Widely Tunable Terahertz Phase Modulation with Gate-Controlled Graphene Metasurfaces

As the basis of a diverse set of photonic applications, such as hologram imaging, polarization, and wave front manipulation, the local phase control of electromagnetic waves is fundamental in photonic research. However, currently available bulky, passive, range-limited phase modulators pose an obstacle in photonic applications. Here, we propose a new mechanism to achieve a wide phase modulation range, with graphene used as a tunable loss to drive an underdamped to overdamped resonator transition. Based on this mechanism, we present widely tunable phase modulation in the terahertz regime, realized in gate-tuned ultrathin reflective graphene metasurfaces. A one-port resonator model, supported by full-wave simulations, explains the underlying physics of the discovered extreme phase modulation and indicates general strategies for designing tunable photonic devices. As an example, we demonstrate a gate-tunable terahertz (THz) polarization modulator with a graphene metasurface. Our findings establish the possibility for photonic applications based on active phase manipulation.

Popular Summary

Holographic imaging relies on controlling the phase of electromagnetic waves, but conventional phase modulators are often large and expensive. Here, we demonstrate wide-range THz phase modulation with metasurfaces integrating magnetic resonators and gate-controlled grapheme, whose thicknesses are roughly one-tenth the wavelength of the incident radiation. We use a one-port resonator model to explain the essential features of the proposed metasurface, and we show that graphene is a gate-tunable loss material that can be used to modulate the critical transition in the resonator and achieve an extremely large phase modulation.

Previous efforts to modulate the phase of electromagnetic waves largely relied on changing the refractive index of materials or using a metasurface-based phase modulator; a drawback of the latter was that it could not be tuned remotely. Furthermore, many previous studies were only able to achieve phase modulation over a narrow range, which limited the applications of this technique. Here, we modulate the optical conductivity of graphene to change the phase of waves reflected off of the graphene metasurface. We employ a five-layer metasurface, and we change the resistance of the graphene by applying a voltage. We use spectroscopy to study both the amplitude and the phase of the electromagnetic radiation that is reflected, and we employ simulations to explore the physics of our technique. We are able to achieve phase modulation of 180 degrees, but we note that our results are susceptible to a reduction in reflectance (i.e., losses) that is due to absorption and radiation leakage. Finally, we use simulations to reproduce and support our experimental findings.

We expect that our findings will pave the way for other photonic applications in the THz regime.

Figure 1

Device geometry and experimental setup. (a) A schematic of the structure of the proposed device. The metasurface consists of an array of Al mesas and a continuous Al film (yellow) separated by an SU8 spacer (blue). CVD-grown monolayer graphene is transferred to the top of the metasurface and subsequently covered by a layer of gel-like ion liquid. The gate voltage applied between graphene and a top gate (not shown) controls the doping level of graphene. (b) An optical image of a typical device viewed from the top. (c) The gate-dependent resistance of CVD-grown graphene transferred to a silicon wafer (blue curve) and the metasurface (red curve). (d) A schematic of the THz time-domain spectroscopy measurement system.

Figure 2

Gate-controlled reflection modulation and the proposed resonator model based on CMT. The variation of reflectance ($R=|r{|}^2$) with the relative gate voltage $\mathrm{\Delta }{V}_g$. A critical transition occurs at $\mathrm{\Delta }{V}_c=0.76\mathrm{V}$ (see text). The reflectances for $\mathrm{\Delta }{V}_g\le \mathrm{\Delta }{V}_c$ and $\mathrm{\Delta }{V}_g\ge \mathrm{\Delta }{V}_c$ are shown in (a) and (b), respectively. The spectra are measured for a device with an $85\text{−}\mu \mathrm{m}\text{−}\text{thick}$ SU8 spacer. The lateral dimensions of the Al mesas are $100\mu \mathrm{m}\times 160\mu \mathrm{m}$, and the mesa array has periods of $240\mu \mathrm{m}$ in the $x$ and $y$ directions, respectively. The spectrum measured at $\mathrm{\Delta }{V}_g=2.02\mathrm{V}$ is used as the reference. (c),(d) Phase modulations for $\mathrm{\Delta }{V}_g\le \mathrm{\Delta }{V}_c$ and $\mathrm{\Delta }{V}_g\ge \mathrm{\Delta }{V}_c$, respectively. Data are obtained for the same device used for measurements in (a) and (b). (e) Smith curves of the reflection coefficient $r$ for the one-port model illustrated in the inset. The blue, black, and red curves represent underdamping, critical damping, and overdamping behavior, respectively. (f) Smith curves of the transmission coefficient $t$ for the two-port resonator model (inset). No critical transition is present, even in the limiting case ${\mathrm{\Gamma }}_i=0$ (broken line).

