We proposed and demonstrated a new metamaterial architecture capable of high speed modulation of free-space space thermal infrared radiation using graphene. Our design completely eliminates channel resistance, thereby maximizing the electrostatic modulation speed, while at the same time effectively modulating infrared radiation. Experiment results verify that our device with area of 100 × 120 µm2 can achieve a modulation speed as high as 2.6 GHz. We further highlight the utility of our graphene metamaterial modulator by reconstructing a fast infrared signal using an equivalent time sampling technique. The graphene metamaterial modulator demonstrated here is not only limited to the thermal infrared, but may be scaled to longer infrared and terahertz wavelengths. Our work provides a path forward for realization of frequency selective and all-electronic high speed devices for infrared applications.
© 2016 Optical Society of America
A remarkable property of electromagnetic metamaterials is their realization of exotic effects difficult or impossible to achieve with naturally occurring materials. The electromagnetic responses attained by metamaterials derives from the geometry of their unit cells, as opposed to their chemical composition, and examples include invisibility cloaking [1, 2], negative refraction [3, 4] and superlensing [5, 6]. Enhanced optical constants values obtained are due to an inductive-capacitive (LC) resonance and these properties are preserved in a macroscopic medium fabricated from their individual units. The dependence of metamaterial properties on the LC resonance, however, enables another salient metamaterials feature, i.e. an ability to achieve their novel properties dynamically. To-date, control of amplitude [7, 8], frequency [9–11], phase [12, 13] and polarization [14, 15] responses have been demonstrated across the electromagnetic spectrum utilizing optical [9, 16], thermal [17, 18], mechanical [19, 20] and electrical [21–24] modulation techniques.
Although much progress has been made in metamaterials research over the last fifteen years, an often unrecognized - and underutilized - aspect of the structured material design paradigm is that metamaterials are multifunctional. The metallic inclusions which constitute metamaterial unit cells are sub-wavelength and resonant thus providing both light concentration and tailorable electromagnetic properties. Metamaterials are thus commonly used in a configuration where the responsive material (semiconductor, liquid crystal, graphene, etc.) is placed in regions where the metamaterial resonant structure focuses the external field. Notably, individual metamaterial unit cells may also be electrically linked to form critical functions of a larger system, for example as the connection in a two or three terminal semiconductor device. Thus multifunctional metamaterials enable utilization of alternative device architectures which may prove superior to typical choices. For example, a metamaterial that functions as a metal-semiconductor junction was shown to not only concentrate incident external fields within the responsive material, but also to provide the Schottky barrier needed for operation as a diode. 
Here we present a new graphene metamaterial device architecture operating as a free-space modulator of radiation in the mid-wave IR (3–8 µm) and long-wave infrared (8–15 µm). Our multifunctional design eliminates channel resistance thereby minimizing parasitics, and thus maximizing modulation speed. We illustrate the advantage of a fast efficient modulator by developing a technology demonstration system, utilizing an equivalent time sampling technique, which increased the sampling rate of a thermal infrared camera by over four orders of magnitude.
2. Results and discussions
The graphene metamaterial modulator consists of a top metamaterial electric LC (ELC) layer, a dielectric spacer and a metallic ground plane - depicted in Fig. 1(a). Single layer graphene is placed between the ELC and insulating layer; the ELC unit cells are electrically connected together and used both to enhance the incident infrared field and also as an Ohmic contact - see Fig. 1(b). Typical graphene modulator designs use source, drain and gate contacts, thus introducing both channel resistance - between source and drain - as well as contact resistance between the graphene and Ohmic contacts. Here we introduce a two terminal architecture where the source and drain are connected, and thus at the same potential, thereby eliminating channel resistance. Application of voltage between the top metamaterial layer and the ground plane, modifies the graphene optical conductivity through a change in carrier concentration. As the conductivity of graphene decreases, the gaps between ELC unit cells become more capacitively coupled, and thus the peak absorptive resonance frequency ω0 shifts to lower frequencies (longer wavelengths) in accord with . The graphene metamaterial modulator operates in reflection mode - a continuous ground plane gives near zero transmission over the range of interest - and a peak in the absorption is obtained where we realize an impedance match to free space radiation. Figure 1(b) shows a scanning electron microscope (SEM) picture of the fabricated metamaterial with dimensions as noted.
