Ultrastrong coupling between molecular vibrations in water and surface lattice resonances

Vibro-polaritons under the USC have been investigated exclusively with Fabry–Pérot optical cavities formed by a pair of facing mirrors with the molecules in between.^31–35 An alternative platform to achieve USC can be found in periodic arrays of scattering metallic or dielectric particles called metasurfaces. These metasurfaces sustain photonic modes known as surface lattice resonances (SLRs), which arise from the enhanced radiative coupling of the scatterers in the array mediated by the in-plane diffracted orders of the array.^36–39 Compared to optically closed Fabry–Pérot cavities, these metasurfaces are open cavities, which are fully accessible for optical characterizations and easier to couple with external radiation. In addition, their tunability and scalability make them relevant for strong and ultrastrong coupling experiments.

In this article, we experimentally demonstrate the VSC between the SLRs of an array of gold microparticles and the OH stretching modes of water molecules; see Fig. 1(b). The symmetric and asymmetric stretching modes of water cause a very broad linewidth of $∼500$ cm⁻¹ and an energy of 3390 cm⁻¹. Several studies have demonstrated the USC of water in the Fabry–Pérot cavity^{22,24,40–42} and water droplets.⁴³ The gold metasurfaces are designed and optimized using Finite-Differences in Time-Domain (FDTD) to obtain an SLR perfectly resonant with the OH modes. Due to the close frequencies between the two stretching modes of water, the SLRs here couple to both modes, leading to the formation of two species of vibrational polaritons. We investigate three different array configurations: an array with a single gold disk per unit cell, an array with a dimer of disks per unit cell, and an array with a bowtie per unit cell. Among these systems, the bowtie array exhibits the largest Rabi splitting because of its highest field confinement. In addition, the optical response of the fabricated array of gold bowties coupled with the OH⁻ bond of water was measured. We recover a Rabi splitting of 564 cm⁻¹, whose coupling strength g is 8% of the vibrational energy of the OH stretching modes. This magnitude of the coupling strength is close to the criterion of USC. The demonstration opens the possibility of using these resonant arrays as a platform to further investigate novel physical and chemical properties under USC.

The light–matter interaction between the OH⁻ molecular vibrations and SLRs is performed on uniform periodic arrays of gold microparticles. To investigate what kind of particle’s geometry and configuration leads to the strongest coupling strength, we analyze three different configurations of particles forming the unit cell: a single disk, a dimer of disks, and a bowtie. The geometrical parameters of both the metallic particles and the arrays have been optimized using the FDTD method. In general, the optimal coupling is achieved when the SLR perfectly overlaps with the molecular resonance. For all three array configurations, a three-layer system is considered: a semi-infinite CaF₂ substrate with frequency-dependent permittivity,⁴⁴ the gold particles with a complex refractive index on top of the substrate,⁴⁵ and 6 μm of dielectric material representing the water layer on top of the array. To simulate the optical response of the bare array without the effect of the molecular vibrations of water, we consider the dielectric material on top of the arrays with the real part of the refractive index of the dielectric material as a constant (n = 1.33) and zero dissipation (k = 0). A hypothetical non-dissipative medium is used for the numerical characterization of the SLR modes in the absence of molecular vibrations [black curves in Figs. 3(a)–3(c)]. By having a real component of the refractive index and no absorption, we can tune the SLRs to the same frequency of the molecular vibrations, which are responsible for the coupling. For the array formed by single disks, the optimization is performed by sweeping over several radii of particles (R) and period of the arrays (a), until a good overlap between the spectral position and linewidth of the SLR and the OH⁻ resonance is achieved. The height of the metallic particles is set at 50 nm. The optimal system obtained from the simulations is an array with a period a = 1.95 μm and disk’s radius of R = 490 nm.

The increased complexity of the array of disk’s dimers requires the consideration of an additional parameter: the gap distance, d, between the disks in the dimer. After optimization of the geometrical parameters, the ideal system is found to have a period a = 1.9 μm, radii of the disks in the dimer of R = 335 nm, and a gap distance of d = 50 nm. Finally, the array configuration with bowties is optimized with the simulations by sweeping over the period, the angle α at the vertex of the triangles, and the height of the triangles h. The optimization yielded an array with a period a = 1.75 μm and a height of h = 670 nm.

