Enhancing vibrational light-matter coupling strength beyond the molecular concentration limit using plasmonic arrays

Vibrational strong coupling is emerging as a promising tool to modify molecular properties, by making use of hybrid light-matter states known as polaritons. Fabry-P\'erot cavities filled with organic molecules are typically used, and the molecular concentration limits the maximum reachable coupling strength. Developing methods to increase the coupling strength beyond the molecular concentration limit are highly desirable. In this letter, we investigate the effect of adding a gold nanorod array into a cavity containing pure organic molecules, using FT-IR microscopy and numerical modeling. Incorporation of the plasmonic nanorod array, that acts as artificial molecules, leads to an order of magnitude increase in the total coupling strength for the cavity filled with organic molecules. Additionally, we observe a significant narrowing of the plasmon linewidth inside the cavity. We anticipate that these results will be a step forward in exploring vibropolaritonic chemistry and may be used in plasmon based bio-sensors.


Introduction
Strong light-matter coupling has attracted considerable attention in the past couple of years due to the potential applications it o ers in physical and chemical sciences. [1][2][3][4] For example, strong coupling of organic molecules has been shown to modify the rate of a photoisomerization reaction, 5,6 increase electronic transport, 7 and expand the length scale of Förster energy transfer. [8][9][10] Not to mention other e ects of strong coupling such as selective manipulation of excited states, 11 suppression of photo-oxidation 12 or reducing photodegradation in polymers. 13 Recently, vibrational strong coupling has come into focus as a promising physical tool to control molecular properties. Since the rst experimental evidences of vibrational strong coupling (VSC) in both solid [14][15][16] and liquid states, 17 the eld has expanded considerably, [18][19][20][21][22][23][24][25] and it has been shown to alter reaction kinetics, [26][27][28][29] control reaction selectivity, 30 allow for intermolecular energy transfer, 31 and modi cation of enzyme activity. 32 Recent progresses in chemical reactions making use of polaritons were summarized by Hirai et al. 33 In order to signi cantly impact chemical reactivity, theoretical investigations has demonstrated that a high coupling strength is required 34,35 and a recent experimental study has shown a non-linear relationship between the coupling strength and thermodynamics of a chemical reaction. 29 Strong light-matter coupling is achieved by interfacing molecules with con ned electromagnetic eld of resonant cavities tuned to a molecular transition. When a molecular vibrational transition is in the strong coupling regime, two new hybrid states, known as polaritons, are formed, 36 separated in energy by the so-called Rabi splitting ℏΩ R . Traditionally, polaritons have been engineered with the use of planar cavities, such as Fabry-Pérot resonators con ning the electromagnetic elds between two mirrors. 14 Reaching large coupling strengths usually requires saturating the cavity volume with the molecular material, and additionally aligning the transition dipole moments with the cavity vacuum eld. [37][38][39] Plasmonics o ers an alternative route to strong coupling by con ning light down to subwavelength scales with the use of metallic nanoparticles and nanocavities. [40][41][42] Only a tight region of space around the metallic cavity needs to be lled with molecules in order to form polaritons. 43 Plasmon resonances of nanoparticles are tunable from the UV to the IR range, and can be used for molecular sensing in the IR range due to nanoscale mode volumes. [44][45][46][47] However, to improve the sensitivity, new approaches for narrowing the plasmon linewidth are desirable.
The magnitude of the Rabi splitting for a given molecular transition is proportional to the square root of the molecular concentration and the lling factor. Furthermore, the maximal achievable magnitude of the Rabi splitting in the case of saturated mode volume is ultimately bounded by the bulk Rabi splitting ℏΩ R ∼ (with being the transition oscillator strength 48 ), which is independent on the cavity type. [49][50][51] Therefore, new approaches are required to increase the Rabi splitting in order to maximize the e ect of the con ned electromagnetic eld onto molecules, as shown by theoretical studies. 34,52,53 In this Letter, we utilize a hierarchical coupling between a Fabry-Pérot cavity, a vibrational absorption band of an organic molecule, and a localized surface plasmon resonance in the mid-IR regime to go beyond the Rabi splitting imposed by the maximal concentration limit 54 . First we show that the coupling of the plasmon and the FP cavity results in an order of magnitude decrease in plasmon's linewidth, an observation rationalized by reduced radiative losses from the plasmon in the cavity 55 . Then, by using numerical and analytical modelling in conjunction to our experimental data, we show a ve to nine-fold increase in the total coupling strength, indicating that the plasmon act as an arti cial molecule that increases the molecular coupling strength. In this study, we report a method to increase the coupling strength above the limit of √ using a hybrid system composed of a Fabry-Pérot (FP) cavity, an organic molecule, and a localized surface plasmon, in a fashion similar to the one introduced by Bisht et al. 54 using two-dimensional transition metal dichalcogenides in the visible regime. All three entities are tuned to the same resonance frequency, thereby coupled amidst themselves, creating hybrid polaritons ( Figure   1a). The Fabry-Pérot cavities used in the following experiments are composed of IR-transparent substrates (CaF 2 and ZnSe) coated with 10 nm of gold ( Figure 1b). The physical distance between the gold mirrors, ranging from 11 to 16 µm, was controlled using a polymer spacer. The cavities were designed with two inlets allowing to inject liquids. The quality factor of an empty cavity was The plasmon resonances were broad (FWHM = 621-1120 cm −1 ) due to radiative losses. This is an intrinsic feature of plasmon arrays in the mid-IR, hampering its use.  We will rst describe the coupling between the cavity and the two molecules, then the cavity and plasmon, and lastly, the complete coupled system with the FP cavity, the plasmon and the two molecules. Figure  for the C ---N band.

