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

  • Scientific Reports 6, Article number: 32144 (2016)
  • doi:10.1038/srep32144
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Abstract

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.

Introduction

Collective conduction electron oscillations in metals (plasmons) provide the means to locally enhance the electromagnetic field of light within nanometer-scale regions, well below the optical wavelength1. In particular, plasmons in noble metal nanostructures can resonate at visible and near-infrared (vis-NIR) frequencies, thus holding great potential for photonic technologies. This has stimulated a great deal of work over the last decade aiming to tailor the spatial and spectral properties of plasmons2, with applications such as metamaterial design3,4, optical biosensing5,6,7, spectrophotometry8,9,10, photocatalysis11,12,13,14,15,16, and coloring17,18,19,20,21,22. Control over the plasmon characteristics generally relies on the design of optimized nanostructure composition and morphology. However, active control through external stimuli based on these principles is limited to relatively long response times, which are nonetheless useful for tunable metamaterial designs23, including externally driven phase transitions24,25. This scenario has substantially evolved with the advent of two-dimensional crystals, which can undergo radical changes in their optical response under electrical doping26,27,28. For example, electrical modulation of graphene plasmons has been demonstrated to produce octave-scale frequency shifts29. This potential has been recently exploited to improve optical sensing7. Unfortunately, intrinsically fast plasmon-based modulation has only been demonstrated at long wavelengths within or beyond the midinfrared (mid-IR) region, while its extension to shorter wavelengths imposes severe demands on the level of doping and the reduction in size of the structures, the combination of which still remains a challenge.

A possible strategy to achieve vis-NIR light modulation consists in exploiting the switching off of graphene absorption when it transits from undoped to doped states: indeed, undoped graphene absorbs 2.3% of the incident light over the vis-NIR range30,31; in contrast, when doped to a Fermi energy EF, an optical gap of size 2EF opens up in which absorption is drastically reduced26,27. Electrical gating has been used to show EF ~ 1 eV doping27, which in principle enables intrinsically fast vis-NIR light modulation. However, the poor amount of absorption produced by this material is limited by its atomic thickness, and consequently, order-one modulation requires coupling it to either strong optical resonances or large structures in which a substantial effect builds up. The latter strategy has been followed to demonstrate active modulation in the NIR light transmitted through graphene-loaded waveguides32 and photonic crystals33,34, although the resulting structures are rather bulky and extend over many optical wavelengths. Alternative approaches have been suggested, including coupling to Mie modes, lattice singularities in periodically patterned surfaces, and Fabry-Perot resonances35, 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 difference36,37,38,39,40. 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 strength41.

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 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 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 transitions35, while the optical gap opened in doped graphene leaves the plasmons nearly intact below ~2EF. 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.

Figure 1: Tunable plasmon quenching in ultrathin graphene-metal hybrid films (UGMs).
Figure 1

(a) Sketch of an UGM consisting of a graphene monolayer on top of an ultrathin silver film (thickness t = 1 nm), supported in turn by a silica substrate (). (b) Plasmon dispersion of the structure in (a) when the graphene is either undoped (EF = 0, left) or highly doped (EF = 0.7 eV, center; EF = 1 eV, right), as illustrated by the photon-energy and parallel-wave-vector dependence of the reflectance for p polarization. Interband transitions produce strong plasmon quenching in the undoped structure and also in the doped structure when the photon energy exceeds 2EF (i.e., above the yellow lines). We model graphene with the local-RPA conductivity42 assuming a mobility μ = 2000 cm2/(V s) throughout this work, while silver is described by its measured permittivity46. The light cone (dashed lines) is shown as a reference.

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 ribbon42, 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 EF. 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 EF = 1 eV. The effects of doping are consistent with the suppression of damping channels (interband transitions) at photon energies below 2EF. 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.

Figure 2: Optical switch based upon a periodic array of silver/graphene UGM ribbons.
Figure 2

(a) Scheme of the structure under consideration. The ribbon array (metal thickness t = 1 nm, width W = 50 nm, period P = 100 nm, embedded in silica, ) is illuminated under normal incidence with transversal polarization. (b,c) Extinction (b) and reflection (c) spectra for either doped (red curves, EF = 1 eV) or undoped (blue curves, EF = 0) graphene, showing ~26% (~36%) modulation depth in extinction (reflection) at 0.92 eV photon energy. Full numerical simulations (dashed curves) are in good agreement with analytical theory (solid curves, see Methods).

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 films43. Additionally, the modulation depth inferred from these results can be as high as ~23% in absorption and ~59% in reflection.

