Sub‑Diffraction‑Limit Structural Color Filters with Uncoupled LSPPs: 141 000 dpi, Wide Gamut, and Polarization Independence

Abstract

The continuous shrinkage of pixel pitch on modern image sensors has outpaced the capabilities of conventional dye‑based color filters, which typically span several micrometres and therefore limit achievable spatial resolution. We report a plasmonic structural colour filter that exploits a circular nanohole‑nanodisk hybrid lattice, producing a single‑pixel colour response with an area of only 180 × 180 nm²—corresponding to a theoretical resolution of ~141 000 dpi. The key to this performance lies in uncoupled localized surface plasmon polaritons (LSPPs), which allow each nanostructure to act as an independent colour generator. Experimental measurements and numerical simulations confirm that the filter offers a broad colour gamut, a wide viewing angle, and insensitivity to the incident light’s polarization. These attributes make the approach attractive for high‑density optical data storage, secure microscale imaging, and next‑generation nanoscale optical filters.

Introduction

Digital imaging technology is pushing sensor elements down to the sub‑50 nm regime, yet the optical components that translate light into colour—particularly colour filters—have lagged behind. Traditional filters rely on organic dyes or pigments and therefore require pixel sizes of several micrometres, which inevitably overlaps multiple sensor pixels and degrades spatial fidelity. In 2015, a vertical nanorod array sensor with a 50 nm pitch was demonstrated, underscoring the gap between sensor miniaturisation and filter resolution.

Structural colour offers a pathway to bridge this gap. Unlike pigment‑based systems, structural colours arise from the interaction of light with nanostructured metal or dielectric patterns, enabling sub‑wavelength pixel dimensions. The extraordinary optical transmission (EOT) phenomenon, discovered in 1998, has been instrumental in designing plasmonic structural colour filters (SCFs) that can approach the diffraction limit. Over the past decade, various SCF architectures—sub‑wavelength hole arrays, nanodisk ensembles, hybrid nanohole‑nanodisk configurations, and metal gratings—have been reported. However, achieving simultaneously a small pixel size, wide colour gamut, large viewing angle, and polarization independence remains a challenge.

While many plasmonic SCFs rely on coupling between adjacent resonators—thereby limiting pixel miniaturisation—our design exploits uncoupled localized surface plasmon polaritons in a circular nanohole‑nanodisk hybrid lattice. This strategy yields individual pixel colours at 180 × 180 nm² while preserving a wide gamut and angular robustness. The following sections detail the fabrication, optical performance, underlying physics, and practical demonstration of this approach.

Methods

The plasmonic filters consist of a square‑lattice array of circular nanodisk‑nanohole hybrids fabricated on a silicon substrate (Fig. 1a). A 25 nm silver layer is deposited directly onto 120 nm polymethyl methacrylate (PMMA) pillars with a 1 nm chromium adhesion layer. Silicon is chosen for its high conductivity, which facilitates electron‑beam lithography (EBL). Silver is selected for its low extinction coefficient and the presence of a thin (~2–3 nm) native oxide layer that only marginally shifts the resonance.

a Illustration of the circular nanodisk‑nanohole hybrid array on silicon. b Fabrication flowchart: (i) spin‑coat 120 nm PMMA, (ii) expose with 100 kV, 100 pA EBL, (iii) develop in MIBK/IPA, (iv) deposit 1 nm Cr + 25 nm Ag, (v) lift‑off. c SEM images of arrays with period P = 200 nm and diameter D = 130 nm; inset shows a magnified view. Scale bars: 1 µm (left) and 200 nm (right).

In detail, the PMMA resist is spin‑coated onto the silicon wafer and patterned using a high‑resolution NanoBeam Limited nB5 system (100 kV, 100 pA). After development in MIBK and rinsing in IPA, the resist pillars are annealed under nitrogen. Subsequently, a 1 nm Cr adhesion layer followed by a 25 nm Ag film is evaporated using an electron‑beam source. The resulting structures are characterised by scanning electron microscopy (SEM) to confirm dimensions and uniformity.

Results and Discussion

Wide Colour Gamut

Figure 2a shows a colour palette generated by varying the nanodisk diameter D (70–140 nm) and lattice period P (150–240 nm). Mapping the reflected colours onto the CIE 1931 chromaticity diagram (Fig. 2b) confirms coverage of the cyan‑magenta‑yellow (CMY) primaries. Reflectivity spectra were recorded with a NOVA‑EX spectrometer (400–800 nm) and an Olympus BX53 microscope (NA = 0.9, 100×). The experimental spectra (Fig. 2c) exhibit red‑shifting minima as D increases, matching the finite‑difference time‑domain (FDTD) simulations (Fig. 2d). Minor discrepancies arise from fabrication tolerances and material parameters.

