Vibrational strong 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–Pérot optical cavities because the design can strongly couple with all molecules on the surface of the substrate regardless of molecular orientation. We demonstrate that the plasmonic substrate provides strong coupling with the C=O vibrational stretch of deposited films of PMMA. We also show that the large linewidths of the plasmon resonance allow 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 Rabi splitting from 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.

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.1–5 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 the understanding of the underlying dynamics of polariton chemistry, such as relaxation lifetimes,7 energy transfer,8 and the role of density of states in 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 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 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 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.15 This near-field concentration is created by an external optical field driving the free electrons in the metal into a collective oscillation, which leads to a localized surface plasmon resonance (LSPR). Furthermore, plasmons can be tailored to exhibit resonances through the visible and mid-infrared (IR) regime 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 that 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 of coupling excitons produced by quantum dots,16–18 J-aggregates,19–24 semiconductors,25 or molecular transitions26–28 to plasmons, there is significantly less work that has studied vibrational coupling of bulk molecular systems to plasmonic structures.29,30

In this study, we developed a plasmonic nanodisk substrate with a resonance that is tunable throughout the mid-IR spectrum and that exhibits no angle dispersion. That is, the plasmonic mode couples equally with all dipole orientations. We used a Salisbury screen design,31 which takes advantage of constructive interference in the dielectric layer of a metal–insulator–metal (MIM) to create an absorber mode that, in combination with the LSPR from the plasmonic nanodisks, also show angle-independent, near-unity IR absorptivity and emissivity32 (Fig. 1). Prior work has shown that these geometries have angle-independent resonances that can be tuned in the IR regime.33–35 We hypothesized that these substrates may be an ideal platform for studying vibrational strong coupling because (1) deposited films on the substrate surface can couple to the plasmon regardless of molecular orientation and (2) coupling occurs in sub-diffraction limited volumes, maximizing the coupling strength in the system.

FIG. 1.

Experimental design and fabrication of the plasmonic coupling platform: (a) Schematic of the plasmonic substrate. The nanodisk height is held constant at 100 nm. The gap spacing is held constant at 250 nm so that the pitch P changes only as a function of nanodisk diameter d. (b) Scanning-electron-microscope image of a nanodisk array with d = 680 nm. The scale bar is 1 µm. (c) Optical image of the entire 200 × 200 µm nanodisk square array shown in (b). The scale bar is 20 µm. (d) The nanodisk array shown in (c) with 2 µm of CuSO4(H2O)1 deposited on top. (e) Confocal Raman depth map of the plasmonic substrate with 2 µm of CuSO4(H2O)1 deposited. (i) Schematic of the plasmonic substrate with CuSO4(H2O)1 on top. The red dotted lines show the Raman map region. (ii) The Raman depth map with horizontal dashed lines indicating the boundaries of the different regions. The scale bar is 4 µm. (iii) A spectrum obtained by the Raman map above the substrate. (iv) A spectrum obtained from the film region showing the prominent peaks of CuSO4(H2O)1 at 1118 and 1048 cm−1.

FIG. 1.

Experimental design and fabrication of the plasmonic coupling platform: (a) Schematic of the plasmonic substrate. The nanodisk height is held constant at 100 nm. The gap spacing is held constant at 250 nm so that the pitch P changes only as a function of nanodisk diameter d. (b) Scanning-electron-microscope image of a nanodisk array with d = 680 nm. The scale bar is 1 µm. (c) Optical image of the entire 200 × 200 µm nanodisk square array shown in (b). The scale bar is 20 µm. (d) The nanodisk array shown in (c) with 2 µm of CuSO4(H2O)1 deposited on top. (e) Confocal Raman depth map of the plasmonic substrate with 2 µm of CuSO4(H2O)1 deposited. (i) Schematic of the plasmonic substrate with CuSO4(H2O)1 on top. The red dotted lines show the Raman map region. (ii) The Raman depth map with horizontal dashed lines indicating the boundaries of the different regions. The scale bar is 4 µm. (iii) A spectrum obtained by the Raman map above the substrate. (iv) A spectrum obtained from the film region showing the prominent peaks of CuSO4(H2O)1 at 1118 and 1048 cm−1.

