Hybrid architectures for terahertz molecular polaritonics

Atoms and their different arrangements into molecules are nature’s building blocks. In a regime of strong coupling, matter hybridizes with light to modify physical and chemical properties, hence creating new building blocks that can be used for avant-garde technologies. However, this regime relies on the strong confinement of the optical field, which is technically challenging to achieve, especially at terahertz frequencies in the far-infrared region. Here we demonstrate several schemes of electromagnetic field confinement aimed at facilitating the collective coupling of a localized terahertz photonic mode to molecular vibrations. We observe an enhanced vacuum Rabi splitting of 200 GHz from a hybrid cavity architecture consisting of a plasmonic metasurface, coupled to glucose, and interfaced with a planar mirror. This enhanced light-matter interaction is found to emerge from the modified intracavity field of the cavity, leading to an enhanced zero-point electric field amplitude. Our study provides key insight into the design of polaritonic platforms with organic molecules to harvest the unique properties of hybrid light-matter states.

Strong light-matter interactions can modify fundamental properties of some physical systems leading to applications beyond fundamental science.In general, the light modes used in such experiments range from the visible into the region of mid-infrared.In the visible regime, where light couples to electronic transitions, experiments have e.g.shown modifications of charge conductivity [1,2], photochemistry [3,4] or single-molecule branching ratios [5,6].The condition for observing coherent exchanges between light and matter requires the coupling strength, also known as the vacuum Rabi splitting (VRS), to exceed all of the various loss rates in the system.To mitigate optical loss, high finesse optical resonators are utilized: standard designs in early pioneering efforts have made use of distributed Bragg reflector (DBR) microcavities with active media consisting of either an inorganic semiconductor quantum well design [7] or organic semiconductors [8,9].
In the THz regime (wavelengths from 0.1 to 1 mm), light can also directly couple to intra-and inter-molecular vibrational modes [10][11][12].This led to emerging applications in chemistry through the modification of ground state potential landscapes allowing for the manipulation of chemical reactions pathways and rates [13][14][15].However, for the purpose of studying  light-matter coupling involving far-infrared light and low-energy vibrational transitions of molecules, the DBR design becomes unpractical since most dielectrics are absorptive in this region and their required thickness exceeds the capacity of most nanofabrication equipment.In this context, other types of optical resonators have been demonstrated such as standard Fabry-Perot (FP) cavities with planar mirrors, where a VRS on the order of 68 GHz has been reached [16].
We propose here alternative architectures where structural resonances in the THz regime are interfaced with vibrations in ensembles of organic molecular quantum emitters.On the electromagnetic side, this can refer to single plasmonic emitters/antennas [17,18], metallic waveguides [19][20][21], or metasurfaces (MSs) [22][23][24].On the matter side, we focus on glucose which has a strong relevance to biological processes including metabolism and photosynthesis.More specifically, we propose a set of four hybrid architectures illustrated in Fig. 1 to achieve a regime of strong light-matter interactions with a sharp vibrational resonance of glucose.In a first step, we demonstrate similar performance of both plasmonic MSs and standard FP cavities in achieving strong light-matter couplings.This is due to the stronger spatial confinement of a photonic mode allowed by the evanescent field of the MS which enables a reduction in the number of molecular emitters in comparison to the FP cavity.The combination between the two platforms can then lead to an improvement in the overall finesse of the system [25].
We focus on providing strong confinement of an electromagnetic mode around a vibrational transition of glucose at 1.43 THz which has a linewidth around 100 GHz, while ensuring a limited mode volume where the glucose layer is placed.In addition, full control of the resonance frequency and linewidth can be achieved by a tailored design of subwavelength arrays of metallic elements [26,27] with engineered periodicity and geometry of its constituent elements as a function of the surrounding media.This renders the MS as a frequency-selective mirror (analogous e.g., to subradiant optical mirrors realized with trapped atoms [28]) which can be integrated in standard FP configurations to achieve better cavity finesse [25].A spray coating technique is used to deposit a layer of crystalline sugar directly on a MS, allowing for both the optimization of interaction with the plasmonic field as well as for the tuning of the plasmonic resonance [29].The light-matter interaction strength, i.e., the vacuum Rabi splitting, is detected in the transmission of the hybrid system via a time-resolved THz spectroscopy technique which allows for the reconstruction of the full oscillating electric field.Rabi splittings in the range of 140 GHz proving strongly coupled light-matter dynamics are observed which are in good agreement with theoretical simulations based on the transfer matrix approach.

