Twisted Bilayer Photonic Crystals

• Twisted bilayer photonic crystals are vertically stacked, rotated photonic structures that generate long-range moiré patterns and induce band folding.
• They enable precise control of optical dispersion, interlayer hybridization, and flat-band formation for enhanced light localization and modulation.
• Advanced material platforms and nanofabrication techniques make these systems promising for applications in nonlinear optics, lasing, and quantum photonics.

Twisted bilayer photonic crystals are vertically stacked photonic-crystal systems in which one patterned layer is rotated relative to the other, generating a moiré superlattice that reshapes optical dispersion, radiative coupling, and field localization. In the literature, the term encompasses dielectric photonic-crystal slabs, crossed gratings, bilayer photonic graphene based on spoof surface plasmons, and true heterobilayers assembled from distinct materials. A central distinction is between genuine multilayer bilayers and single-layer “merged-pattern” approximations, because the former retain independent layer thicknesses, materials, and interlayer spacing as photonic design variables (Wang et al., 6 Mar 2025, Tang et al., 2023, Oudich et al., 2021).

1. Conceptual definition and structural taxonomy

A twisted bilayer photonic crystal is a bilayer photonic crystal in which two periodic photonic layers are stacked with a relative in-plane rotation. In true bilayer implementations, the two patterned layers remain physically distinct in the vertical direction. This differs from single-layer merged-pattern moiré photonic crystals, where the geometry of two twisted lattices is merged into one 2D pattern and etched into a single slab (Wang et al., 6 Mar 2025).

The terminology used across the field is comparatively precise. A bilayer photonic crystal denotes two photonic-crystal layers stacked vertically. A heterobilayer photonic crystal denotes a bilayer whose two patterned slabs are made from different materials, as in graphite/Si$_3$N$_4$. A moire photonic crystal denotes a photonic structure whose emergent long-period modulation arises from the interference of two periodic lattices. In graphene-inspired platforms, the local stacking landscape is commonly described in terms of AA, AB, and BA registries, with AA regions often identified as the loci of strongest localization (Wang et al., 6 Mar 2025, Oudich et al., 2021).

The field also spans several geometrical classes. One branch uses 2D photonic-crystal slabs with honeycomb or square lattices, directly paralleling twisted bilayer graphene or moiré photonic slabs. Another uses crossed 1D gratings, which still generate an effectively 2D twisted superlattice and support moiré band folding, flat bands, and chiral responses. Taken together, these studies suggest that “twisted bilayer photonic crystal” is best understood as a family of layered periodic photonic systems rather than a single canonical geometry (Salakhova et al., 2022, Choi et al., 8 Oct 2025).

2. Moiré geometry, reciprocal-space folding, and localization mechanisms

The most elementary geometric consequence of twist is the appearance of a long-period moiré scale. In the hexagonal heterobilayer photonic crystal realized in graphite/Si$_3$N$_4$, the moiré periodicity is

$\Delta_m=\frac{a}{2\sin(\theta/2)},$

with $a=330$ nm, and the measured periods for $2^\circ$, $4^\circ$, $6^\circ$, and $8^\circ$ closely follow that relation (Wang et al., 6 Mar 2025). In the twisted bilayer dielectric-grating problem, the analogous reciprocal-space scale is the moiré Bragg vector

$_4$0

which defines new moiré Brillouin-zone boundaries and new diffraction-assisted hybrid modes (Salakhova et al., 2022).

A recurring physical picture is moiré-induced band folding plus interlayer hybridization. In optical square-lattice Si$_4$1N$_4$2 bilayers, twist introduces moiré reciprocal vectors $_4$3 that scatter incident light into guided slab resonances according to $_4$4, producing repeated iso-frequency contours and twist-dependent parabolic bands in momentum space (Tang et al., 2023). In dielectric bilayer gratings, the moiré superlattice introduces new reciprocal vectors $_4$5, folds guided resonances toward the moiré zone center, and yields moiré-assisted hybrid quasiguided resonances whose linewidth can become extremely small when the relevant diffraction channel is closed and the interlayer scattering is mediated only by weak evanescent harmonics (Salakhova et al., 2022).

