Ultra-narrowband and rainbow-free mid-infrared thermal emitters enabled by a flat band design in distorted photonic lattices

Thermal radiation from hot bodies is naturally broadband and incoherent, which limits efficiency in applications such as gas sensing where narrow spectral features are needed. Narrowband thermal emitters based on photonic nanostructures can improve temporal coherence but typically suffer from a rainbow effect: the emission wavelength strongly depends on output angle due to steep dispersion of high-Q modes, broadening the collected spectrum and reducing efficiency. The research question addressed here is how to design a thermal emitter that maintains ultra-narrow bandwidth (high temporal coherence) while eliminating angle-dependent spectral shift (rainbow effect) to enable efficient collection with lenses over wide angles. The authors propose a flat-band photonic lattice approach that folds guided modes to the Γ point to achieve angle-insensitive, high-Q resonances in the mid-infrared (MIR).

Prior approaches include: surface phonon polariton emitters (e.g., SiC) enabling coherent emission but limited to Reststrahlen bands; moiré-based structures offering tunability but with complex fabrication and uncontrolled radiation; bull’s eye plasmonic gratings with directionality but high losses; and metal–insulator–metal (MIM) metamaterial emitters that are easy to fabricate but have broad linewidths due to metal loss (Q < 20). All-dielectric metasurfaces using high-Q resonances such as bound states in the continuum (BICs) and quasi-guided modes (QGMs) can yield ultra-narrowband emission, even with evaporated amorphous films, but still exhibit steep dispersions leading to rainbow effects. Existing flat-band methods (moiré crystals, symmetry breaking, plasmonic BICs, high-order Mie resonances) face trade-offs among fabrication complexity, losses, and limited Q-factors. Thus, achieving a wide-wavevector flat band with simultaneously high Q remains challenging.

Design: Start from a square lattice of high-index Ge disks (single-disk structure, SDS) on an Al2O3 spacer over thick Au. Introduce period-doubling perturbations along x to form a double-disk structure (DDS), halving the first Brillouin zone (FBZ). Two perturbations are combined: (1) change disks to ellipses and rotate every second column by 90°, and (2) slightly alter center-to-center distance to a−δ. This folds guided modes (GMs) at the X edge back near Γ, where they couple with existing guided-mode resonances (GMRs), producing band splitting and enabling a flat band with low group velocity. A slight symmetry breaking converts a symmetry-protected BIC into a quasi-BIC (QBIC) with finite but high Q and y-polarized coupling. Numerical simulations: Finite element method (COMSOL Multiphysics) with Floquet periodic boundary conditions laterally and PMLs along z. Emissivity E(λ)=A(λ)=1−R(λ) (since T=0 with thick Au). Temporal coupled-mode theory: E = 4γγ0 / [(ω−ω0)^2 + (γ+γ0)^2], with Qrad = ω0/2γ and Qabs = ω0/2γ0 = n/(2k). Critical coupling (perfect absorption/emission) when Qrad = Qabs. Qrad tuned via asymmetry (Δ=A−B) and period-doubling strength; Qabs tuned via material loss and Al2O3 thickness. Dispersion and group velocity computed (v_g = df/dk) to quantify flatness. Geometries used (typical): lattice a=2 μm; Ge thickness h=0.6 μm; Al2O3 thickness t=0.45 μm; initial circular D=1.45 μm. DDS perturbations: δ=0.25 μm; elliptical axes A=1.54 μm, B=1.35 μm (Δ=190 nm for critical coupling). Fabrication: On Si substrate deposit Ti(5 nm)/Au(100 nm)/Ti(3 nm) by electron-beam evaporation (EBE), then Al2O3(450 nm) and Ge(600 nm) by EBE. Pattern with 180 nm PMMA via electron-beam lithography (50 kV), deposit 20 nm Al2O3 hard mask, lift-off, transfer pattern into Ge by inductively coupled plasma-enhanced reactive ion etching. SEM verifies DDS quality. Optical measurements: Emissivity measured by FTIR (Bruker Vertex 80-V) with liquid-nitrogen-cooled MCT detector. Sample heated using Bruker A540 emission adapter; blackened steel plate used as blackbody reference. Polarization characterized with MIR wire-grid polarizer. Angle-resolved emission measured using a 3D rotating stage with 2° steps along x and y directions. Temperature series: 175–275 °C. Finite-size and lens collection modeled numerically using a Gaussian beam to emulate NA≈0.25 (angles −14.5° to 14.5°) on a 6×12-unit-cell array.