II. SETUP AND APPROACH
MSs are constructed using a photolithography and metal evaporation process in which arrays of crossshaped aluminium elements are fabricated onto a THz transparent 188 µm-thick cyclo-olefin copolymer, commercially branded as Zeonor, with a measured index of refraction of 1.53 (at 1 THz).The photolithography procedure utilizes a negative tone resist to etch the array design, followed by an aluminium deposition through direct current sputtering and a subsequent lift-off process.The dimensions of the metallic elements and the periodicity of the array, schematically shown in Fig. 1(a), are optimized to achieve a sharp THz plasmonic resonance causing a distinctive dip in the spectral transmission.The four-fold symmetry of the cross-shaped elements is chosen to ensure a response insensitive to the polarization state of the THz radiation.A spray coating technique (see Appendix C for details) is used to deposit a glucose layer [30].
In a first experiment, the layer is deposited directly on the MS as shown schematically in Fig. 1(a).In a second experiment, two partially reflective mirrors (R ≈ 0.85), fabricated by sputtering 9 nm of gold on a semiconductor substrate, form a FP cavity in the THz region (Fig. 1(b)).The semiconductor substrate is 650 µm-thick undoped GaAs with a refractive index of 3.6 (at 1 THz).In a third and fourth experiment, we explore hybrid architectures, schematically shown in Figs.1(c),(d), where one mirror of the FP cavity is replaced by a MS.We investigate the THz transmission response when a glucose layer is deposited on the planar mirror (H1) or on the MS (H2) with a thickness of 210 µm and 90 µm, respectively.
Characterization of the different architectures is performed with a THz time-domain spectroscopy (THz-TDS) technique, depicted in the setup shown in Fig. 2. In brief, an ultrafast source operating at 1030 nm with a pulse duration of 170 fs and a repetition rate of 1.1 MHz is split into a pump and gating beams.The pump generates a THz transient through optical rectification in a 2 mm-thick GaP crystal.A standard electro-optic sampling scheme resolves the THz pulse using another 2 mm-thick GaP crystal.
In order to observe a sizeable VRS, both the linewidths of the photonic device and that of the molecular ensemble have to be optimized.Saccharides, like glucose, are known to have a distinctive narrow radiative transition in the THz region originating from collective intermolecular vibrations due to the hydrogen bonding networks in the crystalline phase [31].The complex refractive index of glucose is measured with time-resolved THz spectroscopy.The inset of Fig. 2 shows the measured absorption spectrum with a prominent vibrational resonance at 1.43 THz and background absorption increasing towards higher frequencies.The real part of the refractive index is n g = 1.9 at 1.43 THz.We used these values to model the spectral transmission of the MS with the Lumerical FDTD solver [32] and the response of the devices including a photonic cavity with a theoretical analysis based on the transfer matrix method (see Appendix A for details).
The description of the interaction between an electromagnetic mode (angular frequency ω c ) and an ensemble of N = ρV (in a volume V with number density ρ) molecular vibrational dipoles (angular vibrational frequency ν) is given by the Tavis-Cummings Hamiltonian (setting ℏ = 1) where â, bj are the bosonic annihilation operators for the cavity mode and the jth molecular dipole, respectively.The position-dependent coupling g j = µEf (r j )ε j µ • ε c is given by the product of the dipole moment of the vibrational transition µ, the zero point electric field amplitude E (inversely proportional to 1/ V opt -where V opt is the cavity mode volume) and a spatial function f (r j ) evaluated at the position of the molecule r j .The unit vectors ε j µ and ε c account for the relative orientation between the molecular dipole and the cavity polarization, respectively.Assuming, for simplicity, the case where all couplings are identical g j = g, the Hamiltonian describes the coupling of a single collective bright mode B = j bj / √ N to the cavity field with a collective cou- pling strength g N = g √ N .This is the so-called vacuum Rabi splitting (note that the splitting between the peaks is actually 2g N ) and describes the strength of the lightmatter coherent exchanges.In the limit where this rate dominates any loss processes, the system is said to be in the collective strong coupling regime.We remark that the Hamiltonian presented in Eq. ( 1) assumes the rotating wave approximation (RWA) which is valid as long as the collective coupling strength is much smaller than the transition frequency.
A very simple alternative to derive the Rabi splitting, even beyond the RWA, is to perform a linear response analysis via the transfer matrix approach.In this way, the splitting is obtained as the difference between the light-matter hybridized states (polaritons) in the transmission profile as a function of the incoming laser frequency (see Appendix D).

