Data from: Strong interlayer coupling and chiral flat-band cascades in twisted bilayer gratings
Data files
Jul 28, 2026 version files 312.02 MB
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README.md
8.74 KB
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TBG_data_set.zip
312.01 MB
Abstract
From atomic crystals to macroscopic material structures, twisted bilayer systems have emerged as a promising route to control wave phenomena. In few-layer van der Waals (vdW) materials, however, the intrinsically weak interlayer coupling typically demands fine control of small twist angles to reach magic-angle conditions. Here, we show that one-dimensional photonic crystal bilayers can overcome this limitation by accessing a regime of strong interlayer coupling—comparable to intralayer coupling. This strong coupling enables flat-band formation over a broad angular range even at large twist angles. We experimentally realize this regime by stacking WS₂ gratings via a two-step lithography method, yielding ultra-wide chiral flat-band cascades in magic-angle twisted bilayer gratings. Our work not only provides a platform for designing photonic applications with a tunable localization but also explores a new regime of physics that is unattainable in conventional solid-state-based moiré systems.
Dataset DOI: 10.5061/dryad.fxpnvx16v
Description of the data and file structure
This dataset: TBG_data_set.zip contains simulated angle-resolved transmittance and circular-dichroism spectra, photonic band-structure calculations, near-field electric displacement field profiles, and magic-angle/flat-band-width parameter sweeps for twisted bilayer photonic gratings, together with supplementary substrate-material comparisons and complex refractive index data. All data were generated by rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulation and are stored in Excel format, with one file per main-text or supplementary figure and one sheet per panel or parameter value.
Files and variables
File: Fig1_Data.xlsx
Description: This file provides angle-resolved transmittance spectra and near-field electric displacement field profiles for the twisted bilayer grating. "Fig1_c_10degree", "Fig1_c_35degree", "Fig1_c_44degree", and "Fig1_c_64degree" provide transmittance as a function of incidence angle and photon energy at twist angles of 10°, 35°, 44°, and 64°. Sheets "Fig1_d_44degree_xy_bottom", "Fig1_d_44degree_xy_top", and "Fig_1d_44degree_xz" provide the electric displacement field distribution in the xy (bottom and top layer) and xz cross-sections at a 44° twist angle. Sheets "Fig1_e_64degree_xy_bottom", "Fig1_e_64degree_xy_top", and "Fig_1e_64degree_xz" provide the corresponding field distributions at a 64° twist angle.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
- X, Y, Z (nm) – spatial coordinates
- Electric displacement field (a.u.)
File: Fig2_Data.xlsx
Description: This file provides simulated photonic band structures of the twisted bilayer grating. Sheets "Fig2_c_Uncoupled" and "Fig2_c_Coupled" provide the k_x–energy dispersion of the uncoupled and coupled bands at one twist angle. Sheets "Fig2_d_Uncoupled" and "Fig2_d_Coupled" provide the corresponding uncoupled and coupled bands at a second twist angle. Sheet "Fig_2_e" provides the twist-angle dependence of the band separation parameter (s) for the 1st and 2nd bands. Sheet "Fig_2_f" provides the twist-angle dependence of the flat-band width for the 1st and 2nd bands.
Variables
- k_x – in-plane wavevector component
- Energy (eV)
- s – Dimensionless scaling factor for effective coupling strength
- Twist angle (degree)
- Flat band width
File: Fig3_Data.xlsx
Description: This file provides angle-resolved transmittance spectra of the twisted bilayer grating at different twist angles. Sheets "Fig3_d_38degree" through "Fig3_d_44degree" provide transmittance maps at twist angles of 38°, 40°, 42°, and 44°. Sheets "Fig3_e_57degree" through "Fig3_e_66degree" provide transmittance maps at twist angles of 57°, 60°, 63°, and 66°.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
File: Fig4_Data.xlsx
Description: This file provides circularly polarized transmittance and circular dichroism (CD) data. Sheet "Fig4_a" provides the CD map as a function of incidence angle and energy. Sheets "Fig4_b_left" and "Fig4_b_right" provide the corresponding left- and right-handed circularly polarized transmittance maps. Sheet "Fig4_c" provides the four circular-polarization-resolved transmittance spectra (T_LL, T_LR, T_RR, T_RL) at a fixed incidence angle. Sheet "Fig4_d" provides the same four transmittance spectra under a different condition.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- CD – Circular dichroism
- Transmittance
- T_LL, T_LR, T_RR, T_RL – circular-polarization-resolved transmittance
File: Fig4_E_LCP.txt
Description: This file provides the electric field energy density distribution in the xy plane for the left circular polarization excitation.
