Angle-Independent Plasmonic Substrates for Multi-Mode Vibrational Strong Coupling with Molecular Thin Films

Strong vibrational coupling of molecules to optical cavities based on plasmonic resonances has been explored recently, because plasmonic near-fields can provide strong coupling in sub-diffraction limited volumes. Such field localization maximizes coupling strength, which is crucial for modifying the vibrational response of molecules and, thereby, manipulating chemical reactions. Here, we demonstrate an angle-independent plasmonic nanodisk substrate that overcomes limitations of traditional Fabry-Perot optical cavities, because the design can strongly couple with all molecules on the surface of the substrate regardless of molecular orientation. We also show that the large linewidths of the plasmon resonance allows for simultaneous strong coupling to two, orthogonal water symmetric and asymmetric vibrational modes in a thin film of copper sulfate monohydrate deposited on the substrate surface. A three-coupled-oscillator model is developed to analyze the coupling strength of the plasmon resonance with these two water modes. With precise control over the nanodisk diameter, the plasmon resonance is tuned systematically through the modes, with the coupling strength to both modes varying as a function of the plasmon frequency, and with strong coupling to both modes achieved simultaneously for a range of diameters. This work may aid further studies into manipulation of the ground-state chemical landscape of molecules by perturbing multiple vibrational modes simultaneously and increasing the coupling strength in sub-diffraction limited volumes.


Introduction
Strong coupling of molecular vibrational modes to optical (infrared) cavities has been explored increasingly in recent years as an avenue to modify the intrinsic vibrational response of molecular systems and, thereby, the chemical properties associated with the vibrating bond. [1][2][3][4][5] When molecules are inside an optical cavity, the two systems can coherently exchange radiative energy if the frequency of the cavity resonance is tuned to the molecular vibrational mode. When the exchange of energy occurs faster than the damping rates of the cavity and of the vibration, the system is said to be in the strong coupling regime. 6 Energy splitting of the original eigenstates, otherwise known as Rabi splitting, gives rise to hybrid polariton modes with higher and lower frequencies than the original resonance, with consequent modification of the bond energy. 3 Optical cavities based on Fabry-Pérot (F.P.) resonances have been the primary optical platform used to promote vibrational strong coupling to date, due to their high quality factor, Q.
Recently, this platform has helped to increase understanding of the underlying dynamics of polariton chemistry, such as relaxation lifetimes, 7 energy transfer, 8 and the role of density of states on polariton-modified reactions. 9 However, even though F.P. geometries are useful due to their low loss, they have intrinsic limitations, and overcoming these is the focus of this report. Because the magnitude of vibrational strong coupling is directly proportional to both the number of molecules present and the dot product between the electric field vector of the cavity and the vibrational dipole moment, 3,4,10 coupling with an entire ensemble of molecules cannot be achieved unless all of the vibrating bonds are aligned with the electric field inside the cavity. Another limitation of F.P. cavities is that the optical field concentration is diffraction limited. Prior work has shown that coupling strength is inversely proportional to the square root of the electric field mode volume. 11,12 Physically, this means that the highest degree of coupling occurs when the electric field density is largest, or equivalently, when the mode is volume is as small as possible.
In F.P. cavities, the maximum electric field density is constrained by the wavelength-scale limit on the minimum mode volume.
As an alternative, plasmonic metal nanomaterials are quickly gaining attention as a new strategy for vibrational strong coupling. [13][14][15][16][17] Although plasmonic devices are lossy in comparison with F.P. resonances, they may overcome their lower Q-factors and out-compete damping processes by taking advantage of the intense optical near-fields at the metal surface, which can enhance and concentrate light by many orders of magnitude in sub-diffraction-limited volumes. 18 This near-field concentration is created by driving the free electrons in the metal into a collective oscillation, also known as a surface plasmon resonance, or plasmon. Further, plasmons can be tailored to exhibit resonances through the visible and mid infrared (IR) spectrum, and with much greater flexibility regarding the suitable molecular dipoles that can couple with them (i.e. lower momentum matching constraints), compared with cavities based on far-field optical resonances.
The enhanced fields created in sub-diffraction-limited volumes suggest the plasmonic devices can allow for higher coupling strengths than F.P. cavities, overcoming their broader resonant linewidths (i.e. higher damping rates), in order to enable multi-mode strong coupling as we describe below. While there have been several studies coupling excitons produced by quantum dots, 19-21 J-aggregates, [22][23][24][25] or semiconductors 26 to plasmons, there is significantly less work that has studied vibrational coupling of bulk molecular systems to plasmonic structures. 27,28 In this study, we developed a plasmonic nanodisk substrate with a resonance that is tunable throughout the near-IR spectrum and that exhibits no angle dispersion. That is, the plasmonic mode couples equally with all dipole orientations. Our design is based on metal-insulator-metal (MIM) plasmonic nanodisk geometries (Fig. 1). Prior work has shown that these geometries have angleindependent resonances that can be tuned in the IR regime. [29][30][31] We hypothesized that these substrates may be an ideal platform for studying strong vibrational coupling, because (1) deposited films on the substrate surface can couple to the plasmon regardless of molecular orientation, (2) coupling occurs in sub-diffraction limited volumes, maximizing the coupling strength in the system.
Additionally, because of the broad linewidth of the plasmonic mode, the substrates allow for strong coupling to multiple vibrational modes simultaneously. Previous studies with F.P.
cavities have shown coupling to multiple, spectrally isolated modes using multiple optical resonances, 32,33 while others have shown polariton hybridization of different molecular species with similar spectral frequencies. 34 Related work from Menghrajani et al. demonstrated coupling of three different vibrational modes in PMMA to both a F.P. cavity and a plasmonic grating, although only one polariton mode reached the strong coupling regime. 35 Building from these previous reports, this study shows how a plasmonic substrate can strongly couple to two, orthogonal vibrational modes simultaneously, potentially opening the door for more sophisticated coherent energy transfer between a cavity and chemical system.
To study strong coupling effects, copper sulfate monohydrate [CuSO4(H2O)1] was deposited as a thin film on the substrate surface. This molecule was analyzed because it is easy to characterize using Raman and IR spectroscopy and has strong, spectrally isolated vibrational modes in the mid IR regime. 36,37 Copper sulfate is also particularly interesting because the most prominent absorption band near 3200 cm -1 is due to two distinct, orthogonal symmetric and asymmetric stretching modes of the associated water molecule, giving insight into how the plasmonic substrate may couple to both modes at room temperature. We also analyzed the total hemispherical absorptivity of the substrate to demonstrate that the plasmon resonance is indeed angle-independent, suggesting that all molecules in the optical near-field can participate in strong coupling with the substrate. Finally, a three-coupled-oscillator model was developed that fits to the coupling data based on the assumption the plasmon couples to the two orthogonal water stretching modes simultaneously, due their close spectral spacing. We observed that, in general, the plasmon mode couples more strongly to the asymmetric water stretching mode, likely due to the stronger transition dipole of the that molecular vibration. Our study confirms that strong coupling can be obtained for the water symmetric and asymmetric stretching modes simultaneously due to the unique design of the plasmonic substrate.

