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Vibrational Strong Coupling Controlled by Spatial Distribution of Molecules within the Optical Cavity Wonmi Ahn, I. Vurgaftman, Adam D Dunkelberger, Jeffrey C. Owrutsky, and Blake S. Simpkins ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b00583 • Publication Date (Web): 29 Sep 2017 Downloaded from http://pubs.acs.org on October 3, 2017

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Vibrational Strong Coupling Controlled by Spatial Distribution of Molecules within the Optical Cavity

Wonmi Ahn,1 Igor Vurgaftman,2 Adam D. Dunkelberger,3 Jeffrey C. Owrutsky,3 and Blake S. Simpkins3,* 1

National Research Council Postdoctoral Associate, U.S. Naval Research Laboratory, Washington, DC

20375, United States 2

Optical Sciences Division, U.S. Naval Research Laboratory, Washington, DC 20375, United States

3

Chemistry Division, U.S. Naval Research Laboratory, Washington, DC 20375, United States

*E-mail: [email protected]

Abstract: Similar to excitonic materials interacting with optical cavity fields, vibrational absorbers coupled to resonantly-matched optical modes can exhibit new hybridized energy states called cavity polaritons. The delocalized nature of these hybrid polaritonic states can potentially modify a material’s physical and chemical characteristics, with the promise of a significant impact on reaction chemistry. In this study, we investigate the relationship between the spatial distribution of vibrational absorbers and the cavity mode profile in vibrational strong coupling by systematically varying the location of a 245-nm-thick poly(methyl methacrylate) (PMMA) film within a few-micrometer-thick Fabry-Perot cavity. Angle-tuning the cavity reveals that the 1st- and 2nd-order cavity resonances couple to molecular absorption lines of PMMA (the C=O and C-H stretching bands at 1731 and 2952 cm-1, respectively), resulting in quantifiable vacuum Rabi splittings in the dispersion response. These splittings, as extracted from experiment, transfer-matrix calculations, and an analytical treatment, display a consistent and strong dependence on the molecular spatial distribution within a cavity. Furthermore, we demonstrate the response of two physically separated molecular layers by measuring and calculating the vacuum Rabi splitting for cavities loaded with single and widely spaced pairs of 1 ACS Paragon Plus Environment

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PMMA layers. The results provide evidence that extended cavity polariton modes sample these separate layers simultaneously and, more broadly, provide guidance for controlling the coupling strength, and potentially chemical reactivity, of a given region through modification of the cavity mode profile or through introducing a remotely located molecular layer.

Keywords: Vibrational strong coupling, Hybrid polariton, Delocalized states, Vacuum Rabi splitting, Fabry-Perot cavity

Generating new light-matter states through strong coupling is a fascinating and impactful means to tailor a material’s physical and chemical character. A material excitation placed in an optical cavity may interact with a cavity optical mode (e.g., via dipolar interaction) if the two are spectrally matched.1,2,3,4 If the coupling rate outpaces all decay and dephasing processes, the system is said to be in the strong-coupling regime, and new hybrid light-matter states (polaritons) are observed at energies above and below that of the uncoupled material excitation.5,6 The presence of these polariton states can have a profound and varied impacts on the material’s physical and chemical properties. Applying cavity coupling to excitons in semiconductors and dyes has led to polaritonic lasing,7 photon blockade,8 Bose-Einstein condensate formation,9 improved carrier mobility in organic semiconductors,10 and enhanced non-radiative energy transfer between dyes.11 All of these examples result from the material excitation acquiring some cavity-photon character, which modifies fundamental properties such as excitation lifetime and effective mass. Recently, strong coupling to molecular vibrations12,13 has been explored as a means to selectively alter the behavior (e.g., chemical reactivity,14 excited state lifetime,15 and Raman scattering16,17) of specific molecular bonds within a larger molecule. Vibrational strong coupling (VSC) is broadly analogous to excitonic coupling, sharing behaviors such as vacuum Rabi splittings that scale with the square root of the oscillator 2 ACS Paragon Plus Environment