Contour maps (Fig. 2e,f) reveal that period P has a modest effect on spectral features, whereas diameter D predominantly governs the resonant wavelength—a contrast to many previous SCF designs where P was the main tuning parameter. This behaviour enables colour definition with a single nanostructure, paving the way for ultra‑compact pixels.

a Colour palette as a function of period P and diameter D. b CIE 1931 diagram with experimental points. c Experimental reflectance spectra. d FDTD spectra. e Reflection contour vs. wavelength and period (P = 180–240 nm, D = 100 nm). f Reflection contour vs. wavelength and diameter (P = 230 nm, D = 70–140 nm). White asterisks mark spectral minima; dashed lines trace the fitted minima.

Physical Mechanism

In periodic nanostructures, inter‑particle coupling can shift and split plasmonic resonances, limiting the smallest viable pixel size. The short propagation length of short‑range surface plasmon polaritons (SRSPPs) and the decay of localized surface plasmon polaritons (LSPPs) means that, when the separation exceeds ~150 nm, coupling is negligible. FDTD simulations of arrays with large (Fig. 3a,b) and small (Fig. 3c,d) inter‑particle distances confirm this: large‑spacing arrays confine the field to the edges of the disks and holes, while small‑spacing arrays show strong field localisation in the gaps, evidencing SRSPP and LSPP coupling.

Because our design deliberately maintains a large inter‑particle gap, the observed colour originates mainly from uncoupled LSPP modes. The resonant wavelength is therefore governed by the nanodisk diameter, explaining the strong D‑dependence seen in the experimental data and the relative insensitivity to period P.

a,b Field maps at spectral minima (P = 180 nm, D = 80 nm). c,d Field maps at λ = 600 nm (P = 180 nm, D = 160 nm). White dashed lines outline the Ag layer.

Polarisation Independence and Large Viewing Angle

The circular symmetry of the nanostructures ensures that the reflected spectrum does not depend on the polarisation of the incident light. FDTD simulations using the Broadband Fixed Angle Source Technique (BFAST) confirm that both s‑ and p‑polarised illumination produce virtually identical spectra up to ± 40° incidence (Fig. 4a,b), indicating a wide angular tolerance suitable for imaging applications.

Simulated angle‑resolved reflectance for (a) p‑polarisation and (b) s‑polarisation at P = 180 nm, D = 80 nm.

Super‑High Resolution

To verify the sub‑diffraction‑limit performance, we fabricated a series of checkerboard patterns with 1–5 × 1–5 pixel blocks (P = 180 nm, D = 80 nm). Even a single nanostructure (1 × 1) produced a vivid magenta colour (Fig. 5a‑i), demonstrating that each pixel functions independently. This translates to a theoretical resolution of ~141 000 dpi, well above conventional colour filter limits.

a Resolution test pattern (SEM on right). b Sub‑wavelength colour printing of “Nature” and “Science” (6 µm × 9 µm). Scale bars: a‑i 1 µm, a‑ii 500 nm, b‑i 200 nm, b‑ii 1 µm, b‑iii 500 nm.

The printed letters “Nature, Science” showcase the ability to render fine detail at the single‑nanostructure level, underscoring the potential for high‑density optical storage and covert microscale imaging.

Conclusions

We have demonstrated a plasmonic structural colour filter that operates at a pixel size of 180 × 180 nm²—equivalent to ~141 000 dpi—using uncoupled LSPPs in a circular nanohole‑nanodisk lattice. The filter offers a full CMY colour gamut, a large viewing angle (± 40°), and polarization independence. Because each pixel is a single resonator, the design supports truly sub‑diffraction‑limit resolution, as verified by both simulation and experimental colour printing. The approach holds promise for next‑generation nanoscale imaging, secure microscale graphics, and high‑density optical data storage.

Availability of Data and Materials

The datasets that underpin the conclusions of this article are included within the article.

Abbreviations

BFAST:

Broadband Fixed Angle Source Technique

CMY:

Cyan, magenta, yellow

dpi:

Dots per inch

EBL:

Electron‑beam lithography

EOT:

Extraordinary optical transmission

FDTD:

Finite‑difference time‑domain

IPA:

Isopropyl alcohol

LSPPs:

Localized surface plasmon polaritons

MIBK:

Methyl isobutyl ketone

PMMA:

Polymethyl methacrylate

SCFs:

Structural colour filters

SPPs:

Surface plasmon polaritons

SRSPPs:

Short‑range surface plasmon polaritons