Close modal

Additionally, because of the broad linewidth of the plasmonic mode, the substrates allow for strong coupling to multiple vibrational modes simultaneously. This is in contrast to F.P. cavities, which usually have narrow optical modes (i.e., low damping rates). While a narrow F.P. mode is useful for strong coupling due to the low loss of the system, it limits the cavity’s ability to couple to multiple, closely spaced vibrational modes. Instead, previous studies with F.P. cavities have shown coupling to spectrally isolated modes taking advantage of multiple optical resonances,36,37 while others have shown polariton hybridization of different molecular species with similar spectral frequencies.38 Related work by 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.39 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 a chemical system.

To study multi-mode 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.40,41 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. Recently, Vergauwe et al. showed that by strongly coupling to one water stretching mode with a F.P. cavity, the rate of an enzymatic hydrolysis reaction was modified.42 We hypothesize that by strongly coupling to both water symmetric and asymmetric stretching modes simultaneously, the potential energy landscape of the molecule may be perturbed even more than what can be achieved with single mode coupling to a F.P. resonance, leading to an increased modification of reaction rates. We note that in pure liquid water, the symmetric and asymmetric stretching modes are not as well isolated as in CuSO4(H2O)1.

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 that 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.

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 Al2O3 to model an adhesion layer used in fabrication. Air (n = 1) was used as the surrounding dielectric. Figure 1(a) shows 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 that the pitch P varied only as a function of the disk diameter d. The gold refractive index used was from the work of Babar and Weaver43 because it extends the refractive index from the visible to IR regime, and the refractive index for Al2O3 used was from the work of Kischkat et al.44 for similar reasons. The refractive index for chrome was obtained from the work of Rakić et al.45 

The total hemispherical absorptivity of the structures was obtained from the FEM simulations by integrating the absorptance of the substrate from θ = 0° to θ = 80° and ∅ = 0° to ∅ = 90°, where θ 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:46,47

a(λ,θ,)=00θλ1λ2[1Rλ,θ,]IBB(λ)cos θdλdΩ00θλ1λ2IBB(λ)cos θdλdΩ,

where R(λ, θ, ∅) is the reflectance of the substrate, 1−R(λ, θ, ∅) is the absorptance a(λ, θ, ∅) of the substrate, IBB 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 = sin θdθd∅ is the solid angle. In our system, the transmittance of the substrate was 0 due to the gold back reflector.

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 a 1 × 1 cm2 silicon chip. A 100 nm gold layer was thermally evaporated (Lesker PVD electron-beam evaporator) onto the silicon chip. After the gold was deposited, a 40 nm layer of Al2O3 was deposited using RF sputtering (Lesker PVD RF sputterer). Electron-beam lithography was used to fabricate 200 × 200 µm2 square nanodisk arrays, with each array’s nanodisk diameters corresponding to the desired plasmon resonance. 950 PMMA A4 was used as the e-beam resist. Finally, a 5 nm chrome adhesion layer was deposited on top of the unfilled nanodisks developed into the resist, and then, a 100 nm gold layer was deposited on top of the chrome, which is the height of the nanodisks. Liftoff was performed in acetone using a combination of acetone pumping with a glass pipet and sonication. The resulting nanodisk array is shown in Fig. 1(b) (SEM) and in Fig. 1(c) (optical). The array appears dark due to the absorbing nature of the plasmonic nanodisks in the visible regime.

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 the required temperature, the 25 mM solution was drop cast on top of the entire substrate, and water was allowed to evaporate quickly, leaving behind only a CuSO4(H2O)1 thin film. Due to the crystallinity of CuSO4(H2O)1, the thin film is a homogeneous, uniform layer. Thus, the thin film has an approximately constant number of molecules participating in the coupling across the surface region studied spectroscopically. An optical image of the deposited molecular thin film is shown in Fig. 1(d). Note the color change in the nanodisk array from Figs. 1(c) and 1(d) due to the change in the refractive index of the surrounding medium.

