## Introduction

Infrared (IR) and Raman spectroscopies provide complementary probes of molecular vibrations, and are widely used to sense molecules. However, only one in a million photons are inelastically scattered by the Raman process, and the interaction of vibrational transitions with IR light is an order-of-magnitude weaker than with electronic transitions in the visible region1. This limits the ability of conventional IR and Raman spectroscopies to measure trace analytes and demonstrates the need for an effective way to strengthen light-matter interactions in order to measure picomolar concentrations. Plasmonic constructs enhance the interaction of light with molecular vibrations2 using micron-scale resonant antennae3, metamaterials4, and nanoparticle aggregates5, and have been used to detect molecular structure and conformation via surface-enhanced IR absorption (SEIRA) spectroscopy6 for various chemical, biological, and security applications. Infrared confinement is also useful in light-harvesting for photovoltaics7 or photocatalysis, thermal management metasurfaces8,9, and in the design of new infrared sources and detectors10. Metal plasmonic nanocavities are highly efficient in reducing the mode volume of light, operate across a broad spectrum from the UV to THz11,12,13, and can be fabricated via self-assembly14,15,16,17,18,19 unlike surface phonon-polaritons20 and acoustic graphene plasmons21. However, for wavelengths λ in the mid-infrared (MIR), plasmonic cavity mode volumes achieved so far are on the order of (λ)3 in microcavities3 or 100∙(λ)2 in patch antennae22/superlattices19. Plasmonic nanoparticle resonances can be tuned towards the infrared by assembling nanoparticle chains11, which creates a collective super-radiant mode that saturates at λ ~ µm12 due to their intrinsic coupling. By extending the lateral extent14,15,16,17 and number of layers to create well-ordered superlattices19 or superparticles13, these resonances can be pushed beyond 1 µm. However, highly-ordered nanoparticle superlattices are difficult to fabricate with small gap sizes, and the tortuosity of their gaps and interstices makes bringing analyte molecules into optical hotspots difficult. Randomly deposited gold nanoparticle aggregates23 and rough gold substrates24 possess broad enhancements in the infrared spectral window for SEIRA, and lack specific resonances. The need to develop better SEIRA-active substrates has been identified2 (since developments lag behind SERS substrates), as well as to develop combined SERS-SEIRA platforms.

Here we show giant (>90% extinction) mid-infrared plasmonic resonances which have much smaller mode volumes of 10−8 (λ)3 and are highly tuneable. These are created by hierarchical self-assembly of amorphous gold nanoparticle multilayer films on a mirror (NPnML-on-mirror). Each layer is a disordered two-dimensional nanoparticle aggregate made by linking gold nanoparticles (AuNPs) with the molecular glue cucurbit[5]uril (CB[5])25, with the layers then sequentially deposited onto a gold mirror. These multilayer NPnML-on-mirror films, with n indicating the number of layers, possess dual resonances in the visible and infrared regions. Their dominant infrared resonance can be tuned beyond λ > 11 µm by increasing the AuNP size and number of layers, and is remarkably robust to disorder. Furthermore, free-space coupling of light into these nanogaps is efficient, making them practical for realistic SEIRA applications. The amorphous AuNP arrangement with precise nanogap sizes25 localizes visible and infrared light to sub-wavelength volumes, improves in/out-coupling of light, and allows giant SEIRA (>106) and SERS (106) enhancements to be obtained greatly exceeding all existing self-assembled platforms (benchmarked in Supplementary Tables S1 and S2).

## Results and discussion

### Tuning collective plasmonic modes to the mid-infrared

Millimeter-wide monolayers of nanoparticles with diameter D = 20–100 nm are fabricated by drop-casting a concentrated aqueous solution of AuNPs that are aggregated with CB[5] and concentrated in chloroform (see “Methods”). Since aggregation occurs at the chloroform-water interface, a two-dimensional AuNP sheet is produced with fill fraction ~65%. The resulting films are characterized to determine their surface morphology (Fig. 1a–c), showing separate regions with 1 or 2 layers. These dense layers are built from disordered AuNP networks (Supplementary Information Section S1) forming connected clusters with many vacancies. Cucurbituril-binding is crucial to achieve d = 0.9 ± 0.05 nm gap sizes25 that result in prominent resonances deep in the MIR. The gap size inhomogeneity when instead using salt or acid aggregation results in much broader modes (Supplementary Information Section S2). By depositing NP droplets sequentially after each previous one dries, NPnML multilayers (n = 1–9) can be rapidly constructed with a layer-number-dependent optical response (Fig. 1d, e).

