakes of varying thicknesses – often present on the same substrate after exfoliation – and fit a permittivity model to the extracted values at selected frequencies. These permittivity values serve as the basis for our transfer matrix simulations.

We conducted FTIR micro-spectroscopy measurements using a Bruker Hyperion II microscope coupled with a Bruker Vertex 80 FTIR spectrometer equipped with a MCT detector. A ×36 Cassegrain objective was employed for collection. We utilized a linear ZnSe holographic wire grid polarizer from Thorlabs and a CdSe wave plate from VM-TIM GmbH. The size of the measured area was controlled using the knife-edge aperture of the microscope.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this work, the authors exploit the natural optical anisotropy of van der Waals α-MoO₃ crystals to experimentally demonstrate that twisted bilayer structures break inversion-rotation symmetry, thereby exhibiting intrinsic chirality. Through direct thermal emission measurements of microscopic twisted bilayers, they show that these heterostructures can generate chiral light via incandescence. Notably, the twisted configurations of van der Waals materials eliminate the need for lithographic fabrication, presenting a scalable platform for chiral filters and thermal light sources that extends beyond conventional metamaterial-based architectures. Although there is the demonstrated chirality, the presented result is not that impressive, with an experimentally measured peak chirality of only 0.20 as shown in Figure 4A. Therefore, I cannot accept this manuscript to be published the prestigious journal, like nature communications. Before the authors submitted this work to somewhere, the authors should address the following issues.\n1. The authors need to look at the limited chirality seriously and carry out the possible experiments to improve the chirality to be close to 1, experimental. Without this improvement, this paper has limited impact.\n2. In Figure 5, the authors plotted out the modified S3, which is defined by Eq. (3). This plot is very confusing. Instead, the authors should stick to the standard S3 parameter, which is well defined and well known for the research community. In comparison, the inset of Figure 5 represents the standard S3/S0 for the simulation results. What is the experimentally measured S3/S0?\n3. For Figure 2A, would like to suggest the author to split it into two sub-figures. One sub-figure is on the refractive index, n, along the two anisotropic axis with respect to wavelength. Meanwhile, the other sub-figure is on the absorption coefficient, k.\n4. For Figure 2B and 2C, label it clearly on the figure captions that these results are simulations.", "reviewer_2": "This paper by Enders et al. reports an experimental demonstration of incandescent chiral emission by a twisted layer heterostructure formed by the stacking of alpha molybdenum trioxide. This Van der Walls material exhibits a strong in-plane anisotropy close to 12 microns, due to the Reststrahlen effect. Introducing a (non-trivial) twist angle between adjacent layers of material amounts allows to break mirror symmetry, and therefore induces chirality in absorption and emission.\nThe key aspect of the paper is the experimental demonstration of the effect, that has been already proposed, numerically simulated, optimized and discussed in several of the papers that are indeed referenced in the paper. In that sense, this paper reports original work on a challenging experiment, and represents a noteworthy advance in the field.\nA first set of experiments reports measurements of CD in absorption, and a second set performs the spectroscopy of thermal emission and analysis of the polarization via Stokes polarimetry. Both experiments indeed report some circular dichroism and a non-zero of circular polarization, as displayed by the S3 component of the Stokes vector : the calims are therefore correctly supported by the work reported.\nThe methodology behind both experiments is explicitly and extensively discussed, with detailed explanations of the experimental procedures in the supplementary material, with both numerical simulations and analytical results on the one hand (regarding estimation of CD in bilayer systems of various thicnkesses and twst angles, and experimental procedures and data processing (for the analysis of polarization state in the infrared domain in particular) on the other hand. The authors exhausitvely discuss the limitations of performing infrared measurements on tiny signals, requiring to include the influence of reference and background measurements in their data processing procedure, and explaining how detector drift affect measurement accuracy when performing long acquisitions. The authors make a strong point by taking into account as many sources of undertainties as possible, and it gives a strong credibility to their methodology. In addition, the amount of information displayed is sufficient for the work to be reproduced by readers.\nMy global impression of the paper is positive at this stage, though I have questions and comments for the authors.I may recommend publication of the paper after revision.\n- In the introduction of the paper, the authors claim, refering to previous examples of thermal emission of chiral light : \"their large-scale thermal excitation entails considerable technical challenges as well\". This seems to suggest that the work presented in the paper is somewhat able to overcome this limit, which looks rather unsure, given the limited size of the twisted hetereostructure. Can the authors be more explicit or comment this statement ?\n- The authors state \"Instead of relying on external structural modifications as in the case of metamaterials, we harness the natural, intrinsic in-plane optical anisotropy observed recently in several emerging van der Waals materials...\". This is merely a question of semantics, but I guess that the fabrication of a VdW heterostructure can still be considered as an \"external structural modification\" allowing the emergence of chirality, and not that \"natural\". In that sense, I raise a (modest) respectful dissent in the terminology used in the paper, that I find slightly misleading in its effort to make a (legitimate) distinction between \"chirality from periodic, symmetry-broken metasurface\" and what is achieved in the paper.\n- \"The reported chiral effects additionally remain present even in the case of twisted monolayers, enabling two-dimensional chirality.\" This is most probably true, but is not the point of the paper, and is not even reported : with layers hundreds of nanometer thick, we are very far from this situation. I suggest the authors to clarify in order to remove any ambiguity.\n- It is unclear to me at which extent the authors were able to control (or lucky enough) to identify and find flakes fitting the appropriate thicknesses (between 800 nm and 1 um) optimizing CD, as discussed in their numerical simulations. The total CD, for a given twist angle, seems to be rather strongly dependent on the thicknesses ; which can be a challenge or not depending on how reproducible are the fabrication/exfoliation processes. Can the authors comment on this point.\n- My most important question is about measurements in emission and the definition (and interpretation of normalized S3). I agree that the spectral variations of normalized S3 are reliable in describing the spectral variation of the \"real\" S3. Now with the quantitative aspect, while I understand that providing a clear estimation of the degree of circular polarization of the light exclusively emitted by the flakes is a challenge, it is extremely difficult to interpret a \"modified S3\" with values above 1 - and it feels rather arbitrary. As the authors explain, it is expected that the \"real\" S3 is somewhat less sensitive to external contributions from the reference and background, since chirality is expected only from the sample. Choosing this \"modified S3\" makes it absolutely impossible to compare the plot with the reference plot in inset of S3/S0, which would make still make sense having in mind all the precautions highlighted by the authors in the experimental and data processing procedure. The uncertainties are as well difficult to interpret.\nSo my questions are : what does it mean for this normalized component to be above 1 ? Can the authors provide a measurement of the S3 component with no modification, to have an idea of the DCP of the light emitted by the entire system (including substrate and reference contribution) ? Since the system is based on heating the bulk of the substrate AND the twisted heterostructure, this is the relevant parameter in the hypothetical perspective of making this an actual sourcer of chiral light.\n- In the same line, the inset of Fig 5. is interesting, but a precise value of the maximum expected value of S3/S0 would be interesting to know ; it is not present on the graph, which cannot be compared quantitatively to the other graph because of this modified S3.\n- Also, I find the displayed ellipse a bit misleading, in the sense that the complete state of emitted polarization is not a perfectly polarized state, but has most probably a modest degree of polarization, event when restricted to the emission of the twisted flake only. I humbly suggest that the author remove it.