III. COUPLING WITH A METASURFACE RESONATOR
The spectral transmission of a plasmonic MS does not only depend on the geometry and periodicity of its metallic elements, but also on the background media surrounding its interface.The design shown in Fig. 1(a) presents a Zeonor substrate underneath the MS and glucose or air on the top surface.The structure is opti-mized to allow strong coupling between the molecular resonance at 1.43 THz and a resonant plasmonic mode.A rendered depiction of the sample is shown in Fig. 3(a) with an inset zoom-in that defines the MS geometry in terms of periodicity (P ), cross arm length (L) and cross arm width (W ).Since the coupling strength scales with N/V opt = ρV /V opt , the glucose layer must ideally fill up the plasmonic mode volume to ensure that the largest number of emitters are coupled with the electromagnetic mode.Further addition of glucose will not increase the coupling, which is obviously limited by the density ρ, but instead only brings detrimental effects due to the increased absorption.We therefore iteratively deposit thin layers of glucose (height d g , cross section A) while monitoring the transmission properties.A cross sectional diagram of the coated MS is illustrated in Fig. 3(b) where three coating thicknesses are picked to showcase the improvement of the light-matter interaction.
The complex frequency-dependent transmission coefficient for the hybridized MS-glucose system can be obtained from transfer matrix theory as (neglecting effects of the substrate) with c the speed of light and ζ hyb describes the so-called polarizability of the hybridized MS.The expression for ζ hyb derived in Appendix E shows that the Rabi splitting increases with the thickness of the glucose layer and eventually saturates once the thickness exceeds the plasmonic mode volume as characterized by the penetration depth z 0 .The collective coupling can then be expressed as g N = g 0 ρAz 0 (1 − e −2dg/z0 )/2 where g 0 is the average coupling strength of a single emitter directly at the metasurface.
The measured intensity transmission of the coated MS is plotted in Fig. 3(c).The bare MS (black dashed curve) initially has a plasmonic resonance at 1.6 THz corresponding to the narrow spectral dip in transmission.As we gradually deposit layers of glucose on the surface, we observe a red-shift of the resonance to (1) 1.52 THz, (2) 1.49 THz, and (3) 1.43 THz (colored solid lines) with contributions of the Rabi splitting, leading to a maximum peak separation of 90 GHz at close to zero detuning.The response of an equal thickness coating of glucose on the substrate in an area with no MS elements is also plotted (colored dashed lines).The shift of the resonance can be understood as a gradual increase in the effective index of the medium on the top of the MS as we increase the thickness of the glucose layer.Consistent to the theoretical prediction, we also have observed that further increasing the volume of glucose to exceed the plasmonic mode volume will no longer yield a redshift or an improvement in the Rabi splitting, but instead only increased absorption by glucose.The vibrational resonance frequency of the targeted glucose mode is plotted for clarity (vertical dashed line).

IV. COUPLING WITH A STANDARD FABRY-PEROT CAVITY
A rendered depiction of a FP cavity filled with glucose is shown in the top row of Fig. 4(a).The flat mirror cavity is created from partial mirrors formed by sputtered gold on GaAs.One of the mirrors is coated with glucose using the aforementioned spray coating technique.THz-TDS measurements are taken at 5 µm increments of spacing between the cavity mirrors.This effective spacing is given by d eff (ω) = d air + d g n g (ω), where d air is the air space between the mirrors and n g (ω) is the refractive index of glucose.Analytically, one can deduce the expression for the transmission where ζ describes the polarizability of the gold mirrors which we assume to be frequency-independent.This expression is then used to fit the experimental results (see Appendix F).
Experimental results are presented in Fig. 4(a).The middle row shows a scan of the transmission as a function of frequency for varying cavity spacings.Around the 1.43 THz resonance of glucose, one of the cavity modes displays an anti-crossing behavior that is characteristic of strong light-matter coupling.The corresponding Rabi splitting at around 140 GHz is observed in the bottom row of Fig. 4(a).