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strength,18 Rabi oscillations with a period equal to the inverse of the Rabi splitting energy,15 and polariton linewidths that appear immune to inhomogeneous broadening of the material excitation.12,19 Although position-dependent coupling, the focus of the present work, has been demonstrated with electronic transitions in a cavity,20 there are considerations unique to vibrations. These include higher excited-state transitions such as overtones and hot-bands, with energies anharmonically shifted from the ground-state absorption, excitations that are localized on the molecular scale and that may benefit greatly from formation of delocalized polaritons, and the potential to modify intermolecular energy transfer through selective modification of targeted bonds within a molecule.21,22,23 It can also be argued that vibrational coupling is more universally applicable than excitonic coupling since vibrations are present in virtually all molecules, whereas excitonic coupling is limited to materials with strong electronic transition such as J-aggregates or quantum dots.20,24 These differences highlight the importance of developing a complete understanding of fundamental VSC processes. In particular, the present work describes how the relationship between the spatial distribution of vibrational absorbers and the cavity-mode profile determines the coupling strengths. Since the light-matter interaction is governed by the overlap between the spatially varying cavity field and the material of interest, molecular position and modal profile offer degrees of freedom that can be employed to control coupling strength. Furthermore, while the reduced mode volume of a strongly subwavelength optical mode may increase coupling and offer the potential for single-molecule coupling, these come at the price of a dramatically increased spatial variation of the mode intensity. Understanding the relationship between the location of the molecule within a spatially varying mode and the resulting coupling is thus critical, not only for the use of highly confined optical modes, but also for schemes of cavitymediated excitation transfer between spatially separated regions10,11 and cavities including multiple distinct oscillators.25

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In this report, we evaluate the relationship between cavity mode field profile and spatial distribution of material excitations by placing a slab of vibrational absorbers at various locations within a Fabry-Perot cavity. The vacuum Rabi splittings are measured and compared to the results of transfer-matrix calculations as well as to an analytical treatment. Both experiment and modeling show a strong dependence of vacuum Rabi splittings on molecular distribution within a cavity and on the mode character (s- versus p-incident polarization), confirming that the molecular interaction with the cavity follows the cavity mode profile. Finally, we demonstrate cavity-mediated sampling of two physically separated molecular layers by measuring and calculating the vacuum Rabi splitting for cavities loaded with single molecular layers and pairs of these layers. An ability to control coupling strength of a given region in the cavity through modification of the field profile or through introduction of a second, remotely located layer opens up new possibilities for all-optical modulation of chemical reactivity.

Results and Discussion Fabrication of Au/SOG/PMMA/SOG/Au Fabry-Perot Cavity with Variable PMMA Film Positions. We used spin-on glass (SOG) spacer layers to place the PMMA layer at the desired position within the cavity. SOG is a methylsiloxane polymer ([H3CSiO2]m[SiO2]n-m) that can be spin-coated on a substrate to a desired thickness from tens to thousands of nanometers and thermally cured to form an amorphous oxide film with a refractive index close to that of SiO2.26,27 SOG is also a favorable choice for this work because it does not produce infrared absorption bands that interfere with the carbonyl absorption bands of PMMA (1731 cm-1, Figure S1) and is tolerant to the baking temperature for the PMMA film. We used two different SOG solutions, one for making thicker (~536 nm) and another for thinner SOG films (~270 nm), both of which are described in detail in Supporting Information. The planar Au mirrors were created by electron-beam evaporation on undoped Si substrates, with the PMMA (4% dissolved in anisole, molecular weight of 950 kDa) and SOG films, each prepared according to spin/bake 4 ACS Paragon Plus Environment

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recipes shown in Table S1 (Supporting Information), comprising the optical cavity. The targeted thicknesses for the Au and PMMA layers were 20 and 245 nm, respectively, while the thickness of SOG was varied to place the PMMA film at desired locations relative to the cavity center as shown in Figure 1a. The total cavity thickness was designed to be ~2.4 µm for all cavities in order to tune the first-order cavity resonance near the PMMA carbonyl stretching band at 1731 cm-1. Multiple spin coating and baking processes were required to produce a single cavity. We found that gradual cooling minimized the thermal stress between SOG films, significantly reducing the formation of cracks and delamination. The resulting full cavity linewidths at normal incidence were ~31 cm-1 and 56 cm-1 for the 1st- and 2nd-order modes, respectively. A detailed description for the Au/SOG/PMMA/SOG/Au cavity fabrication can be found in the Methods section. Controlling Cavity-Vibration Coupling with Variable Molecular Position. In order to verify the dependence of cavity-vibration coupling on molecular distribution within the cavity, we consider the two lowest-order modes (m = 1 and 2) of a Fabry-Perot cavity that support λ/2 and λ standing waves, respectively. The 1st (2nd)-order cavity mode supports one (two) antinode(s) and two (three) nodes. Field profiles were calculated using the transfer-matrix method (see the Methods section) and are shown for the s-polarized and p-polarized 1st-order modes (Figure 1a and 2a, respectively) and s-polarized 2nd-order mode (Figure 3a). As the Fabry-Perot cavity is angle tuned, the 1st-order resonance sweeps through the molecular absorption of the PMMA C=O stretching band at 1731 cm-1 (linewidth ~29 cm-1), and the 2nd-order mode sweeps through the PMMA C-H stretching band at 2952 cm-1 (linewidth ~33 cm-1), allowing for simultaneous monitoring of the vibrational coupling of two different vibrational modes to two different cavity modes. Note that the 2nd order resonance frequency is not exactly twice that of the 1st due to spectral dependence of the refractive index. Figure 1a shows a schematic diagram of the Au/SOG/PMMA/SOG/Au Fabry-Perot cavities used in this work. Five different cavities were prepared, each with a single PMMA slab 5 ACS Paragon Plus Environment