To study coupling with a single vibrational mode, we spin coated 950 PMMA A4 at 1500 RPM to create a ∼300 nm thin film on top of a new nanodisk substrate. A diameter, d = 1200 nm, was used in order to target the C=O stretch with the plasmon resonance, which is located at 1728 cm−1 and is spectrally isolated from other vibrational modes.

A Witec RA300 confocal Raman microscope was used to determine the CuSO4(H2O)x thin film thickness. A 532 nm laser was directed through a 50× (numerical aperture 0.55) objective lens with an optical power of 360 µW. A Raman spatial scan, like that shown in Fig. 1(ei), was obtained by performing a depth profile map. The map started at z = +10 µm and moved in the −z direction in −1 µm increments to a final depth of z = −10 µm. The horizontal y-direction started at y = −10 µm and moved to y = +10 µm in +1 µm increments on each subsequent z-step of the depth profile. An integration time of 0.5 s was used on each step. The resulting cross sectional depth map is shown in Fig. 1(eii). The signal was filtered to select the 1119 cm−1 peak—the prominent spectral signature of CuSO4(H2O)1—indicating that the bright areas are showing only the signal from CuSO4(H2O)1.48 By selecting specific pixels in the depth profile, we observed that the dark area above the substrate is air [Fig. 1(eiii)] and the bright area on the substrate is a thin film of CuSO4(H2O)1 [Fig. 1(eiv)], further supported by the prominent peaks at 1118 and 1048 cm−1.48 These Raman peaks show no signature of coupling because the plasmon resonant frequencies of our structures were made to range from 1500 to 4200 cm−1, which is not resonant with the copper sulfate Raman peaks. Raman spectra of the molecules on and off the substrate are shown in Fig. S1 (supplementary material). From the depth map, the CuSO4(H2O)1 thin film layer was determined to be ∼2 µm thick.

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 Log10 (absorptance), and then, the spectra were normalized to the highest spectral peak on a scale from 0 to 1. All datasets were averaged over 40 collected spectra at one position.

For our substrate design, we have adapted the work of Abbas et al.,33 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 vs the diameter of plasmonic gold nanodisks on top of Al2O3 with a gold back reflector. Gold was used rather than silver to reduce the effects of substrate oxidation, and 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. 2(a). 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. S2a.

FIG. 2.

Spectral tunability and angle independence of the plasmonic resonance. (a) Simulation (FEM) of the nanodisk array spectral absorptance as a function of diameter. The red vertical dashed line indicates the resonant frequency of 3333 cm−1 for d = 680 nm. (b) Corresponding experimental absorptance spectrum of the fabricated plasmonic substrate with d = 680 nm (red dashed) and the absorptance spectrum of CuSO4(H2O)1 (blue). The substrate is in resonance with both the symmetric and antisymmetric water stretching modes located at 3145 and 3330 cm−1, respectively. (c) The calculated total hemispherical absorptivity of the nanodisk substrate from (b) in red compared to an ideal blackbody in black. The absorptance was integrated from θ = 0 to θ = 80° and from ∅ = 0° to ∅ = 360° over the entire hemisphere above the substrate.

FIG. 2.

Spectral tunability and angle independence of the plasmonic resonance. (a) Simulation (FEM) of the nanodisk array spectral absorptance as a function of diameter. The red vertical dashed line indicates the resonant frequency of 3333 cm−1 for d = 680 nm. (b) Corresponding experimental absorptance spectrum of the fabricated plasmonic substrate with d = 680 nm (red dashed) and the absorptance spectrum of CuSO4(H2O)1 (blue). The substrate is in resonance with both the symmetric and antisymmetric water stretching modes located at 3145 and 3330 cm−1, respectively. (c) The calculated total hemispherical absorptivity of the nanodisk substrate from (b) in red compared to an ideal blackbody in black. The absorptance was integrated from θ = 0 to θ = 80° and from ∅ = 0° to ∅ = 360° over the entire hemisphere above the substrate.