The optical properties of the NP1ML-on-mirror monolayer films vs NP diameter D are measured in a custom-built visible (VIS) to near-infrared (NIR) reflectance spectrometer (Fig. 1d). Two plasmonic modes are found in the VIS and NIR, both redshifting with increasing NP size. A AuNP diameter of 100 nm is sufficient to tune the single layer resonance to λ = 1.7 µm. By then increasing the film thickness using n from 1–9 layers, the resonance tunes further into the MIR, out to λ = 11 µm (27 THz, 900 cm−1 in Fig. 1e). These resonances also display near complete extinction, with reflectance < 5%. Simultaneously, the infrared absorption bands of the CB[5] molecules embedded in the nanogaps are enhanced significantly when the MIR resonance passes through their vibrational transitions (Fig. 1e).

### Origin of mid-infrared mode tuning

Individual nanoparticle plasmons within well-ordered face-centered cubic AuNP superlattices couple with each other to form a collective plasmonic mode $$\widetilde{\omega}_p$$18,26. A simple estimate of the 1 ML plasmon frequency (Fig. 1d) from a generalized circuit model in the small gap limit27 indicates that $$\widetilde{\omega}_p$$ is set by the capacitance of the AuNP nanogaps (Supplementary Information Section S3), but does not change significantly with gap size. This collective plasmon $$\tilde \omega _p$$ then hybridizes with propagating light within the film $$\omega _l\left( {k_n} \right) = ck_n/n_{{{{\mathrm{eff}}}}}$$ (where neff is the effective dielectric constant in this material), forming a bulk plasmon-polariton mode (ωBPP) with dispersion set by the light-plasmon interaction strength (Ω)18,26:

$$2\omega _{{{{\mathrm{BPP}}}}}^2(k) = \omega _l^2\left( k \right) + \widetilde{\omega} _p^2 + 4{{\Omega }}^2 - \sqrt {\left[ {\omega _l^2\left( k \right) + \widetilde{\omega} _p^2 + 4{{\Omega }}^2} \right]^2 - 4\widetilde{\omega}_p^2\omega _l^2\left( k \right)}$$
(1)

In a multilayer of finite thickness, plasmon-polaritons reflect off the bottom and top surfaces to form standing waves, giving rise to pronounced Fabry-Perot-like optical resonances18,19. The giant absorption of NPnML-on-mirror films (reflection < 5%), relative to the perfectly ordered case (Supplementary Information Fig. S8), is due to the bottom mirror preventing transmission and the disorder-induced scattering loss28. The mirror at the bottom surface enforces a field-null here, which sets the fundamental Fabry-Perot mode resonant condition λn = 4 L, where $$L = \sqrt {\frac{2}{3}} nD$$ is the thickness of the NPnML18. This NPnML-on-a-mirror metamaterial slab confines a quarter-wavelength within it (Fig. 2a), resulting in wave-vector kn = 2π/(4L) of the collective plasmonic mode (Fig. 2b).

Using this condition, the observed plasmon resonances for n = 1–9 ML (Fig. 1e) compare well with the dispersion model of Eq. (1) (Fig. 2b), explaining the red shift with increasing nanoparticle diameter and layer number (Fig. 1d, e). A good fit is obtained (Fig. 2b black line) with neff = 1.3, $$\widetilde{\omega}_p$$ = 0.71 eV, and Ω = 0.51 eV (similar to that in highly-ordered AuNP superlattices18). When ωBPP becomes resonant with the CB[5] C = O stretch at ωm = 1765 cm−1 (Figs. 2b and 3b), an additional anticrossing/coupling of ωBPP with ωm occurs. As we will show below, the MIR light trapped in these modes occupies extremely small mode volumes, giving strong SEIRA spectra near resonance (Fig. 1e).