\nTypos :\n-Page 3, \"unitl cells\"\n-Page 10, \"Fig. 5shows\"", "reviewer_3": "In this manuscript, the authors demonstrate that in a twisted double layer of MoO3, chiral thermal emission can be observed without any lithographic patterning requirement. The key idea appears to be valid and the experimental method and analysis employed to demonstrate the same is sound, for the most part (see point 4 below). The work has significant importance for the field and experimental results on such non-lithographic platform is currently lacking. I have a few questions which need to be addressed before I can recommend this manuscript for publication:\n1) Fig. 2A: it is unclear in the manuscript whether this is the measured refractive index for the samples in question? If yes, could you provide details of the measurement method? This is important because typically the same shortcomings (such as larger IR spot size compared to flake size) would make this measurement less accurate.\n2) Figure 2C: Comparing figures 2B and 2C, it appears that the thickness optimization does not really increase the CD. However, there seems to be several combinations of the two thicknesses which lead maxima in CD. While the simulational results look okay, I feel the authors need to provide certain “design rules” based on the physics of the interplay between Fabry Perot modes and symmetry breaking. This will be incredibly useful to the community and will generalize the results to other anisotropic layers.\n3) In the discussion of Figure 4A and B, the authors attribute the discrepancy between experiment and simulation (a multiplicative factor of 2) to the larger IR spot size compared to the flake size. Actually it is very much possible to simulate the setup with actual dimensions using a finite element approach. This will perhaps match the experimental situation closer than the ideal case transfer matrix calculations employed by the authors. I would strongly recommend that the authors include such a calculation since most IR characterization setups currently will suffer from this spot size problem anyway. It will also help identify if the source of discrepancy is something other than the spot size.\n4) The emission data is currently presented for a temperature of 300 degrees C. Although there are experimental difficulties in precise measurements of S3 in this case, I think the variation of thermal emission chirality (S3 spectrum) for a few different temperatures is critical to present the potential of this platform. The reason I ask for this is because the comparison of experiment to simulation in Figure 5 appears a bit shaky since there are several additional spectral features in the experimental data, which are not present in the simulation. Just an overall broad feature seems to be matching."}, "author_response": "Response to Reviewer Comments for Manuscript “Mid-IR chirality and chiral thermal emission through\ntwisting”, by M. Enders, M. Sarkar, E. Klironomou, M. F. Picardi,\nR. Bertini, A. Deeva, G. T. Papadakis\nWe thank all three reviewers for carrying out a comprehensive review of our manuscript and providing constructive\nfeedback. Below, we respond to all reviewer comments (green) and outline corresponding changes to our revised\nmanuscript (orange). In Part A we address a matter raised by all reviewers: that of the selection, physical meaning,\nand amplitude of the experimental observable related to chirality in thermal emission measurements, S . In Part B,\n3\nwe address a point raised by reviewer #1, pertaining to the magnitude of the reported chiral signal and measured\ncircular dichroism. In Part C, we address all other points raised by the reviewers.\nPart A\nUpdated experimental characterization and analysis of S parameter\n3\nchirality in light emission. The reason for presenting its modified version, instead of the standard representation\nthat is S / S , pertains to the experimental challenges in measuring thermal emission from a sample with very small\n3 0\nlateral dimensions. The small size of the sample yields a low emitted signal as compared to the background thermal\nradiation from all optical components in the FTIR instrumentation. In particular, as shown below, and in Fig. S4\nof the revised Supplemental Information of our manuscript, the active, or twisted, area of the flakes does not exceed\nroughly 40% of the field of view as taken with the FTIR microscope.\nFigure 1: Figure S4 of supplemental information – The active (twisted) area of the flakes does\nnot exceed 40% of the field of view of the microscope\nIn relation to this challenge, the following comments were made by the reviewers:\n• Reviewer 1: “… the authors should stick to the standard S3 parameter, which is well defined and well known\nfor the research community. In comparison, the inset of Figure 5 represents the standard S3/S0 for the simulation\nresults. What is the experimentally measured S3/S0?”\n• Reviewer 2: “…I agree that the spectral variations of normalized S3 are reliable in describing the spectral\nvariation of the \"real\" S3. Now with the quantitative aspect, while I understand that providing a clear estimation\nof the degree of circular polarization of the light exclusively emitted by the flakes is a challenge, it is extremely\ndifficult to interpret a \"modified S3\" with values above 1 - and it feels rather arbitrary. As the authors explain,\nit is expected that the \"real\" S3 is somewhat less sensitive to external contributions from the reference and\nbackground, since chirality is expected only from the sample. Choosing this \"modified S3\" makes it absolutely\nimpossible to compare the plot with the reference plot in inset of S3/S0, which would make still make sense having\nin mind all the precautions highlighted by the authors in the experimental and data processing procedure. The\nuncertainties are as well difficult to interpret.\nSo my questions are: what does it mean for this normalized component to be above 1? Can the authors provide\na measurement of the S3 component with no modification, to have an idea of the DCP of the light emitted by\nthe entire system (including substrate and reference contribution)? Since the system is based on heating the bulk of the\nsubstrate AND the twisted heterostructure, this is the relevant parameter in the hypothetical perspective of making\nthis an actual source of chiral light.\nIn the same line, the inset of Fig 5. is interesting, but a precise value of the maximum expected value of S3/S0\nwould be interesting to know; it is not present on the graph, which cannot be compared quantitatively to the\nother graph because of this modified S3.”\n• Reviewer 3: “The emission data is currently presented for a temperature of 300 degrees C. Although there are\nexperimental difficulties in precise measurements of S3 in this case, I think the variation of thermal emission\nchirality (S3 spectrum) for a few different temperatures is critical to present the potential of this platform. The\nreason I ask for this is because the comparison of experiment to simulation in Figure 5 appears a bit shaky since\nthere are several additional spectral features in the experimental data, which are not present in the simulation.\nJust an overall broad feature seems to be matching.”\nAction taken in relation to S\n➔ We have carried out new sets of experimental measurements, and have updated our data analysis. In our revised\nmanuscript, Fig. 6, we now present the standard Stokes parameter: S / S , as all reviewers recommended, and as is\n3 0\ncustomary in reporting the degree of chirality in light emission.\n➔ This resolves the confusion of values of normalized S above unity in our initial submission, raised by reviewer\n3\n#2.\n➔ In addition, we carried out the extraction of S / S at four different temperatures (300, 350, 400 and 450 degrees),\n3 0\nas reviewer #3 recommends, and obtained consistent results across all cases. This demonstrates the validity of our\ncharacterization approach.\n➔ In addition, based on the comment of reviewer #3, in the supplemental material, we present the un-normalized\nparameters S , S , S , S , as a function of temperature. From these measurements, as expected, we see that as\n0 1 2 3\ntemperature increases, the total intensity of emitted light increases (Figure S7, panel A – parameter S ).\n(Supplementary Note 3), but they are also discussed below in a concise manner. We thank the reviewers for raising\nthese points that made us more proficient in carrying our Stokes parameters extraction in light emission from small\nsamples, which improved the quality of our work.\nImprovement of experimental detection of S\n3 0\nemission measurements and address, with much more caution, the sources of noise in the FTIR setup.\nTo achieve this, first, we re-aligned the entire system to ensure that the optical paths for reflection (or absorption)\nand emission fully overlap as they ought. This guarantees that we probe the exact same region of the sample under\nthe microscope in both configurations, thereby reducing the contribution of background relative to the signal.\nWhile the background noise remains larger than the signal, we characterized it in detail and confirmed that it is:\n• additive,\n• sample-independent, and\n• primarily originates from the scanner in the FTIR interferometer.\nIn addition, we identified that:\n• the window of the temperature stage introduces extra noise around 13.5 µm.\n• Importantly, we found that the background, noted as B in our original manuscript and below,\nis stable over time, which allowed us to use it as a reference.