Close modal

Figure 2(b) shows the experimentally measured IR absorptance spectrum of the CuSO4(H2O)1 thin film on top of a 40 nm layer of Al2O3 on top of a gold back reflector. The dominant vibrational modes are the water bending mode of CuSO4(H2O)1 near 1510 cm−1 and the water symmetric and asymmetric stretching modes at 3145 and 3330 cm−1, respectively.40,41 Each of these vibrational modes in the mid-IR regime can be targeted individually by using the appropriate nanodisk diameter. In order to target the water stretching modes for these studies, a substrate was fabricated with a nanodisk of diameter d = 680 nm, an Al2O3 dielectric thin film layer with thickness t = 40 nm, and an optically thick Au back reflector. This geometry is indicated by the red dashed line in Fig. 2(a). Figure 2(b) 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.46 That is, by integrating the spectral absorptance over the entire hemisphere, the frequencies in which the most radiation is absorbed over all angles were 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. 2(c). The angle-independent plasmon resonance behavior of MIM nanodisks was also reported in previous work.33,34 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.19,24,27,49 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 film layer of CuSO4(H2O)1 was deposited on top of the substrate. The substrates were fabricated based on the simulation in Fig. 2(a) to tune the plasmon resonances systematically through the water stretching modes as a function of the nanodisk diameter. Figure 3 shows the spectral positions of the plasmonic resonances without CuSO4(H2O)1 on them (red dashed), with each individual panel showing a separate substrate. Diameters ranged from d = 560 nm to d = 760 nm. Six substrates were fabricated that tuned the plasmon resonance from 4274 to 2994 cm−1. After the bare substrate spectra had been obtained, the CuSO4(H2O)1 thin film was deposited on the surface. The spectra of CuSO4(H2O)1 on top of only Al2O3 and the gold back reflector are illustrated by the blue solid lines in Fig. 3. The prominent peaks at 3145 and 3330 cm−1 are the same symmetric and asymmetric water stretches observed in Fig. 2(a); however, this time, the spectra were normalized by the maximum. Note that the thin film peak locations are located at the same spectral positions in all six panels of Fig. 3, meaning that each deposited salt film is in the same hydration state.

FIG. 3.

The spectral absorbance (normalized) of a bare plasmonic substrate (red dashed), a CuSO4(H2O)1 thin film on Al2O3 with a gold back reflector (blue), and the combined spectra of the CuSO4(H2O)1 thin film on top of the plasmonic substrate (black). The panels correspond to plasmon resonant frequencies (with approximate nanodisk diameters) at (i) 4274 cm−1 (d = ∼560 nm), (ii) 3865 cm−1 (d = ∼600 nm), (iii) 3595 cm−1 (d = ∼670 nm), (iv) 3534 cm−1 (d = 680 nm), (v) 3248 cm−1 (d = ∼720 nm), and (vi) 2994 cm−1 (d = ∼760 nm). The maroon vertical dashed lines show the shifted plasmon resonance frequency when the surrounding medium is CuSO4(H2O)1.

FIG. 3.

The spectral absorbance (normalized) of a bare plasmonic substrate (red dashed), a CuSO4(H2O)1 thin film on Al2O3 with a gold back reflector (blue), and the combined spectra of the CuSO4(H2O)1 thin film on top of the plasmonic substrate (black). The panels correspond to plasmon resonant frequencies (with approximate nanodisk diameters) at (i) 4274 cm−1 (d = ∼560 nm), (ii) 3865 cm−1 (d = ∼600 nm), (iii) 3595 cm−1 (d = ∼670 nm), (iv) 3534 cm−1 (d = 680 nm), (v) 3248 cm−1 (d = ∼720 nm), and (vi) 2994 cm−1 (d = ∼760 nm). The maroon vertical dashed lines show the shifted plasmon resonance frequency when the surrounding medium is CuSO4(H2O)1.