### Coupling of molecular vibration to collective plasmon

For NP7ML-on-mirror films, the broad plasmonic resonance (~2100 cm−1) results in a giant enhancement of the nearby ωm = 1765 cm−1 carbonyl (C = O) barrel-stretch mode of CB[5] (Supplementary Information Section S5). The IR absorption bands display a highly asymmetric Fano lineshape due to coupling and interference with the plasmonic mode29. From X-ray photoelectron spectroscopy measurements of these films (Supplementary Information Section S6), the upper limit of CB[5] coverage is 0.89 nm−2 (inter-molecular spacing = 1.14 nm). Comparing to infrared transmission spectra of 5 mM CB[5] in water gives a lower bound of the SEIRA enhancement factor (EF) as (1.2 ± 0.1) × 106 (Supplementary Information Section S7), performing better than state-of-the-art SEIRA platforms3,30,31,32 which only reach enhancement factors between 102-104 (detailed comparison in SI Tables S1 and S2).

By extracting the location of the molecular Fano dip and the center of the broad plasmonic resonance (Supplementary Information Fig. S18), an anticrossing can be seen as the plasmonic resonance tunes across the 1765 cm−1 vibration (Supplementary Information Fig. S19a, with changing film thickness around 7–8 ML). The optomechanical (vibration-plasmon) coupling strength g = 102 ± 8 cm−1 (Supplementary Information Fig. S19b) is comparable to many realizations of carbonyl bond (C = O) vibrational strong coupling with previous g ranging from 3033, 5422, 6434, to 7535 cm−1. However, due to the large linewidth of the plasmon (γc ~ 770 cm−1) and small molecular linewidth (γm ~ 70 cm−1), the coupled system remains in the weak coupling regime36, defined by 2g/γc ~ 0.3 (thus <1). On the other hand, the effective cooperativity factor C = 4g2/γcγm 0.8 is comparable to single-molecule strong coupling in the visible37 and mid-infrared collective strong coupling33.

The Fano lineshape can be fitted by a modified coupled oscillator model38, which accounts for the change in refractive index of the plasmonic system due to coupling with molecular resonances in the local Green’s function (Supplementary Information Section S8) as a modified polarization,

$$P\left( \omega \right) \propto \frac{{\left( {{{{\mathrm{\nu }}}} + q} \right)^2 \,+ \,B}}{{\left( {{{{\mathrm{\nu }}}}^2 + 1} \right)}}$$
(2)

with normalized detuning $${{{\mathrm{\nu }}}} = \left[ {\omega ^2 - \left( {\omega _m + \delta \omega _L} \right)^2} \right]/\omega \gamma _m$$, Fano asymmetry parameter $$q = 2(\delta \omega _L - \delta \omega _L^\prime )/\gamma _m$$ and $$B = \left( {\gamma _m^\prime /\gamma _m} \right)^2$$, where ω is the incident frequency, ωm the molecular transition frequency, $$\delta \omega _L$$ the molecular Lamb shift, γm the molecular decay rate, and $$\delta \omega _L^\prime$$, $$\gamma _m^\prime$$ the multipolar plasmonic modifications to the Lamb shift and decay rates respectively (see ref. 43 and Supplementary Information Section S8). Fitting Eq. (2) allows coupling parameters to be extracted as a function of detuning (Fig. 3d, e).

