Tunable rainbow light trapping in ultrathin resonator arrays

The study addresses the challenge of achieving tunable, spatially controlled, and spectrally precise rainbow light trapping with very high localized field strengths in plasmonic nanostructures. Conventional rainbow-trapping designs composed of resonator arrays (nanoparticles and nanocavities) lack analytical models for accurate prediction of resonant properties, requiring extensive simulations, and are limited by fabrication gap sizes typically ≥50 nm, which constrains field enhancement. The purpose is to develop an analytical, rapid design framework and a compatible fabrication method for metal–insulator–metal (MIM) nanogroove arrays that enable precise control over resonant wavelengths via groove width and length, achieving ultrathin gaps (down to 5 nm) and extreme local field enhancements across the visible spectrum. The significance spans sensing (SERS, PEF, SEIRA), nonlinear and super-resolution optics, and photo-enhanced catalysis, where strong, position-dependent field enhancement is critical.

Prior work has demonstrated plasmonic field enhancement using nanoparticles and nanocavities across applications such as SERS, PEF, SEIRA, nonlinear optics, super-resolution, and photocatalysis. Multi-resonant particles and cavities have been combined to realize position-dependent rainbow trapping. However, absence of analytical solutions for resonator behavior necessitates iterative simulations, and fabrication methods have limited minimum gaps (~50 nm), reducing achievable enhancement due to the inverse scaling of plasmonic enhancement with gap size. Length-graded nanogroove arrays have been explored, but with limited control and larger feature sizes. These gaps motivate an analytical, versatile design method and fabrication capable of ultrathin features.

Analytical modeling: Each MIM nanogroove (Ag–MgF2–Ag) is modeled as a Fabry–Perot resonator supporting the symmetric SPP mode. The standard resonance condition L = m·λ_spp/2 is modified to include a non-negligible boundary phase shift due to near-field energy storage at the open ends, leading to L = (m − φ/π)·λ_spp/2. The reflection coefficient r = |r|e^{iφ} and the phase φ are determined analytically from field integrals over the groove width, accounting for thin-dielectric (w < λ) effects. Phase shift is computed versus groove width, and resonant length versus width is obtained with and without phase correction.

Numerical validation: 2D COMSOL Multiphysics wave optics simulations are performed for selected geometries. For fixed groove width and wavelength, groove length is swept to locate resonance (maximal internal field intensity), validating analytical predictions that include the boundary phase shift.

Array design and simulations: Three array configurations are designed using the analytical resonance maps (first to fourth modes across the visible): (1) Length-graded arrays: constant width (e.g., w = 25 nm), groove lengths 40–120 nm with ~8 nm steps, 11 grooves, 70 nm Ag separation; (2) Width-graded arrays: constant length (L = 120 nm), widths 5–35 nm in 3 nm steps, 11 grooves; (3) Bigradient arrays: both length (60–220 nm) and width (35→5 nm) varied simultaneously. COMSOL simulations compute average |E|^2/|E_i|^2 inside grooves and surface field maps across 400–700 nm.

Fabrication: Arrays are fabricated via RF magnetron sputter deposition of alternating Ag and MgF2 layers to set ultrathin groove widths with near-nanometer precision, followed by focused ion beam (FIB) milling to define groove lengths (width-graded and bigradient designs demonstrated). Material choices (Ag for plasmonic performance; MgF2 for low index and confinement) are used, but the approach is compatible with other materials.

Experimental characterization: Rainbow trapping is demonstrated with far-field hyperspectral microscopy, and results are compared to simulations for positional and spectral agreement of field enhancement maxima.

• Analytical inclusion of boundary phase shift is essential: It reduces the resonant length by tens of nanometers relative to the simple Fabry–Perot model, especially at larger widths, and matches COMSOL simulations for the first mode.
• Tunability via width and length: Both parameters independently and jointly tune resonant wavelengths; resonance maps (for m = 1–4) enable rapid array design across the visible spectrum.
• Length-graded arrays (e.g., w = 25 nm; L = 40–120 nm): Provide rainbow trapping with position of maximum field enhancement shifting to longer grooves for longer wavelengths; observed multimode behavior at 400 nm (first and second order). Achieve normalized field enhancements on the order of 10^3.
• Width-graded arrays (L = 120 nm; w = 5–35 nm): Capture the full visible range with multiple trapped modes; ultrathin 5 nm grooves yield peak |E|^2/|E_i|^2 up to ~1.5 × 10^3; comparable spectral uniformity to length-graded arrays and more spectral peaks due to multiple modes.
• Bigradient arrays (L = 60–220 nm; w = 35→5 nm): Support a greater number of trapped modes than single-parameter graded arrays while maintaining high field strengths; spatial maxima correlate with analytical intersection points.
• Fabrication achievement: Realization of groove widths as small as 5 nm via multilayer deposition and FIB, an order of magnitude smaller than prior rainbow-trapping studies, enabling extreme localized enhancement.
• Experimental confirmation: Hyperspectral microscopy demonstrates rainbow trapping with spatial and spectral profiles in agreement with simulations.
• Application relevance: Near-field energy storage at groove boundaries enhances light–matter interactions at accessible surfaces, promising for sensing and nanoscale optics.

By incorporating boundary phase shifts into an analytical Fabry–Perot model of MIM grooves, the work provides an accurate, fast design tool for tailoring resonant conditions via groove width and length. This directly addresses prior limitations of iterative simulation-only design and limited feature control. The validated model guides creation of length-graded, width-graded, and bigradient arrays that produce position-dependent field maxima across the visible spectrum, achieving strong, localized fields (up to ~10^3–1.5×10^3 in normalized intensity) desirable for SERS, PEF, SEIRA, and other plasmon-enhanced processes. Experimental hyperspectral microscopy corroborates the simulated spatial progression of enhancement maxima with wavelength and the presence of multiple mode orders. The capability to fabricate 5 nm grooves drastically increases field strengths and expands the design space. Bigradient arrays, offering two degrees of freedom, further increase modal density and adaptability, though they require more stringent fabrication control. The framework is flexible in groove count, spacing, and targeted spectral regions and can extend beyond the visible, indicating broad relevance in integrated photonics and sensing.

The paper introduces a versatile analytical framework for designing rainbow-trapping MIM nanogroove arrays by leveraging both groove width and length, with essential inclusion of boundary phase shifts for accurate resonance prediction. Combined with multilayer deposition and FIB milling, the approach realizes ultrathin grooves down to 5 nm and extreme local field enhancements (~10^3–1.5×10^3). Length-graded, width-graded, and bigradient arrays are designed and validated via simulations and hyperspectral microscopy, showing tunable, spatially resolved enhancement across the visible. The paradigm enables rapid, predictive design for applications in sensing and nanoscale optics. Future directions include optimizing array geometry (groove number, spacing) for tailored spatial responses, extending operation into the near-infrared, and exploring alternative material systems to target specific spectral regions or application constraints.

• The analytical and numerical validation emphasized the first few resonant modes (m = 1–4) and geometries within the visible spectrum; behavior at higher orders and broader spectral ranges was not exhaustively explored.
• Simulations were 2D for rectangular grooves; full 3D effects, fabrication imperfections, and coupling between adjacent grooves beyond fixed spacing were not comprehensively studied.
• Experimental evidence is presented via far-field hyperspectral microscopy; direct near-field measurements and quantitative enhancement factors at the nanoscale were not detailed in the provided text.
• Bigradient arrays, while offering enhanced tunability, impose significant fabrication challenges requiring precise control over two geometric parameters.
• Complete affiliation details for some contributors and full fabrication tolerances/yield statistics are not provided in the excerpt.