Sample design

The design of our graphene/hBN/nanoarray modulator is shown in Fig. 1a. The gold plasmonic nanostripe array is separated from the graphene/hBN by an air gap (d). Using the graphene as a broadband, transparent and extremely tough electrical contact, a gate voltage can be applied across the structure. In this work the nanostripe array had a periodicity a=1,570 nm, stripe width w=550 nm, stripe height h 2 =80 nm and gold sublayer of thickness h 1 =65 nm (Fig. 1b)—see Methods for device fabrication details. A representative scanning electron microscopy micrograph is shown in Fig. 1c. Such plasmonic nanoarrays can be tuned to give narrow, diffraction-coupled resonances that arise when the wavelengths of diffracted light modes, running along the air–substrate boundary (known as Rayleigh cutoff wavelengths), are recaptured as electron oscillations in the plasmonic nanostructures5. These resonances can be further narrowed by adding a metallic sublayer26. Our nanostructure was designed to produce a narrow plasmon resonance around the telecom wavelength of λ ∼1.5 μm, although higher-order diffraction-coupled modes exist throughout the near-infrared and visible spectrum. An hBN flake (∼110 nm thick) and single-layered graphene were then mechanically exfoliated and transferred on to the plasmonic nanostructure (see Methods). Hexagonal boron nitride is an ideal dielectric for graphene devices because it is an atomically flat crystal with a similar lattice constant to graphene27. Within the modulator region of our device the initial air gap between the hBN and nanostripe array was ∼300 nm. An optical image of the completed device is shown in Supplementary Fig. 1. Atomic force microscopy data confirming the device dimensions is shown in Supplementary Fig. 2.

Figure 1: Nanomechanical electro-optical modulator structure. (a) Schematic of our device with air gap height d. (b) Geometric design parameters for our gold nanostripe array. (c) Representative scanning electron microscopy (SEM) micrograph of the nanostripe array (scale bar 2 μm). (d) The working principle of the device. The coloured wave represents an unperturbed standing wave for different wavelengths observed under reflection from the nanostructured mirror. Full size image

Spectroscopic ellipsometry and reflectometry

Devices were studied using spectroscopic ellipsometry and reflectometry (see Methods). Figure 2a shows the ellipsometric reflection spectrum (Ψ) of a device from the mid-ultraviolet through to the near-infrared, when illuminated at an incident angle of θ=70°. We attribute the broad absorption peaks in the wavelength range 280 nm<λ<590 nm to Fabry–Perot (FP) interference in the air gap, whereas the sharp feature at λ=275 nm is caused by the complex, multi-peaked ultraviolet absorption spectrum of hBN28. The remaining strong features from 590 nm<λ<1,600 nm primarily arise from the nanoarray and correspond to the Rayleigh cutoff wavelengths for air, determined by , where a is the array periodicity, m is an integer and n the refractive index of air5. The absorption peaks at λ≈620, 780, 1,030 and 1,520 nm can be associated with the m=5, 4, 3 and 2 diffraction-coupled modes, respectively. The m=4, 5 features each consist of two peaks because of a mismatch between the inverse polarizability and retarded dipole sum of individual nanoparticles in the plasmonic nanoarray in this spectral region29, caused by the presence of the hBN.

Figure 2: Device characterization using spectroscopic ellipsometry. (a) Ellipsometric reflection spectrum Ψ of our graphene/hBN/plasmonic heterostructure (V g =0 V, θ =70°). (b) Colour map of Ψ as a function of wavelength and V g . Full size image

Figure 2b plots Ψ as a function of both wavelength and gate voltage V g , showing how the various features from the ultraviolet to near-infrared respond to electrical biasing of the device. As V g is raised from 0 to ±150 V we see dramatic changes in the FP resonances, along with a red-shift of the Rayleigh resonance wavelengths. These changes in reflection happen because of motion of the hBN/graphene heterostructure—the applied gate voltage creates an electrostatic force within the device, acting to reduce d. The Maxwell stresses caused by induced electrical charges can be of the order of 10 atmospheres (see Supplementary Note 1). We note that Casimir interactions between the graphene and gold are negligible at this length scale30. It is worth noting that, in general, the opto-electro-mechanical response of the structure is symmetric with respect to the sign of V g and there is a threshold of ±50 V before which application of V g produces no change in optical reflection (no motion of the heterostructure). One exception to the above mechanism occurs near λ=1.6 μm for large negative V g . In this region the absorption changes because of electrical gating of graphene, moving its charge neutrality point and the spectral onset of optical Pauli blocking3. This results in an increase in the measured value of Ψ at the highest wavelengths for the largest negative V g . It is worth noting that one can distinguish the effect of hBN motion and that of the Pauli blocking by the symmetry of the response (the effect of hBN motion is symmetric with respect to the sign of the applied voltage, whereas the Pauli blocking effect is not symmetric because of the initial doping of graphene) and by the wavelength range at which these effects are observed (see the discussion in Supplementary Note 2).

The response to V g in the ultraviolet region measured in s-polarized reflection (R s ) is shown in Fig. 3a. Note that the hBN absorption feature at λ=275 nm is relatively insensitive to V g (and hence d) as the wavelength is approximately equal to the optical path length within the hBN. However, as V g is increased (and d decreased) the adjacent FP absorption features are dramatically altered. This cavity modulation effect occurs over the entire measured ultraviolet range (λ >250 nm) and gives a peak modulation depth of ∼10% at λ ∼310 nm. This compares favourably with prior attempts at ultraviolet modulation that have usually relied on wide band gaps31 or excitonic effects32 in semiconductor devices.

