Hybridization of graphene-gold plasmons for active control of mid-infrared radiation

Many applications in environmental and biological sensing, standoff detection, and astronomy rely on devices that operate in the mid-infrared range, where active devices can play a critical role in advancing discovery and innovation. Nanostructured graphene has been proposed for active miniaturized mid-infrared devices via excitation of tunable surface plasmons, but typically present low efficiencies due to weak coupling with free-space radiation and plasmon damping. Here we present a strategy to enhance the light-graphene coupling efficiency, in which graphene plasmons couple with gold localized plasmons, creating novel hybridized plasmonic modes. We demonstrate a metasurface in which hybrid plasmons are excited with transmission modulation rates of 17% under moderate doping (0.35 eV) and in ambient conditions. We also evaluate the metasurface as a mid-infrared modulator, measuring switching speeds of up to 16 kHz. Finally, we propose a scheme in which we can excite strongly coupled gold-graphene gap plasmons in the thermal radiation range, with applications to nonlinear optics, slow light, and sensing.


Introduction
Devices operating in the mid-infrared region of the electromagnetic spectrum find significant applications in imaging, sensing, communication, and astronomy due to the presence of unique molecular "spectral fingerprints" and atmospheric transparency windows between 3-5 μm and 8-12 μm.However, the development of mid-infrared technology has been hindered by the lack of materials with a small enough bandgap and the requirement to operate at lower temperatures.Graphene, with no bandgap in a chargeneutral state, can absorb 2.3% of light across the THz and mid-infrared range, as determined by the finestructure constant 1 .Although this is an impressive value for a single-atom-thick material, for applications such as metasurface modulators this value is insufficient 2,3 .Nevertheless, nanostructured graphene can couple to light through localized surface plasmons and enhance light absorption and scattering [4][5][6][7][8] .
Moreover, graphene plasmon resonances can be tuned across a significant part of the mid-infrared through charge injection.The coupling, however, is inefficient due to wavevector mismatch, the thinness of graphene, plasmon damping, and interaction with the substrate 5,6 .In particular, direct patterning of the graphene introduces defects at the edges which render the edges electrically inactive 6 .Measured midinfrared extinction rates in graphene nanostructures have been consistently smaller than 10% [4][5][6][9][10][11][12] , with a notable exception showing an extinction of 40% at high (0.8 eV) doping in a top-gated scheme with a highcapacitance ion-gel as the gate dielectric 11 .
More recently, alternative schemes have been proposed to enhance absorption, making use of gold antennas or slots to interact with graphene plasmons [13][14][15][16] .Kim et al. showed near perfect absorption in a graphene nanoribbons metasurface by engineering mirror charges on a low permittivity substrate and demonstrated a mid-infrared modulator operating in reflectance 15 .Zeng et al. demonstrated a metasurface mid-infrared modulator with reflection modulation depth of up to 90% and a spatial light modulator device 16 .These other exciting results have showed the viability of using graphene as a platform for active mid-infrared optical elements and devices.
Here we propose an alternative approach, based on hybridization of gold-graphene plasmons, in which their strong near-field interaction can create tunable and sharp plasmonic resonances across the mid-infrared range.In this scheme, the graphene itself does not need to be etched (avoiding the creation of inert regions of graphene), and the gold rods enhance the coupling with light.We demonstrate a metasurface in which a hybrid, graphene-like plasmon resonance can be tuned through the application of an external voltage, allowing for high differential transmission rates of 20% under moderate doping conditions.We also explore the potential application of such a device as an electro-optic modulator by applying an oscillating voltage source to the gate and measuring the optical modulation.Finally, we propose a design for a metasurface operating in the thermal radiation range showing strong coupling between graphene and gold plasmons, with potential applications in sensing and nonlinear optics.