\nConsequently, the measured FTIR signal takes the form:\n𝐼 +𝐵 𝐼\n𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑎𝑚𝑝𝑙𝑒\n𝑆𝑖𝑔𝑛𝑎𝑙 = = +1\n𝐹𝑇𝐼𝑅 𝐵 𝐵\nfrom which we can reliably extract S/B (see Supplementary Note 3) and the normalized Stokes parameter S /S ,\n3 0\nsince B cancels out (see revised manuscript).\nBased on the reviewers’ comments about the simulation results presented in the original Fig. 5 of the initial\nmanuscript, we agree that they did not serve for a direct comparison with the initial experiment. In the revised\nmanuscript, the simulation results can be directly compared to the experimental results.\nPart B\nMagnitude of circular dichroism and S as compared to molecular systems and\n3\nprevious generations of metamaterials\nReviewer #1\nIn this work, the authors exploit the natural optical anisotropy of van der Waals α-MoO₃ crystals to experimentally\ndemonstrate that twisted bilayer structures break inversion-rotation symmetry, thereby exhibiting intrinsic chirality.\nThrough direct thermal emission measurements of microscopic twisted bilayers, they show that these\nheterostructures can generate chiral light via incandescence. Notably, the twisted configurations of van der Waals\nmaterials eliminate the need for lithographic fabrication, presenting a scalable platform for chiral filters and thermal\nlight sources that extends beyond conventional metamaterial-based architectures.\nAlthough there is the demonstrated chirality, the presented result is not that impressive, with an experimentally\nmeasured peak chirality of only 0.20 as shown in Figure 4A. Therefore, I cannot accept this manuscript to be\npublished the prestigious journal, like nature communications. Before the authors submitted this work to\nsomewhere, the authors should address the following issues.\n1. The authors need to look at the limited chirality seriously and carry out the possible experiments to improve the\nchirality to be close to 1, experimental. Without this improvement, this paper has limited impact.\nAuthors’ Response 1.1\nWe thank the reviewer for carefully reviewing our manuscript.\nWe take considerable exception to the criticism that the values of peak chirality are not that impressive or small. To\nunderstand this, it is useful to contextualize the value CD of 10% - 20% reported in our manuscript and to compare\nit to both:\na) what is naturally available (e.g. in molecular chiral systems) as well as\nb) what is available with artificial media, e.g. metamaterials and metasurfaces.\nWith respect to these, it is critical to emphasize that:\na) the reported values of CD in our work exceed what is available with natural molecular systems by orders of\nmagnitude and\nb) the introduced design platform of twisted anisotropic layers is radically different from previous-generation\nmetamaterial-based architectures.\nThe novelty of our work lies in that it is the first experimental demonstration of chirality, in any spectral\nrange, in addition to chiral thermal emission, in a design platform completely novel and different from\ntraditional metamaterial- and metasurfaces. Below, we provide references and explain these arguments.\na) Comparison with naturally available chiral substances and molecular systems\nIn molecular systems, the differential absorbance between left- and right-circularly polarized light in the mid-\ninfrared range is typically five orders of magnitude smaller than the absorbance of unpolarized light. Please see:\n[1] L. A. Nafie, Vibrational Optical Activity: Principles and Applications; John Wiley & Sons Ltd. (2011)\n[2] W. Ma, L. Xu, N. A. Kotov et al., Chiral Inorganic Nanostructures, Chemical Reviews 117, 8041-8093 (2017)\n– See, for example, Figs. 4 C, 5F and H, Figs. 6 B, 7 E and F, for DNA-functionalized assemblies.\n[3] C. Yang, Y. Xu, Probing Chiral solute-water hydrogen bonding networks by chirality transfer effects: A\nvibrational circular dichroism study of glycidol in water, The Journal of Chemical Physics, 130, 16 (2009)\nOur achieved CD of 0.2 thus represents a multiple-orders-of-magnitude enhancement over natural systems,\ndemonstrating the effectiveness of twist-induced chirality in bilayer α-MoO3.\nb) Comparison with metamaterial-based architectures\nOptimized metamaterial-based motifs, realized through extensive lithographic patterning, that were heavily\nexplored over the past decades, can indeed achieve CD values close to unity. However, such engineered\nmetamaterials require complex top-down fabrication and design (e.g., multi-layer lithography and sophisticated\nnano-antenna-like geometries). In addition, they operate based on either diffraction and/or the electromagnetic\ncoupling between meta-atoms [B. Wang, J. Zhou, T. Koschny, M. Kafesaki, C. Soukoulis, Chiral Metamaterials:\nSimulations and Experiments, Journal of Optics A: Pure and Appplied Optics 11, 114003 (2009)].\n➔ By contrast, the chirality induced via twisting anisotropic layers, as demonstrated in our manuscript, represents\na radically different material platform that relies on different physics, namely, wave interference, and requires no\nlithographic patterning.\nAdditionally, we note that the majority of previously reported chiral metamaterial designs pertain to the visible and\nnear-IR spectral range. While there exists some volume of experimental works in the spectral range between 4 and\n8 microns (see [4]-[9] below), the spectral range above 11 micrometers has remained largely unexplored, even with\nconventional metamaterials. That spectral range (λ>11 micrometers) is central to applications in thermal\nmanagement, spectroscopy, detection, and others, since the blackbody spectrum at near-room temperatures is\nmaximal there. Our work is the only one, to our knowledge, that introduces a scalable approach to engineering\nchirality in the mid-IR range.\n[4] J. R. Nolen et al., Local Control of Polarization and Geometric Phase in Thermal Metasurfaces, Nature\nNanotechnology 19, 1627 (2024)\n[5] X. Wang et al., Observation of Nonvanishing Optical Helicity in Thermal Radiation from Symmetry-Broken\nMetasurfaces, Science Advances 9, eade4203 (2023),\n[6] A. Nguyen et al., Large circular dichroism in the emission from an incandescent metasurface, Optica 10, 232-\n238 (2023),\n[7] X. Zeng et al., Mid-Infrared Chiral Metasurface Absorbers with Split-Ellipse Structures, Optics\nCommunications 525, 128854 (2022),\n[8] M. S. Mahmud et al., Chiral Plasmonic Metasurface Absorbers in the mid-infrared wavelength range, Optics\nLetters 45, 5382 (2020),\n[9] X. T. Kong et al., Mid-infrared plasmonic circular dichroism generated by graphene nanodisk assemblies, Nano\nLetters 17, 5009 5105 (2017),\nAction taken 1.1\nWe have clarified these points in more detail in the introduction and conclusion of our manuscript, and have cited\nthe aforementioned works [1]-[9].\nPart C\nResponse to all other reviewer comments\nReviewer #1(continuation)\n2. In Figure 5, the authors plotted out the modified S3, which is defined by Eq. (3). This plot is very confusing.\nInstead, the authors should stick to the standard S3 parameter, which is well defined and well known for the research\ncommunity. In comparison, the inset of Figure 5 represents the standard S3/S0 for the simulation results. What is\nthe experimentally measured S3/S0?\nAuthors’ Response 1.2\nThis is a critical point. It is addressed in detail in Part A of this report.\nReviewer #1 (continuation)\n3. For Figure 2A, would like to suggest the author to split it into two sub-figures. One sub-figure is on the refractive\nindex, n, along the two anisotropic axis with respect to wavelength. Meanwhile, the other sub-figure is on the\nabsorption coefficient, k.\nAuthors’ Response 1.3\nWe agree with the reviewer that directly presenting the refractive indices and absorption coefficients along both\naxes of the crystal will improve the clarity and readability.\nAction Taken 1.3\nWe now present the real and imaginary parts of the refractive index separately in Fig. 3 in the revised manuscript.\nReviewer #1 (continuation)\n4. For Figure 2B and 2C, label it clearly on the figure captions that these results are simulations.\nAction Taken 1.4\nWe have completely revised the figures to place greater emphasis on the underlying design principles, while\nensuring that it is clearly indicated that the presented results are simulations.\nReviewer #2\nThis paper by Enders et al. reports an experimental demonstration of incandescent chiral emission by a twisted layer\nheterostructure formed by the stacking of alpha molybdenum trioxide. This Van der Walls material exhibits a strong\nin-plane anisotropy close to 12 microns, due to the Reststrahlen effect. Introducing a (non-trivial) twist angle\nbetween adjacent layers of material amounts allows to break mirror symmetry, and therefore induces chirality in\nabsorption and emission.\nThe key aspect of the paper is the experimental demonstration of the effect, that has been already proposed,\nnumerically simulated, optimized and discussed in several of the papers that are indeed referenced in the paper. In\nthat sense, this paper reports original work on a challenging experiment, and represents a noteworthy advance in\nthe field.\nA first set of experiments reports measurements of CD in absorption, and a second set performs the spectroscopy\nof thermal emission and analysis of the polarization via Stokes polarimetry. Both experiments indeed report some\ncircular dichroism and a non-zero of circular polarization, as displayed by the S3 component of the Stokes vector:\nthe calims are therefore correctly supported by the work reported.