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located at one of five locations within the cavity (labeled Z1 – Z5 in Figure 1a). The positions include one near the node of the 1st-order cavity mode (Z1), one at its antinode (Z5), and several in between. First, s-polarization was used, whose mode profile (solid blue curve) is overlaid on the schematic diagram of the cavity. The cavity-vibration coupling between the 1storder cavity mode and the carbonyl stretching band of PMMA manifested as Rabi splittings in the transmission spectra taken as a function of incident angle θ (Figure S2) and an avoided crossing between the upper branch (UB) and lower branch (LB) in the dispersion response (Figure S4 and S5). Dispersion curves in the angular domain (Figure S4) were converted into the in-plane wavevector domain, kǁ, (Figure 1b and Figure S5) in order to account for the different internal wavevectors of the hybridized modes for a given angle of incidence. Cavity dispersions clearly show vacuum Rabi splittings as a result of coupling between molecular vibrations and optical cavity modes (selected cavity responses Z1, Z3, and Z5 shown in Figure 1b). Dispersion curves also show that this Rabi splitting is smallest when the PMMA slab is at Z1 (node) and increases as the slab moves to the center of the cavity (Z5, antinode), confirming that the molecular interaction with the cavity follows the cavity field intensity. The relationship between the spatial distribution of the molecules and the cavity mode profile was analyzed quantitatively by fitting the upper and lower polariton dispersions to a coupled-oscillator expression. The 2×2 matrix describing this coupling28,29,30 (Eq. 1) produces a determinant with two roots (Eq. 2), corresponding to the upper and lower polaritons:

−

=

=0 −

(1)

± − + 4

(2)

The resonances of the cavity and vibration are denoted as Ecav and Ev, λ is the polariton energy, and V is the coupling strength, which is half the Rabi splitting and referred to as the Rabi frequency in quantum-optics literature. We globally fit Eq. 2 to the upper and lower polariton dispersions of all of the data sets (solid red curves in Figure 1b), simultaneously yielding the 6 ACS Paragon Plus Environment

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experimental Rabi splitting values (further details about data processing are shown in Figure S8a, b). The measured vacuum Rabi splittings (filled red circles in Figure 1c) compare very well to values predicted by transfer-matrix calculations (empty red circles) and faithfully follow the 1storder s-polarized mode profile (solid blue curve). Depending on the position of the slab of vibrational absorbers within a Fabry-Perot cavity, the vacuum Rabi splitting varied from 20.8 cm1

(Z1) to 70.8 cm-1 (Z5). Although the dependence of excitonic coupling strength on the

distribution of dyes within a cavity has been reported,20,

31, 32, 33

a strong dependence of

vibrational coupling strength on molecular distribution within a cavity may have novel and important implications for flow cell or other integrated designs, which attempt to utilize cavity coupling for chemistry modification.34 Assuming a collective dipole in the entire slab and neglecting any permittivity variation as well as finite cavity lifetimes and molecular dephasing times, the vacuum Rabi splitting, Ω, for a discrete slab of oscillators within a cavity is given by the following analytical expression (the derivation is found in the Supporting Information): Ω=

!" #

% $&

+

0

2

0

2

'( *+,-./ 1 134' *+,-./ 1 ' 134 5 ( .

