Miniature computational spectrometer with a plasmonic nanoparticles-in-cavity microfilter array

The study addresses the challenge of achieving high spectral performance in miniature spectrometers. Traditional dispersive spectrometers (e.g., grating-based or Fourier transform systems) are bulky due to movable components and large optical elements, limiting portability and response time. Computational spectrometers that sample spectra with wavelength-selective components and reconstruct signals algorithmically are promising for miniaturization, especially when paired with CMOS/CCD image sensors that offer millions of pixels in compact formats. However, building large-scale arrays of spectrum-disparate filters with high transmittance, scalability, and low fabrication cost remains challenging. The research proposes a plasmonic nanoparticles-in-cavity (NPs-in-cavity) microfilter array coupled to a CMOS sensor and a machine learning reconstruction method to overcome the trade-off between device size and spectral resolution, enabling subnanometer visible-light spectral measurements in a compact system.

Prior miniaturized and computational spectrometers have used thin-film filters, perovskite films, single and superconducting nanowires, tunable van der Waals junctions, folded metalenses, integrated photonic chips, and wavelength-selective photodetectors. CMOS/CCD image sensor-based approaches are especially compelling because spatial multiplexing enables many filter elements, improving resolution via longer coding sequences. Various microfilters have been explored: quantum dots, photonic crystals, plasmonic encoders, rainbow chips, metamaterials/metasurfaces, liquid crystals, random structures, multilayer interference/etalon films, and 3D-printed optics. While multilayer film filters can tailor spectral responses, their multi-step deposition/patterning hinders scalability for large, distinct arrays. Nanophotonic metastructures can achieve subnanometer resolution but often require time-consuming, expensive nanolithography (e-beam lithography or nanoimprinting), limiting the number of distinct filters and throughput. Plasmonic chirped gratings demonstrate dual-function spectro/polarimetry but typically operate in reflection due to low transmittance, limiting compact transmissive designs. Hence, scalable, transmissive, and highly diverse microfilter arrays without ultrafine nanolithography are needed.

Design and operating principle: A plasmonic nanoparticles-in-cavity microfilter integrates size-controlled silver nanoparticles (AgNPs) within Fabry-Pérot (FP) thin-film microcavities. Strong coupling between the FP cavity modes and the AgNPs’ localized surface plasmon/Mie resonances induces Rabi splitting and modulates transmission peaks across the visible spectrum. Both AgNP size and FP cavity length are independently tunable, enabling n × m distinct microfilters from n cavity lengths and m nanoparticle sizes. Numerical modeling with COMSOL treats AgNPs as dense random (modeled as periodic) layers; coupling-induced splitting depends on nanoparticle layer density and inversely on the square root of cavity length. Design parameters include 25 nm Ag mirrors for balanced transmittance and FP resonance strength, a 43.5 nm SiO2 protective layer, and a 10 nm TiO2 photocatalytic layer between the AgNPs and the bottom Ag mirror. Simulations explore polymer (photopolymer) layer thicknesses from ~50–500 nm and AgNP diameters from 0–60 nm, showing Rabi splitting, anticrossing behavior, and opposite shifts of FP peaks around the plasmonic resonance near 400 nm.

Fabrication workflow (five steps): (1) Sputter deposition of bottom Ag/SiO2 layers on quartz; (2) Sol–gel spin-coating of a TiO2 nanolayer; (3) Direct printing of size-controlled AgNPs via precision photoreduction; (4) Grayscale patterning and nanoscale tuning of polymer FP cavities using digital UV lithography; (5) Sputter deposition of top Ag/SiO2 layers. Key advances include digital UV exposure using a DMD for both nanoparticle printing and cavity thickness control.

AgNP printing by precision photoreduction: UV light (365 nm) is projected through a coverslip and an ethylene glycol-based silver nitrate solution onto the TiO2 photocatalytic layer atop the Ag mirror. Material formulation was adjusted (ethylene glycol as solvent/reducing agent; removal of PVP) to suppress undesired solution photoreduction and mitigate light scattering during growth, stabilizing patterning. A DMD (1920×1080, optical resolution ~297 nm, peak intensity ~1803 mW/cm^2, exposure 1–60 s) loads grayscale patterns to control AgNP size (0–50 nm diameters). Substrates are rinsed (DI water, IPA) and dried (N2).