V. COUPLING WITH HYBRID CAVITY ARCHITECTURES
While strong coupling can be achieved in both setups described above, integrating MSs with flat mirrors might bring a few advantages.One stems from the convolution of the MS's narrow frequency response with the cavity transmission window to design sharper resonances [25] and thus sharper polaritonic peaks.Secondly, the coupling between the three resonances involving glucose, MS and cavity, leads to a richer polaritonic physics beyond the standard upper and lower polaritons typical of strong coupling experiments.We therefore test two scenarios, depicted in Figs.4(b) and (c).
The H1 architecture involves an uncoated MS with a resonance frequency of 1.45 THz merged with a glucose coated flat mirror with a coating thickness of 210 µm.Results are depicted in the middle row density plot of Fig. 4(b).In the density plot, one can see an anti-crossing region forming around the 1.43 THz vibrational resonance of glucose.Additionally, as a cavity mode shifts towards the MS/vibrational resonance, the linewidth of the cavity mode can be shown to narrow slightly.The MS is functioning as a strongly frequencydependent mirror with an approximately Lorentzian response.The bottom row of Fig. 4(b) compares the transmission characteristics of the H1 architecture when a cavity mode is overlapped with the MS/vibrational resonance (on-resonance) versus when a cavity mode is spectrally far from the MS/vibrational resonance (offresonance).We observe a narrowing of the resonance as well as the formation of polariton peaks when the cavity mode is resonant with the MS/vibrational resonance.The splitting between the peaks in the on-resonance transmission is measured to be 135 THz, comparable to the splitting observed in the case of the flat mirror cavity with the same glucose coating thickness.
The architecture of H2, depicted in the top row of Fig. 4(c), is particularly suited for the study of complex polaritonic systems as it couples the glucose resonance to both the cavity-delocalized mode and to the MS resonance.This is observed in the middle plot as an interesting anti-crossing behavior.Distinct dark anti-crossing regions can be seen when the cavity mode is spectrally far from the polaritonic modes of the MS/glucose.This off-resonant case corresponds to the transmission response of just the coated MS.In contrast, when the mirror spacing is set so that the cavity mode begins to interact with the polaritons, the anti-crossing region morphs into three dark regions.This interaction can be observed more clearly by looking at slices of the transmission when the cavity mode is on-resonance (overlapping with the polaritons) versus off-resonance (spectrally far from the polaritons).
Transmission spectra for the on-and off-resonant cases are plotted in the bottom row of Fig. 4(c).We can observe how in the on-resonant case, the response of the H2 architecture shows an enhancement of the MS-glucose interaction which leads to an effectively larger Rabi splitting of 200 GHz for the MS-glucose polaritons.

VI. THE NATURE OF THE HYBRID CAVITY ENHACEMENT
To better understand the competition between the cavity-glucose and MS-glucose coupling for the H2 cavity architecture, we show in Fig. 5(a) a plot of the transfer matrix simulation results with increasing MS-glucose coupling strength g eff , while keeping all other parameters fixed.When geff is small, the cavity-glucose interaction can be seen from the formation of two weak polariton peaks symmetrically shifted from the dominant glucose resonance.In fact, when g eff = 0, we retrieve the transmission response observed for the H1 architecture (black curve).When increasing the MS-glucose coupling, which is the case for H2 architecture, two dips appear, corresponding to the MS-glucose polaritons.Most importantly, the exhibited splitting is now roughly a factor of two larger than the case of coupling only to the MS.This enhancement can be traced back to the fact that the hybrid architecture leads to an increase in the zeropoint electric field amplitude of the intra-cavity mode around the position where the glucose is added.To prove this point, we incorporate FDTD simulations, shown in Fig. 5(b), of an empty hybrid cavity.The electric field strength is monitored in one-dimension along the MScavity axis and normalized to the incident field.The design consists of an infinitely periodic planar array of metallic crosses with a perfectly reflecting mirror plane at a distance (cavity spacing) above.In the plot, the orange dashed line indicates the position of the MS and the green, purple, and brown dashed lines indicate the various positions of the mirror planes.Three different cavity spacings are compared to showcase when a cavity mode is completely overlapped (green curve), partially overlapped (purple curve), and not overlapped (brown curve) with a cavity mode.The electric field is monitored at the resonance frequency of the plasmonic array.Positive monitor positions are within the cavity and negative monitor positions are outside of the cavity.The resultant field profiles obtained from these simulations clearly show that the field strength at the MS interface of a hybrid cavity can be significantly enhanced (for example a factor around 1.8 close to the interface and even larger further away from it) when a cavity mode is resonant to a plasmonic mode.As aforementioned, the coupling strength, g, is linearly proportional to the local electric field given by the product of the zero-point electric field amplitude and the spatial function of the mode supported by the photonic resonator.

