# Tailoring Flatband Dispersion in Bilayer Moiré Photonic Crystals

Chirine Saadi, Sébastien Cueff, Lydie Ferrier, Aziz Benamrouche, Maxime Gayrard, Emmanuel Drouard, Xavier Letartre, Hai Son Nguyen, Ségolène Callard

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Chirine Saadi, Sébastien Cueff, Lydie Ferrier, Aziz Benamrouche, Maxime Gayrard, et al. Tailoring Flatband Dispersion in Bilayer Moiré Photonic Crystals. Laser and Photonics Reviews, 2025, 19 (22), pp.e01038. 10.1002/lpor.202501038 . hal-05370170

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# Tailoring Flatband Dispersion in Bilayer Moiré Photonic Crystals

Chirine Saadi, Sébastien Cueff, Lydie Ferrier, Aziz Benamrouche, Maxime Gayrard, Emmanuel Drouard, Xavier Letartre,* Hai Son Nguyen, and Ségolène Callard

In this study, the photonic dispersion in 1D moiré structures formed by stacking two photonic crystal slabs with slightly different periods, separated by a carefully controlled subwavelength optical spacer, is experimentally investigated. Angle-resolved reflectivity measurements reveal moiré bands arising from the interplay between intra- and inter-layer coupling mechanisms of guided modes mediated by the moiré superlattice corrugation. By precisely adjusting the refractive index contrast through the filling factor of the photonic crystals, intralayer coupling is continuously tuned while keeping interlayer coupling constant. Consequently, the evolution of moiré minibands into flatbands characterized by minimal dispersion bandwidth is experimentally demonstrated. All experimental results show good agreement with numerical simulations. The findings not only confirm theoretical predictions but also provide a practical approach for realizing photonic flatbands in silicon-based moiré superlattices operating in the telecom wavelength range. This work paves the way toward harnessing flatband physics in advanced optoelectronic applications such as lasers and optical sensors.

## 1. Introduction

Flatbands are dispersionless energy bands in periodic media, characterized by macroscopic degeneracy and suppressed transport under standard conditions.[1–3] They typically emerge in finite-range hopping lattices where destructive interference preserves compact localized states and inhibits wavefunction delocalization. These features make flatbands ideal for studying

strongly correlated phases and exotic quantum phenomena. Photonic platforms have recently become a promising arena for flatband physics. Early studies focused on Lieb and Kagome photonic lattices based on tight-binding analogs of supra-wavelength photonic “atoms”.[4–7] More recently, in subwavelength-scale photonic crystals, “local” flatbands have been realized in specific regions of the Brillouin zone, arising from vertical symmetry breaking[8] or lattice distortion that mimics photonic Landau levels.[9,10]

To go beyond local flattening and achieve flatbands across the entire Brillouin zone, moiré engineering has emerged as a powerful strategy. This approach draws inspiration from twisted bilayer graphene, where flatbands appear at magic angles due to moiré hybridization gaps that isolate them from Dirac bands, enabling unconventional

superconductivity,[11–14] quantum Hall effects,[15] and topological phases.[16] Theoretical studies predict that similar mechanisms in twisted 2D photonic crystals can lead to flatbands and enhanced confinement,[17–20] with strong interlayer coupling supporting robust, potentially topological, flatbands even at large twist angles.[21] Additional moiré-induced phenomena include chiral emission[22,23] and vortex generation.[24] Experimentally, most work has focused on effective moiré potentials rather than true bilayer superlattices. Initial demonstrations used monolayer architectures with superimposed lattices, enabling lasing[25,26] and harmonic generation,[27] where flatbands boost confinement and nonlinear effects. However, continuous tuning of dispersion and direct observation of bandwidth collapse at magic angles remain unrealized. Full control over intra- and interlayer coupling requires bilayer structures with true geometric degrees of freedom. Recent efforts have fabricated twisted bilayer photonic crystals, demonstrating twist-angle–tunable dispersion and moiré scattering in microwave[28] and telecom[29,30] regimes. Yet, despite high tunability, flatbands have not yet been experimentally observed.