\nThe methodology behind both experiments is explicitly and extensively discussed, with detailed explanations of the\nexperimental procedures in the supplementary material, with both numerical simulations and analytical results on\nthe one hand (regarding estimation of CD in bilayer systems of various thicnkesses and twst angles, and\nexperimental procedures and data processing (for the analysis of polarization state in the infrared domain in\nparticular) on the other hand. The authors exhausitvely discuss the limitations of performing infrared measurements\non tiny signals, requiring to include the influence of reference and background measurements in their data\nprocessing procedure, and explaining how detector drift affect measurement accuracy when performing long\nacquisitions. The authors make a strong point by taking into account as many sources of undertainties as possible,\nand it gives a strong credibility to their methodology. In addition, the amount of information displayed is sufficient\nfor the work to be reproduced by readers.\nMy global impression of the paper is positive at this stage, though I have questions and comments for the authors.\nI may recommend publication of the paper after revision.\nAuthors’ Response 2.1\nWe thank the reviewer for their extensive studying of our manuscript.\nReviewer #2 (continuation)\n- In the introduction of the paper, the authors claim, referring to previous examples of thermal emission of chiral\nlight: \"their large-scale thermal excitation entails considerable technical challenges as well\". This seems to\nsuggest that the work presented in the paper is somewhat able to overcome this limit, which looks rather unsure,\ngiven the limited size of the twisted heterostructure. Can the authors be more explicit or comment this statement?\nAuthors’ Response 2.2\nWe agree with the reviewer that this comment, as was stated, was confusing. Both approaches entail challenges;\nLarge-scale (macroscopic) metamaterial-type samples require larger electrical power densities to raise and maintain\ntheir temperature, due to larger lateral dimensions and larger thickness. The micron-scaled surface areas of our\nexfoliated flakes, on the other hand, also entail challenges, specifically in thermal emission detection, as explained\nthoroughly in the manuscript and as reviewer 2 noticed already.\nAction Taken 2.2\nTo avoid misinterpretation and for the sake of conciseness, we have removed this comment.\nReviewer #2 (continuation)\n- The authors state \"Instead of relying on external structural modifications as in the case of metamaterials, we\nharness the natural, intrinsic in-plane optical anisotropy observed recently in several emerging van der Waals\nmaterials...\". This is merely a question of semantics, but I guess that the fabrication of a VdW heterostructure can\nstill be considered as an \"external structural modification\" allowing the emergence of chirality, and not that\n\"natural\". In that sense, I raise a (modest) respectful dissent in the terminology used in the paper, that I find\nslightly misleading in its effort to make a (legitimate) distinction between \"chirality from periodic, symmetry-\nbroken metasurface\" and what is achieved in the paper.\nAuthors’ Response 2.3\nIndeed, we agree that this is a matter of semantics. In traditional metamaterials, a chiral response is achieved with\nsymmetry-broken meta-atoms, composed of conventional materials. That symmetry is broken via lithography. Here,\na chiral response is achieved, instead, by twisting highly anisotropic bilayers with respect to each other.\nAction Taken 2.3\nTo improve clarity, we have replaced the phrase “external structural modifications” with “external lithographic\npatterning along the in-plane directions”, and we hope that the distinction is now clear.\nReviewer #2 (continuation)\n- \"The reported chiral effects additionally remain present even in the case of twisted monolayers, enabling two-\ndimensional chirality.\" This is most probably true, but is not the point of the paper, and is not even reported: with\nlayers hundreds of nanometer thick, we are very far from this situation. I suggest the authors to clarify in order\nto remove any ambiguity.\nAuthors’ Response 2.4\nAlthough the reviewer is correct that the chiral effects remain present even in the limit of monolayers, we agree\nthat this comment does not serve the clarity of the manuscript and could create ambiguity.\nAction Taken 2.4\nWe have removed this comment from the manuscript and have focused on the micron-thick layers of a-MoO ,\n3\nwhich is the range of thicknesses considered in our experiments.\nReviewer #2 (continuation)\n- It is unclear to me at which extent the authors were able to control (or lucky enough) to identify and find flakes\nfitting the appropriate thicknesses (between 800 nm and 1 um) optimizing CD, as discussed in their numerical\nsimulations. The total CD, for a given twist angle, seems to be rather strongly dependent on the thicknesses;\nwhich can be a challenge or not depending on how reproducible are the fabrication/exfoliation processes. Can the\nauthors comment on this point.\nAuthors’ Response 2.5\nWe thank the reviewer for raising this important point. In practice, we identify candidate flakes in the 800 nm to\n1000 nm thickness range directly under an optical microscope. Thick flakes tend to have larger lateral dimensions,\nwhich makes them easier to spot, while thinner ones can be distinguished by their slightly different interference\ncolors. Visual inspection provides a reliable indication of when to stop the exfoliation process.\nPromising flakes are then measured by AFM to determine their exact thickness. Based on these measured values,\nwe select the appropriate twist angle guided by our simulations. While adjusting the twist angle is relatively\nstraightforward in our setup, the main experimental challenge lies in transferring one flake on top of another and\nensuring sufficient adhesion between them.\nIn this work, our primary aim was to establish a proof-of-concept demonstration of twist-induced chirality, rather\nthan to target the exact thickness that maximizes CD. As such, we did not attempt to optimize systematically for\nthe highest possible CD.\nAction Taken 2.5\nA similar comment was raised by reviewer #3. Thereby, we decided to dedicate a section in our revised manuscript\nwhere we provide concrete design rules for inducing chirality based on the considered principle: twisting anisotropic\nbilayers. In the revised manuscript, we clearly explain the role of each layer, the role of loss and dichroism, as well\nas that if birefringence. Please see updated Figure 2, and corresponding section “Design rules for circular dichroism\nin twisted bilayers”.\nReviewer #2 (continuation)\n- My most important question is about measurements in emission and the definition (and interpretation of\nnormalized S3). I agree that the spectral variations of normalized S3 are reliable in describing the spectral variation\nof the \"real\" S3. Now with the quantitative aspect, while I understand that providing a clear estimation of the degree\nof circular polarization of the light exclusively emitted by the flakes is a challenge, it is extremely difficult to\ninterpret a \"modified S3\" with values above 1 - and it feels rather arbitrary. As the authors explain, it is expected\nthat the \"real\" S3 is somewhat less sensitive to external contributions from the reference and background, since\nchirality is expected only from the sample. Choosing this \"modified S3\" makes it absolutely impossible to compare\nthe plot with the reference plot in inset of S3/S0, which would make still make sense having in mind all the\nprecautions highlighted by the authors in the experimental and data processing procedure. The uncertainties are as\nwell difficult to interpret.\nSo my questions are: what does it mean for this normalized component to be above 1? Can the authors provide\na measurement of the S3 component with no modification, to have an idea of the DCP of the light emitted by\nthe entire system (including substrate and reference contribution)? Since the system is based on heating the bulk of the\nsubstrate AND the twisted heterostructure, this is the relevant parameter in the hypothetical perspective of making\nthis an actual source of chiral light.\n- In the same line, the inset of Fig 5. is interesting, but a precise value of the maximum expected value of S3/S0\nwould be interesting to know ; it is not present on the graph, which cannot be compared quantitatively to the\nother graph because of this modified S3.\nAuthors’ Response 2.6\nThese are critical points. They are all addressed in detail in Part A of this report.\nReviewer #2 (continuation)\n- Also, I find the displayed ellipse a bit misleading, in the sense that the complete state of emitted polarization is\nnot a perfectly polarized state, but has most probably a modest degree of polarization, event when restricted to the\nemission of the twisted flake only. I humbly suggest that the author remove it.\nAction Taken 2.7\nWe agree. The polarization ellipse is removed in the updated manuscript.\nReviewer #2 (continuation)\nTypos:\n-Page 3, \"unitl cells\"\n-Page 10, \"Fig. 5shows\"\nAction Taken 2.8\nThey are corrected in the revised manuscript.