(3)

where 67 is the vacuum permittivity, 89 is the average refractive index in the cavity, µ is the dipole moment, N/V is the volume density of absorbers, W is the slab thickness, L is the full cavity length, and : is the position of the center of the slab along the cavity axis. The product of the squared dipole and the volume density can be estimated from the measured slab absorption outside of the cavity. The constant A, (Eq. 4), is needed to treat the p-polarized mode since this mode contains an angle-dependent component polarized in the propagation direction (the ppolarized results will be discussed fully later) as well as an in-plane polarized component: ; = tan ?sin' /

*+, BC 3D

(4)


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where EF is the angle of incidence between the p-polarized probe beam and the surface normal. A = 0 for s-polarized probing. This relatively simple analytical approach provides quantitative values for the Rabi splitting (empty red squares in Figure 1c) that agree reasonably well with the data. The systematic underestimate of the splittings for slab positions closer to the mirror likely results from the use of a simple cosine functional form to describe the cavity field, which neglects the penetration into the mirrors and hence underestimates its magnitude near the mirrors. The dependence of coupling strength on the molecular position is a direct consequence of the molecules sampling the cavity mode distribution. This implies that one can manipulate coupling, not only by moving the molecular slab, but also by utilizing different mode profiles supported by the Fabry-Perot cavity. It is well established that under off-normal incidence, sand p-polarizations result in different mode profiles.35 S-polarized incident light can couple only to an in-plane electric field (normal to the plane of incidence, yz plane in Figure 1a) with cosinelike functional form, i.e., peaking at the cavity center and nearly vanishing at the mirror faces (Figure 1a). On the other hand, p-polarized light can couple to a component along the propagation direction, G (parallel to yz plane), which is non-zero at the mirror boundaries, i.e., sine-like rather than cosine-like (Figure 2a). This is because the electric displacement along the propagation direction, HG = 6G , where 6 is the permittivity, must be continuous across the metal mirror interface. Since the metal permittivity is much larger than that inside the cavity, a large change in G can take place at the boundary. Since both field components (in-plane and propagation-direction) supported under p-polarization couple to the isotropic molecular vibrations, the measured vacuum Rabi splitting for a slab placed near the mirror should be higher for p-polarized conditions than for the s-polarized conditions, which is indeed observed in our experiments. Sample dispersion was measured under p-polarized conditions (Figure 2, S3, S6, and S7). While the light polarization effects were nearly negligible in our previous work in which the 8 ACS Paragon Plus Environment

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entire cavity was filled with PMMA,12 they play an important role in the present work with active slabs much thinner than the cavity length. As described earlier, the p-polarized mode includes two field components, one polarized in-plane (dotted green curve) and the other polarized along the propagation direction (dotted orange curve; Figure 2a). The vacuum Rabi splittings obtained from experiment (filled red circles), transfer-matrix calculations (empty red circles), and the analytical treatment described above (empty red squares) followed the sum of the two components under p-polarization (solid blue curve, Figure 2a and c). The slight disagreement in the vacuum Rabi splittings found for experiment and theory is attributed to misplacement of the PMMA slab within the cavity, which may have been caused by multiple spin-coating and baking processes performed to create a single cavity. The layers, deposited early in the process flow, experienced multiple baking sessions during subsequent layer depositions, potentially altering their thicknesses. It is informative to compare the response of the system under s- and ppolarized probing. The vacuum Rabi splittings for samples with the slab at the cavity center exhibited very little polarization dependence (Ω = 70.8 and 65.0 cm-1 for s- and p-polarized modes, respectively). However, cavities with the slab located near the mirror displayed strong sensitivity to mode polarization, varying by a factor of 2 (20.8 cm-1 and 42.1 cm-1 for the s- and p-polarized modes, respectively). This knowledge provides a tool to selectively enhance or inhibit the coupling of molecular vibrations to optical modes through the selection of mode character as well as the molecular position within the cavity, which may find important applications for the detection and characterization of molecules in optical cavities. The location of molecules within the cavity and its influence on the vibrational coupling were further demonstrated with the 2nd-order cavity mode (λ mode). The 2nd-order cavity mode aligned well spectrally to two different vibrations, the PMMA C-H stretching band at 2952 cm-1 and the -CH3 symmetric vibration mode of the SOG spacer at 2973 cm-1 (Figure S1). Extraction of the coupling strength to the PMMA slab thus necessitated fitting the response in this region to a three-oscillator model25,36,37 (Eq. 5) with three real roots for the polariton energy, λ (Eq. 6): 9 ACS Paragon Plus Environment

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$

−

− 0

0 5=0 −

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(5)

I − J − − K − − − L = 0

(6)