To simplify the fabrication challenges while preserving essential physical phenomena, an alternative approach is employing 1D crystals instead of 2D structures. In our previous theoretical work, we showed that periodic mismatches between two stacked 1D photonic crystals can also yield photonic moiré superlattices. In these structures, the interplay between intra- and inter-layer

<footnote>C. Saadi, S. Cueff, L. Ferrier, A. Benamrouche, M. Gayrard, E. Drouard, X. Letartre, H. S. Nguyen, S. Callard
Ecole Centrale de Lyon, INSA Lyon
Université Claude Bernard Lyon 1, CPE Lyon, CNRS, INL, UMR5270
Ecully 69130, France
E-mail: xavier.letartre@ec-lyon.fr</footnote>

<footnote>H. S. Nguyen
Institut Universitaire de France (IUF)
Paris F-75231, France</footnote>

<footnote>ID The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/lpor.202501038</footnote>

<footnote>© 2025 The Author(s). Laser & Photonics Reviews published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>

<footnote>DOI: 10.1002/lpor.202501038</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** a) Schematic representation of a 1D moiré structure formed by two gratings with different periods $a_1$ and $a_2$, where the optical modes are governed by intralayer coupling $U_{1,2}$ and interlayer coupling V. The two layers are separated by a distance L. The moiré period is given by $\Lambda = a_1(N + 1) = a_2N$. b) 3D view of the structure composed of an upper layer of amorphous silicon (a-Si) and a lower layer of crystalline silicon (c-Si), deposited on a 2µm SiO$_2$ layer atop a silicon substrate. The upper and lower gratings have periods $a_1$ and $a_2$, respectively, and share the same height h and filling factor f. The two layers are separated by a SiO$_2$ layer of thickness L.</figcaption></figure>

coupling of guided modes depends strongly on the separation distance between layers.[31] Indeed, interlayer separation directly affects coupling strength, and photonic flatbands have been observed at specific “magic distances,” critical separations at which light confinement is significantly enhanced and which can be effectively described by a tight-binding framework.[31] Subsequent numerical studies have explored various facets of these systems, including finite-size effects on light localization,[32] the robustness of flatbands,[33,34] and the implementation of staggered potentials.[35] However, from an experimental standpoint, tuning the interlayer separation to achieve these “magic distances” is impractical, as each separation requires a distinct multilayer stack fabricated via standard planar processes. To overcome this limitation, a recent experimental study introduced an alternative strategy: tuning the moiré supercell period to achieve flatbands in structures with enlarged supercells.[36] While successful in generating flatbands, this approach inherently reduces the Brillouin zone size, leading to a trivial flattening of all minibands. Furthermore, as the moiré period depends on discrete numbers of period repetitions within each layer, this approach does not allow continuous observation of band flattening evolution. Consequently, an experimental demonstration of flatband tuning arising specifically from competition between intra- and inter-layer coupling in bilayer photonic crystals remains elusive.

Here, we report on the experimental dispersion engineering of moiré bands in bilayer moiré structures based on 1D silicon photonic crystals, demonstrating continuous tailoring of photonic flatbands. These bilayer structures were fabricated through a double lithography technique with high-precision alignment. The optical spacer separating the two photonic crystal layers is precisely controlled and significantly smaller than the operating wavelength, thus ensuring strong interlayer coupling. By systematically varying the refractive index contrast of the photonic crystals through adjustments in their filling factors, we effectively tuned intralayer coupling while keeping the interlayer coupling fixed by maintaining a constant interlayer spacing. Angle-resolved reflectivity measurements clearly reveal the evolution of moiré minibands in the optical dispersion diagram, arising from the competition between interlayer and intralayer coupling mechanisms. Numerical simulations using Rigorous Coupled-Wave Analysis (RCWA) strongly support our experimental observations, showing excellent agreement. Importantly, we experimentally demonstrate a flatband dispersion characterized by a significant reduction in bandwidth at a specific filling factor, consistent with theoretical predictions. These findings represent a critical step toward the precise control of photonic flatbands in bilayer moiré superlattices, offering promising applications in integrated photonics and advanced optical signal processing.