As the coupling strength depends on the electric field of the metasurface, we simulated for all the optimized configurations the electric field enhancement under normal illumination with a plane wave polarized along the x-direction. The results are shown in Fig. 2. Schematic illustrations of the unit cell with the parameters that are optimized with the simulations are shown in Figs. 2(a),2(e), and 2(i). Figures 2(b)–2(d) show the field enhancement in a unit cell of the array formed by single disks. The largest field enhancement is located on the edges of the particle with a 20-fold enhancement. In addition, field enhancements above 2, which are associated with the SLR, extend up to 1 μm above the CaF₂/water interface.

Compared to the array of single particles, the configuration with the disk dimers shows a higher field enhancement of 30 in the gap between the disks, as shown in Figs. 2(f)–2(h). The SLR in the array of bowties gives the highest field enhancements with a maximum value of 155 [Figs. 2(j)–2(l)]. Notably, at the bases of the triangles, a high-field enhancement is also present with a value of 20, comparable to the highest fields of the previous two configurations.

The coupled systems are simulated by replacing the dielectric material without absorption with the material with the complex refractive index of water.⁴⁶ Note that the molecular density and the random orientation of water molecules are taken into account by the complex refractive index of bulk water. The simulated extinction spectra E, defined as E = 1 − T (where T is the transmission), of the coupled systems are shown for the investigated arrays in Figs. 3(a)–3(c) (red curves) as a function of the wavenumber. The extinction of the SLRs of the bare arrays is shown in the same figures as a black curve. All three configurations clearly show Rabi splitting, indicating the formation of vibro-polaritons. Note that the VSC here fulfills the Savona et al. criterion: 4g > |γ_c − γ_m|, where γ_c and γ_m correspond to the losses of the photonic modes and the molecular resonator.^47,48 For the array of the single microdisks, we retrieve the energies of the lower and upper polaritons to be 3130 and 3610 cm⁻¹, respectively. The Rabi splitting is 480 cm⁻¹. In the case of the array of dimers of disks, the lower polariton has an energy of 3150 cm⁻¹ and the upper polariton has an energy of 3603 cm⁻¹, with a Rabi splitting of 453 cm⁻¹. The coupled array of bowties and water shows the polaritons at 3119 cm⁻¹ for the LP and 3645 cm⁻¹ for the UP. For this configuration, the Rabi splitting is 526 cm⁻¹, which is $∼17%$ of the energy of the molecular vibration. These results show that the array of bowties gives the highest light–matter coupling strength together with the most intense field enhancement [Fig. 3(d)]. As a result, we choose the array of bowtie as the platform to experimentally achieve vibrational ultrastrong coupling. Interestingly, the comparison between the single-microdisk array and the array of microdisk dimers indicates that high local field enhancements are not directly associated with high coupling strength. This is because the disk dimer causes fewer averaged field enhancements on top of the disks, where the majority of the molecules are located, compared to the single disk (Fig. S2).

The particle array has been fabricated using electron beam lithography (see Sec. S1 of the supplementary material) on a disk-shaped CaF₂ substrate with 1-inch diameter and 1 mm thickness. A scanning electron microscope (SEM) image of a portion of the array is shown in Fig. 4. The dimensions of the array are 9 × 9 mm². After fabrication, the sample is placed in a Harrick Scientific demountable liquid cell with a 6 μm polytetrafluoroethylene (PTFE) spacer and a 2 mm thick CaF₂ window on top. We use a Bruker v70 Fourier Transform Infrared Spectrometer (FTIR) to measure the IR extinction spectra.