\nReviewer #3\nIn this manuscript, the authors demonstrate that in a twisted double layer of MoO3, chiral thermal emission can be\nobserved without any lithographic patterning requirement. The key idea appears to be valid and the experimental\nmethod and analysis employed to demonstrate the same is sound, for the most part (see point 4 below). The work\nhas significant importance for the field and experimental results on such non-lithographic platform is currently\nlacking. I have a few questions which need to be addressed before I can recommend this manuscript for\npublication:\n1) Fig. 2A: it is unclear in the manuscript whether this is the measured refractive index for the samples in\nquestion? If yes, could you provide details of the measurement method? This is important because typically the\nsame shortcomings (such as larger IR spot size compared to flake size) would make this measurement less\naccurate.\nAuthors’ Response 3.1\nWe thank the reviewer for carefully studying our manuscript. Indeed, these are our own measurements of the\nrefractive index of the samples used. The reviewer is correct; measuring the refractive index of micrometer-wide\nflakes at IR frequencies is a challenge. We have developed a comprehensive method to overcome this challenge,\nwhich can be found here: https://www.researchsquare.com/article/rs-7037943/v1. Please note that this method and\nmanuscript is currently also under review. In that work, the challenge of measuring flakes with sizes smaller than\nthe IR beam is discussed extensively.\nAction Taken 3.1\nIn our revised measurements, we have clarified that these are measured values of the refractive index of a-MoO ,\n3\nand provided some details on the method used. We have also cited the method.\nReviewer #3 (continuation)\n2) Figure 2C: Comparing figures 2B and 2C, it appears that the thickness optimization does not really increase the\nCD. However, there seems to be several combinations of the two thicknesses which lead maxima in CD. While the\nsimulational results look okay, I feel the authors need to provide certain “design rules” based on the physics of the\ninterplay between Fabry Perot modes and symmetry breaking. This will be incredibly useful to the community and\nwill generalize the results to other anisotropic layers.\nAuthors’ Response 3.2\nWe thank the reviewer for these observations, and we agree that a set of design rules will improve the quality of the\nmanuscript.\nAction Taken 3.2\nWe have introduced a section solely devoted to the design rules for maximizing CD. In the section “Design rules\nfor circular dichroism in twisted bilayers”, we now explain clearly identify the requirements for inducing high-CD\nin twisted bilayers: high birefringence in the bottom flake, dichroism in the top flake, twisting for symmetry\nbreaking, and proper thickness selection to maximize interference.\nReviewer #3 (continuation)\n3) In the discussion of Figure 4A and B, the authors attribute the discrepancy between experiment and simulation\n(a multiplicative factor of 2) to the larger IR spot size compared to the flake size. Actually it is very much possible\nto simulate the setup with actual dimensions using a finite element approach. This will perhaps match the\nexperimental situation closer than the ideal case transfer matrix calculations employed by the authors. I would\nstrongly recommend that the authors include such a calculation since most IR characterization setups currently will\nsuffer from this spot size problem anyway. It will also help identify if the source of discrepancy is something other\nthan the spot size.\nAuthors’ Response 3.3\nWe thank the reviewer for this comment, which is indeed important. Instead of investigating the source of the\ndiscrepancy using numerical tools, we directly verified that it primarily originates from the small size of the flakes.\nBelow, we present microscope images of two flakes of a-MoO with drastically different lateral dimensions,\n3\nexfoliated onto the same gold substrate. As can be seen from the large flake with lateral dimensions approaching\n150 microns along the x-axis of the crystal (panel a), the transfer matrix calculations agree with the experimentally\nmeasured reflection (panel b). By contrast, the smaller flake (panel c), with lateral dimensions nearly 40 microns\nalong the x-axis of the crystal, yields considerable disagreement with the transfer matrix method (panel d). We note\nthat the thickness of these flakes was determined with atomic force microscopy, and the reference FTIR\nmeasurement for both flakes pertains to the same gold surface.\nWe have verified these findings in a plethora of additional flakes, measured for the sake of another ongoing work\nthat can be found in: https://www.researchsquare.com/article/rs-7037943/v1; the disagreement with the transfer\nmatrix consistently increases as the lateral dimensions of the flake decrease.\nAs the reviewer accurately states, this is a well-known and significant challenge in mid-IR photonics. Additional\nfactors that contribute to discrepancies between theory (transfer matrix) and experiments, especially in the case of\nstacked and twisted flakes, pertain to each flake’s uniformity - especially the top flake of the twisted bilayer - as\nwell as small deviations of the gold substrate from being a perfect reflector.\nAction Taken 3.3\nWe clarify these points in the revised manuscript.\nReviewer #3 (continuation)\n4) The emission data is currently presented for a temperature of 300 degrees C. Although there are experimental\ndifficulties in precise measurements of S3 in this case, I think the variation of thermal emission chirality (S3\nspectrum) for a few different temperatures is critical to present the potential of this platform. The reason I ask for\nthis is because the comparison of experiment to simulation in Figure 5 appears a bit shaky since there are several\nadditional spectral features in the experimental data, which are not present in the simulation. Just an overall broad\nfeature seems to be matching.\nAuthors’ Response 3.4\nWe thank the reviewer for this comment. The points raised by the reviewer are all addressed in Part A of this report."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The manuscript has been improved significantly. For the response to Reviewer #1 Response 1.1 and Action 1.1, would like to suggest the authors to make a benchmarking figure of this paper, with respect to the References 1-9, in terms of chirality and wavelength range for different designs.", "reviewer_2": "I would like first to thank the authors for the considerable amount of efforts they put in improving their experimental procedure, their derivation of a more understandable metric of S3/S0 - i also highlight the detailed and convincing explanation of their experimental procedures. I do believe the methodology is sound and provided with enough detail to be reproduced.\nA strong point of the paper is now to consistently retrieve in all measurements in absorption and emission the similar expected bump in circular dichroism expected from the simulations. It is however difficult to escape the fact that the measured circular dichroism in emission reaches probably a maximum of around 0.05 only - the text of the paper refers to a qualitative agreement without mentioning explicitly the max value of S3/S0.\nTherefore, the strongest point of the paper cannot really be the absolute value of observed CD ; but there is very interesting matter in the design/engineering part. These elements support a mixed picture of the potential impact of the paper. I would be happy to provide a more positive answer with additional elements of discussion that would validate in more depth their approach in CD engineering.\nIn the part of the paper intitled « Design rules for circular dichroism in twisted bilayers », the authors spend a considerable amount of time discussing CD optimization in numerical situations that do not correspond to their experimental devices 1 and 2, by a far amount. On fig 2, I see simulations with d1=0.2um and d2 = 2 um, while on fig 3, we have d1=0.19 um and d2=2 um (I am not sure why these two have to be different), and it is clear that the experimental devices work with d1=0.6 um and 0.8 um and d2=1.1 um or 0.85 um. The reason is clarified in their rebuttal letter :\n« […] Promising flakes are then measured by AFM to determine their exact thickness. Based on these measured values, we select the appropriate twist angle guided by our simulations. While adjusting the twist angle is relatively straightforward in our setup, the main experimental challenge lies in transferring one flake on top of another and ensuring sufficient adhesion between them.\nIn this work, our primary aim was to establish a proof-of-concept demonstration of twist-induced chirality, rather than to target the exact thickness that maximizes CD. As such, we did not attempt to optimize systematically for the highest possible CD. »\nIt took me quite some time to fully understand that the actual degree of freedom that the authors use to maximize the highest obtainable CD is the twist angle, once they have the info of the flakes thicknesses. While I understand Fig 2 as a general discussion on the physical vision of the situation (dichroic emitter+ waveplate), Fig 3 is, in my opinion, confusing - it could be used to actually simulate the impact of twist angle for the actual thicknesses used in devices 1 and 2, therefore showing at which extent, even for modest expected CD, the authors do try to maximize CD in their actual samples, and not in hypothetical ones. I do think that the statements in the rebuttal letter are essential to clearly understand the progression from the first paragraph « Design rules… » to the actual discussion « Absorption spectroscopy… » in the next section. I humbly suggest the authors to further clarify the connection between these two parts by writing more explicitly what they do indeed use as degrees of freedom to engineer circular dichroism, and to maybe complete FIg3 with simulations used to select the appropriate twist angle, as suggested in the rebuttal letter.