## 2. Eruption of Flatbands in Moiré Structures

The studied system is a bilayer moiré photonic crystal, created by stacking two silicon photonic gratings of thickness h and separated by an interlayer distance L (Figure 1a). The two gratings present slightly different lattice periods, $a_1$ and $a_2$, satisfying the commensurate conditions $\frac{a_1}{a_2} = \frac{N}{N+1}$: N is an integer that defines the size of the moiré supercell (or moiré period) $\Lambda = Na_2 = (N+1)a_1$. For each grating, the periodic pattern is defined by the same filling factor f, representing the proportion of high-index material in the gratings. This structure generates periodic regions at the edges of the supercells where the unit cells of the top and bottom layers are perfectly aligned (AA stacking) and regions at the centers of the supercells where the unit cells of the upper layer are displaced relative to those in the bottom layer (AB stacking) (see Figure 1a). These variations in stacking alter the local electromagnetic field environment and give rise to the unique characteristics of the moiré potential.

In our prior theoretical work, we showed that for a given moiré period (defined by N), light propagation and confinement in the structure are strongly influenced by the interplay between intra-layer and inter-layer couplings $U_{1,2}$ and V in Figure 1a, respectively.[31] These couplings can be tuned through structural design. The inter-layer coupling V, mainly governed by the overlap of the evanescent tails of co-propagating guided modes in each layer, decreases exponentially with the layer separation. In contrast, the intra-layer couplings $U_{1,2}$, arising from diffraction between counter-propagating modes within the same layer, strongly depend on the periodic pattern and refractive index contrast of each grating. Numerical simulations have demonstrated that, in the regime of evanescent coupling, when $L < a_0$ (with $a_0 = \frac{a_1+a_2}{2}$), mode hybridization between the two layers leads to
the emergence of minibands within the bandgap of the uncou-
pled layers.[31] These minibands, analogous to those found in
semiconductor superlattices, correspond to Bloch modes defined
by the supercell periodicity and are subsequently referred to as
moiré bands. Furthermore, adjusting the ratio between inter-
layer and intra-layer coupling strengths allows the moiré band's
bandwidth to be tuned and significantly reduced. Notably, in the
so-called “magic” configurations, the band becomes strongly flat-
tened. This behavior can be effectively captured using a simple
tight-binding model of an atomic chain in the Wannier basis of
moiré supercells.[31,32] Within this model, light confined in the
Wannier states tunnels to nearest neighbor ones to form moiré
bands. Notably, in the magic configurations, photon tunneling
between moiré Wannier states within each supercell is canceled
due to an accidental destructive interference between inter-layer
and intra-layer couplings. As a result, a flatband emerges, leading
to unconventional localization of photonic states within each su-
percell.

Dispersion engineering of moiré bands can be achieved ei-
ther by tuning the inter-layer coupling through variation of the
separation distance L, or by tuning the intra-layer coupling via
adjustment of the refractive index contrast through the filling
factor *f*. In this study, we adopt the latter strategy for several
reasons: first, varying *L* is practically challenging, as it requires
fabricating separate layer stacks for each distance, and because
the inter-layer coupling decreases exponentially with *L*,[31] mak-
ing fine-tuning difficult. Conversely, adjusting the filling factor *f*
can be performed continuously across different structures on the
same stack, and enables precise control of the coupling strength,
thanks to the linear variation of intra-layer coupling with *f*.[31]

