Full-range Gate-controlled Terahertz Phase Modulations with Graphene Metasurfaces

Local phase control of electromagnetic wave, the basis of a diverse set of applications such as hologram imaging, polarization and wave-front manipulation, is of fundamental importance in photonic research. However, the bulky, passive phase modulators currently available remain a hurdle for photonic integration. Here we demonstrate full-range active phase modulations in the Tera-Hertz (THz) regime, realized by gate-tuned ultra-thin reflective metasurfaces based on graphene. A one-port resonator model, backed by our full-wave simulations, reveals the underlying mechanism of our extreme phase modulations, and points to general strategies for the design of tunable photonic devices. As a particular example, we demonstrate a gate-tunable THz polarization modulator based on our graphene metasurface. Our findings pave the road towards exciting photonic applications based on active phase manipulations.

Phase modulation of electromagnetic (EM) waves plays a central role in photonics research. This is best illustrated by Huygens' Principlethe far-field EM wave-front is essentially determined by the phase distribution on a given near-field plane 1 . The ability to control the local EM phase underpins important applications such as holographic imaging [2][3][4][5] , polarization manipulations 6 , and wave-front controls [7][8][9] . Such phase modulation was conventionally achieved via modulating the refractive index of bulk materials (including both natural materials 10 and recently studied metamaterials (MTM)) [11][12][13][14] . The dimension of such systems is typically on Page 3 of 20 the order of wavelength 2,10 , and therefore too bulky for optical integrations.
In this Letter, we experimentally demonstrate full-range gate-tunable THz phase modulation that is realized by an ultra-thin meta-system (thickness 10 /  ) integrating graphene and a specially designed metasurface. We show that a gate bias applied on graphene through ion liquid tunes its optical conductivity, turns the coupled system from an under-damped resonator to an over-damped one, and induces drastic modulation on the phase of the reflected wave. We develop an analytical model based on coupled-mode theory 19 (CMT) that captures the essence of our phase-modulation mechanism: a one-port resonator, i.e. a resonator with only reflection channel, is able to drive the phase of the reflected wave across a 180  transition when the losses in the resonator are fine-tuned (in our case by graphene).
This is in stark contrast to the two-port resonator (with both reflection and transmission channels) commonly used in previous studies 20 , where only a small phase modulation was possible. Our findings represent a significant advance over previous attempts on photonic devices with tunable responses 21-34 , and our method points to new design strategies for future active phase modulators. As an example, we present an experimental realization of a tunable THz polarization modulator based on our gate-controlled graphene metasurface.
Page 4 of 20 The structure of our graphene metasurface is shown schematically in Fig. 1a. The metasurface is a five-layer structure that we fabricate sequentially, starting from the bottom layer. An aluminum (Al) film is first evaporated onto a 2 SiO /Si substrate (not shown in Fig. 1a), and serves as a totally reflective surface for the incident THz wave from above. We then coat a layer of cross-linked photoresist SU8 (MicroChem), followed by an array of Al mesas (100 μm 80 μm  rectangles, shown in Fig. 1b Fig. 3a and 3b, respectively). This is made possible by the fact that gate doping modulates the phases from ~180  to  0 at frequencies right above the resonance in device A (Fig. 3a), and at the same time suppresses the phase from ~180 to  0 at frequencies just below the resonance in device B (Fig. 3b). As a result, an enormous phase modulation is induced within the frequency interval between the two resonances (shaded region in Fig. 3a and 3b), with a maximum modulation range of 243 at 0.48 THz. We note that the range of modulation, although already large, can be further improved by decreasing the overall absorption of graphene and the SU8 spacer (see Supplementary Information). Armed with these results, a plethora of phase-modulation-based applications (such as gate-tunable wave-front control, holographic imaging, and perfect absorber) are now within reach.
How do we interpret the gate-induced critical transition in our graphene metasurfacesthe foundation of our observed large phase modulation? A coherent picture emerges if we treat our system as a one-port resonator within the framework Page 7 of 20 of CMT 19 . In what follows, we first establish a generic model for our metasurface and then discuss the crucial role of gate-tunable graphene in governing its behavior.
The resonance formed between the Al mesa and the Al plane in our metasurface can be modeled by a one-port resonator (with resonance frequency 0 f ), driven by an incident wave at frequency f . Here the Al plane entirely eliminates the transmission through the resonator, and only the reflection channel needs to be considered (hence the name 'one-port'). The loss in the resonator comes from two sourcesabsorption within the resonator and radiation to external modes. The former is denoted as the intrinsic loss i  , and the latter the radiation loss r  . Analysis based on CMT shows that the reflection coefficient r of such a system can be generally expressed as 19 : The evolution of r is best viewed as the Smith curvestraces of r on the complex plane as frequency f increases from 0 to  . The curves all start and end at points close to 1 r  (Fig. 2e). But they cross the real axis (when in resonance, i.e. Finally, as a demonstration we present a gate-tunable polarizer based on graphene metasurface as shown in Fig. 5e. Here the Al mesas are replaced by stripes, so that the system exhibits magnetic resonance only for the polarization || Ex . Upon gating, graphene significantly modulates both the reflectance and the phase spectra ( Fig. 5a and 5b), due to the critical transition accompanied by a large phase modulation. On the other hand, the reflection for waves polarized along y direction is hardly tuned by graphene (See Supplementary Information) due to the lack of a resonance. Such an anisotropic response can be readily utilized for polarization control. As shown in Fig.   5c and 5d, the reflectance ratio / respect to the x axis. The reflected wave is now elliptically polarized due to the anisotropic response of our polarizer. The polarization of the reflected wave, characterized by two parameters (namely the ratio between short-and long-axes of the ellipse ( / SL ) and the angle  of the long axis, Fig. 5e inset), is now drastically tuned by graphene under gate-control (Fig. 5f).
In conclusion, we demonstrate full-range THz phase modulation tuned by a gate.
This is achieved on metasurfaces integrating magnetic resonators with gate-controlled graphene, with overall thickness down to deep sub-wavelength regime. A one-port resonator model is able to capture the essential features of our metasurface. The model further reveals the important role of graphene as a gate tunable loss that modulates the critical transition in the resonator, leading to extreme phase modulation.
Our full-range tunable local phase control opens the door to exciting photonic applications in the THz regime. A gate-tunable polarizer is presented as an early demonstration of the capability of our graphene metasurfaces.