Figure 3

Full-range gate-controlled phase modulation. Gate-dependent reflection phase spectra of (a) device A with a mesa size of $110\mu \mathrm{m}\times 160\mu \mathrm{m}$ and (b) device B with a mesa size of $100\mu \mathrm{m}\times 160\mu \mathrm{m}$. For both devices, the thickness of the SU8 spacer is $60\mu \mathrm{m}$, and the mesa array has a period of $240\mu \mathrm{m}$ in both the $x$ and $y$ directions. The incident THz wave is polarized along the short axis of the mesa. The spectrum measured on an Al mirror is used as the reference. A large phase modulation is obtained in the shaded region.

Figure 4

Reflectance and phase modulation for metasurfaces with different spacer thicknesses. Reflectance modulations measured as a function of both gate voltage and frequency for devices with SU8 spacer thicknesses of (a) $85\mu \mathrm{m}$, (b) $60\mu \mathrm{m}$, and (c) $40\mu \mathrm{m}$. Data from these three devices are normalized to spectra measured at $\mathrm{\Delta }{V}_g=2.02\mathrm{V}$, $\mathrm{\Delta }{V}_g=2.03\mathrm{V}$, and $\mathrm{\Delta }{V}_g=1.73\mathrm{V}$, respectively. (d)–(f) Reflection phase modulations measured as a function of the gate voltage and frequency for the same three devices considered in (a)–(c). All three devices have a mesa size of $100\mu \mathrm{m}\times 160\mu \mathrm{m}$, and the mesa array has a period of $240\mu \mathrm{m}$ in both the $x$ and $y$ directions. The incident THz wave is polarized along the long axis of the mesa.

Figure 5

A gate-tunable THz polarizer. (a) A reflectance modulation and (b) reflection phase modulation as a function of the gate voltage and frequency measured on the polarizer [shown in (e)]. The incident THz wave is polarized perpendicular to the stripes of the polarizer. (c) The reflection amplitude ratio and (d) phase difference between waves with polarizations in the $x$ and $y$ directions measured as a function of the frequency at different gate voltages. Both parameters are effectively modulated by the gate voltage. (e) An optical image of the polarizer. The stripes have a width of $60\mu \mathrm{m}$, and they are spaced $60\mu \mathrm{m}$ apart. (f) The polarization state (see inset) of the reflected THz wave, characterized by the elliptical axis ratio ($S/L$, red curve) and the rotation angle $\theta$ (blue curve), measured as a function of the gate voltage. The working frequency is 0.63 THz. The gate causes a drastic modulation of the polarization state.

Figure 6

FDFD simulations for the experiments described in Fig. 2. (a),(b) Variation of the reflectance ($R=|r{|}^2$) with the relative gate voltage $\mathrm{\Delta }{V}_g$. A critical transition occurs at $\mathrm{\Delta }{V}_c=0.76\mathrm{V}$. The reflectances for $\mathrm{\Delta }{V}_g\le \mathrm{\Delta }{V}_c$ and $\mathrm{\Delta }{V}_g\ge \mathrm{\Delta }{V}_c$ are shown in (a) and (b), respectively. The spectrum calculated at $\mathrm{\Delta }{V}_g=2.02\mathrm{V}$ is used as the reference. (c),(d) Phase modulation for $\mathrm{\Delta }{V}_g\le \mathrm{\Delta }{V}_c$ and $\mathrm{\Delta }{V}_g\ge \mathrm{\Delta }{V}_c$, respectively. The simulated system has geometrical parameters identical to those of the system studied in Fig. 2.

Figure 7

FDTD simulations for the experiments described in Figs. 4. (a)–(c) Reflectance modulation as a function of both gate voltage and frequency for the devices with SU8 spacer thicknesses of 85, 60, and $40\mu \mathrm{m}$, respectively. Data from these three devices are normalized by the spectra calculated at $\mathrm{\Delta }{V}_g$ values of 2.02, 2.03, and 1.73 V, respectively. (d)–(f) Reflection phase modulation as a function of the gate voltage and frequency for the same devices in (a)–(c). The simulated devices have geometrical parameters identical to those of the devices shown in Fig. 4.