To numerically investigate the evolution of the moiré band as
the filling factor *f* varies, we calculate the energy-momentum dis-
persion of the modes using the RCWA method. The structure
is designed to operate in the transverse magnetic (TM) mode
regime around 1.2 µm for *N* = 13. To ensure a realistic design,
the bilayer rests on a 2 µm silica layer on a silicon substrate
(Figure 1b). The lower grating is composed of crystalline silicon
(c-Si) and silica with a period of *a*₂ = 317 nm, while the upper
grating consists of amorphous silicon (a-Si) and air with a pe-
riod of *a*₁ = 342 nm. A double-period perturbation of 5 %, simi-
lar to the designs in Refs. [8, 31], is implemented for each grating
so that the modes of interest, originally near the X point of the
BZ, are brought to the center of the BZ and can be probed by
plane-wave excitations in RCWA. The thickness *h* of each grat-
ing is 220 nm. The two gratings are separated by a *SiO*₂ layer
fixed at *L* = 80 nm to ensure the evanescent coupling condition
(*L* < *a*₀ with *a*₀ = *a*₁+*a*₂/₂ ≈ 330 nm). The refractive indices of all
materials used in the simulations were obtained from ellipsom-
etry measurements. In the spectral range of interest, they are:
n<sub>a-Si</sub> = 3.53, n<sub>c-Si</sub> = 3.51, n<sub>SiO<sub>2</sub> (SOI)</sub> = 1.45, and n<sub>SiO<sub>2</sub> (spacer)</sub> = 1.44.
The filling factor *f* varies from 0.5 to 0.8 to enable fine-tuning of
the intra-layer couplings.

**Figure 2** presents numerical results highlighting the evolution of photonic bands as the filling factor *f* varies from 0.5 to 0.8, with emphasis on the isolated moiré band (marked in yellow). At lower filling factors ($f = 0.5$ and $f = 0.6$), clear and distinct moiré bands emerge within the band structure, indicating new energy states introduced by the moiré corrugation (Figure 2a). As the filling factor increases to $f = 0.7$, the moiré band exhibits significant

flattening, reflecting a balance between interlayer and intralayer
coupling. However, further increasing the filling factor to *f* = 0.8
causes the band to become dispersive again, suggesting that the
minimum bandwidth (flatband condition) is achieved at a filling
factor close to 0.7. The band flattening has a direct impact on the
spatial distribution of the electromagnetic field in the structure.
Figure 2c shows the computed map of the field intensity (|*H*<sub>y</sub>|<sup>2</sup>)
for a filling factor of *f* = 0.7, corresponding to the flatband con-
figuration. The results clearly illustrate strong field localization
at AB sites, whereas AA sites exhibit comparatively weaker con-
finement. These findings confirm that the moiré flatbands arise
from the intricate interplay of interlayer and intralayer interac-
tions and are tunable via the filling factor *f*.

**3. Fabrication and Characterization of Moiré Photonic Crystals**

To fabricate the moiré sample, we employed a monolithic fab-
rication process involving double nanostructuring with precise
alignment, enabling accurate definition of photonic crystal lay-
ers. These structures were patterned using conventional planar
microelectronics techniques. The process began by nanopattern-
ing the lower gratings from a commercial 220 nm silicon-on-
insulator (SOI) substrate (Figure 3a). Multiple gratings, each with
the same period *a*₂ = 342 nm but different filling factors *f* were
defined. The size of each grating is 80 × 80 µm. These patterns
were initially created in an 80 nm thick AR-P resist layer using
electron beam lithography, then transferred to the c-Si layer via
ionic dry etching. Subsequently, a two-phase planarization pro-
cess was performed: first, a silica (SiO₂) layer was deposited by a
sol-gel process, followed by controlled ionic dry etching precisely
planarize the surface and achieve the desired 80 nm spacer be-
tween the two gratings. Ensuring this uniform surface is crucial
for accurate control over the optical properties and to minimize
irregularities that could affect device performance.

The upper grating, consisting of a-Si gratings (h = 220 nm) deposited by plasma-enhanced chemical vapor deposition (PECVD), was fabricated through a second electron beam lithography step, accurately aligned with the lower grating to form the moiré pattern. Precise alignment is essential, as a tilt between the two gratings could cause significant misalignment, impacting device efficiency. Regarding the lateral alignment, numerical simulations confirmed that horizontal shift up to 20 nm between the grating rods has negligible effects on optical frequencies when the number of moiré periods *N* is sufficiently large (*N* ≫ 1) (see supporting information). Moreover, even larger global shift of a few micrometers does not affect the optical performance due to the inherent periodicity of the moiré pattern.