Hybridization model
The concept of hybridization in plasmonics was introduced by Prodan et al. to explain plasmon resonances in metallic nanostructures 17 .Originally applied to metallic nanoshells, it has been used to explain and design plasmon resonances in a myriad complex structures [18][19][20] , including in nanostructured graphene 10,21 .This powerful concept borrowed ideas from hybridization in chemistry to provide an intuitive picture to explain the plasmon resonances and visualize charge distribution.In our case, the metasurface design, depicted in Fig. 1(a), will be based on hybridization between graphene and gold plasmons.It consists of gold nanorods deposited on a graphene surface in a periodic configuration.Mid-infrared light excites localized surface plasmons (LSPs) in the gold nanorods, which in turn excite graphene LSPs confined in the gaps between the tips of the gold rods 22,23 .Due to their proximity, they strongly couple, forming hybrid modes.We can control the detuning between graphene and gold LSP frequencies through their geometry and gate voltage.We will consider two cases separately: when these two resonances are far apart, and when they match.Figure 1(b) shows the concept for hybridization in our design.Graphene and gold plasmons will couple through near-field, giving rise to two new hybrid modes, depending on their charge density configuration.In the bonding (symmetric) mode, the charge density will be concentrated mostly on graphene, while in the antibonding (antisymmetric) mode the charges will be distributed on both graphene and gold rods.The picture is equivalent to that of a coupled harmonic oscillator, but the hybridization concept provides a microscopic description of the coupling origin.The resonances will be calculated from electromagnetic simulations, including a model for the each material permittivity or surface conductivity (see supplementary information).

Detuned resonances
We begin by considering the scenario where the LSPs of both gold and graphene are detuned.The design is presented in Fig. 2(a) and the calculated spectra for varying graphene Fermi level are presented in 2(b).
When the Fermi level is set to 0, the spectrum displays only a broad resonance of the gold rod, peaked at 4 µm and 9.6 μm.The additional features in the spectrum will be explained in the experimental section later.
By adjusting the Fermi level of graphene, resonances centered around 7.5 µm and in the 11-13 µm range can be observed.The original peak around 4 µm is also shifted by the coupling to the graphene LSP, though this effect is more limited.While the modes are hybridized, the graphene and gold LSPs generally retain their original character within the range of chemical potentials that we can access.Therefore, for detuned resonances, we will refer to these hybrid modes as graphene-like and gold-like, respectively.In Fig. 2(c), the calculated charge distribution on this metasurface at 7.5 µm confirm that this resonance is graphenelike.Figure 3(a) shows an SEM image of the fabricated metasurface, using e-beam lithography on a CVD-grown graphene field-effect transistor device 24 (see methods section).The total area of the metasurface is 250x250 µm 2 .The spectral response of the fabricated device was measured using a Fourier Transform Infrared Spectrometer (FTIR) and is shown in Fig. 3(c).The gate voltage was adjusted to tune the graphene chemical potentials from 0 to 0.35 eV. Figure 3(d) shows the differential extinction, defined here as Δ(  ) = 1 − (  )/  , where (  ) and   are transmittances at the graphene's Fermi level   and at charge neutrality point (CNP,   = 0), respectively.This metric is useful for comparing the performance of our graphene metasurface at a given doping level to that of graphene at the CNP.The FTIR data shows a strong differential extinction of 17% at 11.5 μm, which corresponds to an atmospheric window, and 11% at 7.5 μm.These two resonances correspond to a graphene-like plasmon.Some negative differential transmission can be seen where the gold-like LSP shifts, which results in higher transmission.The gold rod resonances peak around 4 and 9.6 μm, and coupling with the silica phonons 5,6 in the 9.6 μm region results in a surface enhanced infrared absorption (SEIRA) effect 25,26 .A second peak around 12.8 μm is sensitive to the tuning of the graphene chemical potential, which is the result of splitting of the resonance due to the silica surface optical phonon around 12.4 μm 27 .The linewidths of the graphene-like LSPs are narrower than the gold LSPs due to the lower losses in graphene.Additionally, we conducted an electro-optical modulation experiment by applying an alternating voltage source to the gate over a range of modulation frequencies while measuring the transmission modulation at a select wavelength.The wavelength was selected using a mid-infrared band-pass filter, and the measurements were taken with a lock-in amplifier.The transmission modulation data (Fig. 3(e)) shows strong modulation depths of up to 23% of 11.5 μm light and remains within 3 dB (50%) of the maximum modulation depth up to around 16 kHz.This demonstrates the device's potential as an electro-optic modulator or as a laser noise eater.The sensing application is especially promising given that the device is operable in an atmospheric window while in contact with the ambient atmosphere and at room temperature.These results were achieved using CVD graphene on standard substrates (silica on silicon) that was processed through several rounds of lithographic processes, and thus represent a reasonable picture of such a device produced at scale.The extinction spectrum of the device is significantly affected by the type of substrate used as well as the mobility of graphene.Our experiments showed that using a silica substrate, the device produced multiple resonances due to the dispersion of the refractive index 28 , but the tunability of the spectrum was limited.
To address this limitation, we conducted numerical simulations for Al2O3, which are presented in Supplementary Figure 1.These simulations showed that by using Al2O3 substrate, we could tune the graphene resonances from 9 to 6.5 µm, providing greater spectral tunability.Additionally, we found that even with low mobility graphene, we were still able to achieve a significant response