Here, E1 and E2 are the uncoupled PMMA and SOG vibrations (i.e., 2952 and 2973 cm-1), and V1 and V2 are the coupling strengths between the cavity and the PMMA and those between the cavity and the SOG vibrations, respectively. The peak maxima are culled from the dispersive spectra and fit to the three roots of Eq. 6 to provide the cavity-vibration coupling strengths as a function of PMMA slab position. Raw data and example fits are presented in the Supporting Information (Figure S8c, d). The coupling strength between the PMMA C-H band and the 2ndorder cavity mode tracked well the field profiles of this mode for s-polarization (Figure 3b), although we note that, unlike for the 1st-order cavity mode, the PMMA couplings observed for the 2nd-order mode are not in the strong-coupling regime, with branch splittings ranging from 18.1 cm-1 at Z3 (antinode) to 3.6 cm-1 and 3.5 cm-1 at Z1 and Z5 (nodes), respectively. In addition to providing further demonstration that coupling strength track the modal form, this result suggests novel functionality such as multiple vibrational modes of a molecule simultaneously experiencing cavity coupling (e.g., C=O coupled to the 1st-order cavity mode and C-H to the 2nd), which may be yet another feature differentiating VSC from cavity coupling to electronic transitions. One can envision position-sensitive control where a desired band becomes cavity coupled when the molecule is at a particular location, while a different vibration is activated when the molecule finds itself at a second location. Also, energy transfer between two distinct vibrational modes may be facilitated by their coupling to the cavity, opening up new vibrational relaxation mechanisms. Cavity-mediated energy transfer between dye molecules has been observed11, 38 although, in that case, both species were coupled to the same cavity mode. Coupling to Two Remote Molecular Layers via Cavity Fields. One of the most exciting phenomena associated with cavity coupling is delocalization of the hybrid light-matter


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polariton state. The matter excitation (a molecular vibration, in the present work) on its own is clearly localized within the material. However, the hybrid light-matter polariton occupies the same volume as the optical mode (i.e., the entire cavity), which can greatly extend the range of vibrational excitations. In fact, polariton delocalization has been reported for excitonic coupling to surface plasmon polaritons39,40 whispering-gallery-mode polaritons,41 photonic-crystal nanocavities,42 and for coupling localized and delocalized surface plasmon-polaritons in graphene.43 We now demonstrate that the presence of a slab of molecules can affect the coupling experienced by a second slab, located well away from the first, by examining a cavity with two widely separated PMMA slabs. Figure 4a shows the two systems used in our experiment. In these cases, two physically separated PMMA slabs are located at either ‘Z1a + Z1b’ (green) or ‘Z3a + Z3b’ (blue) positions. The two molecular layers here were positioned at the mirror-image locations with respect to the 1st-order cavity mode. However, this arrangement is not required for the influence to take place. Once again, we employ both s and p light polarizations. The dispersions in Figure S9b (with spolarization) and S9c (with p-polarization) reveal that the vacuum Rabi splittings are larger for these pairs than those measured for single layers at the same position (compare the splitting seen for ‘Z1a’ to ‘Z1a+b’). The increase in the vacuum Rabi splitting for the double-layer cavities is plotted in Figure 4b (s-polarization) and 4c (p-polarization), from which we find that these cavities show an increased splitting by a factor of ~1.3 compared with the single-layer cavities. The 1.3-fold increase in splitting is consistent with a doubling of the number of molecules, since the Rabi splitting is proportional to the square root of the number of molecules in the cavity, (√2~1.4). The increased vacuum Rabi splitting associated with the insertion of a second molecular layer shows that the coupling between a given slab and the cavity can be enhanced by the presence of another slab positioned relatively far from the first (Figure 4). This is because the new light-matter polaritons take on the extended nature of the cavity photons. Even without 11 ACS Paragon Plus Environment

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physical contact between the two layers, the presence of a second layer influences the cavity coupling to the first via their simultaneous interactions with the cavity field. This experiment paves an exciting path for controlling the coupling strength of a given region through modification of a remotely located layer, either actively or statically, as well as the prospect of intermolecular interactions and energy transfer for molecules that are spatially separated. By analogy with an optical buffer that modulates transport of optical signal in optical interconnects,44 cavities with individual molecular layers should be able to trigger a specific chemical reaction in a remotely confined region of a cavity through strong coupling with cavity modes.