Results & discussions
Let us now consider the plasmonic arrays inside the FP cavity. With increasing rod length, the plasmon resonance shifts to lower energies (Figure 2d), and the rod length can therefore be viewed as a method of tuning the resonant condition. Moreover, due to intrinsic anisotropy of the rods, the microcavity-plasmon polaritons are formed only along the long axis of the rods, while along the short axis, the bare cavity is recovered. This polariton anisotropy can be probed using polarization-resolved transmission spectroscopy. As shown in Figure 3a, we observe a normal mode splitting of the bare plasmon absorption when the plasmonic arrays are placed inside the FP cavity and the polarizer axis was aligned along the rods. Here, the modes dispersing linearly with the rods length are the polaritonic modes, whereas the vertical modes are uncoupled FP modes, which arise due to polarizer artefacts, as we explain below. Furthermore, we observe an order of magnitude decrease in the linewidth of the resulting polariton compared to the bare plasmon. Similar narrowing was observed in our previous experiments with plasmonic arrays ultra-strongly coupled with FP cavities in the visible to mid-IR range. 55 The linewidth of closely packed metallic nanorods in the IR region is dominated by radiative losses; but when placed inside a closed cavity, the radiation from the nanorods does not instantaneously leave the cavity, instead bouncing between the mirrors and thus reducing the total resonance linewidth. Consequently, the FWHM of the plasmon polaritons drops to ca. 70 cm −1 for all the rods' lengths, as a result of signi cantly suppressed radiative damping. Observing that the FWHM of the FP modes are 84 ± 7.3 cm −1 , the linewidth of the cavity is the main limitation of the linewidth of the plasmon polariton (Table S2).
By adding molecules into the cavity, a third coupling component is introduced to In order to gain further understanding of the experimental results, we performed numerical modelling of the coupled systems using FDTD (Figure 3d-f, Figure S1-3). Simulated normalincidence transmission spectra demonstrate a good agreement with the experimental spectra for both plasmonic structures, and composite plasmon-molecule ones. Speci cally, the observed polaritonic modes linearly disperse with the rods length, however, the dispersion is less pronounced than for uncoupled rods (gray dots). This is a consequence of intermixing between highly dispersive plasmonic modes and non-dispersive FP modes (all arrays were placed in the same FP cavity).
The results also suggest that uncoupled FP transmission peaks found in the measured spectra are an artifact resulting from non-ideal polarization alignment. To con rm that, we simulated transmission spectra of the coupled systems illuminated with plane wave polarized linearly at an angle of 20 degrees with respect to the nanorod longer axis. The resulting spectra clearly exhibit uncoupled FP resonances ( Figure S2). Next, to ensure that the observed dispersions are a result of the interaction between the three components in the hybrid system, transmission spectra of the system with a polarizer perpendicular to the nanorods' long axis were measured. The results are shown in Figure S6 (numerical modeling in Figure S1). As expected, when the contribution of the plasmonic array is removed by the polarizer, the transmission spectra are the same as when probing the system beside the array (Figure 2b and c). Likewise, the values of ℏΩ R with a perpendicular polarizer are 46 cm −1 and 101 cm −1 for the C ---N and C --O vibrations, respectively, which are the same values as we observed when when probing next to the plasmonic array.