All lower grating structures have a period of $a_z = 342$ nm with filling factors ranging from $f = 0.53$ to 0.78, while the upper grating has a period of $a_1 = 317$ nm with similar filling factors (for more details on the fabrication, see the Supporting Information). A double-period perturbation of 10% is also implemented in the design of the fabricated structures, allowing the photonic modes to be probed via far-field spectroscopy (angle-resolved reflectivity).

A microscopic image was captured to access the fabrication
quality of the moiré structure (Figure 3a, top panel). This image
<figure><img src="image_4.png" /><figcaption>**Figure 2.** a) Simulations for the moiré structure with the upper layer completely etched to 220 nm for filling factors *f* = 0.5, 0.6, 0.7, and 0.8. The yellow box indicates the band of interest that varies with the filling fraction. b) The spatial distribution of the magnetic field component *H*<sub>y</sub> in the moiré structure with the upper layer fully etched is shown for a filling factor *f* = 0.7 at the wavevector *k* = 0 (Γ-point), with AA and AB sites labeled.</figcaption></figure>

clearly shows the superposition of the two membranes with negligible tilt: the lower layer, outlined in blue, and the upper layer, outlined in red, with the resulting moiré supercell measuring approximately 4 µm, closely matching the theoretical prediction given by Λ = 4.4 µm. It is important to point out that due to the positive nature of the resist, outside of the overlap region, both lower and upper stack is still a bilayer stack, but only one layer is patterned: lower stack consists of an unpatterned a-Si slab on top a c-Si grating, and upper stack consists of an a-Si grating on top of an unpatterned c-Si slab (Figure 3a, lower panels).

To assess the quality of planarization atomic force microscopy (AFM) measurements of the lower stack, taken over a span of 5 µm were performed. The result (Figure 3b), top panel, show a modulation depth of approximately 6 nm, confirming successful planarization from an initial modulation depth of 220 nm of the patterned c-Si grating in air down to 6 nm. Moreover, ellipsometry measurements outside the patterned regions (see Supporting Information) further confirmed the precise thickness of the silica spacer, validating the accuracy of the etching process in the planarization step.

AFM analysis of the upper stack indicates a modulation depth of around 130 nm, smaller than the total a-Si thickness of 220 nm (Figure 3b). This partial etching likely resulted from altered etching dynamics due to the presence of the lower grating. Nonetheless, as demonstrated later, this partial etching minimally affects dispersion engineering and flatband formation in the moiré structures. Finally, AFM analysis of the moiré structure over a 20 µm span reveals that a residual modulation caused by the planarization step results in a topographic beat of approximately 6 nm (Figure 3c). Such beating, of period 4.4 µm, consistent with the moiré period identified in the microscopic image (Figure 3a), and alinging well with theoretical prediction.

## 4. Experimental Measurement of Moiré Flatbands

To measure the band diagram of our structure, a white light beam is focused onto the sample via a microscope objective (NA = 0.8). The reflectivity is collected using the same microscope in a confocal geometry
<figure><img src="image_5.png" /><figcaption>**Figure 3.** a) Image captured by an optical microscope showing the formation of a moiré supercell from the superposition of two layers. The lower layer (outlined in blue) and the upper layer (outlined in red) create an interference pattern visible as the moiré supercell. b) Height profiles of the upper and lower layers are shown separately. Below the profiles, a combined plot illustrates the periodic variations in height across a 5 µm span, with the red and blue lines representing the upper and lower layers, respectively. c) Height profile of the moiré supercell structure is shown. The profile illustrates the periodic modulation of the moiré pattern over a (20 µm) span. The lower plot provides the height variation along the x-axis, highlighting the periodic nature of the moiré interference pattern, with the moiré periodicity denoted as (Λ ≈ 4 µm).</figcaption></figure>

and is then projected into Fourier space before being directed to the en-
trance slit of a spectrometer. Finally, the signal is captured by the sensor
of an infrared camera at the spectrometer output[37] (see Supporting In-
formation).