The strength of the plasmon-molecule interaction is observed in the magnitude of the Fano peak-to-dip extinction (RFano), which can be almost as large as the plasmon mode extinction (Fig. 3a, c, d), and the molecular Lamb shift ($$\delta \omega _m$$), which can reach up to 40 cm−1. This greatly exceeds any existing SEIRA platforms which have RFano of only a few percent3,30,31,32 (SI Table S1 and S2). Furthermore, there is a strong multipolar contribution to the near-field Green’s function, beyond the dipolar approximation38, which introduces an additional Lamb shift ($$\delta \omega _L^\prime$$) and linewidth broadening ($$\gamma _m^\prime$$). This results in an asymmetric spectrum at zero-detuning Δ = ωBPPωm ~ 0 (Fig. 3c), where a symmetric one is normally expected. Hence, the largest $$\delta \omega _m$$ and RFano do not occur at zero detuning, but at Δ ~ 200 cm−1. Finally, the Fano asymmetry parameter (q) of the SEIRA peaks flips sign39 as expected, depending on the detuning Δ (Supplementary Fig. S19c).

From the coupling strength and radiative decay rates (Supplementary Information Section S9), the effective radiative Purcell enhancement factor $$F_p = (\gamma _m - \gamma _{{{\mathrm{m}}}}^\prime )/\gamma _{{{\mathrm{m}}}}^{{{\mathrm{s}}}} = 4g^2/\gamma _{{{\mathrm{c}}}}\gamma _{{{\mathrm{m}}}}^{{{\mathrm{s}}}}$$ can be found38, where the spontaneous radiative decay rate of CB[5] outside the cavity is $$\gamma _m^s$$. This spontaneous molecular radiative decay can be extracted from the oscillator strength of the CB[5] vibration ($$\gamma _m^s$$ = 1.1 × 10−6 cm−1, Supplementary Information Section S9), and the decay within the cavity from fitting the spectrum in Fig. 3a (γm = 62 ± 5 cm−1, $$\gamma _m^\prime$$ = 49 ± 4 cm−1). The resulting average Purcell factor FP = (6 ± 1) × 106 is large (even exceeding 107) and comparable to many single nanostructure Purcell factors in the visible regime40. The mode volume (Vm) reduction compared to free-space corresponding to this Purcell factor is Vm = 1.5 × 10−8 λ3 (Vm = 2900 nm3). The extracted mode volume thus implies light confinement within ~7 gaps assuming typical 25 nm diameter facets27 and d = 0.9 nm gap widths defined by CB[5]. This is consistent with the number of gaps within a AuNP septamer, which forms the typical structural motif in the disordered film (Fig. 1b and Supplementary Information Fig. S1), and approaches the limit of tightest confinement possible within this nanostructure. Squeezing the near-field into consistent gaps of spacing 0.9 nm accounts for the large optomechanical coupling strength g, the dip strength Rnorm, Lamb shift $$\delta \omega _{\it{m}}$$, and the giant SEIRA enhancement factors measured.

### SEIRA—SERS comparison on a single substrate

In the following, we compare the SEIRA and SERS spectra from a NP7ML-on-mirror film. While the SEIRA spectrum is dominated by the portal C = O stretch of CB[5] in the gaps (Fig. 4a), the SERS-active vibrations have different selection rules and instead are dominated by the expected 830 cm−1 peak from the CB[5] ring-breathing mode41 (Fig. 4b). In addition, multiple peaks from the citrate capping agent used to stabilize AuNPs are observed only in the SERS spectrum. Hyperspectral IR and Raman maps of the same substrate show substantially different enhancements in the bands associated with CB[5]. The SEIRA C = O map (Fig. 4c) has different local intensities due to the heterogeneity in number of AuNP layers which locally tunes the ωBPP resonance. The SERS map (Fig. 4d) is more homogeneous because the SERS enhancement depends more on the local septamer structure of the AuNPs in the visible regime and the homogeneous nanogap sizes.