Conclusion We have demonstrated the influence of spatial overlap between the location of vibrational absorbers and the optical modal profile on the resulting vacuum Rabi splitting. This was demonstrated using several mode profiles (s- and p-polarized 1st- and 2nd-order cavity modes) supported in Fabry-Perot cavities containing a slab of PMMA located at different positions. Generally, coupling increases when absorbers are placed in regions of high modal intensity (i.e., coupling strength follows the mode profile). Notably, molecules near the cavity face (i.e., the mirror) couple twice as strongly to the p-polarized mode as to the s-polarized mode. This is due to p-polarized modes supporting a component polarized along the propagation direction, which are non-zero at the mirror face. This is an angle-dependent effect, which increases for cavities tuned to be resonant with the absorber at higher angles and disappearing completely for cavities tuned to be in resonance with the absorber at normal incidence. The experimental vacuum Rabi splittings under all conditions agree well with those obtained from transfer-matrix calculations as well as from an analytical expression developed in this work, which reinforces the concept that the coupling strength depends strongly on the molecular distribution within a 12 ACS Paragon Plus Environment

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cavity. Finally, the examination of cavities consisting of two remotely located PMMA layers within the cavity reveal that the coupling between each individual layer and the cavity strengthens when both layers independently couple to the cavity field. These results will have even greater importance when examining the use of subwavelength-confined optical modes, which may exhibit extreme modal spatial variation. The delocalized nature of hybrid polaritonic states may provide a simple yet powerful method to modify chemical reactions, and the understanding of the dependence of light-matter coupling on molecular spatial distribution brings the community closer to controllable and active modification of chemical reactivity using vibrational strong coupling.


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(c)

PMMA positions

Field intensity Emax

Z1 Z2 Z3 Z4 Z5

Polarizer s-pol. θ θ = 0 – 70˚ z x

0

y

-1000 -500

0 500 Z (nm)

PMMA positions

Undoped Si -1

Unpolarized

Au

Branch splitting (cm )

(a)

70 60 50 40 Experiment Transfer matrix Analytical

30 20 -1200

1000

-800

-400

0

Z (nm)

2000

(b)

Z1

Wavenumber (cm -1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Z3

Z5

1900 1800 1700 1600 1500 0

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x103

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Figure 1. Influence of the mode profile on cavity-vibration coupling with the 1st-order cavity mode under s-polarization. (a) A schematic diagram of a Fabry-Perot cavity that allows variable location of a PMMA slab within the cavity (Z1 through Z5). The simulated 1st-order s-polarized mode intensity profile at the angle of the strongest coupling is overlaid on the cavity diagram (solid blue curve). The cavity and mode profile are drawn roughly to scale. (b) Cavity dispersion curves plotted versus in-plane wavevector for selected cavities with a PMMA slab located at Z1, Z3, and Z5 positions. An avoided crossing between the upper branch (UB) and lower branch (LB) is clearly shown in each cavity as an indication of vibrational coupling between the carbonyl stretching band of PMMA centered at 1731 cm-1 (dashed white line) and the cavity mode. Upper and lower polaritons were fit to a two-coupled-oscillator expression (fits shown as solid red curves). Additional splittings occurring at ~1630 cm-1 are due to SOG spacers, as verified by a control cavity entirely filled with SOG only (Figure S4f – S7f). (c) Rabi splittings acquired experimentally (filled red circles), by a transfer-matrix calculation (empty red circles), and an analytical treatment (empty red squares) are plotted versus PMMA position relative to cavity center. The 1st-order s-polarized mode profile is shown as a solid blue curve.


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(c)

Unpolarized

Au

Z1 Z2 Z3 Z4 Z5

Field intensity

Polarizer

Emax

p-pol. θ θ = 0 – 70˚ z x

0

y

-1000 -500

0 500 Z (nm)

PMMA positions

Undoped Si 65

-1

PMMA positions


(a)

60 55 50

Experiment Transfer matrix Analytical

45 40 -1200

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Z (nm)

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(b)

Z1

Wavenumber (cm-1)

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x103

(cm-1)

Figure 2. Influence of the mode profile on cavity-vibration coupling with the 1st-order cavity mode under p-polarization. (a) The p-polarized mode consists of two field components, one polarized in-plane (dotted green curve) and the other polarized along the propagation direction (dotted orange curve). The sum of the two field intensities is shown in a solid blue curve. The field profiles were calculated at the angle of the strongest coupling. (b) Cavity dispersions plotted versus in-plane wavevector for selected cavities, Z1, Z3, and Z5, showing that Rabi splitting at 1731 cm-1 (dashed white line) is smallest for Z1 (node) and increases as the PMMA slab moves toward the center of the cavity (Z5, antinode). Fits to a two-coupled-oscillator expression are shown as solid red curves. (c) Rabi splittings acquired experimentally (filled red circles), by a transfer-matrix calculation (empty red circles), and an analytical treatment (empty red squares) are plotted versus PMMA position relative to cavity center. The 1st-order ppolarized mode profile is shown as a solid blue curve.


