Active modulation of visible light with graphene-loaded ultrathin metal plasmonic antennas

Electro-optical modulation of visible and near-infrared light is important for a wide variety of applications, ranging from communications to sensing and smart windows. However, currently available approaches result in rather bulky devices, suffer from low integrability, and can hardly operate at the low power consumption levels and fast switching rates required by microelectronic drivers. Here we show that planar nanostructures patterned in ultrathin metal-graphene hybrid films sustain highly tunable plasmons in the visible and near-infrared spectral regions. Strong variations in the reflection and absorption of incident light take place when the plasmons are tuned on- and off-resonance with respect to externally incident light. As a result, a remarkable modulation depth (i.e., the maximum relative variation with/without graphene doping) exceeding 90% in transmission and even more dramatic in reflection (>600%) is predicted for graphene-loaded silver films of 1–5 nm thickness and currently attainable lateral dimensions. These new structures hold great potential for fast low-power electro-optical modulation.

modes, lattice singularities in periodically patterned surfaces, and Fabry-Perot resonances 35 , which again require relatively bulky structures. More compact designs can be made by coupling to plasmonic particles, as recently demonstrated in the mid-IR, taking advantage of the relatively low absorption of noble metals in that spectral region, where graphene can make a big difference [36][37][38][39][40] . However, the small thickness of graphene is still a key limitation that prevents the extension of these methods toward the visible regime. This suggests the possibility of reducing the relative volume of the plasmon-supporting metal, which can in fact go down to a single monolayer while retaining a large optical strength 41 .
Here, we show through realistic simulations that ultrathin graphene-metal hybrid films (UGMs) can undergo order-one modulation in vis-NIR light transmission and reflection. We present attainable designs consisting of 50 nm wide ribbons formed by a thin noble metal film of thicknesses in the 1-6 nm range supported on monolayer graphene. These results open a viable route toward fast electro-optical modulation within that technologically important frequency range.