\nMore comments :\n- The « Design rules… » part is rather hard to follow at some extent. One reason is that I strongly suspect that some « kappa » are sometimes replaced with « k » such as in « In this idealized system, since k2,y = n1,y = 0, by misaligning the in-plane crystal axe of the layers by an in-plane rotation of angle α … ». I suggest the authors to carefully proofread this part of the paper.\n- I sincerely think that some parts of this discussion are unnecessarily complex. It is sometimes because of the phrasing :\n« When the bottom layer exhibits in-plane dichroism (κ2,x ̸= κ2,y), it emits preferentially in either the x or y direction. » : i\nsuppose « emits preferentially linearly polarized light either along the x or y direction » would be more appropriate.  This\ncomment also highlights that, in the same way that the authors describe the top layer as the « quarter wave plate » of their\nsystem, they could also as well describe their bottom layer as an absorbing polarizer - wire grid polarizers in the IR for\ninstance, can emit linearly polarized light when heated, see https://doi.org/10.1038/s41467-021-21752-w for instance). The\ncombination of a quarter wave plate and an absorbing polarizer at 45° of its axis is…a circular polarizer. The concept of\n« lossy dichroic emitter » makes sense in this emission picture, but the definition of having very anisotropic in-plane losses\nis the very definition of a simple, absorbing polarizer. The key ingredients for this scheme to operate « ideally » do not\nrequire to assume n1,y=n2,y=0 -- I do think there is a loss of generality when assuming such an « exotic » condition that\ndoes not fit what is discussed next.\nMaybe a clearer way to formulate everything is to use real and imaginary parts of the permittivity instead of the complex\nindex of refraction. The birefringence of the top layer juste requires a notable difference in real part of the permittivity along x\nand y (which of course translates into a difference in real part of the optical index).\nLossy dichroic medium requires a strong difference in the imaginary part of the permittivity along x and y - it is slightly\ndifferent from looking for a difference in kappa x and kappa y. These quantities are misleadingly attributed to optical losses :\n« the role of the optical loss in each layer – κ1,x - and κ2,x. […] ». The case of perfect, lossless metals, is the illustration of\nthe difference between optical losses and attenuation through evanescence. I do agree with the rest of the discussion\nregarding the fact that some balance has to be found to optimize absorption within the bottom layer, which is equivalent to\nlooking for a critical coupling condition.\nI do believe the whole discussion would be more straightforward and convincing by sticking to this vey well known and\nunderstandable situation of a combination of linearly polarized emission then quarter wave plate without the need to\nintroduce abstract zero-index conditions that drives the reader away from the key message : alpha MoO3 is a material that\ncan provide both contrasts in real and imaginary permittivities.\n- Finally, the authors conclude their measurements by experiments performed at various temperatures, where they do not\nobserved a change in their reported, small DCP. They write By contrast, since neither the underlying single α-MoO3 flake\nnor the substrate exhibit chiral emission, S3, the circular polarization component, arised arose only from the twisted region\nwhich is the only one that breaks inversion-rotation symmetry thereby emitting chiral light. »  I agree on this statement, but it remains fuzzy what the twisted region is. Also since the reported S3/S0 is small, it would be extremely interesting to compare the \"size\" of this twisted region favoring absorption of circularly polarized light compared to the size of the whole volume of absorption (from simulations perspective).\nIn order to support their claim, and to reconnect the experimental results with their whole engineering/design procedure, and\nto provide a strong argument to explicitly illustrate why the CD is low experimentally, I humbly suggest the authors to\ncompute a map of the local rate of absorption within their stack (product of squared modulus of the field times imaginary part\nof the permittivity), in order to visualize where, exactly, absorption of circular polarized light occur in the system, and where\nthe rest of absorption occur. By showing on a map that, using the best twist angle for given thicknesses of the flakes) the\nauthors manage to slightly better localize absorption of right-circularly polarized light in the bottom layer, the authors would\nstrongly support the concept of a bottom absorbing layer on top of a waveplate retarder, with also an illustration,\nthrough reciprocity, of the unbalance between signal and background in their system.", "reviewer_3": "The authors have addressed my conerns and the results are significant to the field. I support the publication of this manuscript."}, "author_response": "Response to reviewer comments (second round of review) of manuscript “Mid-IR chirality and chiral thermal emission through twisting”, by M. Enders, M. Sarkar, E. Klironomou, M. F. Picardi, R. Bertini, A. Deeva, G. T. Papadakis\nWe thank all three reviewers for carrying out a second round of comprehensive review of our manuscript and providing constructive feedback. Below, we respond to reviewer comments (green) and outline corresponding changes to our revised manuscript (orange).\nReviewer #1\nThe manuscript has been improved significantly. For the response to Reviewer #1 Response 1.1 and Action 1.1,\nwould like to suggest the authors to make a benchmarking figure of this paper, with respect to the References 1-9,\nin terms of chirality and wavelength range for different designs.\nAuthors’ Response\nWe thank the reviewer for reviewing our manuscript a second time. With respect, we find that devoting a whole\nfigure to prior art, benchmarking our work with respect to others in terms of design, wavelength range, and values\nof CD may be more appropriate for a review article, whereas our work represents original work. Most importantly,\nour work is the only one reporting chirality in thermal emission at wavelengths above 7 micrometers, thereby\ncomparing with different wavelength ranges would go beyond the scope of the manuscript.\nAction taken\nè In the introduction of our revised manuscript, as a reference to the reader, we quoted the values of CD observable\nwith naturally occurring molecular substances (References 1-3 as mentioned by the reviewer) as compared to those\nreported within our manuscript (in the section Absorption Spectroscopy).\nè In the section Emission Spectroscopy, we have identified the most relevant thermal emission experiments\nconducted with metamaterials and metasurfaces (from References 4-9 as mentioned by the reviewer, as well as\nothers recently published ones), and have quoted the values of measured S /S within the text. These values can be\n3 0\ndirectly contrasted to our measurements (Fig. 6).\nWe once again thank the reviewer for their constructive feedback.\nReviewer #2\nI would like first to thank the authors for the considerable amount of efforts they put in improving their\nexperimental procedure, their derivation of a more understandable metric of S3/S0 - i also highlight the detailed\nand convincing explanation of their experimental procedures. I do believe the methodology is sound and provided\nwith enough detail to be reproduced.\nAuthors’ Response\nWe thank the reviewer for providing comprehensive comments for our manuscript and for acknowledging the\nsignificant amount of work we have carried out to improve it.\nReviewer #2 (continuation)\nA strong point of the paper is now to consistently retrieve in all measurements in absorption and emission the\nsimilar expected bump in circular dichroism expected from the simulations. It is however difficult to escape the\nfact that the measured circular dichroism in emission reaches probably a maximum of around 0.05 only - the text\nof the paper refers to a qualitative agreement without mentioning explicitly the max value of S3/S0..\nTherefore, the strongest point of the paper cannot really be the absolute value of observed CD;\nAuthors’ Response\nIn relation to the magnitude of S /S , we have already addressed this point in the first round of reviews, since it was\n3 0\nraised by reviewer #1. In the end of the present document (Part B), we append our previous responses to the initial\nfeedback we received. There, we addressed:\nè The novelty of our work in relation to previous works (see below references A, B, C). We emphasize\nthat our work is the first and only one we are aware of where measurements of thermal emission from\nmicroscopic flakes of a van der Waals material are conducted, and inside a microscope.\nè The range of CD reported in naturally occurring molecular systems is at least three orders of\nmagnitudes smaller and conventional metamaterial designs require significant efforts in lithography.