Optical measurements were performed in three distinct regions to
analyze the response of the three different stacking configurations: the
upper stacking, the lower stacking, and the moiré region (Figure 4). The

dispersion diagrams corresponding to the optical response of the upper
and lower stackings exhibit the well-known characteristic 1D photonic
crystal band structures (Figure 4a,b), albeit slightly modified with respect
to the band structures of single gratings due to the presence of the layered
stack (see Supporting Information for RCWA simulations of the upper
and lower structures). In contrast, the moiré region exhibits a markedly
different optical response compared to the individual gratings. Interlayer
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Experimental dispersion diagrams obtained from angle-resolved reflectivity measurements at different regions of the bilayer moiré photonic crystal. The maps show the filtered differential reflectivity signal ΔR (a.u.); see Supporting Information for details. a) Dispersion of the upper grating, b) dispersion of the lower grating, and c) dispersion in the moiré region, where moiré bands emerge due to interlayer interactions. The yellow box highlights the isolated moiré flatband observed around E = 1.1 eV.</figcaption></figure>

interactions between the two gratings induce significant modifications in the photonic dispersion, leading to the emergence of moiré bands. Experimental results reveal the formation of distinct moiré bands, notably an isolated band (highlighted in yellow) around E = 1.1 eV, which is the band of interest in this study (Figure 4c).

This band highlighted in yellow evolves as the filling factor *f* is progressively tuned, as shown in Figure 5. At *f* = 0.53, the band exhibits noticeable dispersion. As *f* increases, a transition toward minimal dispersion occurs, leading to the formation of a flatband around *f* = 0.7. At *f* = 0.72, the experimental data clearly reveal a significantly flattened band, confirming the emergence of a moiré flatband.

To further support this observation, we compare our experimental findings with RCWA simulations of the fabricated structures with partially etched upper grating (Figure 5b). The simulated energy-momentum dispersion closely matches the experimental band positions and their evolution as *f* increases, validating the robustness of our fabrication and measurement approach. Theoretical simulations predict that the formation of flatbands in these structures is closely tied to variations in the filling factor *f*. In a previous study,[31] this behavior was modeled using a tight-binding approach that considers the nearest-neighbor couplings. In this model, the moiré structure is represented as a periodic chain of supercells, where the energy profile between *k* = 0 and *k* = π/Λ (corresponding to the Γ and X points in the first Brillouin zone) is given by:

$$E(k) = E_0 + 2J \cos(\Lambda k), \quad (1)$$

where $E_0$ is the central energy of each supercell, *J* is the tunneling rate governing the coupling between neighboring supercells, and Λ is the moiré period. The global spectral bandwidth Δ, defined as Δ = 4*J*, serves as a

figure of merit to evaluate the flatness of the moiré minibands. A smaller bandwidth Δ corresponds to a flatter band, indicating minimal dispersion. In this equation, the energy deviation relative to the central energy $E_0$ is given by ΔE = E(k) – $E_0$, where ΔE characterizes the energy variation within the band. In Figure 5a, the yellow lines represent cosine fits derived from the tight-binding model (Equation (1)). These fits closely match the experimental band dispersion, confirming the periodic modulation of energy.