Close modal

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 panels (i) and (vi) of Fig. 3. In all six panels of Fig. 3, the red dashed curves show the original plasmon substrate without CuSO4(H2O)1 on it, the blue curve shows CuSO4(H2O)1 when deposited on a control region of the substrate without plasmonic nanodisks, and the black curve shows the spectra of CuSO4(H2O)1 on top of the nanodisk array, illustrated in Figs. 1(d) and 1(e). From panels (i) and (vi) of Fig. 3, the black curve clearly shows the red shift in the plasmonic substrate due to the change in the refractive index. If we focus on panel (i) of Fig. 3, the line shape of CuSO4(H2O)1 is completely retained, and the plasmon peak is clearly observed at 3880 cm−1, corresponding to a red shift of −394 cm−1. Similarly, in panel (vi) of Fig. 3, a red shift of −183 cm−1 is observed from an original plasmon frequency of 2939 to 2756 cm−1. From these peak shifts, in combination with full-wave simulations, the refractive index of CuSO4(H2O)1 was extracted as a function of wavenumber, and the results are shown in Fig. S2 (supplementary material). The refractive indices range from n = 1.27 farther from the water modes to n = 2 near the modes, indicating that the plasmon red shifts more when the plasmon position is in closer resonance with the vibrational peaks. This trend corroborates the expected Lorentzian line shape of the dielectric function close to a molecular absorption mode, as expected for a damped harmonic oscillator, and this trend is also confirmed in the more sophisticated three-coupled-oscillator fitting model describedbelow.45,50,51

In panels (ii)–(v) of Fig. 3, the plasmon resonances are not as easy to discern. Furthermore, the CuSO4(H2O)1 symmetric and asymmetric water stretches are not clearly observed either. Instead, new line shapes are observed at a similar spectral position as the CuSO4(H2O)1 modes, with a FWHM that is significantly broader than either the plasmon or CuSO4(H2O)1 modes individually. In fact, panels (ii)–(v) of Fig. 3 show two characteristically different absorption features with peak positions at higher and lower frequencies than the original CuSO4(H2O)1 modes, separated by a local minimum where the CuSO4(H2O)1 frequencies were originally located. This behavior is clear indication of strong coupling.6,52–54 When the plasmon and CuSO4(H2O)1 spectrally overlap, coherent energy exchange is established between the two systems, resulting in two new hybrid polariton modes with higher and lower frequencies than the un-coupled modes. Thus, the plasmon resonance red shifts into resonance with the water vibrational modes, causing vibrational strong coupling to occur. The shifted plasmon resonance is depicted by the maroon vertical dashed lines in Fig. 3, as determined by the fitting equation discussed below.

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. Several methods have been developed to account for coupling between molecular transitions and optical cavities including the transfer-matrix method, fitting matrix method, and full-wave electrodynamic simulations.52 Here, we adopted a semi-classical analytical approach from prior work, where the spectral line shape 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 the supplementary material for details).55–57 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 ωvm, the fit deviates significantly from the experimental data. For example, Fig. 4(a) shows an attempt to fit this model to the data in panel (iv) of Fig. 3; the fit largely resembles the line shape of a single vibrational mode coupled to a plasmonic system established in prior work.20,24,27,58 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.39 

FIG. 4.

The fits to panel (iv) of Fig. 3 using the (a) two-coupled-oscillator model and (b) three-coupled-oscillator model. The experimental data are shown in black, and the fit from each model is shown by the green dotted line. The coupling strength, g, is also indicated.

FIG. 4.

The fits to panel (iv) of Fig. 3 using the (a) two-coupled-oscillator model and (b) three-coupled-oscillator model. The experimental data are shown in black, and the fit from each model is shown by the green dotted line. The coupling strength, g, is also indicated.

Close modal

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 the supplementary material for details). The use of this three-coupled-oscillator model is for describing situations where two separate orthogonal modes become coupled primarily via a strong coupling interaction with a third radiative mode. Similar strategies have been described in other works.36,38,39 The resulting fits provide a much better description of the data, as illustrated in Fig. 4(b). 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 g-values, g1 and g2, 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 the following equation:55,59

g>14γpl+γvm.