VII. CONCLUSION
In summary, we have shown strong coupling between a vibrational resonance of glucose and a plasmonic MS mode in the THz regime where powerful spectroscopic methods based on the THz-TDS technique can be exploited for system characterization.Furthermore, we suggest that this work can open avenues in designing light-matter interfaces based on hybrid architectures.We have shown experimentally, and with support from analytics tested against numerical simulations, the emergence of strong light-matter coupling in a variety of geometries, ranging from the standard FP cavity to more complex hybrid configurations interfacing a MS with a planar mirror.We have demonstrated the enhancement of light-matter coupling strength brought on by the hybrid cavity design and directly connected it to the increase in the zero-point electric field amplitude stemming from the interference between the MS evanescent field and the standing wave field of the cavity at the location of the glucose layer.Further investigations in this direction hold the promise of identifying mechanisms for the design of higher-finesse cavities as well as providing platforms for the exploration of the richer physics of multi-polariton systems.
We instead use a spray coating technique to place a large concentration of glucose molecules at the interface of the plasmonic array, depicted in the cartoon schematic of Fig. A1(b).The vibrational resonances of glucose observed at 1.43 and 2.09 THz are prominent when glucose is in solid-state form.All glucose-coated MSs and planar mirrors produced for this work were coated using this spray coating technique.Placing many solid-state glucose molecules near the plasmonic interface of the MS requires the crystalline particle size of glucose to be reduced; we achieve this condition utilizing an ultrasonic bath.First, we prepare a mixture of glucose powder in isopropanol, which is non-polar and has a low evaporation temperature.The mixture is then sonicated to produce a stable suspension of glucose in isopropanol with crystalline sizes of ∼ 10 µm.The extracted suspension of fine glucose particulates are loaded into an air spray gun.The sample to be coated is placed onto a hot plate with a temperature set above the boiling point of isopropanol (82.5 • C) to facilitate the rapid evaporation of the solvent.A few sprays of the mixture onto the substrate and subsequent drying results in a relatively uniform layer of solid-state glucose on the substrate.To increase the layer thickness, the cycle of spray coating and drying is repeated.The thickness of spray coated glucose onto the samples is probed using optical microscopy.

(E −
R , E + R ) ⊤ via the transfer matrix T such that Assuming a unit input field entering the system from the left E + L = 1, and no input field from the right, E − R = 0, the transmission coefficient is simply obtained as the inverse of the last entry of the transfer matrix t = 1/T 22 .Furthermore, the complex transmission and reflection amplitudes can always be connected as t = 1 + r.The free propagation through a dispersive medium with index of refraction n(ω) and length d is described by the matrix while the action of a thin mirror or MS is described by Here, the quantity ζ m (ω) = −ir m (ω)/t m (ω) is called the polarizability of the mirror which describes the ratio between the complex reflection and transmission coefficients.This is not to be confused with the polarizability from section A. While this is a strongly frequency-dependent quantity for the MS, we assume the polarizability of the gold mirrors to be constant within the considered frequency range.Assuming a Lorentzian reflectivity for the MS (compare with Eq. (A7)), given by r m (ω) = −iγ m /[(ω − ω m ) + i(γ m + γ l )] and including an additional nonradiative loss channel γ l , the polarizability of the MS simply expresses as In addition, the Fresnel losses at the interface between two layers j and j + 1 can be taken into account by the transfer matrix with the standard Fresnel reflection and transmission coefficients For the purpose of modeling spray-coated glucose, we take a Lorentz-Drude model for the refractive index around the resonance at ν = 2π • 1.43 GHz (note that ω and ν are angular frequencies) with background permittivity ε g,back = 3.61, oscillator strength α g = 0.028, and linewidth γ g = 2π • 85 GHz.The total transmission matrix is then simply obtained by multiplying the matrices of the individual elements.In Fig. A3 we illustrate the potential advantages of hybrid cavity designs by comparing the transmission of a standard FP cavity to that of a hybrid architecture where the left mirror is replaced by an ideal, lossless MS.The hybrid architecture leads to a filtering out of all other resonances while simultaneously showing a reduction in linewidth around the resonance of interest (with a Fano-like profile and a zero of transmission located directly at the MS resonance).The cavity length for both architectures is 348 µm.
Appendix F: Coupled-dipoles approach for glucose-MS coupling While the transfer matrix method describes the forward and backward propagation of plane waves through the structure, it does not per se include the near-field coupling of the glucose layer to the evanescent field of the MS.This coupling can be included by a coupled-dipoles model.To this end, one assumes that each vibrational dipole couples to the MS with a distance dependent rate g j ≡ g(r j ).From the Tavis-Cummings Hamiltonian (Eq.( 1) of the manuscript), supplemented with the proper decay terms, one can then derive equations of motion for the amplitudes of the electric field of the MS and the jth molecular dipole in the glucose layer where η(t) describes some arbitrary input field probing the response of the MS and γ g is the linewidth of the glucose resonance.Solving this set of equations in Fourier domain, one can see that the coupling to the glucose gives rise to a modified MS response .