Sensing analytes with SEIRA is possible by flowing31 them through the CB[5]-scaffolded nanogaps42 (preliminary data in SI Section S13, Fig. S25). However besides the vibrational signals from these nanogaps, it is possible to detect molecular self-assembled monolayers (SAMs) placed onto the mirror, before the NPnML is deposited (Fig. 4e, pink molecular layer). Here, we use a robust SAM molecule 4'-cyanobiphenyl-4-thiol (BPTCN) as a spacer, because of its clearly distinguished vibrational modes from CB[5]. The enhancement of the local fields in the gaps between a NP1ML film and the mirror is clearly seen by the strong SERS from this molecular layer (Fig. 4f), with SERS enhancement factor 1.1 × 106 (Supplementary Information Section S7). A perfectly ordered AuNP superlattice on a mirror has a field null enforced by boundary conditions on the surface, with poor enhancement of SERS signals expected at the superlattice-mirror gap. In contrast, the NPnML-on-mirror films display strong simultaneous SERS and SEIRA enhancements which arises due to the disordered nature of the AuNP layers allowing for high-angle coupling into the gap between the NPnML layer and the mirror via each defect. Supercell calculations of defects in the ordered superlattice confirm this enhanced coupling (Supplementary Information Section S4 and Fig. S12).

To demonstrate the strong enhancements possible here, we also demonstrate sub-picolitre sensing of 1-decanethiol (DT) SAM (0.07 pL of DT in IR microscope spot size) which is typically hard to detect. The SERS and SEIRA spectra (Fig. 4g, h) of the adsorbed DT are extracted by subtracting the spectrum of the bare film and correcting for the plasmonic background (Supplementary Information Section S10). The SERS and SEIRA enhancement factors for 1-decanethiol are 1.2 × 104 and 8.3 × 103 respectively. The observed SEIRA peaks possess different maximum enhancement as a function of relative detuning (Δ) from the plasmon peak (ωBPP). This emphasizes the role of local plasmonic fields, as different vibrations couple in different ways to the local multipolar plasmonic field, resulting in different near-field enhancements.

It is remarkable that the disordered NPnML-on-mirror films display similar bulk plasmon-polariton modes to their highly-ordered parent structures, but with much better SERS and SEIRA enhancement factors19. Previous theoretical results implied highly-ordered structures43 are needed for dipole-dipole coupling to create the collective plasmonic mode26. However, in our case the infrared response is no longer dependent on the precise NP structure, but instead behaves as an effective metamaterial in the homogeneous regime, similar to random AuNP aggregate coupling to ITO plasmons in the near-infrared44. Our work shows that structural order is not necessary, and in fact aids sensing applications as it allows more light to be in/out-coupled.

## Conclusions

In summary, multilayer films of amorphously-arranged AuNPs (NPnML-on-mirror) are fabricated by self-assembly with a precision cucurbit[5]uril molecular glue. The resulting metamaterial displays tunable resonances in the mid-infrared sensing region (λ = 2–10 µm). Our key advance is to show that near- to mid-infrared can be compressed into mode volumes Vm ~ 108 λ3, resulting in strongly enhanced vibrational signatures from gap molecules and plasmonic resonances which are robust to global structural disorder. Instead of using complex microfabricated structures which require combined lithography of µm length-scale antennas with nm gaps, we here utilize facile self-assembly of commercially available AuNPs with molecular scaffolding to define the optimum architecture with precise sub-nanometer gap sizes.

NPnML-on-mirror films display dual SERS and SEIRA enhancements, enabling sensing of molecules with different spectral features in Raman and IR, and can avoid visible fluorescence backgrounds that contaminate Raman spectra. The strong mid-infrared mode, which arises from a bulk plasmon polariton, allows for both significant SEIRA (EF ~ 106) and SERS (EF ~ 106) enhancements, with vibration-plasmon coupling strengths on par with those in vibrational strong coupling. The SERS and SEIRA enhancement factors exceed many state-of-the-art resonant plasmonic antenna structures3,30,31,32 used to confine mid-infrared light for sensing. The strength of the coupling can be attributed to the efficiency with which the NPnML-on-mirror confines MIR light and squeezes it into the locally-ordered nanocavity gaps. The large Purcell factor and extremely small mode volume implies strong confinement of the mid-infrared field within a small number of inter-particle gaps, approaching the limit of confinement possible within such a nanostructure.