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PMMA positions

Au

Emax

s-pol. θ θ = 0 – 70˚ z 0

x y

-1000 -500

0 500 Z (nm)

PMMA positions

-1

Z1 Z2 Z3 Z4 Z5

(b)

Undoped Si


(a)

Field intensity

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15 10 5 -1200

1000

-800

-400

0

Z (nm)

Figure 3. Influence of the mode profile on the cavity-vibration coupling with the 2nd-order cavity mode under s-polarization. (a) Schematic of the Fabry-Perot cavity with variable PMMA slab locations (Z1 – Z5) and the 2nd-order s-polarized mode profile. (b) Experimentally obtained vacuum Rabi splittings (filled red circles) as a function of PMMA slab location Z.


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PMMA positions

Au

(a)

Undoped Si

s- or p-pol. Z 1 θ = 0 – 70˚ a z θ

Z 3 a

Z 3 b

Z 1 b

x y

(b)

(c)

60

s-polarization Experiment Simulation

40 20 0

Z1a

Z1a+b

80 p-polarization Experiment Simulation

-1


80

-1


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Z3a

60

40 5 0

Z3a+b

Z1a

Z1a+b

Z3a

Z3a+b

Sample

Sample

Figure 4. Coupling between two remote molecular layers via cavity fields. (a) Schematic of the Fabry-Perot cavity consisting of two slabs of PMMA layers at positions of either Z1a and Z1b (green) or Z3a and Z3b (blue). Vacuum Rabi splitting values obtained experimentally (solid fill) and via a transfer-matrix simulation (diagonal fill) for each case of single (Z1a, Z3a) and double (Z1a+b, Z3a+b) layers of PMMA under (b) s- and (c) p-polarization. Double-layer cavities showed an increased splitting by a factor of ~1.3 compared with the single-layer cavities.


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Methods Fabrication of Au/SOG/PMMA/SOG/Au Fabry-Perot Cavities with Variable PMMA Film Positions. First, a silicon substrate (undoped, 2 x 2 cm2, 500 µm thickness, University Wafer) was cleaned in a buffered oxide etch solution (10:1, J.T.Baker) for 2 min and rinsed with copious amounts of distilled water. The substrate was blow-dried with N2 and further baked on a 120˚C hot plate for 15 min to remove the adsorbed water and enhance the adhesion of metal films in the following step. The bottom Cr/Au films with thicknesses of 3/20 nm were deposited on the cleaned silicon substrates by electron-beam evaporation (Temescal Model FC-2000) with deposition rates of 1.0 / 2.0 Å/sec for each metal. The metal film thicknesses were monitored by a quartz crystal microbalance during deposition. There were ±0.3 nm differences between the targeted and actual Au film thicknesses. Initial deposition of a Cr adhesion layer improved the adhesion of the Au film to the silicon substrate during the bottom Au mirror fabrication. However, the Cr film was omitted during the evaporation of the top Au mirror (only a 20 nm thick-Au film was deposited). Depending on the cavity design, spin-on-glass layers (SOG, part numbers 315F and 21F, Filmtronics) were repeatedly spin-coated in a bench-top spin processor (Laurell WS400BZ-6NPP/LITE) to obtain the desired film thicknesses and locate a PMMA slab (4% in anisole, molecular weight of 950 kDa) at the desired positions within the cavity. The detailed spin conditions for each sample are listed in Table S1. The SOG 315F and 21F were used to make thick and thin films of SOG, respectively. After spin coating each SOG layer, substrates were baked at 170˚C for 1.5 min with ramp rates of 30 and 3˚C/min for heating and cooling, respectively. The gradual cooling minimized the thermal stress in the SOG films (especially films that require multiple coat and bake) and significantly reduced the formation of cracks and delamination of the SOG film. After PMMA spin-coating, substrates were baked at 170˚C for 15 min with the same ramp rates. The film thicknesses were measured with a profilometer (KLA


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Tencor Alpha Stepper Profilometer) after using a razor blade to cut witness samples prepared under the identical spin and bake conditions.