\nè There is a scarcity of works that have conducted chiral thermal emission measurements in wavelengths\nlarger than 4 um – only few papers exist to our knowledge (see Refs. A-C below).\nè There is absence of any previous work reporting chiral thermal emission in the wavelength range near\n10-13 um, where the blackbody emission is maximized, and its technological relevance.\nReferences\n[A] A. Nguyen et al., Large circular dichroism in the emisión from an incandescent metasurface, Optica (2023)\nè Wavelength range: 4-8 um, Max. reported S /S : approximately 40% - macroscopic samples\n3 0\n[B] J. R. Nolen et al., Local Control of Polarization and Geometric Phase in Thermal Metasurfaces, Nature\nNanotechnology (2024)\nè Wavelength range: 3-5 um, Max. reported S /S : approximately 38% - macroscopic samples\n3 0\n[C] K. Sun et al., Circularly polarized thermal emission driven by chiral flatbands in monoclinic metasurfaces,\nScience Advances (2025) –\nè Wavelength range: 4-5 um, Max. reported S /S : approximately 83% - macroscopic samples\n3 0\nAction taken\nPlease see action taken with respect to the comment from Reviewer 1, above.\nReviewer #2 (continuation)\n… but there is very interesting matter in the design/engineering part. These elements support a mixed picture of\nthe potential impact of the paper. I would be happy to provide a more positive answer with additional elements of\ndiscussion that would validate in more depth their approach in CD engineering.\nIn the part of the paper intitled « Design rules for circular dichroism in twisted bilayers », the authors spend a\nconsiderable amount of time discussing CD optimization in numerical situations that do not correspond to their\nexperimental devices 1 and 2, by a far amount. On fig 2, I see simulations with d1=0.2um and d2 = 2 um, while\non fig 3, we have d1=0.19 um and d2=2 um (I am not sure why these two have to be different), and it is clear that\nthe experimental devices work with d1=0.6 um and 0.8 um and d2=1.1 um or 0.85 um. The reason is clarified in\ntheir rebuttal letter:\n« […] Promising flakes are then measured by AFM to determine their exact thickness. Based on these measured\nvalues, we select the appropriate twist angle guided by our simulations. While adjusting the twist angle is\nrelatively straightforward in our setup, the main experimental challenge lies in transferring one flake on top of\nanother and ensuring sufficient adhesion between them.\nIn this work, our primary aim was to establish a proof-of-concept demonstration of twist-induced chirality, rather\nthan to target the exact thickness that maximizes CD. As such, we did not attempt to optimize systematically for\nthe highest possible CD. »\nAuthors’ Response\nWe thank the reviewer for comprehensively studying the new section of our manuscript on “Design Rules”.\nThe reason why the numerical examples in Fig. 2 of our manuscript do not correspond to the experimental devices\na-MoO3) is that we aimed to compose the “Design Rules” section in a didactic manner, using a materials-agnostic\napproach, as is customary. Our aim is to explain to the reader that the conducted experiments are just one possible\nway of achieving chiral thermal emission with twisted bilayers, and to indicate that similar chiral emission results\ncould be achieved with other in-plane anisotropic materials that have birefringence (Δn=n -n ) and dichroism\nx y\n(Δk=κ -κ ). It is for this reason that in Fig. 2 we carry out a broad parameter sweep over these parameters, n , n ,\nx y x y\nκ , κ as well as the twist angle and respective thicknesses, rather than focusing on a specific material. We consider\nx y\nit to be the most didactic approach.\nΤhe thicknesses selected for Figs. 2 and 3 are almost identical. The minor modification by 0.01 um in d1 was carried\nout in order to present optimized results in Fig. 3.\nAs the reviewer explains accurately, the reason why the experimental devices have thicknesses that differ from the\noptimal ones is because it is challenging to target specific a-MoO3 thicknesses with exfoliation. This is already\nclarified in the manuscript.\nAction taken\nIn our revised manuscript, the thicknesses in Figs. 2 and 3 are now identical (d1 is now equal to 0.2um in both\nfigures), as per the reviewer’s recommendation. As expected, since d1 was only modified by 5%, the results look\nidentical to the previous Fig. 3.\nReviewer #2 (continuation)\nIt took me quite some time to fully understand that the actual degree of freedom that the authors use to maximize\nthe highest obtainable CD is the twist angle, once they have the info of the flakes thicknesses. While I understand\nFig 2 as a general discussion on the physical vision of the situation (dichroic emitter+ waveplate), Fig 3 is, in my\nopinion, confusing - it could be used to actually simulate the impact of twist angle for the actual thicknesses used\nin devices 1 and 2, therefore showing at which extent, even for modest expected CD, the authors do try to\nmaximize CD in their actual samples, and not in hypothetical ones\n. I do think that the statements in the rebuttal letter are essential to clearly understand the progression from the\nfirst paragraph « Design rules… » to the actual discussion « Absorption spectroscopy… » in the next section. I\nhumbly suggest the authors to further clarify the connection between these two parts by writing more explicitly\nwhat they do indeed use as degrees of freedom to engineer circular dichroism, and to maybe complete FIg3 with\nsimulations used to select the appropriate twist angle, as suggested in the rebuttal letter.\nAuthors’ Response\nFigure 3 presents theoretical predictions with twisted flakes of a-MoO3 with optimized thicknesses, unlike the\nexperiment where we have little control over the thickness of the flakes. The calculations in Fig. 3 are carried out\nusing experimentally measured refractive indices of a-MoO3. We find it important that Fig. 3 remains unchanged,\nin order to clearly address to the reader what is the maximal CD that can be obtained with this material.\nAction taken\nIn our revised manuscript, we have clarified that the results in Fig. 3 pertain to calculations that were restricted to\noptimal thicknesses for maximizing CD.\nWe have also followed the reviewer’s recommendation and commented on the connection between the “Design\nRules” section with the next (experimental) ones, explicitly stating that we use the twist angle as a degree of\nfreedom.\nReviewer #2 (continuation)\nMore comments :\n- The « Design rules… » part is rather hard to follow at some extent. One reason is that I strongly suspect that\nsome « kappa » are sometimes replaced with « k » such as in « In this idealized system, since k2,y = n1,y = 0, by\nmisaligning the in-plane crystal axe of the layers by an in-plane rotation of angle α … ». I suggest the authors to\ncarefully proofread this part of the paper.\nAuthors’ Response\nThis was indeed a typo. We thank the reviewer. We have proofread the section on Design Rules and there was no\nother typo.\nAction taken\nWe have corrected the typo.\nReviewer #2 (continuation)\n- I sincerely think that some parts of this discussion are unnecessarily complex. It is sometimes because of the\nphrasing : «When the bottom layer exhibits in-plane dichroism (κ2,x ≠ κ2,y), it emits preferentially in either the x\nor y direction. » : i suppose « emits preferentially linearly polarized light either along the x or y direction » would\nbe more appropriate. This comment also highlights that, in the same way that the authors describe the top\nlayer as the « quarter wave plate » of their system, they could also as well describe their bottom layer as an\nabsorbing polarizer - wire grid polarizers in the IR for instance, can emit linearly polarized light when heated,\nsee https://doi.org/10.1038/s41467-021-21752-w for instance). The combination of a quarter wave plate and an\nabsorbing polarizer at 45° of its axis is…a circular polarizer. The concept of « lossy dichroic emitter » makes\nsense in this emission picture, but the definition of having very anisotropic in-plane losses is the very definition of\nan absorbing polarizer. The key ingredients for this scheme to operate « ideally » do not require to assume\nn1,y=n2,y=0 -- I do think there is a loss of generality when assuming such an « exotic » condition that does not fit\nwhat is discussed next.\nAuthors’ Response\nWe thank the reviewer for providing an alternative description for the lossy dichroic emitter. We agree that this\nsection can be shortened and simplified.\nAction taken\nIn our revised manuscript:\nè we have added the phrase “absorbing polarizer” as an alternative description of the lossy dichroic emitter,\nè we have added the phrase in relation to emission of linearly polarized light, and\nè we have slightly shortened and simplified the section on Design Rules.\nReviewer #2 (continuation)\nMaybe a clearer way to formulate everything is to use real and imaginary parts of the permittivity instead of the\ncomplex index of refraction. The birefringence of the top layer juste requires a notable difference in real part of\nthe permittivity along x and y (which of course translates into a difference in real part of the optical index).