Figure 3: Electromechanical modulation from ultraviolet to near-infra red regions. Measured reflection spectra (left column) of the graphene/hBN/nanoarray for (a) s-polarized light (R s ) in the ultraviolet/blue range and (b) p-polarized light (R p ) in the visible. (c,d) Ellipsometric reflection in the near-infrared. All spectra were measured with θ=70°. Modelling results (right column) reveal that the electrically induced reflection modulation is explained by a changing air gap. The sharp reflection minima in (a) (centred at λ=275 nm) stems from the complex ultraviolet absorption spectrum of hBN. The features in (b–d) correspond to the fourth-, third- and second-order Rayleigh cutoff wavelengths of the nanoarray, respectively. Full size image

Moving to the visible and near-infrared ranges (for the same device) we have observed strong modulation of the diffraction-coupled resonances in the plasmonic nanoarray produced by graphene gating. Figure 3b shows the changes in p-polarized reflection spectra for the λ=780 nm resonance, whereas Fig. 3c,d show Ψ of ∼1,030 and 1,520 nm respectively. In all three cases the reflection minima are shifted by up to 10 nm for |V g |=150 V—as the hBN moves closer to the nanoarray the local fields increase and the refractive index of the ambient medium (ordinarily n=1 for air) is effectively changed. This in itself produces a strong modulation effect, simply because the plasmonic resonances are so narrow. Even though the minimum Ψ value in the vicinity of λ=1,520 nm (Fig. 3d) remains approximately constant (∼26–27°), its shifting wavelength with increasing |V g | leads to a modulation depth of 20% at λ=1,536 nm. This is significantly higher than the near-infrared absolute modulation depths previously reported in graphene- and plasmonic-based devices23,33,34,35: for example, Li et al.35 reported an absolute modulation depth of ∼9% at telecom wavelengths using a graphene-clad microfibre. The modulation frequency in our devices could be reasonably high ∼100 kHz and could be further improved to 100 MHz by a dedicated design (see the detailed discussions in Supplementary Notes 3 and 4).

Reflection spectra obtained experimentally are described well by rigorous coupled-wave analysis (RCWA) modelling (see Methods), in which the graphene/hBN heterostructure is displaced vertically, reducing d from 300 to 200 nm. The right-hand panels in Fig. 3a–d show the results of this modelling in the ultraviolet, visible and near-infrared regions of interest. Both the functional form and behaviour of the blue-shifting FP and red-shifting Rayleigh resonances are reproduced by the model. The differences between the experimental and modelled spectra can be attributed to impurities in, and roughness of, our gold nanostripe arrays. In addition, the height of the suspended area is not constant over the beam spot that leads to resonances smearing. Further modelling, of even smaller air gaps, reveals that as d approaches zero the Rayleigh resonance wavelengths become increasingly sensitive to changes in d (see Supplementary Fig. 3). With this knowledge future devices might be deliberately engineered with smaller initial air gaps, potentially greatly enhancing the achievable modulation depths.

Infrared reflection spectra were measured using Fourier transform infrared spectroscopy (see Methods). Figure 4a shows the strong modulation feature observed in the mid-infrared wavelength range produced by graphene gating. At such long wavelengths, incident light is not influenced by the grating structure, instead effectively experiencing a planar gold surface. On the long wavelength side of its Reststrahlen band, just beyond the transverse optic phonon wavelength of ∼7.35 μm, hBN displays strong light absorption and spectral dispersion. In this region we observe a broad reflection minimum, with reflection values falling to 33% at λ ∼7.6 μm (Fig. 4a). The electromechanical reduction of d induces a narrowing of this feature and a blue shift of the reflection minimum by over 100 nm. The reflection minimum also falls to ∼15%. As a result, large absolute reflection modulation depths are possible for a given wavelength—up to 30% at λ=7.5 μm. This represents a dramatic improvement on existing mid-infrared graphene-plasmonic modulator results22,36,37: for example, Yao et al.37 have previously reported an absolute reflection modulation depth of ∼20% at ∼7.6 μm. Comparing the device dimensions (total height ∼450–550 nm) with the wavelength of this absorption feature reveals the high degree of light confinement within the structure. As a consequence of this confinement—on the order of ∼λ/10—the device is capable of modulating light with an optical interrogation volume of as little as λ3/10. (The actual modulation volume of our device was ∼λ3 at mid-infrared frequencies. It can be reduced to the optical interrogation volume by using smaller suspended areas.)

Figure 4: Modulation and modelling of hexagonal boron nitride’s Reststrahlen band. (a) Measured (upper panel) and modelled (lower panel) reflection spectra close to the transverse optical (TO) phonon energy in hBN. The broader measured resonance width stems from the Fourier transform infrared (FTIR) reflecting objective that provides a range of incidence/measurement angles simultaneously (θ=12–24°) compared with the modelled θ=15°. (b) The air gap is significantly smaller than the mid-IR wavelengths; however, close to the TO phonon energy, light is highly compressed within the hBN because of its large index of refraction. Full size image

As with shorter wavelengths, RCWA simulations agree very closely with the measured mid-infrared behaviour (Fig. 4a). The basic existence of the absorption feature at λ ∼7.5 μm is attributable to material absorption in hBN. Hence, a similar reflection minimum also occurs in simulations of free-standing thin hBN films, and could be modulated simply by changing the hBN thickness (for example, from 110 to 140 nm). However, the hBN thickness is fixed experimentally. Instead, we observe an analogous modulation effect arising from the motion of the hBN slab with respect to the gold mirror. Altering d leads to changes in the optical field overlap with the hBN, as the field diminishes to zero at the gold surface (Fig. 4b). Although the nanostripe array was included in the above RCWA calculations, a much simpler Fresnel reflection-based model of a planar Au/air/hBN/graphene structure confirmed that it is not necessary for the observed mid-infrared modulation.