- Flat-band formation: Period doubling folds GM bands to Γ and strongly couples them with GMRs, producing avoided crossings and enabling a flat band with ultra-low group velocity near the I (Γ) point; v_g remains near zero up to ~0.1π/a, contrasting with rapidly increasing v_g in SDS. - High-Q QBIC control: In lossless case, Q diverges at Δ=0 (BIC) and follows inverse-quadratic decay with Δ. With realistic evaporated amorphous films, Q can still approach ~10^7 numerically. Critical coupling achieved at Δ=190 nm where Qrad=Qabs. - Simulated performance: Under y polarization, near-unity emissivity with ultra-narrow linewidth of 5.94 nm at λ0≈5.131 μm; multipole decomposition shows magnetic dipole dominance; emission is linearly y-polarized. - Angle insensitivity (simulation): Emissivity peak shows negligible spectral shift and robust narrow linewidth for output angles −17.5° to 17.5° in both x and y directions; Q decreases slightly at larger k due to increased radiation. - Experimental performance: Ultra-narrowband MIR emission with FWHM = 23 nm (Q ≈ 224) at λ0 ≈ 5.144 μm, maintained over a broad range of output angles (−17.5° to 17.5°). Emission intensity increases with temperature (175–275 °C). Polarization measurements confirm strong y-polarized emission and vanishing x-polarized output. - Temperature tuning: Center wavelength shifts nearly linearly with temperature due to Ge thermo-optic effect; linewidth remains nearly constant with temperature, enabling convenient fine tuning without degrading temporal coherence. - Angle-resolved measurements: For DDS, negligible wavelength shift up to ≈18° (y) and ≈10° (x); beyond, blue/redshifts occur but linewidth remains nearly unchanged. A control symmetry-broken SDS (SB-SDS) with similar normal-incidence Q exhibits strong redshift with angle and significant linewidth broadening (rainbow effect). - Power advantage: Using a lens with NA≈0.25 to collect emissions from the rainbow-free emitter can increase collected power by roughly two orders of magnitude compared to using a spatial filter on a rainbow-prone emitter to maintain ~10 nm bandwidth. - Finite-size device: A 6×12-unit-cell DDS under Gaussian-beam collection (NA≈0.25) preserves ultra-narrow linewidth; slight linewidth increase and emissivity reduction arise from edge scattering and Qabs–Qrad mismatch.

The work demonstrates that engineering a flat dispersion band via period-doubling in a dielectric metasurface can eliminate the rainbow effect while preserving high-Q resonances for ultra-narrowband thermal emission. Folding guided modes to Γ and coupling them with GMRs creates a flat band with near-zero group velocity over a wide wavevector range, so many output angles correspond to the same emission frequency. This directly addresses the challenge of angle-dependent spectral shifts that broaden collected spectra when using lenses, thereby enabling efficient power collection without spectral filtering and preserving temporal coherence. The emission is linearly polarized (y), exhibits near-unity emissivity under critical coupling, and maintains narrow linewidth across temperature and angle variations. Comparisons with a traditional QBIC-based emitter confirm that the flat-band DDS design is significantly less sensitive to output angle. The observed temperature-dependent spectral shift provides a practical tuning mechanism to match target absorption lines (e.g., in NDIR), while robustness to finite-size effects suggests scalability for larger devices.

By combining two geometric perturbations in a square lattice to induce Brillouin zone folding and controlled symmetry breaking, the authors realize a flat-band, high-Q QBIC in a distorted photonic lattice, enabling ultra-narrowband, rainbow-free MIR thermal emission. Numerically, linewidths of ~6 nm with near-unity emissivity at ~5.13 μm are achieved; experimentally, a 23 nm FWHM at ~5.144 μm is maintained over ±17.5° output angles, with linear polarization and temperature-tunable center wavelength. This design overcomes angle dispersion limitations of previous high-Q thermal emitters, allowing lens collection without spectral broadening and providing substantial power advantages. Future work can focus on improving material quality to further reduce linewidth, extending the flat-band approach to control full polarization states (including circular polarization via intrinsic chirality and vertical symmetry breaking), and scaling device size while minimizing edge scattering for practical sensing and energy applications.

- Material quality: All films were deposited by EBE, yielding amorphous Ge and higher absorption losses; emissivity and Q are limited compared to single-crystal materials. - Surface/sidewall roughness: Fabrication-induced scattering reduces emissivity and can mismatch Qabs and Qrad. - Angular range: Angle insensitivity is demonstrated up to ~±17.5° (experiment) with some direction-dependent limits (≈18° in y, ≈10° in x before noticeable shifts). - Finite-size effects: Small arrays show slight linewidth broadening and emissivity reduction due to edge scattering; alleviated in larger metasurfaces. - Temperature drift: Center wavelength shifts with temperature (thermo-optic effect), though this can be used for tuning; requires stabilization or calibration for certain applications. - Fabrication tolerance: A 20 nm geometric error leads to ~0.04 μm spectral shift; manageable via temperature tuning but still a consideration for precision applications.