\nLossy dichroic medium requires a strong difference in the imaginary part of the permittivity along x and y - it is\nslightly different from looking for a difference in kappa x and kappa y. These quantities are misleadingly\nattributed to optical losses : « the role of the optical loss in each layer – κ1,x - and κ2,x. […] ». The case of\nperfect, lossless metals, is the illustration of the difference between optical losses and attenuation through\nevanescence. I do agree with the rest of the discussion regarding the fact that some balance has to be found to\noptimize absorption within the bottom layer, which is equivalent to looking for a critical coupling condition.\nI do believe the whole discussion would be more straightforward and convincing by sticking to this vey well\nknown and understandable situation of a combination of linearly polarized emission then quarter wave plate\nwithout the need to introduce abstract zero-index conditions that drives the reader away from the key message :\nalpha MoO3 is a material that can provide both contrasts in real and imaginary permittivities.\nAuthors’ Response\nThe selection of refractive indices over permittivities is intentional: There is a very large number of recent\npublications on a-MoO3 demonstrating exotic effects (cited in our manuscript), all arising from the hyperbolicity\nof this material (Re(ε ) \times Re(ε )<0). By contrast, the results of our manuscript are unrelated to hyperbolic\nx y\nmaterials. We feel that diverting the discussion to permittivities instead of refractive indices could mislead the\nreader into believing that chirality is only achievable with the condition Re(ε ) \times Re(ε )<0, which is not true –\nx y\nplease see Fig. 2 – the results of the manuscript are more general than that.\nThe zero-index discussion is merely a simplification of an otherwise quite complex situation. In addition, setting\nthe index to zero does not reduce the generality of the concept discussed. Diverting from the zero-index condition\nintroduces an additional phase upon propagation, which is well-understood.\nReviewer #2 (continuation)\n- Finally, the authors conclude their measurements by experiments performed at various temperatures, where they\ndo not observed a change in their reported, small DCP. They write By contrast, since neither the underlying single\nα-MoO3 flake nor the substrate exhibit chiral emission, S3, the circular polarization component, arised arose only\nfrom the twisted region which is the only one that breaks inversion-rotation symmetry thereby emitting chiral\nlight. » I agree on this statement, but it remains fuzzy what the twisted region is. Also since the reported\nS3/S0 is small, it would be extremely interesting to compare the \"size\" of this twisted region favoring absorption\nof circularly polarized light compared to the size of the whole volume of absorption (from simulations\nperspective).\nAuthors’ Response\nWe respectfully do not believe that it “remains fuzzy” what the twisted region is. It is shown in Fig. 1C of the main\ntext of our manuscript, Fig. S4 of the supplemental material of our manuscript, and it was also discussed in Part.\nA of the initial response to reviewer comments, appended in the end of the present document.\nIn relation to the second comment about the size of the twisted region, it has been addressed in: Author’s Response\n3.3 in our initial response to reviewer comments, appended in the end of the present document. The action taken to\nimprove our manuscript is also discussed there.\nReviewer #2 (continuation)\nIn order to support their claim, and to reconnect the experimental results with their whole engineering/design\nprocedure, and to provide a strong argument to explicitly illustrate why the CD is low experimentally, I humbly\nsuggest the authors to compute a map of the local rate of absorption within their stack (product of squared\nmodulus of the field times imaginary part of the permittivity), in order to visualize where, exactly, absorption of\ncircular polarized light occur in the system, and where the rest of absorption occur. By showing on a map that,\nusing the best twist angle for given thicknesses of the flakes) the authors manage to slightly better localize\nabsorption of right-circularly polarized light in the bottom layer, the authors would strongly support the concept\nof a bottom absorbing layer on top of a waveplate retarder, with also an illustration, through reciprocity, of the\nunbalance between signal and background in their system.\nAuthors’ Response\nThe dependence of CD on the twist angle is shown in Fig. 3 of our manuscript. Given CD remains relatively high\nfor almost all twist angles between 0 and 90 degrees (but not equal to neither) as shown in panel C of Fig. 3, the\ntwist-angle dependence isn’t strong for the range of thicknesses considered. This is expected and can be understood\nusing symmetry arguments: as long as the twist angle isn’t zero, mirror and rotational symmetries are broken, hence\nthe chiral response is expected and well-understood. Thereby, we do not believe that more simulation results are\nnecessary to support our claims.\nFinally, the S3/S0 reported in emission is not small if one considers the size of the flakes that we measure. The\nmagnitude of reported CD is also not small as compared to both previous generation metamaterials and biological\nchiral substances. Please see Part B of the initial response letter appended with this document.\nAction taken\nIn the end of the section “Emission spectroscopy” of our manuscript, we have added discussion about this issue."}, {"round": 3, "reviewer_comments": {"reviewer_2": "I thank once again for the time and effort the authors put into their manuscript. I understand their different points, and do not have major concerns. I can recommend publicaton, similarly to other reviewers.\nA short comment on the identification of the twisted region, because it is obvious that my comment was also quite \"fuzzy\" and was not clear enough, my sincere apologies. It is clear that the chiral emission comes from the region where the two flakes are twisted and stacked on top of each other. My point was to try to connect the results obtained with Devices 1 and 2 with the engineering/design procesure described in the first part of the manuscript : the first part suggests maximizing polarized emission form the botton flake, so it becomes phase shifted when propagating through the top flake. My comment was on the possibility for the authors to elucidate which part of the stack contribute to chiral emission using reciprocity arguments and simulation\n(does it originate from the top or bottom flake, at which depth ? - the question was not about where in the lateral region in the whole field of view of the microscope).\nThe new version of the manuscript does not study in more details the behavior of the devices, but this is not a big deal as it is not a fundamental point for the claims of the paper : I agree that the reported findings and results are in line with the main claims, and do not have further comment."}, "author_response": "Response to Reviewer Comments (third round of review) for Manuscript “Mid-infrared chirality and chiral thermal emission from twisted α-MoO ”, by M. T. Enders, M. Sarkar, E. Klironomou, M. F. Picardi,\nWe thank Reviewer #2 for extensively studying our manuscript and providing constructive feedback. Below we respond to the final comments of Reviewer #2 (green).\nReviewer #2\nI thank once again for the time and effort the authors put into their manuscript. I understand their different points,\nand do not have major concerns. I can recommend publicaton, similarly to other reviewers.\nA short comment on the identification of the twisted region, because it is obvious that my comment was also quite\n\"fuzzy\" and was not clear enough, my sincere apologies. It is clear that the chiral emission comes from the region\nwhere the two flakes are twisted and stacked on top of each other. My point was to try to connect the results obtained\nwith Devices 1 and 2 with the engineering/design procesure described in the first part of the manuscript : the first\npart suggests maximizing polarized emission form the botton flake, so it becomes phase shifted when propagating\nthrough the top flake. My comment was on the possibility for the authors to elucidate which part of the stack\ncontribute to chiral emission using reciprocity arguments and simulation\n(does it originate from the top or bottom flake, at which depth ? - the question was not about where in the lateral\nregion in the whole field of view of the microscope).\nThe new version of the manuscript does not study in more details the behavior of the devices, but this is not a big\ndeal as it is not a fundamental point for the claims of the paper : I agree that the reported findings and results are in\nline with the main claims, and do not have further comment.\nAuthors’ Response\nWe thank the reviewer for clarifying the question.\nArgument based on simulations: Indeed, as the thickness of the top flake increases, resonant absorption can occur\nin the top flake. Consequently, a heat map similar to the one shown in Fig. 3c would then be determined by the two\nresonances corresponding to the bottom and top flakes, with the resonance frequencies set by their respective layer\nthicknesses. This behavior can be exploited to achieve a stronger dependence of the spectral position of the CD\nmaximum on the twist angle.\nArgument based on symmetry: Based on symmetry, it is not possible to identify the bottom or the top flake as the\none responsible for the chiral emission. By contrast, it is the combination of the two flakes that is required in order\nto break rotation symmetry, and thereby induce chirality."}]

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