(F3)
Assuming the field to fall off exponentially from the MS, can write g j = g(z j ) = g 0 e −zj /z0 where z 0 is the penetration depth of the field into the glucose layer (≈ 15 µm) and g 0 is the coupling strength directly at the MS (considering that we already averaged over the field distribution in the xy plane).Considering a total number of N molecular emitters coupling to the MS (N = Ad g ρ, with A the cross section of the glucose layer, d g the thickness of the glucose layer and ρ the density of molecules), the sum over the coupling strength can be turned into an integral where N z0 describes the number of emitters within the mode volume N z0 = Az 0 ρ.From this, we can define the effective coupling strength (Rabi frequency) as g eff (d g ) = j g 2 j .In Fig. A4 we make use of Eq. (F3) to fit the transfer matrix result to the experimentally measured transmission (parameters in caption).

Appendix G: Experiment -Transfer matrix theory comparison
In Fig. A5 we show a comparison between the experimental results and transfer matrix simulations.For the hybrid architectures, we used the MS fit described in Section E.More details can be found in the figure caption.

FIG. 1 .
FIG. 1. Hybrid architectures for light-matter coupling.(a) Plasmonic metasurface (MS) as an array of cross-shaped metal elements coated with a (90 ± 10) µm-thick glucose layer.(b) Fabry-Perot (FP) cavity where one mirror is coated with a (210 ± 10) µm-thick glucose layer.(c) and (d) Hybrid cavity designs in which one mirror of the FP cavity is replaced by a MS, and where the glucose layer either covers the mirror (H1) or the MS (H2).

FIG. 2 .
FIG. 2. THz-TDS setup and the THz absorption coefficient of glucose.Schematic of the THz time-resolved spectroscopy setup.An ultrafast laser source is used to generate THz through optical rectification in a GaP crystal.The detection process uses a partially reflected pulse from the same optical source to perform standard electro-optic sampling (EOS) inside another GaP crystal.In brief, the THz electric field is revealed by resolving THz-induced birefringence in the nearinfrared gating pulse, which is monitored as a function of time delay with the THz pulse with a quarter-wave plate (λ/4), Wollaston prism (WP) and a pair of balanced photodiodes (PD).(inset) Absorption spectrum of a 300 µm-thick glucose (C6H12O6) pellet measured with time-resolved THz spectroscopy and featuring a prominent vibrational resonance at 1.43 THz.

FIG. 3 .
FIG. 3. Strong light-matter coupling with a glucosecoated MS.(a) Schematic of a MS designed from an array of cross-shaped aluminium elements (shown in dark yellow color for clarity) with a glucose coating covering half the structure.The inset is a zoom-in defining the structural dimensions: the periodicity (P ), cross arm length (L), and cross arm width (W ), which are optimized to provide a narrow plasmonic resonance.(b) A cross-sectional schematic of the MS with three thicknesses of glucose layers: (1) 30 µm, (2) 60 µm, and (3) 90 µm, deposited with successive spray coating passes.(c) THz-TDS measurements taken of these three structures (lines) and the bare glucose layer on Zeonor (without the MS) (dashed lines).The transmission spectrum of the uncoated MS is provided for comparison (black dots).