I. Preparation of CVD-grown graphene
We grow monolayer graphene on copper foils (Alfa Aesar) using standard chemical vapor deposition (CVD) technique 1, 2 . The graphene sample is then transferred onto the target surface following the wet transfer method described in Ref 3,4. The sample remains uniform after being transferred, and the optical image of a typical graphene sample on SiO 2 /Si substrate (SiO 2 thickness 300 nm) is shown in Fig.  S1 inset. Raman spectroscopy measurement (Fig. S1) confirms that the graphene sample is monolayer.
A gate voltage applied between graphene and a side gate modulates the doping level of our graphene sample, with ion-gel serving as the gate medium 5

II. Critical transition modulated by hole-doped graphene
The critical transition in our metasurfaces discussed in the main text can also be modulated by graphene on the hole side of the doping. Here we present data obtained from the same devices studied in Figs. 2 and 4, now with the graphene doped with holes instead of electrons. We find that the metasurfaces exhibit similar behavior as the thickness of the SU8 spacer layer is varied. Specifically, metasurfaces with 85-µm-thick spacer layer (Fig. S2) and 60-µm-thick spacer layer (Fig. S3) feature gate-controlled critical transitions, but the critical transition is not accessible for the metasurface with a 40-µm-thick spacer layer (Fig. S4). We note that the critical gate voltages relative to the charge neutral Dirac point are not strictly the same for electron and hole doping. This is possibly due to the fact that the electron and hole sides of graphene band structure are not exactly symmetric, especially at high doping levels.