Grayscale photopolymerization for FP cavities: A DPHA acrylate resin (Easepi 7300) with 2% TPO-L photoinitiator and surfactant is spin-coated (500 rpm/6 s; 2000 rpm/30 s), prebaked (80°C, 2 min), and grayscale-exposed using the DMD (1–10 s). Oxygen inhibition introduces a vertical polymerization gradient; post-development (acetone/IPA) removes low-polymerized oligomers, followed by baking (120°C, 2 h) to stabilize film thickness. This enables micrometer-scale lateral patterning with nanometer-scale vertical control, yielding FP cavity lengths from tens to hundreds of nanometers, validated by cross-sectional SEM.

Array and device integration: A 1152-element microfilter array was fabricated (each 38.1 µm × 38.1 µm; total array 2.914 mm × 2.690 mm). The array was mounted at the image plane of a telecentric lens (DTCM110-16.6) to project the transmitted microfilter pattern onto a monochrome CMOS camera (ASI178MM; Sony IMX178 sensor; 14-bit; 3096×2080). A beam splitter divides the monochromator output: one arm monitored by a reference spectrometer (USB4000), the other through the microfilter array to the camera. Image preprocessing includes dark/bias correction, pixel binning, and filtering to enhance SNR.

Machine learning-based spectral reconstruction: Training uses a series of single narrow-peak spectra from a tunable monochromator to build a basis of spectra x_j(λ) and corresponding CMOS responses y_j. Assuming linearity, an unknown spectrum x̃(λ) is reconstructed via weights w solving a convex optimization that minimizes a least-squares CMOS discrepancy plus regularization terms: LASSO (L1), ridge (L2), total variation (TV), and quadratic variation (QV). Hyperparameters c1, c2, c3,p, c4,q control sparsity, stability, edge-preserving, and smoothness behaviors. CVXPY solves for w; x̃(λ) is then reconstructed as Σ w_j x_j(λ). Different hyperparameter sets are used for narrowband and broadband testing; a hybrid variant combining LASSO-like and ridge/TV terms was also employed.

Characterization and measurement: Transmission/reflection spectra of microfilters were measured (USB650/USB4000) with a 50× objective; polarization dependence assessed with a switchable linear polarization input. Imaging used a commercial metallurgical microscope and SEM for structural verification. Simulations and measurements evaluated Rabi splitting, peak density, FWHM distributions, and cross-correlation among filter responses to inform algorithm design.

• Fabrication and diversity: A 1152-element plasmonic nanoparticles-in-cavity transmissive microfilter array was fabricated using DMD-enabled UV processes. The array exhibits 2436 transmission peaks across approximately 425–850 nm, with FWHMs from 12.2 to 88.3 nm (average 23.8 nm), and sharp, diverse transmission features spanning ~400–900 nm.
• Strong coupling effects: Simulations and measurements confirm Rabi splitting between FP modes and AgNP Mie resonances, anticrossing behavior as cavity length varies, and opposite-direction shifts of adjacent FP modes around the plasmonic resonance (~400 nm). Measured splitting depth is less than simulations, attributed to AgNP size variation.
• Polarization insensitivity: Polarization dependence of transmittance is ~0.086 dB for 0–180° linear polarization, indicating polarization-insensitive operation.
• Spectral orthogonality: Cross-correlation analysis shows ~70.6% of filter-pair correlations lie between 0.2 and 0.6, motivating robust regularized reconstruction.
• Narrowband performance: With training on ~0.54 nm FWHM single-peak spectra, the system accurately reconstructs peak wavelengths over 395–725 nm with peak RMSE ≈ 0.03 nm; reconstructed average FWHM ≈ 0.65 nm (close to input 0.54 nm). The spectrometer resolves dual peaks separated by ~0.8 nm; with narrower training spectra, resolution improves to ~0.6 nm.
• Broadband performance: For asymmetric broadband inputs (bandwidths ~22–85 nm) and broader training (~8.6 nm FWHM), reconstructed spectra achieve high cosine similarities: 0.9981, 0.9958, 0.9941, and 0.9983.
• Algorithm comparison: Ridge shows better peak-wavelength accuracy, LASSO better FWHM fidelity; a hybrid regularization set achieves average FWHM ~0.48 nm (matching ~0.44–0.54 nm inputs) and peak RMSE ~0.018 nm in tests.
• Scaling with filter count: Spectral resolution improves markedly as the number of filters increases up to ~500, with diminishing returns beyond; benefits taper near ~1152–1440 filters for the tested configurations.
• Noise sensitivity: Reducing RMSE noise from 3.13% to 0.31% improves achievable resolution from ~2.16 nm to ~0.71 nm, highlighting the need for high SNR and denoising.
• Portable demonstration: A smartphone-based prototype measures ~50 nm bandwidth spectra well; narrow-peak performance is limited by sensor contrast. Overall, the miniature CMOS-based computational spectrometer achieves sub-nanometer resolving capability with an average resolution near 0.65 nm across the visible range, enabled by a scalable, highly diverse microfilter array and regularized reconstruction.