In-tune resonances
We now focus our attention to the case where gold and graphene plasmonic resonances have the same frequency.Gold and graphene are materials whose optimal plasmonic resonances fall in different parts of the electromagnetic spectrum and are considered to be complementary 29,30 .While gold presents outstanding performance in the visible and near-infrared ranges, in the mid-infrared its optical extinction coefficient is too high and the resonances are broad.Graphene plasmons, on the other hand, can be fine-tuned to the midinfrared up to around 6.4 µm, beyond which they decay due to optical phonons 6 .Here, we will make use of gap plasmons to tune the gold rod resonance to the 8-10 µm window.The concept of gap plasmons has been thoroughly studied and documented [31][32][33][34] , and the mechanism for shifting the resonance to the midinfrared is similar to that of hybridization 31 .
The design is shown in Figure 4(a).The gold rods are separated from a gold plane by a thin 15 nm dielectric (Al2O3) layer and graphene.When coupled to light, the rods induces mirror charges on the metal plane beneath it, and the plane and the rods couple.As a result, the bonding mode arising from this interaction falls in the mid-infrared around 9.1 m, as seen in the spectrum in Fig. 4(c) for a graphene Fermi level of 0 eV.By increasing the Fermi level of graphene, graphene plasmons are excited and hybridization between graphene-gap and gold-gap plasmons takes place.We can observe the new two hybridized modes, and the charge density distribution and near-field images shown in Figs.4(e) and 4(f) is in line with the hybridization picture in Fig. 1.By using doping as the detuning parameter, we observe an anti-crossing behavior, and at the point of minimal detuning (EF = 0.18 eV), the separation between the hybrid modes is 2 = 23.0 meV.
We compare this coupling value to the widths of the resonances of the hybrid modes  + =24.9 meV and  − = 8.3 meV.In this design, the coupling rate 2 > ( + +  − )/2, indicating the system is in the strong coupling regime.In this regime, the two modes exchange energy at a rate faster than their dissipation rate, resulting in longer-lived plasmons and narrowed resonances.This is evident from the comparison of the widths of gold gap plasmons at EF = 0 (26.6 meV) and hybridized resonances.In our assumptions above, we slightly underestimate the coupling strength between gold and graphene plasmons.This is because tuning graphene's Fermi level also changes the damping rate of graphene plasmons.Specifically, at lower doping the interband damping is more pronounced, which inhibits the coupling strength.the coupled harmonic oscillator model, the frequency of the hybrid (normal) modes, are given by 35,36  ± =  0 −  ( where in our case,  0 is the resonance frequency at EF = 0 eV,   and   are the damping rates of gold and graphene plasmons respectively, and Ω is the gold-graphene plasmons interaction potential (Ω = 2g for   =   ).Therefore, the frequency of the hybrid modes should be equidistant to  0 .This occurs at EF = 0.27 eV, in which  + =149.7 meV,  − = 123.5 meV, and the coupling rate 2g = 26.2meV.
Finally, as we increase the Fermi level, the charge density distribution is still concentrated on graphene for the bonding mode (graphene-like, right panel of Fig. 4(f)), as expected by the hybridization picture provided in Fig. 1(c).For the antibonding mode however, the charge density is distributed on gold and graphene (left panel of Fig. 4(f)), assuming a truly hybrid character.In the left charge density map of Fig. 4f, we can observe a spatial modulation of the charge density.This is caused by propagating graphene plasmons, which are launched by the gold rods along the x-axis, and interfere with the localized plasmons between the rods (along the y-axis).