IV. Performance of our devices referenced to Al mirror
In the main text, all spectra are referenced against the reference spectra measured under highest doping. While this is enough to illustrate the phase modulation effect (which does not need an absolute reference), one cannot retrieve the working efficiencies of our devices. Here we provide additional data on the absolute reflectance of our devices (referenced to Al mirror). Figure S6 shows the absolute reflectance spectra of the two devices (device A and B) studied in Fig. 3. We also measured the absolute reflectance spectra of the tunable polarizer (the same device studied in Fig. 5), and then retrieved the working efficiency (i.e., the power ratio between the reflected and incident waves) of our device under the experiment condition described in Fig. 5(f). The working efficiency of our device at 0.63 THz is found to be ~ 40% within the range of ours applied gate voltage (Fig. S7).
Figure S6 | Reflectance spectra referenced to Al mirror. a and b, Reflectance spectra of device A and B (the same devices studied in Fig. 3), respectively, as the gate voltage is varied. Figure S7 | Working efficiency of the tunable polarizer. The efficiency is measured as a function of relative gate voltage, and the data are obtained from the same polarizer studied in Fig. 5 of the main text.

A. Simulation model
The conductivity of graphene in the THz regime can be described by the linear-response theory under random phase approximation that only includes intra-band contributions 6 : where f v is the Fermi velocity of electrons in graphene (~5 9 10 / m s × ) 7 , n is the two-dimensional (2D) electron density of graphene and Γ is a phenomenological constant accounting for the electron scattering rate (damping). In our FDTD simulations, graphene is modeled as a thin dielectric layer with thickness d that exhibits an anisotropic dielectric function 8 diag[ , ,1] , with α being the gate capacitance of the ion-gel-based gating scheme and 0 n the residue carrier density 9 , determined by fitting experimental data. We treat Al as lossy metal in our FDTD simulations. Best simulation results are obtained when the electric conductivity of Al is set as 6 10 / S m , which is much smaller than the bulk value 7 3.5 10 / S m × (Ref. 10). Such a difference between bulk and thin-film Al has also been observed by previous THz measurements 11 . The SU8 spacer is treated as a dielectric insulator with Re( ) 3.5 ε = and Im( ) 0.28 ε = . All these parameters were determined through carefully comparing the FDTD results with experimental data on various samples (metasurfaces without graphene).

B. Simulation results and discussions
We performed extensive FDTD simulations to study all the cases experimentally characterized in the main text. Figures S8 and S9 show the FDTD results corresponding to the cases presented in Fig. 2 and Fig. 4 in the main text, respectively. In our simulations, we set    Fig. 4. a, b and c, Reflectance modulations calculated as a function of both gate voltage and frequency for devices with SU8 spacer thicknesses of 85 μm , 60 μm and 40 μm , respectively. Data from these three devices are normalized to spectra calculated at 2.02 V , respectively. d, e and f, Reflection phase modulation calculated as a function of gate voltage and frequency for the same three devices measured in a, b and c. All three devices has a mesa size of 160 μm 100 μm × , and the mesa array has a period of 240 µm in both x and y directions.
To gain a deeper understanding on the nature of the resonance in the under-damped and over-damped regimes, we employed FDTD simulations to calculate the field patterns for two representative cases. The field patterns in the under-damped and over-damped metasurfaces are shown in Fig. S10(a) and Fig.  S10(b) respectively. In the case of the under-damped resonator (Fig. S10(a)), waves penetrate deep inside the metasurface to establish the near-field coupling between the two metallic layers, and establish a magnetic resonance. In contrast, waves are directly reflected back by the top mesa layer before they could enter the metasurface (Fig. S11(b)). This picture naturally explains why our metasurface, when located in the over-damped region, behaves as an electric reflector because essentially only the top mesa layer is working to reflect THz waves.
Figure S10 | Comparison of the field patterns in under-damped and over-damped resonators. a, Simulated y H distribution in the x-z plane for our graphene metasurface with a 60μm -thick SU8 spacer layer. The size of the Al mesa is 160 μm 120 μm × , and the mesa array periodicity is fixed at 240 μm 240 μm × (only one mesa is shown here). Carrier density in graphene is set at 11 2 2.0 10 cm − × , which puts the resonator in the under-damped region. b, Simulated field distribution when the resonator is in the over-damped region (graphene carrier density 13 2 1.45 10 cm − × ). In both cases, the devices are illuminated by normally incident plane waves polarized with || E x  