To further ensure that the three-coupled-oscillator model accurately describes a system with multiple coupled vibrational modes, we also ran a control experiment with the plasmonic substrate coupled to the isolated, single mode of the C=O vibrational stretch of PMMA. Similar to prior work that studied PMMA coupled to F.P. cavities,60 we fit the data to a simpler, two-coupled oscillator model. Normalized absorbance spectra of the original plasmon resonance, PMMA on top of an Al2O3 control substrate, and the spectrum when PMMA was deposited on the plasmonic substrate are shown in Fig. 5(a). The shifted plasmon resonance spectral position due to the change in the refractive index was obtained by the fit. Again, we observed peak splitting indicative of vibrational strong coupling. The high quality of the fit with a two-coupled-oscillator model is shown in Fig. 5(b). We found that this system is in the strong coupling regime since the fitting gave a coupling strength g=0.008 eV>14(γpl+γvm), where γpl = 0.013 eV and γvm = 0.002 eV. This study provides further evidence that (1) the two-coupled-oscillator model is physically descriptive for a single vibrational mode coupled to a single plasmon resonance, (2) the two-coupled-oscillator model cannot be applied to a multi-coupled-oscillator system and provide a robust fit, and (3) the three-coupled-oscillator model accurately describes the multi-coupled system of the plasmon resonance coupled to two separate vibrational modes, as depicted in Fig. 4(b).

FIG. 5.

A two-coupled-oscillator model applied to the plasmon substrate (d = 1200 nm) coupled to a single vibrational mode of PMMA. (a) The spectral absorbance (normalized) of a bare plasmonic substrate (red dashed), a PMMA thin film on Al2O3 with a gold back reflector (purple), and the combined spectra of the PMMA thin film on top of the plasmonic substrate (black). The maroon vertical dashed line shows the shifted plasmon resonance frequency when the surrounding medium is PMMA. The absorbance band of PMMA at 1728 cm−1 is the spectral signature of the C=O stretching mode. (b) The two-coupled-oscillator model applied to the “combined” curve in (a). The coupling strength is also indicated.

FIG. 5.

A two-coupled-oscillator model applied to the plasmon substrate (d = 1200 nm) coupled to a single vibrational mode of PMMA. (a) The spectral absorbance (normalized) of a bare plasmonic substrate (red dashed), a PMMA thin film on Al2O3 with a gold back reflector (purple), and the combined spectra of the PMMA thin film on top of the plasmonic substrate (black). The maroon vertical dashed line shows the shifted plasmon resonance frequency when the surrounding medium is PMMA. The absorbance band of PMMA at 1728 cm−1 is the spectral signature of the C=O stretching mode. (b) The two-coupled-oscillator model applied to the “combined” curve in (a). The coupling strength is also indicated.

Close modal

Figure 6 shows the three-coupled-oscillator model applied to all the spectra in panels (i)–(vi) of Fig. 3. Note that the model in green fits extremely well to the experimental data in black, reproducing well the line shape even in the case of large plasmon detuning in Fig. 6, panels (i) and (vi). Moreover, the high quality of the fits indicates that all the molecules in the thin film on the surface of the substrate that contribute to the far-field spectra participate in coupling when the plasmon resonance is tuned to the vibrational modes because the three-coupled-oscillator model does not account for any uncoupled molecules. That is, the spectra we observe do not appear to be a linear combination of both coupled and uncoupled molecular spectra. This can be explained, in part, by considering the electric field mode volume of the plasmonic substrate compared with the thin film thickness. While the CuSO4(H2O)1 thin film thickness extends to ∼2 µm above the substrate, the electric field enhancement factor |E/E0|2 produced by the plasmonic substrate extends to similar heights. The volume average of the field enhancement contained at various heights above the substrate and the associated field map were obtained from FEM simulations and are shown in Fig. S3 (supplementary material). Although the highest field enhancement resides within 500 nm of the substrate surface, some degree of enhancement also extends up to at least the height of the thin film. This means that all molecular dipoles in the thin film on the substrate surface can be influenced by the enhanced electric field, allowing for some vibrational coupling to occur. Our experiments indicate that any molecules not participating in the coupling interaction, if present, do not contribute significantly to the measured spectra.