Theoretical analysis
In order to extract coupling strengths and con rm that the plasmonic array acts as an arti cial molecule to enhance the total coupling strength of the system, we turn to theoretical analysis of the experimental results. This analysis is essentially based on the coupled harmonic oscillator algebra in the simplest possible implementation. Furthermore, this analysis requires several rather crude assumptions, which may be false in general, but are satisfactory for the goal of extracting the collective coupling constants.
In view of the above remark, we describe the cavity by a set of orthogonal Fabry-Pérot eigenmodes with equidistant frequencies = 1 , each coupling to the molecular resonance with a certain coupling constant. For pure molecular samples, all the molecules residing within the cavity can be roughly approximated by a single collective harmonic oscillator with the resonant frequency of a single molecule 0 , and the collective dipole moment √ (this approximation is rather crude, but for the purposes of extracting collective molecular, plasmonic, and intermixed situations, is su ciently adequate). As we are far from the ultrastrong coupling regime in this case, we employ the multimode coupled-harmonic oscillator Hamiltonian, including lowest Fabry-Pérot modes, and the single harmonic oscillator describing the collective molecular wherê and̂ are the annihilation operators of the -th cavity mode and that of the molecular resonance, respectively, and is the coupling constant.
The coupling constant to the -th cavity mode is given by the standard expression following from the expansion of the minimal coupling Hamiltonian in the Coulomb gauge: 55,56 = √  0 / , where is the dipole moment of transitions with density , and  is the cavity vacuum eld. Each molecule in the cavity, in principle, will experience a di erent vacuum eld depending on its position. But to simplify the analysis, we will assume that all molecules experience the same average vacuum eld  ∼ ℏ / . Thus, the coupling strength with the -th cavity mode takes the form = 0 ℏ 0 / , where 0 is a scaling constant that includes the molecular dipole moment, the molecular concentration, and the cavity mode volume. In a similar way, we analyze the cavity-nanorod system, except that a single mode collective molecular resonance is now replaced by a single mode plasmonic resonance. The nanorod array can be described by a single harmonic oscillator with energy which disperses with the nanorod length ( Figure S3a). Since it is positioned in a speci c horizontal plane inside the cavity at a height above the bottom mirror, the coupling strength takes the form = 0 ℏ sin 0 / , which takes into account the transverse distribution of the vacuum cavity eld. Strictly speaking, the coupling strength will also disperse with the nanorods length. Longer nanorods will have a larger transition dipole moment, but the increasing length at the same time reduces their surface density. The exact scaling law of the nanorod dipole moment with length is not known, but we will assume for simplicity that the product √ is constant in the studied range of between 1100 and 1500 nm (for comparison, we observed less than 50% variation of this product upon an octave variation of nanorods length in a similar system 55 ). Hence, we replace 0 in the Hamiltonian (Eq.

Conclusion
In summary, our hybrid Fabry-Pérot cavities show that the addition of a plasmonic array to the standard molecular vibro-polaritonic system increases the total coupling strength by almost an order of magnitude for a nitrile absorption band and ve times for a carbonyl absorption band.
Increasing the coupling strength beyond the molecular concentration limit, dismantle the crucial obstacle for reaching the ultra-strong coupling regime using organic molecules. Furthermore, precisely controlling the coupling strength, not only with the molecular concentration, but also with the density of the plasmonic array, allows molecules at small concentrations to reach the strong coupling limit. One can in a sense view the plasmonic array as a form of "catalyst", that enables any on-resonance molecular transition, regardless of molecular concentration and transition dipole moment strength, to reach the strong coupling regime. Furthermore, the cavity reduces the radiative damping from the plasmon, sharpening the polariton linewidth with more than an order of magnitude. Together with the spectral tuning ability, such sharp linewidths may allow for mode-selective chemical sensing in the mid-IR. The approach described here is not limited to infrared transitions, but can also be transposed to electronic transitions. For these reasons, we suggest that our hybrid system will be an ideal platform to explore the promising potential of polaritonic chemistry, the ultra-strong coupling regime, as well as provide an approach to mode-selective mid-IR sensing.

Supporting Information Available
The supporting information contains the following sections.
• S1: Methods  with IPA and water, to form the gold nanorods. The physical distance between the mirrors was controlled using a Mylar spacer (Specac) of 6 µm and the ne adjustment of the thickness was done using adjustment screws on the micro uidic cell. Finally, hexanal (Sigma-Aldrich) and 4butylbenzonitrile (Sigma-Aldrich) were injected into the cavity using a syringe connected to the inlet of the cell. All chemicals were used without further puri cation.

S1.2 Optical characterization
Infrared spectra were recorded using an FT-IR microscope (Hyperion 3000, Bruker), using a Schwarzschild-objective 15x objective (NA=0.4) and a linear polarizer parallel and perpendicular along the long axis of the nanorods, connected to an FT-IR spectrometer (Vertex 70v, Bruker) in re ection or transmission mode. All measurements were recorded with a liquid nitrogen cooled MCT detector at a resolution of 4 cm −1 using 512 scans. Furthermore, ATR spectra were recorded using an FT-IR spectrometer (Invenio-R, Bruker) coupled to a PLATINUM ATR accessory (Bruker). The ATR spectra were recorded using a DLaTGS detector with a resolution of 4 cm −1 and 64 scans. Morphology of the samples was characterized using a Zeiss (Germany) scanning electron microscope (SEM ULTRA 55 FEG). In order to obtain the optical response of hexanal and 4-butylbenzonitrile in the infrared region a multi-Lorentz oscillator model was used: 2

S1.3 Numerical modelling
where, is the background refractive index, is the oscillator strength, 0 is the resonant wave vector and is the damping constant, i.e. the full width at half maximum of the th oscillator.

S1.4 Cavity thickness determination
The cavity thickness was measured using the following equation: where, , are the wavelengths of the Fabry-Pérot mode, the refractive index and is an integer number given by = − .  Figure S1.    Figure S3. Simulated transmission spectra with the oscillator strength set to zero of: (a-b) the coupled rods in the FP cavity with hexanal, with the polarisation along the rods axis and perpendicular, respectively; (c-d) the coupled rods in the FP cavity with 4-butylbenzonitrile, with the polarisation along the rods axis and perpendicular, respectively.