Discussion and summary
We have presented a simple design that creates a hybridization between graphene and gold plasmons, offering a microscopic view of their interaction and enabling the creation of more sophisticated structures in the future to improve field localization.Using a commercially available, large-area CVD-grown graphene field effect transistor, we have demonstrated narrow resonances in the mid-infrared region, achieving up to 17% transmission modulation with only a modest 0.35 eV chemical doping.Our device also showed dual band modulation of 20% at a (3dB) rate of up to 16 kHz, with potential improvements in switching speed by reducing the device area and consequently the device's sheet resistivity.
The tunable, narrow resonances of our design make it highly desirable for mid-infrared metasurfaces.A metasurface is composed of an array of subwavelength particles on a surface that can couple with incident light 31,[37][38][39][40][41] .The geometry of each particle in the array can be designed to alter the amplitude, phase, and polarization of the incident light at a subwavelength scale, which can effect such functionalities as lensing 42,43 , beam-steering 41,44 , holography 45,46 , and nonlinearity [47][48][49][50] .Our metal-on-mirror design with matched resonances offers two distinct regions where the amplitude and phase of mid-infrared radiation can be controlled.Moreover, the sharp dip at the center of the spectrum resembles an electromagnetic-induced transparency dip that could be used to observe electrically tunable "slow light" 51 in the mid-infrared range.
The device's extinction rate can be improved by optimizing parameters such as the dielectric gate material, dielectric thicknesses, array dimensions, and index matching between the top and bottom surfaces.
Calculations for a metasurface using Al2O3 as the gate dielectric are presented in the Supplementary Information and showed enhanced extinction rates.When searching for the best parameters, either rational (from hybridization theory) or inverse design methods 52 can be applied, or even a combination of both.
The fact that our design is exposed to air may greatly benefit applications such as biosensing 53 and gas detection 54 .Moreover, the multiple resonances can enhance coherent anti-Stokes Raman signals.Finally, one can visualize applications such as tunable mid-infrared band-pass filters, active control of thermal radiation and cooling.

Figure 1 .
Figure 1.Hybridization between graphene and gold plasmons.a) Design of the hybrid gold-graphene metasurface device.The thickness of the SiO2 dielectric spacer is 90 nm.The graphene layer is placed between the gold rods and the SiO2 spacer.b) Microscopic depiction of the hybridization phenomenon.The incident light is polarized along the long (vertical) axis of the gold rod.The near-field around the gold rods couples to dark plasmons in graphene along the horizontal direction.The gold and graphene plasmons hybridize, forming two new modes, whose energies ħ − and ħ + depend on the charge distribution on graphene.C) Net charge density of antisymmetric ( + ) and symmetric ( − ) modes.The red and blue clouds represent opposite charges.

Figure 2 .
Figure 2. Design of the hybridized gold-graphene metasurface for detuned resonances.a) Parameters of the metasurface: ax = 1210 nm, ay = 70 nm, cx = 270 nm, cy = 150 nm.The height h of the gold rods is 25 nm.Light is polarized along the x-axis.b) Calculated transmittance of the metasurface across the mid-infrared regime for various values of graphene's Fermi level in eV.The gold and purple arrows depict "gold-like" and "graphene-like" resonances, respectively.The damping parameter of Graphene is 0.02 eV c) Charge density map (arbitrary units) calculated at λ = 7.5 µm.The charges are mostly concentrated on the graphene area, and the resonance character is essentially that of graphene plasmons.

Figure 3 .
Figure 3. Characterization of the fabricated metasurface.a) Scanning electron microscopy of a section of the device.b) Transfer curve of the field-effect transistor device.c) Measured transmittance as a function of graphene's Fermi level, given in eV.d) Calculated differential extinction.e) Frequency response characterization of the mid-infrared modulator for sinusoidal gate voltages of 80 V (blue) and 40 V (red) peak-to-peak.The modulation experiment was conducted with an optical bandpass filter at 7.5 μm (top) and 11.5 μm (bottom), which correspond to the yellow bands in (c) and (d).Cutoff frequencies (-3 dB, 50%) compared to max modulation) are marked with vertical black lines.

Figure 4 .
Figure 4. Design of hybridized gold-graphene metasurfaces for in-tune resonances.a) Illustration of the metasurface's crosssection.The parameters of the periodic array (top view shown in Fig. 2(a)) are ax = 1600 nm, ay = 110 nm, cx = 90 nm, cy = 100 nm.b) Calculated reflectivity of the metasurface for three different values of graphene's Fermi level, showing tunable symmetric and antisymmetric modes.The damping parameter of graphene is set to 13 meV c) Reflectivity of the metasurface calculated for a larger range of graphene's Fermi level.d) Resonance peak for several Fermi levels.The minimum separation between the hybrid modes is at 0.18 eV, and corresponds to Δ = 23 meV.e) Calculated near-field distribution of the gap-plasmons for EF = 0 eV and λ = 8.96 µm (left), EF = 0.40 eV and λ = 7.36 µm (center), and EF = 0.40 eV and λ = 9.60 µm (right).The field was calculated at the position x=700nm.f) Calculated charge density map (arbitrary units) for EF = 0.40 eV and λ = 7.36 µm (left), EF = 0.40 eV and λ = 9.60 µm (right).