Finite element method optimization of nanodisk substrate
To determine the optical properties of the nanodisk substrate, full-wave optical simulations (finite element method (FEM), COMSOL) were used. Gold nanodisks with a tunable diameter and with a height of 100 nm were simulated on top of a 40 nm thick Al2O3 layer on top of an optically opaque smooth 100 nm gold substrate. A 5 nm chrome layer was placed between the nanodisks and the Al2O3 to model an adhesion layer used in fabrication. Air (n = 1) was used as the surrounding dielectric. Fig. 1a is a schematic of the substrate. Periodic boundary conditions were applied to simulate an infinite square array of gold nanodisks with a constant gap spacing of 250 nm in the x-and y-directions between adjacent nanodisks, meaning the pitch P varied only as a function of the disk diameter d. The gold refractive index used was from Babar and Weaver 38 because it extends the refractive index from the visible to IR regime, and the refractive index for Al2O3 used was from Kischkat et al. 39 for similar reasons. The refractive index for chrome was obtained from Rakić et al. 40 Determining total hemispherical absorptivity The total hemispherical absorptivity of the structures was obtained from the FEM simulations by integrating the absorptance of the substrate from = 0˚ to = 80˚ and ∅ = 0˚ to ∅ = 90˚, where is the elevation angle from normal incidence and ∅ is the azimuthal angle. The symmetry of the square array implies that the other three hemispherical quadrants from ∅ = 90˚ to ∅ = 360˚ have the same angular absorptance as the first quadrant. The light was simulated as "unpolarized" by taking the average of S and P polarizations at every incident angle. The total hemispherical absorptivity was determined using the following equation: 41,42 where ( , , ∅) is the reflectance of the substrate, 1 − ( , , ∅) is the absorptance ( , , ∅) of the substrate, is the spectral intensity of the energy absorbed by an ideal blackbody as a function of the wavelength, λ, in accordance with Planck's law, and = ∅ is the solid angle. In our system, the transmittance of the substrate was zero due to the gold back reflector.