FIG. 6.

Fits from the three-coupled-oscillator model (green dashed) for all the “combined” spectra from Fig. 3 of the CuSO4(H2O)1 thin film on top of the plasmonic substrate. The data (black) in panels (i)–(vi) correspond directly to data (black) in panels (i)–(vi) of Fig. 3, respectively.

FIG. 6.

Fits from the three-coupled-oscillator model (green dashed) for all the “combined” spectra from Fig. 3 of the CuSO4(H2O)1 thin film on top of the plasmonic substrate. The data (black) in panels (i)–(vi) correspond directly to data (black) in panels (i)–(vi) of Fig. 3, respectively.

Close modal

Further evidence that the substrate couples to all molecular orientations in the surface film is provided in Fig. S4 (supplementary material), which shows that the absolute absorbance of the coupled system is enhanced compared to the uncoupled molecular spectra. This result can be understood as follows: In an uncoupled thin film of molecules, some molecular dipoles will be misaligned with the incident radiation, meaning that the entire ensemble of molecules will not contribute to the measured absorption. However, our angle-independent plasmonic array acts like an antenna, enabling excitation of molecular dipoles along any orientation when the plasmon mode is excited (at normal incidence in our experiments). When the plasmon resonance is tuned to the molecular mode, all molecules within the mode volume of the electric field absorb equally, independent of their dipole orientation. Therefore, the coupled spectra show a greater overall absorbance than the uncoupled system.

The intense fields produced by the plasmonic substrate also give rise to multi-mode coupling. Because the near-field energy density is so large, the plasmonic mode can have large damping rates (large bandwidth) and still couple to both molecular water stretches simultaneously. A summary of the fitted data to both modes is provided in Table I. The fit not only determines the coupling strengths but also determines the red-shifted plasmon frequencies obscured by the polariton line shape. These fitted values are how we report the shifted plasmon resonance positions in Figs. 3 and 5(a). Figure 7 shows the calculated dispersion relation according to the three-coupled-oscillator model with respect to the plasmon frequency ωpl using the fitted parameters of Table I, the average coupling strengths g1 and g2, and the average mode intensities for the cases where the plasmon frequency was in resonance with the water modes [Fig. 6, panels (ii)–(v)]. The cases with large plasmon detuning have been omitted because the coupling strength does not contribute significantly when fitting the model. The black vertical dashed lines show the plasmon frequency that corresponds to the experimental data and fits in panels (ii)–(v) of Fig. 6. The experimental symmetric and asymmetric water frequencies, ωvm1 and ωvm2, respectively, are shown by the green horizontal dashed lines. As the plasmon tunes through the water modes, hybridized polariton modes and anti-crossing behavior are observed, as expected for the three-coupled-oscillator model.

TABLE I.

The experimentally determined values of plasmon γpl, symmetric γvm1, and asymmetric γvm2, mode damping (in bold) based on analysis of uncoupled spectra, as well as the fitted parameters obtained using the three-coupled-oscillator model for analysis of panels (i)–(vi) of Fig. 6. ωpl is the shifted plasmon position according to the fits, and g1 and g2 are the coupling strengths of the plasmon to the symmetric and asymmetric water stretching modes, respectively. The two columns on the right indicate which of the two vibrational modes are in the strong coupling regime on a panel-by-panel basis (in italic). Data labeled N/A (not applicable) cannot be used to determine g-values due to large plasmon detuning.

