Graphene Based Terahertz Phase Modulators

Electrical control of amplitude and phase of terahertz radiation (THz) is the key technological challenge for high resolution and noninvasive THz imaging. The lack of an active materials and devices hinders the realization of these imaging systems. Here, we demonstrate an efficient terahertz phase and amplitude modulation using electrically tunable graphene devices. Our device structure consists of electrolyte-gated graphene placed at quarter wavelength distance from a reflecting metallic surface. In this geometry, graphene operates as a tunable impedance surface which yields electrically controlled reflection phase. Terahertz time domain reflection spectroscopy reveals the voltage controlled phase modulation of {\pi} and the reflection modulation of 50 dB. To show the promises of our approach, we demonstrate a multipixel phase modulator array which operates as a gradient impedance surface.


Introduction
Electromagnetic waves (EMW) are described by vector fields which include polarization degree of freedom and spatial distribution of intensity and phase. Dynamic control of these physical quantities provides means of encoding information. Imaging and communication systems rely on the manipulation of light with electrical signals that can either directly control the generation of light at the source or it can indirectly manipulate the light during the propagation through a medium. For visible and infrared light, electrically controlled sources and rich variety of electro-optical controls have already been developed [1, 2]. These techniques enabled the realization of sophisticated optical devices. For longwavelength light, radio waves and microwaves, the manipulation of the EMW during the propagation is a challenge. For terahertz radiation, this challenge is even more severe due to the requirement of ultrafast electronics and the lack of an active materials. Over the past two decades, a significant amount of research have been devoted to develop active devices which control intensity and phase of terahertz radiation [3][4][5][6][7][8][9]. Early studies are based on cooled-semiconductor quantum wells whose intersubband absorption falls into terahertz energies [10,11]. Depletion of electrons from the quantum wells leads to the reduced absorption and enhanced reflection. Electromagnetic phenomena achieved by metamaterials enhances these interactions. Chen et al. demonstrated metamaterial based intensity and phase modulators [12]. Furthermore, these approaches were used to realize THz imaging systems [13].
Recent developments in the field of 2-dimentional crystals provide alternative solutions to control lightmatter interaction in a very broad spectrum. Since light-matter interaction is mediated by high mobility electrons, electrostatic tuning of charge density on atomically thin layers facilitates new ways to control light. Especially, graphene is a unique material that provides gate-tunable high mobility carriers at room temperature. Graphene's linear band structure yield nearly energy independent spectrum which results in a very broad optical activity ranging from visible [14,15] to microwave frequencies [16].
In a pioneering work by Rodrigues et al, a back-gated graphene transistor was used as a THz intensity modulator [17]. They showed that graphene can be used as an alternative low-loss THz active material.
However, the back-gated transistor geometry yields limited modulation due to insufficient gating (n<2x10 12 cm -2 and EF<200 meV) [17,18]. To overcome this limitation we have been working on electrolyte gating schemes to achieve much higher charge densities. Electrolyte gating with ionic liquids in a supercapacitor geometry produces the most efficient gating with Fermi energy shift larger than 1eV [15,16,19,20]. In our previous works, we showed that graphene supercapacitors can be used to control light from visible to microwave frequencies [21]. Although, these devices show significant intensity modulation, they do not yield considerable phase modulation due to atomically thin optical path. In a recent study, passive metamaterials were integrated with gate-tunable graphene devices to achieve intensity and phase modulation in THz [22] and microwave frequencies [23]. Varying the resistance of graphene introduces electrically tunable loss to the metamaterial modulating reflected intensity and phase of THz waves.