Flat-band and near-flat-band behavior is one of the central organizing themes. In on-chip silicon honeycomb bilayer slabs, twisting or mismatching two photonic-crystal layers generates flat or quasi-flat moiré bands with near-zero group velocity, AA-site-localized Bloch modes, and simultaneous lateral and vertical confinement of light; for the 2D twisted bilayer system, a flat band forms near $_4$6 THz, and at $_4$7 the bandwidth is reduced to $_4$8 around $_4$9 (Tang et al., 2022). In microwave bilayer photonic graphene based on spoof surface plasmons, flat bands are predicted at $_3$0 for $_3$1 and at $_3$2 for $_3$3, with electric-field localization in AA regions of the moiré unit cell (Oudich et al., 2021).

A distinct mechanism, not tied to discrete magic angles, has also been identified. In a general twisted bilayer model with exponentially decaying coupling, continuous lattice dislocation between AA and AB/BA regions creates a macroscopic effective potential well centered at AA, supporting intrinsic localized states at the lowest and highest energies. Because inter-cell coupling is negligible, these states form spectrally isolated superflat bands over a continuous range of small twist angles (Wang et al., 2022). This suggests that moiré photonic localization need not be exhausted by Dirac-cone velocity renormalization alone.

3. Material platforms and fabrication strategies

Several material platforms now define the experimental and numerical landscape. Bilayer photonic graphene at microwave frequencies uses two graphene-like photonic crystals made from hexagonal lattices of metallic cylindrical pillars on metallic plates; the monolayer supports a Dirac cone near $_3$4, and the interlayer coupling is tuned by the air-gap thickness $_3$5, with $_3$6 showing exponential decay (Oudich et al., 2021). Optical-frequency on-chip twisted bilayer photonic crystals use two fully suspended Si$_3$7N$_3$8 square-lattice membranes, each $_3$9 nm thick with circular holes of lattice constant $_4$0 nm and radius $_4$1 nm, separated by an air gap of $_4$2 nm and assembled by flip-chip bonding with $_4$3 alignment precision (Tang et al., 2023). Silicon honeycomb bilayer slabs use two $_4$4 nm crystalline-silicon membranes patterned with triangular air holes of side length $_4$5 nm and pitch $_4$6 nm, separated by a $_4$7 nm PMMA spacer (Tang et al., 2022, Tang et al., 2021). Strong-coupling twisted bilayer gratings use two $_4$8 nm WS$_4$9 gratings with period $\Delta_m=\frac{a}{2\sin(\theta/2)},$0 nm and width $\Delta_m=\frac{a}{2\sin(\theta/2)},$1 nm on quartz, protected and separated by $\Delta_m=\frac{a}{2\sin(\theta/2)},$2 nm Al$\Delta_m=\frac{a}{2\sin(\theta/2)},$3O$\Delta_m=\frac{a}{2\sin(\theta/2)},$4 (Choi et al., 8 Oct 2025).

A particularly important fabrication milestone is the true twisted heterobilayer photonic crystal based on a suspended $\Delta_m=\frac{a}{2\sin(\theta/2)},$5 nm Si$\Delta_m=\frac{a}{2\sin(\theta/2)},$6N$\Delta_m=\frac{a}{2\sin(\theta/2)},$7 slab and a dry-transferred $\Delta_m=\frac{a}{2\sin(\theta/2)},$8 nm graphite flake, each patterned with its own hexagonal lattice of $\Delta_m=\frac{a}{2\sin(\theta/2)},$9 nm and $a=330$0 nm (Wang et al., 6 Mar 2025). The fabrication sequence is bottom-layer EBL and ICP-RIE, KOH underetch of silicon, dry transfer of an unpatterned graphite flake, post-transfer EBL of the second lattice at the chosen twist, and selective O$a=330$1 etching of graphite. The post-transfer patterning step is crucial: if both layers were patterned before stacking, the spatial alignment would rely on optical microscopy with roughly $a=330$2 accuracy, corresponding to about $a=330$3 twist-angle accuracy for a $a=330$4 structure; by writing the top lattice after transfer, the lower lattice can be referenced directly during EBL with about $a=330$5 nm alignment accuracy, corresponding to about $a=330$6. The same work establishes reciprocal selectivity of the dry etches, with Si$a=330$7N$a=330$8 etched by SF$a=330$9:C$2^\circ$0F$2^\circ$1=3:2 at $2^\circ$2 while graphite etching is negligible, and graphite etched by O$2^\circ$3 plasma at $2^\circ$4 while Si$2^\circ$5N$2^\circ$6 is not etched (Wang et al., 6 Mar 2025).