The SLR of the bare array is characterized by measuring the zeroth order transmission with linearly polarized incident light at normal incidence. The dependence of the IR extinction on the polarization angle of the incident light is shown in Fig. 4(b). The band of large extinction around 4000 cm⁻¹ corresponds to the SLR. The white vertical dotted lines indicate the angles at which the polarization of the light is parallel (TE) or orthogonal (TM) to the long axis of the bowties, which leads to a blueshift from 3930 cm⁻¹ (parallel to the long axis) to 4066 cm⁻¹ (orthogonal to the long axis). In Fig. 4(c), the simulated and measured SLRs of the bowtie array are shown for both TE (red) and TM (black) polarizations as a function of the wavenumber. For both simulations and measurements, the nearly equal peak positions of TE and TM modes arise from the same lattice periods along the x and y axes (square lattice) together with the nearly equilateral shape of the triangles forming the bowtie.³⁸ In addition, the blueshift of the SLR from the TE to TM polarization is observed, which is mainly due to the reduction of the capacitive coupling between the two triangles of the bowties across the gap that results from the different charge distributions under TE and TM excitation (see details in Sec. S2 of the supplementary material). In Figs. 4(b) and 4(c), the measurements and simulations are performed in air to characterize the SLR modes. The difference between the simulated and measured SLRs shown in Fig. 4(c) could be due to imperfections during fabrication, the focused illumination of the sample instead of the collimated illumination considered in the simulations, or a difference in the refractive index of the evaporated gold compared to the values from the literature used in the simulations.⁴⁵ The measurements are taken in air as there is no available material that matches the refractive index of water while lacking the OH⁻ vibrational mode.

To investigate the VSC, we fill the cell with demineralized water and measure the transmittance for both TE and TM polarizations with normal incidence excitation. Figure 5 shows the extinction spectra of the coupled system. To remove the signal from dark states and uncoupled molecules, the measurements are normalized by the extinction spectrum of water in the same liquid cell without particle array. After this normalization, the polariton peaks are clearly observed. For TE polarization, the polaritons are found at 3167 cm⁻¹ (LP) and 3734 cm⁻¹ (UP). We retrieve a Rabi splitting of Ω_R = 567 cm⁻¹. Since the coupling strength is 8% of the OH⁻ energy, it is at the onset of USC. In contrast, the spectrum of the extinction for TM excitation shows a larger Rabi splitting. However, this splitting is caused by the detuned SLR from the OH⁻ vibration at normal incidence due to the blueshift for this polarization [see Fig. 4(c)], and not to a larger coupling strength. Indeed, the simulated field enhancement for TM polarization is lower for TM polarization (see Sec. S5 of the supplementary material), which should lead to a weaker coupling.

We have investigated the coupling between surface lattice resonances in arrays made of metallic particles and the hydroxyl bond of water molecules. We have simulated and optimized three arrays with different unit cell configurations: single disks, dimers of disks, and bowties. Among the three configurations, the arrays of bowties show the largest Rabi splitting and the highest field enhancement, making them the perfect candidate to experimentally demonstrate ultrastrong coupling of molecular vibrations in liquid phase. After fabrication of the array of bowties, we have characterized the bare array, finding good agreement between the measurements and simulations. Finally, we have measured the coupled system retrieved a Rabi splitting of 567 cm⁻¹, whose coupling strength is 8% of the energy of the OH⁻ bond stretching of water. These results demonstrate the coupling between the optical modes in metasurfaces and water molecules close to the USC regime. This demonstration in open resonant cavities, in contrast to closed Fabry–Pérot cavities, introduces a novel platform for investigating polaritonic physics and chemistry under ultrastrong coupling.

The supplementary material is available free of charge and includes: the fabrication recipe of the metasurface, the origin of the blueshift of the SLRs for different polarizations of incident light, the angular dispersion of the SLR, the comparison between the field enhancements of the single disk and the dimer along the z direction, and the field enhancement of the bowtie for the TM polarization.

J.G.R. acknowledges the financial support from the Dutch Research Council (NWO) through the talent scheme (Vici Grant No. 680-47-628). Y.-C.W. acknowledges the support from the National Science and Technology Council (NSTC) through the postdoctoral research abroad program.

The authors have no conflicts to disclose.

Francesco Verdelli: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Yu-Chen Wei: Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). Joost M. Scheers: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal). Mohamed S. Abdelkhalik: Methodology (equal); Resources (equal). Masoumeh Goudarzi: Methodology (equal); Resources (equal). Jaime Gómez Rivas: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.