Methods and results
In this work, we show that without using any metamaterial structure, a planar graphene near a metallic surface can be used as an efficient phase modulator. Using terahertz time domain reflection spectroscopy, we studied the modulation of reflection phase from the active devices. To realize phase modulator structure, we placed gated graphene at quarter-wavelength-distance (λ/4) from a reflecting metallic surface. In the literature, this type of structure is known as Salisbury screen or the anti-reflection surface where reflecting signal is highly attenuated due to resonant absorption [24][25][26]. In this way, the phases of two waves, the ones reflected from graphene and metallic surface, have π difference causing destructive interference. While the reflectivity from metallic surface is constant, the reflectivity of graphene is tunable with the gate voltage [27]. Hence, by varying the conductance of graphene via ionic gating, we were able to modulate both phase and intensity of terahertz beam.  gate voltage between graphene and gold electrodes, we were able to control the charge density (~10 14 cm -2 ) and Fermi energy (> 1 eV) of graphene. Figure S2 in the supporting information shows the Fermi energy shift of graphene with respect to applied voltage. We measured the complex THz reflectivity from the device using a time domain terahertz system (Toptica Teraflash System). The system has two fiber-coupled InGaAs antennas which can generate and detect terahertz pulses with >5 THz bandwidth and over 90 dB dynamic range. Using four 1" parabolic mirrors (Toptica THz reflection head), the terahertz pulse is focused on the sample at 10° incidence angle. Figure 1(c) shows the measured time varying electric field of terahertz pulse at gate voltages from 0 to 2 V. As the gate voltage changes, the reflected THz pulse shows a significant temporal shift with diminishing shape, which also indicates the modulation of the phase and intensity [12,28,29].  S3). We observed a clear phase and intensity modulation over a broad spectral range. As the membrane gets thicker, the resonance shifts to longer wavelengths due to longer cavity length. We also observed a slight shift in the resonance frequency with the increasing gate voltage. is the free space impedance and σ(ω) is the frequency dependent optical conductivity of graphene. We can describe the tunable optical conductance of graphene with Drude model as, is the DC conductivity of graphene, is angular frequency, and is carrier scattering time.
Here, the sheet conductivity of graphene, relies on the Fermi energy = ( 2 ℏ 2 ) [30]. For microwave frequencies (ω ≪ τ −1 ), the optical conductivity equals to and the surface impedance of graphene has only real values. However for THz frequencies, the scattering rate is comparable with the excitation frequency (ω~ τ −1 ), hence, resulting in a complex surface impedance. Note that both and varies with charge concentration.   Extracted sheet resistance of single, two, and three layers of graphene as a function of applied voltage.
The minimum resistance for single, bilayer and trilayer graphene are 325, 120 and 100 respectively.
(f) Reflectance versus resistance curves for single, two, and three layers of graphene.
The modulation bandwidth is directly related to the tunability of the resistance of graphene which varies between 0.3 to 1.5 kΩ for single layer. This tunability window is limited by the unintentional doping around Dirac point, and the electrochemical stability of the ionic liquid at high gate voltages. Increasing the number of graphene layers could extend the range of tunability to lower resistance. To test this idea, we fabricated devices with few-layer graphene which were obtained by sequential transfer process of single layer graphene. Figure 5(a) shows the schematic representation of the THz phase modulator with few-layer graphene on 40 µm thick PE membrane. The blue, red, and green colors correspond to single, two, and tri-layer graphene devices, respectively. The small signal model of the device is shown in figure 5  We anticipate that the demonstrated phase modulation could enable new type of THz devices. To show the promises of our approach, we would like to demonstrate a multipixel phased array. substrate) into to 1-dimensional arrays of ribbons. Figure 5(b) shows the photograph of the fabricated device. We grounded the continuous graphene and applied spatially changing gate voltages to each column. Ability to control the local charge density with the pattered electrodes enable us to generate a phase gradient on the surface. Figure 6(c) shows the measured reflection phase from the pixels at three different voltage configurations for 1.1 THz. In the first case, we applied a gradient voltage to generate a linear spatial phase variation from /2 to 0 radians. In a similar way, when we reversed the gate voltage by applying consecutive 1 V to -3 V from first to last columns, the phase modulation changed from 0 to nearly /2 respectively. In the last configuration, we kept the gate voltage at zero for all pixels, and the relative phase change was nearly zero radian at 1.1 THz. Figure 6(d) shows the corresponding reflectance variations measured from multipixel device with respect to applied voltages.
Using photolithography, the pixel size can be miniaturized while extending the density of THz phasedarray. A thin film structure can be regarded as a metasurface if the thickness is much smaller than the wavelength [31]. However in our case, the thickness of the device is quarter of the wavelength which is not suitable to classify our structure as a metasurface. In the pixelated device, the lateral dimensions are much longer than the wavelength. It is more suitable to consider these surfaces as phased arrays.
These devices can be regarded as a metadevice when the pixels size is much smaller than the wavelength.
We anticipate that scaling the lateral dimension of the pixels to sub wavelength scale would provide new possibility to control not only phase but also polarization state of reflected light.

Conclusion
As a conclusion, we demonstrated an efficient THz phase modulator using active graphene devices. Our device comprises electrostatically gated graphene layer placed at quarter-wave distance from a metallic reflector. In this configuration, graphene behaves as a tunable impedance surface modulating reflection phase. At resonance, the phase of terahertz wave undergoes step-like change while the intensity of the wave is highly attenuated (~50 dB). Efficient carrier density generation at graphene surface is a key parameter that enabled us to modulate the phase of THz radiation. We were also able to extract the complex impedance of electrically gated graphene for THz frequencies. Supporting materials for "Graphene Based Terahertz Phase Modulators" Figure S1. Raman spectrum of CVD grown graphene on Si/SiO2 substrate. The intensity ratio of 2D/G is 1.7.   1 V). LCR meter cannot measure accurately the low resistance values; hence, other methods must be applied to measure the sheet resistance of highly doped graphene. Figure S4. Controlling phase without intensity modulation. Variation of the reflection (a) and phase (b) from the device as a function of impedance of the graphene layer. When the impedance matches the free space impedance, the reflection is at minimum value with shift in phase of the THz wave.