Panelγvm1 (eV)γvm2 (eV)γpl (eV)ωpl (cm−1)g1 (eV)g2 (eV)g1>14(γpl+γvm1)g2>14(γpl+γvm2)
0.031 0.029 0.067 3880 N/A N/A N/A N/A 
ii 0.031 0.029 0.056 3274 0.026 0.038 Yes Yes 
iii 0.031 0.029 0.064 3161 0.025 0.037 Yes Yes 
iv 0.031 0.029 0.055 3129 0.027 0.034 Yes Yes 
0.031 0.029 0.046 3119 0.026 0.037 Yes Yes 
vi 0.031 0.029 0.049 2939 N/A N/A N/A N/A 
Panelγvm1 (eV)γvm2 (eV)γpl (eV)ωpl (cm−1)g1 (eV)g2 (eV)g1>14(γpl+γvm1)g2>14(γpl+γvm2)
0.031 0.029 0.067 3880 N/A N/A N/A N/A 
ii 0.031 0.029 0.056 3274 0.026 0.038 Yes Yes 
iii 0.031 0.029 0.064 3161 0.025 0.037 Yes Yes 
iv 0.031 0.029 0.055 3129 0.027 0.034 Yes Yes 
0.031 0.029 0.046 3119 0.026 0.037 Yes Yes 
vi 0.031 0.029 0.049 2939 N/A N/A N/A N/A 
FIG. 7.

The calculated dispersion based on fits to a three-coupled-oscillator model when tuning the substrate plasmon resonance frequency through the water symmetric ωvm1 and asymmetric ωvm2 stretching modes. The plasmon frequency ωpl is depicted by the white diagonal line. The black vertical lines show the plasmon frequencies that correspond to panels (ii)–(v) of Figs. 3 and 6.

FIG. 7.

The calculated dispersion based on fits to a three-coupled-oscillator model when tuning the substrate plasmon resonance frequency through the water symmetric ωvm1 and asymmetric ωvm2 stretching modes. The plasmon frequency ωpl is depicted by the white diagonal line. The black vertical lines show the plasmon frequencies that correspond to panels (ii)–(v) of Figs. 3 and 6.

Close modal

Upon inspection of Table I, three observations are clear. (1) All panels in Fig. 6. where the plasmon is in close resonance with the water modes are in the strong coupling regime, which means that each substrate strongly couples to both vibrational modes. This is also evident from Fig. 7 because the dispersion shows anti-crossing behavior as the plasmon frequency tunes through the vibrational modes. (2) Despite two vibrational modes being present, the coupling 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 line shape of the dielectric function near the molecular modes.45,50,51 (3) The plasmon seems to couple more strongly to the asymmetric water stretch because g2 > g1 for all frequencies. This trend suggests that intrinsic features of these molecular modes cause the plasmon to couple more strongly with the asymmetric water mode. We hypothesize that this is because the asymmetric mode has a smaller damping rate and also a stronger transition dipole moment, as also indicated by the greater peak intensity of that mode in the uncoupled molecular spectrum. We also see that the values of g1 and g2 are relatively constant in all spectra where it is possible to robustly fit for coupling strength, as expected for the coupled-oscillator model.61,62 The variations observed in the coupling strength are likely due to differences in the plasmonic arrays that were fabricated to collect each spectrum, such as variable surface roughness, or changes in the local electric field density when there are different nanodisk diameters.

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 water stretching modes simultaneously in order to analyze the coupling data. 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, g1 and g2, respectively. The magnitude of the coupling strength to either mode as a function of the spectral position of the plasmon resonance was relatively constant, 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. In particular, by showing multimode strong coupling to two water vibrational modes, this work could impact future studies of strong coupling in biological systems since interaction with water is a major feature of biological processes. Furthermore, given that all molecules in the near-field of the surface can, in principle, couple to the substrate, it may be possible to achieve an 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.

See the supplementary material for the on/off resonance Raman signal, studied plasmonic red shifts, three-coupled-oscillator model, simulated mode volumes, and absolute absorbance spectra of resonant substrates.

This work was funded by the Air Force Office of Scientific Research under Award No. FA9550-16-1-0154 and TAMU X-Grants. M.S. also acknowledges support from the Welch Foundation (Grant No. A-1886) and the Gordon and Betty Moore Foundation under Grant No. GBMF6882. M.P. acknowledges support from the National Science Foundation (Grant No. DMR-1905135). We would like to thank Hayley Brawley for help with the development and troubleshooting of the MATLAB code. We would also like to thank Dr. Nicki Hogan, Ethan Morse, and the TAMU Aggiefab staff for their helpful fabrication advice.

The data that support the findings of this study are available within the article and its supplementary material.

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