Figure 8

Comparison of the field pattern between the underdamped and overdamped resonators. (a) Simulated $H_y$ distribution in the $xz$ plane for the graphene metasurface with a $60\text{−}\mu \mathrm{m}\text{−}\text{thick}$ SU8 spacer layer. The size of the Al mesa is $160\mu \mathrm{m}\times 120\mu \mathrm{m}$, and the mesa array periodicity is fixed at $240\mu \mathrm{m}\times 240\mu \mathrm{m}$ (only one mesa is shown here). The carrier density of graphene is set at $2.0\times {10}^{11}{\mathrm{cm}}^{-2}$, which places the resonator in the underdamped region. (b) Simulated field distribution when the resonator is in the overdamped region (graphene carrier density $1.45\times {10}^{13}{\mathrm{cm}}^{-2}$). In both cases, the devices are illuminated by normally incident plane waves polarized such that $\overrightarrow{E}\parallel \overrightarrow{x}$.

Figure 9

Reflection spectra calculated from FDTD and CMT results for the $85\text{−}\mu \mathrm{m}\text{−}\text{thick}$ spacer metasurface for different gating voltages. The CMT parameters ${\mathrm{\Gamma }}_i$ and ${\mathrm{\Gamma }}_r$ differ among the panels. (a),(b) ${\mathrm{\Gamma }}_i=0.285f_0$ and ${\mathrm{\Gamma }}_r=0.223f_0$, (c),(d) ${\mathrm{\Gamma }}_i=0.281f_0$ and ${\mathrm{\Gamma }}_i=0.281f_0$, (e),(f) ${\mathrm{\Gamma }}_i=0.287f_0$ and ${\mathrm{\Gamma }}_r=0.370f_0$.

Figure 10

Critical transition modulated by doping and the spacer layer thickness. We determine ${\mathrm{\Gamma }}_r$ and ${\mathrm{\Gamma }}_i$ by fitting FDTD simulation results with Eq. (1). Three device structures (with spacer layer thicknesses 40, 60, and $85\mu \mathrm{m}$) are examined, and the relative gate voltage is varied from 0 to 1.5 V.

Figure 11

$Q$ factors as a function of the spacer layer thickness. All materials in the metasurface are assumed to be dissipationless. The geometry of the Al mesa layer is identical to the geometry shown in Fig. 4, and only $d$ is varied.

Figure 12

CMT analysis of a two-port, single-mode resonator. Smith curves for $r$ according to Eq. (C1). Four representative cases are plotted: ${\mathrm{\Gamma }}_i=0.05f_0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (blue curve), ${\mathrm{\Gamma }}_i=0.1f_0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (black curve), ${\mathrm{\Gamma }}_i=0.15f_0$ and ${\mathrm{\Gamma }}_i=0.15f_0$, ${\mathrm{\Gamma }}_r=0.1f_0$ (red curve), ${\mathrm{\Gamma }}_i=0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (gray curve).

Figure 13

CMT analysis of a two-port, single-mode resonator. (a),(b) Smith curves for $r$ and t according to Eq. (C2), respectively. Four representative cases are plotted: ${\mathrm{\Gamma }}_i=0.05f_0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (blue curve), ${\mathrm{\Gamma }}_i=0.1f_0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (black curve), ${\mathrm{\Gamma }}_i=0.15f_0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (red curve), and ${\mathrm{\Gamma }}_i=0$ and ${\mathrm{\Gamma }}_r=0.1f_0$ (gray curve). Without loss of generality, the reflection and transmission coefficients of the background medium are set as $r_0=0.6$ and $t_0=-0.8i$.

Figure 14

Numerical simulation of a gate-tunable diffraction grating. (a) Schematics of the device with the stripes A and B, consisting of pixels of the same size as that of the pixels in samples A and B in Fig. 3. (b) Plots of the zero- and first-order reflectances of the device against $V_B$ for $V_A=1.32\mathrm{V}$ and $f=0.48\mathrm{THz}$. The insets depict the normalized scattering patterns of the device for normally incident plane waves at three typical gating voltages ($V_B=0$, 1.29, and 2.34 V).