The simplicity of this self-assembly enables the creation of robust amorphous metasurfaces. Rather than being a burden, disorder is a strength as it aids diffusion of molecules into the gaps for sensing and permits access to strong optical fields between the NPnML film and the mirror, potentially allowing real time SEIRA measurements within microfluidic flow cells (Fig. S25) with a reusable substrate (Fig. S26). Amorphous NPnML-on-mirror films with extremely small mode volumes open up a key platform with broader uses for infrared radiation capture in increasing the efficiency of IR photodetectors10, controlling the spectral reflectance of thermal management surfaces8,9, in display technologies45, to modulate IR emission, and vibrational strong coupling-controlled chemistry46. The dual enhancements in the visible and IR regions also have the potential to increase nonlinear frequency upconversion47 or frequency mixing48 efficiencies.

## Methods

### Multilayer aggregate formation

Disordered AuNP films were formed by adding 500 μL of gold nanoparticles (20–100 nm, citrate capped, BBI Solutions; 200 nm Sigma-Aldrich) to 500 μL of chloroform in an Eppendorf tube. Aggregation was initiated by the addition of 150 μL of CB[5] (cucurbituril-5-hydrate, Sigma-Aldrich), followed by immediate vigorous shaking for 1 min. After shaking, the solution was left to settle for another minute, causing the separation of the immiscible chloroform and aqueous phases. The aggregated gold nanoparticles then settled to the interface between the two phases. The aqueous phase was thrice-washed by the addition and removal of 500 μL of water to dilute the citrate salts. The aqueous phase was then slowly concentrated by removal of water till a dense Au aggregate bead was formed in chloroform. The bead was then deposited on a gold coated glass substrate (thermally evaporated 5 nm Cr and 500 nm Au) and left to dry. Upon drying, the substrate was cleaned with water, isopropanol, and dried in nitrogen gas. SEIRA measurements were performed on monolayers of decane-1-thiol (DT, Sigma-Aldrich) prepared by immersion of Au substrates for 30 h in DT liquid, and subsequent rinsing and cleaning in ethanol and dried in nitrogen gas flow. SERS measurements of 4′-cyanobiphenyl-4-thiol (BPTCN, Sigma-Aldrich) was performed by deposition of AuNP multilayers on a self-assembled monolayer prepared by overnight immersion of gold substrate in 1 mM BPTCN in ethanol, and subsequent rinsing in ethanol and drying in nitrogen gas flow.

### Broadband reflectance spectroscopy

For large scale extinction spectra, a custom-built setup was used to simultaneously measure the visible (Ocean Optics QEPro from 300 nm to 1000 nm), near-infrared (Ocean Optics NIRQuest from 700 nm to 2000 nm), and mid-infrared (FTIR Interspec 402-X from 1700 nm to 20,000 nm) spectrum, using a thermal globar lamp source and ZnSe beam-splitters, and referenced to a clean gold mirror.

### Infrared microscopy

FTIR reflectance spectral mapping (Shimadzu AIM-9000 FTIR microscope, liquid nitrogen cooled MCT detector, Cassegrain 15X objective 0.7 N.A., 20 µm spot size, Happ-Genzel apodization) was performed, referenced to a clean gold mirror.

### Raman microscopy

Raman measurements (Renishaw inVia microscope, 20X objective, 785 nm, 0.1 mW incident power) were collected with a 1 s integration time.

### Characterization

Sample morphology was analysed using scanning electron microscopy (Hitachi S-5500, 10 kV accelerating voltage) and white light vertical scanning profilometry (Bruker Contour GTK) to obtain heights of monolayer and bilayer AuNP film regions. Atomic force microscopy (Asylum Research MFP-3D Origin+) was also used to characterize layer heights. X-ray photoelectron spectroscopy (ThermoFisher Escalab 250Xi) was used to measure the surface chemistry of MLAgg films using a monochromated Al Kα X-ray source.

### Simulations

Finite-difference time-domain (FDTD) simulations (Lumerical FDTD Solutions) of perfectly ordered AuNP superlattices were conducted (for details see SI). Mie scattering simulations were performed with MSTM49 (multiple-sphere T-matrix formalism) with the Au dielectric function of Johnson & Christy (details in SI).