Angle-Dependent Transmittance Measurement using Fourier-Transform Infrared (FTIR)

Spectrometer.

Angle-dependent

transmittance

spectra

of

the

prepared

Au/SOG/PMMA/SOG/Au Fabry-Perot cavities were obtained using a Fourier-transform infrared (FTIR) spectrometer (Thermo Scientific) equipped with a home-built sample rotator (BGM80, Newport), which allowed light to be incident upon the sample at an angle ranging from 0˚ to 70˚. A MCT-High D* detector was used in the FTIR spectrometer and a linear polarizer (WP25H-Z, Thorlabs) was mounted in the light path for the s- or p-polarization experiment. The system was controlled by a LabVIEW program to collect the transmittance spectra of the sample with 1˚ interval in the spectral range of 1200 - 4000 cm-1. A background spectrum was obtained with an empty sample holder under the same acquisition conditions that were used for the sample (number of scans of 128 and resolution of 4). The transmittance spectra measured at varying incident angles of light were compiled using a custom-written Igor program (Igor Pro. v6.3.7.2.) to plot the dispersion curve of the transmission spectra as a function of wavenumber versus angle. The dispersion curves in the angular domain were then converted to the wavenumber domain by plotting them as a function of wavenumber and wavevector. Finally, in order to obtain splitting between the coupled-mode upper and lower branches, the upper and lower branches were plotted in the wavevector domain and globally fitted to a two coupled oscillator expression, resulting in the extracted vacuum Rabi splitting values (see Figure S8 for an example fit).

Transfer-Matrix Calculations. Transfer-matrix calculations were implemented in Mathcad, with a characteristic matrix for each material layer (window, metal mirror, PMMA, SOG, etc.) as a function of the frequency-dependent complex dielectric function of that layer. These characteristic layer matrices were multiplied together to form the complete system matrix, the elements of which allow to extract the transmission and reflection spectra.45 Vacuum Rabi 19 ACS Paragon Plus Environment

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splittings were extracted from such calculations by simulating a series of transmission spectra as a function of incident angle and light polarization. This angle-dependent data set was converted to k-space and peak positions were extracted. The k-dependent peak positions were fitted to upper and lower polariton functions (Eq. 2 in the main text) to yield the vacuum Rabi splitting. Field profiles were generated for an incident angle that closely corresponded to that which gave the best tuning between the cavity and molecular excitation.

Acknowledgements This research was performed while the author, Wonmi Ahn, held a National Research Council (NRC) Research Associateship award at the U.S. Naval Research Laboratory. The work was supported by the Office of Naval Research and the U.S. Naval Research Laboratory Nanoscience Institute.

Associated Content Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Analytical treatment of Rabi frequency for dipoles in resonators, Recipes used for spincoating and baking of SOG and PMMA films, FTIR transmission spectrum of a bare PMMA and SOG film, FTIR transmission spectra of Fabry-Perot cavities with variable PMMA locations within the cavity under s- and p-polarization, Angular dispersion curves of FabryPerot cavities with variable PMMA slab locations under s- and p-polarization, Cavity dispersion curves plotted versus in-plane wavevector for cavities with variable PMMA slab locations under s- and p-polarization, Data analysis for obtaining vacuum Rabi splitting values, Dispersion curves of single and double PMMA layer cavities (PDF).


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For Table of Contents Use Only

Vibrational Strong Coupling Controlled by Spatial Distribution of Molecules within the Optical Cavity

Wonmi Ahn,1 Igor Vurgaftman,2 Adam D. Dunkelberger,3 Jeffrey C. Owrutsky,3 and Blake S. Simpkins3,* 1

National Research Council Postdoctoral Associate, U.S. Naval Research Laboratory, Washington, DC

20375, United States 2

Optical Sciences Division, U.S. Naval Research Laboratory, Washington, DC 20375, United States

3

Chemistry Division, U.S. Naval Research Laboratory, Washington, DC 20375, United States

*E-mail: [email protected]

A relationship between spatial distribution of vibrational absorbers and cavity mode profile was demonstrated for vibrational strong coupling by systematically varying the location of a poly(methyl methacrylate) (PMMA) film within a Fabry-Perot cavity. Both experiment and simulation revealed that the 1st- and 2nd-order cavity resonances couple to molecular absorption lines of PMMA, resulting in vacuum Rabi splittings that show strong dependence on the molecular spatial distribution within a cavity.


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