Additionally, we present the evolution of the bandwidth Δ as a function of the filling factor *f* (Figure 5c) to further quantify this behavior. The graph compares three datasets: experimental measurements (blue curve), RCWA simulations for a partially etched upper layer (red curve), and RCWA simulations for a fully etched upper layer (black curve). The experimental results (blue) show a clear trend where the bandwidth Δ decreases with increasing *f*, reaching a minimum of approximately 2 meV at *f* = 0.72, where the band is nearly flat. For *f* > 0.72, the bandwidth increases again, indicating a gradual return to a more dispersive state. The RCWA simulations of both partially etched and fully etched configurations closely follow the experimental data, showing a sharp decrease in Δ from *f* = 0.5 to a minimum near *f* = 0.7. These findings demonstrate that the filling factor *f* is a critical tuning parameter for controlling the flatness of moiré bands. Despite small discrepancies between the experimental and simulated values—likely due to fabrication-induced variations in the filling factor and etching depth—the general agreement highlights the robustness of the observed behavior. The emergence of a flatband near *f* = 0.72 confirms the theoretical simulations and emphasizes the potential of moiré structures for achieving tunable photonic states with minimal dispersion. The measured bandwidth remained approximately 2 meV, indicating that while the band is relatively narrow, it is not entirely flat.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** a) Experimental measurements for *f* = 0.53 and *f* = 0.72, with cosine fits (yellow lines) derived from the model equation. b) Corresponding RCWA simulations for *f* = 0.53 and *f* = 0.75, showing good agreement with the positions of the experimental photonic bands. These results highlight a progressive transition toward a flatband for *f* = 0.72. c) Variation of the bandwidth Δ (meV) as a function of the filling fraction *f*. The experimental measurements in blue were performed for *f* = 0.53, 0.58, 0.64, 0.69, 0.72, and 0.78. The data points (in blue) are displayed with error bars. The RCWA simulations are shown in red and black.</figcaption></figure>

The ratio of the bandwidth to the central energy (Δ/E₀) was found to be approximately 1:500, highlighting the relatively small bandwidth in comparison to the energy scale. To evaluate the quality factor (Q) of the moiré flatbands, we applied a Lorentzian resonance model to the experimental reflectivity spectra, as explained in the *Supporting Information*. The estimated Q value is approximately 250, indicating a relatively narrow spectral linewidth. This result is in good agreement with numerical simulations based on the finite element method (FEM) and RCWA simulations, which predict Q factors on the order of a few hundred for structures incorporating a 5% double-period perturbation. For comparison, in the absence of such perturbation, simulations indicate that Q factors can reach several thousands.

**5. Conclusion and Perspective**

This study presents the experimental observation of flatbands in 1D moiré photonic crystal structures. By combining RCWA simulations with precise experimental techniques, we confirmed the emergence of flatbands within these structures. The results align well with theoretical expectations, particularly in demonstrating minimal dispersion at specific filling factors. By adjusting key parameters, such as the filling factor, we achieved fine-tuning of intralayer coupling, leading to enhanced light confinement and the formation of localized photonic states. The fabrication process that we developed can also enable the realization of finite-size cavities, opening a promising route toward compact, high-Q resonators.[32] Furthermore, this versatile platform can be extended to investigate topological phenomena in multilayer photonic crystals,[38–40] offering new opportunities for advanced studies of light—matter interactions.

Looking forward, our platform offers exciting prospects beyond passive photonic structures. By incorporating gain media such as III-V semiconductors or 2D materials between the gratings, moiré-based laser cavities could be realized. Furthermore, the strong sensitivity of the flatband regime to the filling factor makes these structures excellent candidates for optical sensing

applications, with the added advantage of broad angular acceptance for detecting gases or liquids.

**Supporting Information**

Supporting Information is available from the Wiley Online Library or from the author.

**Acknowledgements**

This work was supported by Nanolyon platform, a member of the CNRS-RENATECH+ French national network. The authors thank Pierre Viktorovitch, Serge Mazauric, and Xuan Dung Nguyen for fruitful discussions. The authors acknowledged support from the CNRS/IN2P3 Computing Center (Lyon - France) for providing computing and data-processing resources needed for this work.

**Conflict of Interest**

The authors declare no conflict of interest.

**Data Availability Statement**

The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Keywords**

flatband dispersion, moiré, photonic crystals

Received: April 30, 2025

Revised: June 10, 2025

Published online:
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