Results
It is instructive to first discuss plasmons in homogeneous UGMs, whose dispersion relation can be conveniently obtained by plotting the reflectance for p-polarized light as a function of the parallel component of the wave vector k || and photon energy. For the silica-supported sandwich structure depicted in Fig. 1a, the reflection coefficient r p UGM admits an analytical expression, with the optical properties of graphene and the metal modeled through their surface conductivity and permittivity, respectively (see Methods). We plot the resulting reflectance r p UGM 2 for doped and undoped graphene in Fig. 1b. Despite the relatively large thickness of the silver layer compared with the monolayer carbon film, it is clear that undoped graphene produces strong plasmon quenching via coupling to interband transitions 35 , while the optical gap opened in doped graphene leaves the plasmons nearly intact below ~2E F . Electron doping can thus modulate the plasmon strength dramatically in UGMs. Obviously, most of the region explored in Fig. 1b is far from the light cone, and it is indicative of what we should expect when plasmons are accessed by providing a source of additional momentum to externally incident light, for example by nanostructuring the film, as we discuss next. Interband transitions produce strong plasmon quenching in the undoped structure and also in the doped structure when the photon energy exceeds 2E F (i.e., above the yellow lines). We model graphene with the local-RPA conductivity 42 assuming a mobility μ = 2000 cm 2 /(V s) throughout this work, while silver is described by its measured permittivity 46  In order to more efficiently couple incident light to the UGM, we study the effect of patterning it into a periodic array of ribbons. These structures are simulated using a finite element method in the frequency domain (COMSOL), and the results compared to a simple analytical model presented in Methods. We consider the silica-embedded graphene-silver ribbon array shown in Fig. 2a (ribbon width W = 50 nm, array period P = 100 nm, silver thickness t = 1 nm) and study the extinction (1 − T) and reflection of normally-incident light polarized across the ribbons. The resulting spectra exhibit prominent features associated with the lowest-order dipolar mode of the ribbon 42 , roughly corresponding to the condition that the width W is half the plasmon wavelength in the planar film at that energy (i.e., k || ~ π/W in Fig. 1b). The effect of doping is three-fold: (1) the plasmon peak is blue shifted, (2) the extinction and reflection maxima increase, and (3) the resonance line shape becomes narrower for larger E F . As a result, a modulation depth in extinction (reflection) ~26% (~36%) is observed at a photon energy ~0.92 eV when going from undoped graphene to E F = 1 eV. The effects of doping are consistent with the suppression of damping channels (interband transitions) at photon energies below 2E F . Also, the noted blue shift is expected from the increase in available free carriers produced by doping. Remarkably, despite the simplicity of the analytical model (Fig. 2b, solid curves, see Methods), it is in excellent agreement with full numerical calculations (dashed curves), except for a small blue shift of the latter. In particular, the relative effect of doping is predicted to be the same for both types of simulations.
Tunable light modulation in reflection and absorption for the class of structures sketched in Fig. 2a is a robust effect that takes place up to relatively large metal thickness, as we show in Fig. 3. These results clearly illustrate that an increase (decrease) in reflectance (absorbance) occurs when the Fermi energy exceeds approximately half the plasmon energy for each of the three metal thicknesses under consideration. Simultaneously, the plasmon resonance becomes narrower and slightly blue shifted in all cases. Importantly, together with the ribbon width, the silver thickness provides an extra degree of freedom to control the plasmon energy. Incidentally, the absorbance for t = 1 nm and undoped graphene reaches the maximum value of 50% that is possible for optically thin films 43 . Additionally, the modulation depth inferred from these results can be as high as ~23% in absorption and ~59% in reflection. A continuous graphene layer can be advantageous for actual implementations of these ideas, and therefore, we consider the structure shown in the solid box of Fig. 4a as a possible replacement for the one in the dashed box. For this new configuration our numerical simulations (Fig. 4b, solid curves) predict larger modulation depth (~55% at ~0.96 eV) than in the structured graphene (dashed curves). This can be understood as the result of additional optical attenuation in the inter-ribbon regions for undoped graphene. Simultaneously, the doped structure experiences a slightly larger blue shift, also produced by extra polarization due to the inter-ribbon regions.
Although silver is the less lossy of the noble metals in the spectral region under consideration, gold and copper can also do a fairly good job in UGMs. We present in Fig. 5a an overview of the plasmon energy corresponding to peak extinction as a function of metal thickness for these three different metals with and without doping. These results are obtained for the continuous-graphene structure of Fig. 4a (solid box) with W = 50 nm and P = 100 nm. The plasmon energy increases with thickness (i.e., with decreasing aspect ratio of the ribbons) and takes similar values for the three metals, as they also have similar conduction electron densities, although silver plasmons are slightly blue shifted because d-band screening is less efficient in this material. Incidentally, as the thickness increases, the structure is less sensitive to doping because graphene has to compete with a comparatively larger metal volume.
The modulation depth (Fig. 5b), defined as the relative change in transmission (or reflection) between doped and undoped structures (see vertical axis labels), is an important parameter for pondering potential applications. Obviously, this quantity degrades at large metal thickness, again because the weight of graphene is comparatively  smaller, so it is overwhelmed by the metal. In the small thickness limit, the transmittance increases, also giving rise to a reduction in transmission modulation depth, while the modulation of reflection reaches values well above 1 for all three metals, and it approaches ~6 for silver. We thus conclude that optimum modulation in reflection is achieved for the thinnest metal films, while maintaining a reasonable modulation in transmission. Clearly, silver presents the best performance among the noble metals for vis-NIR light modulation, reaching a depth that exceeds 90% in transmission for metal thicknesses in the 1-5 nm range and > 100% in reflection below 3 nm.

Concluding Remarks
In summary, graphene can be used to modulate the optical response of thin metals, taking advantage of both the strong spectral weight of the resulting plasmons in the hybrid structure and the comparatively large volume of the carbon film when the metal thickness is reduced to only a few nanometers. Graphene doping causes a suppression of interband transitions, and in consequence, a reduction of plasmon damping, which is accompanied by blue shifts due to the addition of doping charges. We find a remarkable > 90% modulation depth in transmission by using graphene-loaded silver ribbon arrays for metal thicknesses in the 1-5 nm range and lateral dimensions of tens of nanometers, which are attainable with currently available lithographies. The modulation of reflection is even more dramatic for metal thickness below 3 nm. The plasmon energies cover the 1-1.8 eV photon energy interval for these thicknesses, thus enabling the design of wide-spectral-range devices. Additionally, a continuous graphene layer appears to be advantageous to increase the modulation depth, and thus, only the thin metal film needs to be patterned.
Our proposed structures could be doped by contacting the ribbons at a large distance from the region in which they are intended to produce light modulation; the ribbons would then act as a top gate, with the graphene placed in the lower side, facing a bottom gate (e.g., a doped silicon substrate with an oxide layer); the charge induced in the top gate is then mainly contained within the outermost atomic layer of the conducting structure 44 . Working at a high intrinsic doping (e.g., as obtained by chemical doping) should allow us to modulate high photon energies by just swapping 2E F across the desired spectral region. Additionally, the moderate amount of doping charges involved should enable the design of low power consumption devices. These findings open a new avenue for the development of compact electro-optical components such as tunable light filters, switchers, and sensors in the vis-NIR spectral region.   2 where W is the ribbon width,  is the permittivity of the homogeneous environment, and the surface conductivity σ = σ m + σ g is the sum of metal and graphene contributions. The latter is given by (1), while we calculate the former as   , and P is the array period.