Variables
- X, Y, Z (nm) – spatial coordinates
- Electric displacement field (a.u.)
File: Fig4_E_RCP.txt
Description: This file provides the electric field energy density distribution in the xy plane for the right circular polarization excitation.
Variables
- X, Y, Z (nm) – spatial coordinates
- Electric displacement field (a.u.)
File: FigS3_Data.xlsx
Description: This file provides calculated angle-resolved transmittance spectra at twist angles of 44°, 45°, 46°, 47°, 48°, 61°, 62°, 63°, 64°, and 65°, one sheet per angle.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
File: FigS4_Data.xlsx
Description: This file provides the magic angle and flat-band width as a function of grating layer thickness.
Variables
- Thickness (nm)
- Magic angle (Degree)
- Flat-band width (Degree)
File: FigS5_Data.xlsx
Description: This file provides the magic angle and flat-band width as a function of grating period.
Variables
- Period (nm)
- Magic angle (Degree)
- Flat-band width (Degree)
File: FigS6_Data.xlsx
Description: This file provides angle-resolved transmittance spectra at twist angles of 15°, 20°, 30°, 45°, 60°, and 70°, one sheet per angle.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
File: FigS7_Data.xlsx
Description: This file provides uncoupled and coupled photonic band structures at twist angles of 40°, 45°, 50°, 55°, 60°, and 65°, with separate "_Uncoupled" and "_Coupled" sheets for each angle.
Variables
- Band index
- k_x in-plane wavevector component
- Energy (eV)
File: FigS8_Data.xlsx
Description: This file provides uncoupled and coupled photonic band structures at twist angles of 43°, 44.3°, 47.3°, 49°, 51°, and 53°, with separate "_uncoupled" and "_coupled" sheets for each angle.
Variables
- Band index
- k_x – in-plane wavevector component
- Energy (eV)
File: FigS9_Data.xlsx
Description: This file provides uncoupled and coupled photonic band structures at twist angles of 60.5°, 61°, 61.5°, 62°, 63.3°, and 64°, with separate "_Uncoupled/_uncoupled" and "_coupled" sheets for each angle.
Variables
- Band index
- k_x – in-plane wavevector component
- Energy (eV)
File: FigS10_Data.xlsx
Description: This file provides angle-resolved transmittance spectra for two grating configurations ("M1", "M2") at spacer thicknesses of 0 nm, 40 nm, and 80 nm.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
File: FigS11_Data.xlsx
Description: This file provides the magic angle and flat-band width as a function of interlayer distance. Sheets "FigS11_a" and "FigS11_b" correspond to two different grating configurations.
Variables
- Interlayer distance (nm)
- Magic angle (Degree)
- Flat-band width (Degree)
File: FigS12_Data.xlsx
Description: This file provides circularly polarized transmittance and CD data. Sheet "FigS12_A" provides the CD map as a function of incidence angle and energy. Sheets "FigS12_B_TRR", "FigS12_B_TRL", "FigS12_B_TLR", and "FigS12_B_TLL" provide the corresponding circular-polarization-resolved transmittance maps. Sheets "FigS12_C" and "FigS12_D" provide the four circular-polarization-resolved transmittance spectra (T_RR, T_LL, T_LR, T_RL) at two fixed incidence angles.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- CD – Circular dichroism
- Transmittance
- T_LL, T_LR, T_RR, T_RL – circular-polarization-resolved transmittance
File: FigS15_Data.xlsx
Description: This file provides angle-resolved transmittance spectra for gratings on three different substrate materials: GaP, hBN, and WS2.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
File: FigS16_Data.xlsx
Description: This file provides the complex refractive index of the grating material WS2 as a function of wavelength.
Variables
- Wavelength (nm)
- Real index
- Imaginary index
File: FigS18_Data.xlsx
Description: This file provides angle-resolved transmittance spectra for the y-direction at twist angles from 10° to 70° (10°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65°, 70°), one sheet per angle.
Variables
- Angle (degree) – incidence angle
- Energy (eV) – photon energy
- Transmittance
Code/Software
Any program that will open a spreadsheet, such as Microsoft Excel is recommended.