FIG. 4 .
FIG. 4. Strong light-matter coupling with FP and hybrid cavity architectures.Transmission spectra for (a) standard FP cavity, (b) H1 and (c) H2.Top to bottom row shows the schematics of the cavity architectures, the 2D transmission as a function of relative cavity spacing and frequency as well as cross sections through the transmission profile.In the plots at the bottom, the dashed black curve in (a) shows the transmission of a glucose-coated gold mirror while the red and blue curves show the transmission for different cavity lengths (on-resonance/off-resonance) as indicated by the arrows in the density plot above.The H2 architecture leads to an enhanced polaritonic response, showing a substantially broader Rabi splitting when a cavity mode is overlapping with the polaritons of the coupled MS.

FIG. 5 .
FIG. 5. Transfer matrix and FDTD simulations of the hybrid cavity.(a) Transfer matrix simulation of cavity transmission (on-resonance) for different glucose-MS coupling strengths g eff and dg = 100 µm.The arrows indicate the enhanced Rabi splitting of the MS-glucose interaction due to the cavity configuration.The vertical dashed line shows the location of the glucose resonance.When g eff > 0, the glucose-MS polaritons are dominant and the transmission result resembles experimental observations of the H2 configuration.Otherwise, when g eff = 0, only the cavity-glucose interaction remains, and the transmission result resembles the H1 configuration.(b) A FDTD investigation of an empty hybrid cavity.The position of the mirror, relative to the array interface (0 µm, orange dashed line), determines the cavity spacing and thus the cavity resonance.Reducing the cavity spacing (from brown to purple to green) allows one to bring the cavity mode in resonance to the MS mode.The electric field magnitude within (> 0 µm) and outside (< 0 µm) of the cavity is monitored in one dimension and normalized to the incident field.The green curve shows the field profile obtained when the plasmonic and cavity modes are resonant to each other.The corresponding vertical dashed lines show the positions of the mirror.The enhancement of the field amplitude is consistent with the modified Rabi splitting showcased in (a).
FIG. A1.(a) Extracted refractive index measurement of a glucose pellet with 300 µm thickness created using a hydraulic press.Glucose has an index of 1.9 (real part) at the targeted 1.43 THz vibrational mode.(b) Cartoon schematic of the spray coating technique.A suspension of sonicated glucose powder in isopropanol is air sprayed onto a sample which is placed onto a hotplate.The temperature of the hotplate is set to allow isopropanol to rapidly evaporate, leaving a layer of solid-state glucose on the sample.
FIG. A2.FDTD simulations of field distribution at the air/substrate/MS interface (shown is a single plasmonic element) (a) in the xy plane (z = 0 µm) and (b) in the xz plane (y = 0 µm) spanning 150 µm above and below the interface.(c) Evanescent field strength monitored along z at a position (x = 41.5 µm, y = 0 µm), which is chosen because it shows a distribution representative of the overall field contained within the xy plane above the metasurface.
FIG. A3.Comparison of cavity transmission functions for (a) standard FP cavity with ζ = 2 and (b) hybrid cavity design where one of the mirrors is replaced by a MS with linewidth γm = 2π • 50 GHz and resonance frequency ωm = 2π • 1.43 THz.The cavity length for both architectures is 348 µm.

2 j
FIG. A4.Comparison of transmission between uncoated (black, dg = 0 µm) and glucose-coated (purple, dg = 90 µm) MS.The solid curves show the experimental results while the dashed curves show the transfer matrix fits which also take into account the effects of the Zeonor substrate.The MS is fitted with γm = 2π • 100 GHz, γ l = 2π • 52 GHz, and we assume a coupling strength of g eff = 2π • 45 GHz for dg = 90 µm.The vertical dashed line shows the location of the glucose resonance.
FIG. A5.Comparison between measured transmission spectra (left column) and results obtained from transfer matrix theory (right column) for the different cavity architectures.Each density plot is normalized to the maximum transmission intensity Tmax.The MS is fitted with γm = 2π • 100 GHz, γ l = 2π • 52 GHz, ωm = 2π • 1.43 THz while for the gold mirrors we assume ζ = 0.9.For H2, we assumed an effective MS-glucose coupling strength of g eff = 2π • 45 GHz.The horizontal resonances at approximately 1 THz for the H1 and H2 architectures stem from back reflection in the Zeonor substrate.We neglected back reflection from the GaAs substrate as this is not captured by the THz-TDS measurement.