Nanodisk substrate fabrication
Once optimized nanodisk geometries were determined from the simulations, the structures were fabricated using electron-beam lithography. Base piranha and UV-ozone were used to clean

CuSO4(H2O)x thin film deposition
CuSO4(H2O)5 was mixed with nanopure water to form a 25 mM solution. The fabricated substrate was placed on a hot plate heated to ~310 ˚C. Once the substrate was up to temperature, the 25 mM solution was drop cast on top of the entire substrate, and the water was allowed to evaporate quickly, leaving behind only a CuSO4(H2O)1 thin film. An optical image of the deposited molecular thin film is shown in Fig. 1d. Notice the color change of the nanodisk array from Fig.   1c to 1d due to the change in refractive index of the surrounding medium.

CuSO4(H2O)X thin film thickness
A Witec RA300 confocal Raman microscope was used to determine the CuSO4 ( From the depth map, the CuSO4(H2O)1 thin film layer was determined to be ~2 µm thick.

FTIR absorbance measurements
A Shimadzu AIM-8800 automatic infrared microscope with a 20× objective was used to acquire all IR spectra at normal incidence. A 40 nm Al2O3 thin film on a 100 nm gold reflector was used as the background before acquiring spectra. The aperture was adjusted to acquire only the spectra from the nanodisks. Absorbance spectra were collected, which is the Log10(Absorptance), and then the spectra were normalized to the highest spectral peak on a scale from 0 to 1. All data sets were averaged over 40 collected spectra at one position.