The work addresses the core challenge of combining miniaturization with high spectral resolution by creating a large-scale array of diverse transmissive microfilters without reliance on slow, expensive nanolithography. Strong coupling between FP cavities and AgNP Mie resonances greatly enriches spectral diversity (Rabi splitting, anticrossing, bidirectional FP peak shifts), enabling dense, distinct transmission features over the visible band. Digital UV lithography with a DMD provides precise, rapid, and parallel control over both FP cavity length and AgNP size, scaling the number of disparate filters to over a thousand in a millimeter-scale footprint. Coupled with a convex, regularized machine learning framework that mitigates ill-posedness due to correlated filter responses, the system reconstructs narrow and broadband spectra accurately. Performance analyses reveal that more filters substantially improve resolution up to a few hundred elements, after which gains saturate, and that noise critically limits reconstruction accuracy, underscoring the importance of SNR, denoising, and calibration. The demonstrated subnanometer resolving power and high accuracy validate the approach for compact, portable applications, while the fabrication methodology offers a practical path to further scaling and broadband extension.

The study introduces an AI-empowered miniature computational spectrometer that integrates a CMOS image sensor with a highly scalable plasmonic nanoparticles-in-cavity microfilter array. By independently tuning AgNP size and FP cavity length via digital UV lithography, the authors realized over a thousand spectrum-disparate transmissive microfilters exhibiting strong-coupling phenomena that enrich spectral features. With a regularized convex reconstruction framework, the spectrometer measures visible spectra with average ~0.65 nm resolution, resolves closely spaced peaks (~0.6–0.8 nm), and accurately recovers broadband profiles. This approach reduces dependence on ultrafine nanolithography while enabling compact, high-performance spectrometers suitable for portable and integrated applications. Future directions include: improving AgNP uniformity and cavity fabrication for more uniform, higher-density spectral features; developing reconstruction algorithms more robust to noise; training with narrower-band sources to push resolution; adopting higher-contrast, highly linear image sensors; and extending platforms (e.g., AuNPs, alternative FP stacks) to broaden operational bandwidth.

• Noise susceptibility: Reconstruction is sensitive to measurement and system noise due to ill-conditioning; performance strongly depends on SNR and effective denoising.
• Fabrication variability: Variations in AgNP size and cavity thickness reduce the depth and predictability of Rabi splitting compared to simulations, impacting ideal filter diversity and reconstruction accuracy.
• Resolution vs. training data: Achieved resolution depends on the bandwidth and density of training spectra; narrower training inputs improve resolvability but require more sophisticated or slower training.
• Diminishing returns with filter count: Beyond ~500–1000 filters, further increases yield reduced gains in resolution, implying practical limits without improvements in filter orthogonality or algorithms.
• Sensor limitations: Smartphone demonstrations indicate limited performance for narrow peaks due to lower sensor contrast and potentially lower linearity.
• Algorithm tuning: Reconstruction quality depends on careful hyperparameter selection; overly strong regularization can suppress weak or sharp spectral features.