Taken together, these implementations indicate that the field has moved from analog and numerical prototypes toward materially diverse multilayer nanophotonics: metallic SSP platforms, dielectric suspended slabs, transferred 2D-material heterobilayers, and high-index crossed gratings all realize the same moiré design logic, but with different coupling scales, loss mechanisms, and observables.

4. Analytical, numerical, and perturbative descriptions

Theoretical treatments are correspondingly diverse. In dielectric bilayer gratings, a dedicated Moiré-Adapted Fourier Modal Method (MA-FMM) was introduced to compute the scattering matrix without the large-supercell inefficiency that afflicts standard FEM, FDTD, or reciprocal-space FMM/RCWA at small twist angles. That framework supports both prism-coupled absorption maps for quasiguided-mode dispersion and dipole-emissivity calculations for extracting intrinsic resonance wavelengths and quality factors (Salakhova et al., 2022).

In silicon honeycomb twisted bilayer slabs, 3D finite-element calculations in COMSOL were combined with a Bistritzer–MacDonald-style continuum model. The continuum fit uses intralayer couplings $2^\circ$7 THz and separate effective interlayer tunnelings for upper and lower bands, reflecting the paper’s conclusion that photonic modes are not as tightly bound as electronic orbitals and that the photonic system exhibits larger band asymmetry than twisted bilayer graphene (Tang et al., 2021).

More recently, a general non-Hermitian perturbative framework has been developed specifically for twisted bilayer photonic crystals with far-field response. In that theory, the bilayer Maxwell operator is written as

$2^\circ$8

and the moiré-coupled eigenstate is expanded in generalized Rayleigh–Schrödinger form. The universal interlayer selection rule is

$2^\circ$9

with the coupling strength determined by Fourier components of the single-layer Bloch or Wannier fields. For low-energy states at the $4^\circ$0 point in hexagonal lattices, this reduces to the Bistritzer–MacDonald structure. In the same framework, the first-order far-field solution predicts a four-fold band splitting in the twisted-bilayer spectrum relative to the single-layer case, and reveals that low-energy $4^\circ$1-point states have suppressed scattering toward $4^\circ$2 through the moiré potential (Xu et al., 28 Sep 2025).

These approaches show a distinctive feature of photonic moiré theory: near-field hybridization and far-field radiation cannot be separated cleanly. Inference from the combined literature suggests that this is the primary reason photonic twisted bilayers require both continuum-coupling models and open-system scattering theory, rather than a direct transplantation of electronic moiré Hamiltonians.

5. Experimental signatures and reported optical phenomena

The most direct experimental signature in optical slab platforms is twist-dependent momentum-space dispersion. In suspended Si$4^\circ$3N$4^\circ$4 bilayers, free-space $4^\circ$5-space imaging directly visualizes repeated iso-frequency contours translated by first-order moiré wavevectors, with measured contours at $4^\circ$6, $4^\circ$7, $4^\circ$8, and $4^\circ$9 THz matching analytical Hamiltonian predictions; comparison among single-layer, aligned bilayer, and twisted bilayer spectra shows interlayer-induced splittings of $6^\circ$0 and $6^\circ$1 THz in the aligned case and $6^\circ$2 and $6^\circ$3 THz in the twisted case for the upper and lower TM-like parabolic bands (Tang et al., 2023).

Real-space moiré-site localization has now also been measured. In the graphite/Si$6^\circ$4N$6^\circ$5 heterobilayer, position-dependent micro-photoluminescence using a $6^\circ$6 nm CW laser, $6^\circ$7 spot size, and $6^\circ$8 mW excitation reveals a cavity-like resonance at AA positions centered at $6^\circ$9 nm with FWHM $8^\circ$0 nm, corresponding to $8^\circ$1; the same resonance is strongly suppressed at AB/BA positions, and 3D FDTD reproduces the AA-selective cavity response (Wang et al., 6 Mar 2025). The low $8^\circ$2 is attributed there to graphite absorption, and replacement of graphite by a low-loss 2D dielectric such as hBN is proposed as a route to higher visible-wavelength $8^\circ$3.