Results and Discussion
For our substrate design, we have adapted the work of Abbas et al., 29 which showed that silver nanodisks on SiO2 with a silver back reflector can absorb nearly 100% of incident radiation, are IR tunable, and are angle-independent. Our computational analysis simulated the spectral absorptance versus the diameter of plasmonic gold nanodisks on top of Al2O3 with a gold back reflector. The gold was used rather than silver to reduce the effects of substrate oxidation, and the Al2O3 was used to avoid any mid-IR absorption that would occur with SiO2. The results of the simulation (normal incidence) are shown in Fig. 2a. It is clear that the plasmonic resonance can be tuned across the entire mid-IR regime as a function of nanodisk diameter, and that the substrate absorbs nearly 100% of incident radiation at resonance. At larger diameters, a lower-order plasmon resonance is observed at higher wavenumbers, which is shown experimentally in Fig. S1a.  Fig. 2a. Fig. 2b also shows the experimental absorptance of that substrate geometry without CuSO4(H2O)1 deposited (red dashed). The plasmon peak position was located at 3318 cm -1 , which targeted primarily the asymmetric water stretch. It is clear from the substrate spectrum that the resonance strongly concentrates and, thereby, absorbs nearly 100% of incident radiation over a narrow IR range, as required for strong coupling.
A crucial optical property of this substrate confirmed by computational analysis was the angle independence of the plasmonic resonance. To demonstrate this property, we simulated the total hemispherical absorptivity of the substrate. 41 That is, by integrating the spectral absorptance over the entire hemisphere, the frequencies in which the most radiation is absorbed over all angles was obtained. We observed that the substrate absorbs primarily only over a narrow frequency range and at the same spectral position as the experimentally obtained (normal incidence) spectrum, as shown by the red curve in Fig. 2c. The angle-independent plasmon resonance behavior of MIM nanodisks was also reported in previous work. 29,30 By normalizing the absorptivity to a perfectly absorbing blackbody spectrum (black dashed), we demonstrated that the nanodisk plasmon resonance is nearly as absorbing and as angle-independent (at resonance) as a blackbody, and that the damping rate, i.e. the peak width, is also angle-independent. By establishing this spectral design feature, we hypothesized that our system would demonstrate similar Rabi splitting as described in prior work. 14,15,25,44 Furthermore, due to the angle-independent resonance, nearly 100% of the molecules within the optical near-field could strongly couple to the plasmonic substrate, regardless of molecular orientation.
We next acquired spectra of various plasmonic substrates before and after a ~2 µm thin One important design feature to consider about the plasmonic substrates is that the resonance peak position red shifts as a function of the surrounding medium's refractive index.
When the surrounding medium was air (n = 1), the red dashed spectra were obtained, illustrated in Fig. 3. However, when the surrounding medium was CuSO4(H2O)1, the resonance frequencies red shift. This is shown in Fig. 3  The explanation for the changes in the observed broadening of the two polaritonic peaks as a function of the spectral position of the plasmon resonance can be understood by considering that there are two molecular modes present, the asymmetric and the symmetric water stretches.
Prior work has shown that the spectral lineshape for a single transition coupled to a single plasmon mode can be described quantitatively by modeling the transition (in this case, the molecular vibration) and the plasmon resonance as two coupled, classical harmonic oscillators (see Supplementary Information for details). [50][51][52] If we attempt to fit to this model, assuming only one molecular vibrational mode that is the mean value of the symmetric and asymmetric vibrational modes for , the fit deviates significantly from the experimental data. For example, Fig. 4a shows an attempt to fit this model to the data in panel (iv) in Fig. 3; the fit largely resembles the line shape of a single vibrational mode coupled to a plasmonic system established in prior work. 15,16,25,53 This suggests that the symmetric and asymmetric water stretches are not well described as one vibrational mode coupled with the substrate. Instead, it is important to consider both water stretching modes as separate modes that, while orthogonal in free molecules, can both interact with the plasmonic substrate. Similar multi-coupling spectra have previously been observed when coupling multiple vibrational modes of PMMA to a plasmonic grating. 35 To account for this more complex coupling interaction, the coupled-oscillator model was extended to allow for simultaneous coupling of two independent vibrational modes to the same plasmonic resonance (see Supplementary Information for details). The resulting fits provide a much better description of the data, as illustrated in Fig. 4b. Here, the molecular damping rates and mode frequencies as well as the plasmon damping rates were constrained to the experimentally determined values from the control experiments, and the plasmon frequencies, coupling strengths, and mode amplitudes were left as free fit parameters. Two -values, 1 and 2 , correspond to the coupling strength of the symmetric and asymmetric modes, respectively, with the plasmonic mode.
Each of the modes will be in the strong-coupling regime if its corresponding coupling strength satisfies: 50 Fig. 5 shows the three-coupled-oscillator model applied to all the spectra in the panels of A summary of the fitted data is provided in Fig. 6 and also tabulated in the Supplementary Information (Table S1). The fit not only determines the coupling strengths but also determines the red-shifted plasmon frequencies obscured by the polariton lineshape. These fitted values are how we report the shifted plasmon resonance positions in Fig. 3. Fig. 6 shows the fitted 1 and 2 values versus the shifted plasmon frequencies, only for the cases where a data set had some value of > 0. The rightmost data points correspond to panel (ii), while the leftmost correspond to panel (v). The experimental symmetric and asymmetric water frequencies, 1 and 2 , respectively, are shown by the vertical dashed lines, and their damping rates, 1 and 2 , are shown by the black horizontal lines with bars on the end. The green box indicates which data points from the fit are in the strong coupling regime. Upon inspection of Fig. 6, two observations are clear: (1) Despite two vibrational modes being present, the coupling feature drives the plasmon into resonance with the modes. This suggests that when the plasmon shifts into resonance with the water modes, the modes "pull" the plasmon resonance into a similar spectral position, as expected due to the lineshape of the dielectric function near molecular modes. 40,45,46 (2) The plasmon seems to couple more strongly to the asymmetric water stretch at all frequencies between the water modes. From the figure, it is apparent that 2 > 1 at all frequencies between 1 and 2 . Only once the plasmon red shifted past 1 does the plasmon more strongly couple to the symmetric water mode, i.e., 1 > 2 . This trend suggests intrinsic features of these molecular modes cause the plasmon to couple more strongly with the asymmetric water mode. We hypothesize this is because the asymmetric mode has a stronger transition dipole moment, as also indicated by the greater peak intensity of that mode in the uncoupled molecular spectrum. In conclusion, we have designed and fabricated angle-independent plasmonic nanodisk substrates that simultaneously strongly couple to both the symmetric and asymmetric water stretching modes in a thin film layer of CuSO4(H2O)1 at room temperature. By simulating the total hemispherical absorptivity and field distribution of the structure, we found that the plasmon resonance is angle-independent and extends well above the molecular film, suggesting that all molecules in the deposited film strongly couple to the substrate regardless of molecular orientation.
Furthermore, we developed a three-coupled-oscillator model that accounted for vibrational strong coupling to two modes simultaneously in order to analyze the coupling data both in the case of strong coupling and also for large plasmon detuning. Our model confirmed that all molecules on the substrate surface contributing to the far-field signal were strongly coupled to the plasmonic mode. From the model, we also obtained (1) the shifted plasmon resonance positions that were obscured by the strong coupling and (2) the coupling strengths of the plasmonic substrate with the symmetric and asymmetric water stretching modes, 1 and 2 , respectively. The magnitude of the coupling strength to either mode was a function of the spectral position of the plasmon resonance, and in general, the plasmon appears to couple more strongly to the asymmetric water stretch. The simultaneous strong coupling of multiple vibrational modes to the same plasmonic resonance results in the coherent exchange of energy between the previously orthogonal molecular vibrational modes, via the substrate interaction, potentially providing a new route for control of chemical behavior.
We believe that the substrate design we demonstrated may benefit future studies of vibrational strong coupling, because the substrate is highly tailorable for targeting specific vibrational modes or coupling bandwidths, and the design eliminates the need for molecules to have the appropriate orientation with respect to the optical mode. Given that all surface-deposited molecules in the near field can, in principle, couple to the substrate, it may be possible to achieve even more pronounced modification of the chemical behavior of molecules via vibrational strong coupling, especially if other challenges related to the field inhomogeneity at the substrate surface can be addressed.
MATLAB code. We would also like to thank Dr. Nicki Hogan, Ethan Morse, and the TAMU Aggiefab staff for their helpful fabrication advice.