Figure 3: Tunable light modulation through UGM ribbon arrays.
Figure 3

We show the normal-incidence reflectance (top) and absorbance (bottom) analytically calculated for the structure considered in Fig. 2a (graphene-silver ribbons in silica, width W = 50 nm, period P = 100 nm) with different metal thicknesses t = 1–3 nm (left to right) as a function of graphene Fermi energy (horizontal axis) and photon energy (vertical axis). Light polarization is across the ribbons.

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.

Figure 4: Optical switch based upon a periodic array of ultrathin silver ribbons on a continuous graphene sheet.
Figure 4

We consider the effect of replacing the bottom graphene ribbons by a continuous monolayer graphene sheet (a) and compare the normal-incidence extinction for doped (EF = 1 eV) and undoped (EF = 0) graphene in both configurations (b). The continuous graphene film (solid curves) produces larger modulation depth than the graphene ribbons (dashed curves). Light polarization is across the ribbons. The ribbon thickness, width and period are t=1 nm, W = 50 nm and P = 100 nm, respectively.

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.

Figure 5: Dependence of light modulation on the choice of metal and metal thickness.
Figure 5

We consider the same geometry as in the solid box of Fig. 4a (continuous graphene sheet, W = 50 nm, P = 100 nm). (a) Peak extinction energy with highly doped (solid curves) and undoped (dashed curves) graphene as a function of metal thickness for different noble metals. (b) Metal thickness dependence of the modulation depth for transmission (solid curves, left scale) and reflection (dashed curves, right scale), defined in terms of the normal-incidence, p-polarization transmittance and reflectance coefficients for undoped (T0 and R0) and doped (T1 and R1) graphene, evaluated at the peak photon energy of the doped structure.

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 structure44. Working at a high intrinsic doping (e.g., as obtained by chemical doping) should allow us to modulate high photon energies by just swapping 2EF 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.

Methods

Graphene Conductivity

We model graphene using the local-RPA conductivity42,45

where is the Fermi-Dirac distribution. Throughout this work, we assume room temperature (T = 300 K) and an inelastic decay time calculated for a mobility μ = 2000 cm2/(V s) and Fermi velocity vF ≈ 106 m/s.

Reflection Coefficient of a Continuous UGM

The k||-dependent reflection coefficient for p-polarized light incident on the sandwich structure of Fig. 1a can be simply constructed from the air-graphene-metal reflection () and transmission () coefficients, the metal-graphene-air reflection () and transmission () coefficients, and the metal-silica reflection coefficient (). Here , , and are the permittivities of air, metal, and silica, respectively; is the normal wave vector in medium j = 0, m, s, with the square root chosen such that Im{kj} > 0; and we have defined , , and A = 4πσgk0km/ω. From a simple multiple-scattering analysis, we find , where t is the metal thickness.

Analytical Model for the Optical Response of UGM Ribbons

We approximate the transversal ribbon polarizability per unit length α by the contribution of the lowest-order dipolar plasmon, which yields42

where W is the ribbon width, is the permittivity of the homogeneous environment, and the surface conductivity σ = σm + σg is the sum of metal and graphene contributions. The latter is given by (1), while we calculate the former as

where t and are the thickness and permittivity of the ultrathin metal. We take from optical measurements46.

Analytical Model for Ribbon Arrays

Under the conditions of Fig. 2a, the reflection and transmission coefficients of the array for normal-incidence p-polarized light are29,42

where , , and P is the array period.

Additional Information

How to cite this article: Yu, R. et al. Active modulation of visible light with graphene-loaded ultrathin metal plasmonic antennas. Sci. Rep. 6, 32144; doi: 10.1038/srep32144 (2016).

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Acknowledgements

This work has been supported in part by the Spanish MINECO (MAT2014-59096-P and SEV-2015-0522), the European Commission (Graphene Flagship CNECT-ICT-604391, FP7-ICT-2013-613024-GRASP and FEDER grant TEC2013-46168-R) and AGAUR (2014 SGR 1400 and 1623).

Author information

Affiliations

  1. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

    • Renwen Yu
    • , Valerio Pruneri
    •  & F. Javier García de Abajo
  2. ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, 08010 Barcelona, Spain

    • Valerio Pruneri
    •  & F. Javier García de Abajo

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Contributions

F.J.G.d.A. conceived the idea. R.Y. performed the calculations and prepared the figures. R.Y. and F.J.G.d.A. worked out the theory and wrote the paper. All authors contributed to discuss the results.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to F. Javier García de Abajo.

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