In numerical studies of on-chip silicon moiré slabs, the flat-band regime combines very high $8^\circ$4, small mode volume, and strong spontaneous-emission enhancement. For the 2D twisted bilayer honeycomb slab, the flat-band modes near $8^\circ$5–$8^\circ$6 THz have reported $8^\circ$7; the abstract reports $8^\circ$8 and $8^\circ$9, while detailed values include $_4$00 at $_4$01 and $_4$02 at $_4$03. The same study reports almost three orders of magnitude LDOS enhancement at AA regions relative to AB regions (Tang et al., 2022).

Twisted bilayer photonic systems also support functionalities beyond flat bands and cavities. In a thin patterned dielectric bilayer, unpolarized zero-OAM input light acquires SAM in transmission and OAM in reflection; the transmitted SAM is attributed to helicity-dependent moiré diffraction, while reflected OAM arises from interference of layer-induced SAM–OAM conversion channels, and moiré-diffracted beams themselves can carry strong SAM and OAM (Vyatkin et al., 2024). In a separate beam-steering regime, inverse-designed twisted bilayer photonic crystals route incident power into a single transmitted diffraction order whose direction is set by twist angle, with reported efficiency above $_4$04 across $_4$05–$_4$06 for TE and TM and overall accuracy nearing $_4$07 when averaged across $_4$08–$_4$09 including left- and right-handed polarizations (Roy et al., 2024).

6. Extensions, classification boundaries, and open problems

The topic has broadened into several neighboring subfields. Magneto-optical twisted bilayer photonic crystal slabs combine moiré resonances with gyrotropic splitting of circular polarizations; for a square-lattice magnetic bilayer at $_4$10 twist, a resonance near $_4$11–$_4$12 yields nearly perfectly linearly polarized transmitted zeroth-order light with transmissivities $_4$13, $_4$14, and $_4$15 and rotation angles $_4$16, $_4$17, and $_4$18 for $_4$19, $_4$20, and $_4$21, respectively (Liu et al., 9 Oct 2025). Moiré-enabled structured-light generation has also appeared: AA-localized Bessel-type quasi-BICs in twisted bilayer moiré photonic crystals produce vortex beams with experimentally demonstrated OAM orders from $_4$22 to $_4$23, and distinct OAM values can be selected at a fixed telecommunication wavelength by tuning twist angle and interlayer separation (Zhang et al., 29 Oct 2025).

At the same time, the boundary of the term remains important. Some related twisted-bilayer photonic systems are not photonic crystals in the strict sense. “Spintwistronics,” for example, studies twisted bilayer photonic spin lattices on a surface-plasmon-polariton platform rather than dielectric photonic-crystal slabs (Shi et al., 2024). Reconfigurable twisted $_4$24-MoO$_4$25 trilayers support multiple photonic magic angles and broadband canalization in a twistoptics setting, but they are polaritonic layered media rather than conventional photonic crystals (Duan et al., 2023). These systems are structurally and conceptually adjacent, yet classification remains nontrivial.

Several limitations recur across the literature. Small-angle moiré supercells become very large, which complicates both fabrication and computation and has delayed convincing experimental observation of some predicted photonic magic-angle flat bands in classical-wave analogs (Oudich et al., 2023). Finite disorder, finite sample size, and imperfect angular control broaden resonances and obscure minibands in optical slab experiments (Tang et al., 2023). Material loss can dominate early heterobilayer demonstrations, as in graphite-based visible cavities (Wang et al., 6 Mar 2025). Some of the most dramatic flat-band and ultra-high-$_4$26 results remain simulation-based and assume ideal geometry, ideal refractive indices, or lossless dielectrics (Tang et al., 2022, Salakhova et al., 2022).

The current direction of travel is nevertheless clear. Large-angle high-$_4$27 flat-band cavities have been proposed by combining twisted bilayers with Brillouin-zone-folding perturbations, producing a quasi-BIC ensemble with divergent density of states and possible applications in nonlinear optics, lasing, and quantum optics (Xu et al., 28 Sep 2025). This suggests that the mature form of the subject may not be a single “magic-angle” paradigm, but a broader moiré photonic toolbox spanning multilayer coupling, far-field engineering, chirality, angular-momentum control, and tunable confinement.