Supplementary Information
See supplementary infomation for the studied plasmonic red shifts, three-coupledoscillator model, simulated mode volumes, and table of coupling values for Fig. 6.

Data Availability Statement
The data that supports the findings of this study are available within the article [and its supplementary material].

Plasmon Redshift with Refractive Index
As presented in the results and discussion section, the plasmon frequency redshifts as a function of the surrounding medium's refractive index. Fig. S1 shows the original plasmon frequencies of plasmonic substrates with different nanodisk diameters when the surrounding medium is air (n = 1). When the surrounding medium is CuSO4(H2O)1 the black curves were obtained. In Fig. S1a-b, the black curve clearly still shows the plasmon frequency along with the line shape of the CuSO4(H2O)1, indicating that none of the three panels are in the strong coupling regime. Instead, the exact red shift of the plasmon frequency can be obtained, shown by ∆ .
Clearly, the plasmon frequency shifts differently based on the wavenumber, as expected. However, the exact change in red shift is nonlinear as a function of the frequency. Instead, plasmon resonances near the water stretching modes shift more when near the water vibrational modes or less when spectrally isolated.

Three-coupled-oscillator model
The coupling between a single transition (electronic or vibrational) and a plasmonic resonance has frequently been modeled by treating the transition and the plasmon as a pair of classical harmonic oscillators, coupled through the near field of the plasmon. [1][2][3] The corresponding equations of motion are where is the oscillating dipole of the plasmon; is the plasmon resonance frequency; is the plasmon linewidth; is the transition dipole moment of the plasmon; , , , and are the corresponding quantities for the vibrational mode; is the coupling strength; and is a driving term representing the force of an external optical field on the plasmon. Here, it is assumed that the plasmon cross-section is much larger than that of the vibrational mode, so that direct driving of the vibration by the external field can be ignored. Solving the equations of motion for an external field of form = , we obtain The extinction cross-section is now given by

Plasmon Enhanced Electric Field Mode Volume
The electric field enhancement factor | / 0 | 2 surrounding the plasmonic substrate is a measurement of the localized electric field compared to the incident electric field. 4 It was necessary to calculate the enhancement factor in our simulations in order to determine where the highest field concentration would be above the nanodisk substrate. Only molecules within the enhanced electric field mode volume will couple to the plasmonic substrate because this is the region where the highest field intensity will be, allowing the molecules to resonantly exchange energy with the substrate, creating the conditions for a strongly coupled system. 5 To determine the mode volume, a simulation was conducted of the frequency versus | / 0 | 2 in COMSOL with a nanodisk diameter d = 680 nm. Fig. S2a shows the volume averaged | / 0 | 2 plot at different heights above the substrate, which takes the volume-averaged enhancement factor contained between the specified height and the substrate surface. From the figure, it is clear that the highest electric field concentration at the desired resonance of 3333 cm -1 is near the substrate surface, indicated by the largest | / 0 | 2 value being obtained within 250 nm of the surface. As the integration region extends higher above the substrate surface, | / 0 | 2 decreases; however, 2 µm above the substrate still shows field enhancement.