VI. Graphene as a tunable loss in the metasurface -an analysis based on CMT
To understand the crucial role of graphene in modulating the resonance behavior of our metasurfaces, we analyze the effect of graphene doping based on Eq. (1). We extract the radiative loss and intrinsic loss r Γ and i Γ at different gate voltages by fitting the corresponding FDTD simulation results with Eq. (1). We chose to fit the FDTD simulation results instead of experimental data because a) all experimental features are well reproduced by FDTD simulations, and b) the fitting depends very sensitively on the shape of the curve at the resonance; fluctuations in the measured spectra make fittings of experimental data unreliable. It should be noted that, strictly speaking, the CMT is only valid at frequencies at the resonance. In order to obtain unambiguous fitting results, we perform the fitting procedure in a frequency interval centered at the resonance. We then vary the bandwidth of the interval, and make sure that the obtained fitting results converge and are nearly independent of the bandwidth. Figure S11 shows how the extracted r Γ and i Γ , scaled by the corresponding resonance frequency 0 f , vary with the gate voltage g V ∆ in different devices. Two conclusions can be drawn from this figure. First, increasing the carrier density in graphene (through increasing g V ∆ ) increases the intrinsic loss i Γ , but leaves the radiation loss r Γ almost intact. Second, when the graphene doping level is fixed, metasurface with thinner spacer layer exhibits smaller radiation loss. Therefore, while sections of the resonances in the two metasurfaces with 85μm and 60μm spacer layers locate in the under-damped region, all resonances in the metasurface with a 40μm -thick space layer locates in the over-damped region due to its diminished radiation loss. The latter does not show a transition as g V ∆ is increased because gating can only increase the intrinsic loss which drives the system even further away from the transition boundary. It is already clear from Fig. S11 that different spacer layer thickness results in different radiation loss r Γ . Here we employe FDTD simulations to further quantify the effect of the spacer layer thickness on r Γ . We compute the Q factor (which is inversely propotional to r Γ ) of a series of devices with varying spacer thickness. To spcifically delineate the effect of spacer thickness on the radiation loss, all materials (both metal and SU8) are assumed dissipationless (i.e. intrinsic loss is set to 0). The Q factor as a function of spacer layer thickness is shown in Fig. S12. A thinner spacer layer leads to an enhanced Q factor, which explains why the radiation loss decreases with reduced spacer layer thickness (Fig. S11). Indeed, metasurface with a thinner spacer has a stronger near-field coupling between two metallic layers, leading to an enhanced Q factor, and therefore a smaller r Γ . Such an intriguing effect has already been discussed in a similar system 12 .
Figure S12 | Q factors computed as a function of spacer layer thickness. All materials in the metasurface are assumed dissipationless. The Al mesa layer has exactly the same geometry as those studied in Fig. 4, and only the spacer layer thickness d is varied.

VII. CMT analysis of a two-port resonator
According to the CMT 13 , assuming that the background medium (medium without the resonant structure) is perfectly transparent (i.e., 0 0 1, 0 t r = = ), we have for the two-port, single-mode model: The Smith curves for the transmission coefficient t have already been plotted in Fig.  2(f) in the main text. Here we present the Smith curves for reflection coefficient r in Fig. S13. Again, no critical transition is observed in r however the doping level is varied.