The wavelength dependent absorption is calculated as A(λ)=1-R(λ)-T(λ), where the reflectance R(λ) and transmittance T(λ) was measured using a Fourier transform infrared microscope. (The transmittance was zero across the entire measured spectrum due to the continuous conducting ground plane.) Figure 2(a) shows the measured absorption spectra A(λ) over a wavelength range of 5–11 µm at gate voltages (Vg) ranging from 0 to 100 V. For Vg = 0 V, red curve in Fig. 2(a), the metamaterial shows a strong resonant response with an absorption peak of 94% centered at 7.45 µm. As the applied bias is increased, the resonant frequency monotonically redshifts and, at the maximum applied voltage, the peak absorption is 92.6% at 7.95 µm - corresponding to approximately a 7% shift in wavelength relative to the initial Vg = 0 V state. In Fig. 2(b) we plot a color map showing the absorption as a function of applied voltage and wavelength. As can be observed, the absorption remains high and the full width half max is approximately constant throughout the entire voltage tuning range. It is interesting to note that the voltage dependent wavelength shift of the absorption peak saturates above 80 V, indicating that the graphene Fermi energy is close to the Dirac point. We thus adopt VCNP = 100 V in all simulations and analysis and note our, as fabricated, graphene realizes a charge neutral point (CNP) gate voltage that is positive around 100 V, indicating our graphene is highly p-doped (Appendix B).
In order to elucidate the relationship between the optical properties of graphene and metamaterial absorption, we performed full wave 3D electromagnetic simulations where the graphene layer was modeled as a 2D material with an equivalent surface impedance calculated from the conductivity and based on the random-phase approximation (RPA) , (Appendix B). The dielectric properties of the AlOx spacer layer were extracted from optical measurements (Appendix C) and the wavelength dependent complex permittivity was used for all simulations. The computed absorption spectra as a function of gate voltage are presented in Fig. 2(c) and (d), and we find that the resonant frequency redshifts with increasing voltage. Our graphene model - coupled with our full wave 3D electromagnetic simulations - indicates that the real portion of the 2D conductivity (σ1) increases by a value of 0.8e2/4ħ (from 0.7e2/4ħ at Vg = 0 to 1.5 at Vg = 100 V), whereas the imaginary part (σ2) increases by 2.6e2/4ħ (0 at Vg = 0 to 2.6 at Vg = 100 V) at wavelengths near the absorption peak. (Appendix B) We thus conclude that the primary graphene optical property responsible for shifting of the metamaterial resonance is capacitive in nature and is therefore consistent with our experimental results, i.e. shifting to longer wavelengths for increasing applied bias.
Having now verified the physical mechanism underlying the dynamic behavior, we next turn toward characterization of the modulation performance. Figure 3(a) shows the reflection modulation depth, defined as M(λ) = [R(λ, Vg) − R(λ, Vg = 0)]/Rmax(λ), where Rmax (λ) is the measured maximum reflectivity at each wavelength. Our modulation scheme results in a frequency shift of the absorption peak and thus M(λ) realizes two extrema - one positive and the other negative - with a minimum lying in-between. For example at Vg = 100 V, our modulator realizes |M(λ)| ≅ 85% at both 7.42 µm and 7.98 µm, and M(λ = 7.65µm) = 0. In order to characterize the modulation speed (fmod) of our device, we added an external series resistor to lower the modulation 3dB down point (f−3dB) to be within the capabilities of our instruments. The red symbols in Fig. 3(b) are the experimental points characterized for the graphene metamaterial modulator with the added series resistor, and we find f−3dB = 2 MHz. Our experimental modulated irradiance, defined as , is approximately linear for small voltages (Fig. 3(d)), and thus a lumped element circuit model, shown as the inset to Fig. 3(b), is used to model the device with added external series resistor - see solid blue curve in Fig. 3(b). An excellent agreement between the circuit model and our experimental data is evident. We thus conclude that the intrinsic maximum modulation speed of our graphene metamaterial modulator (calculated from our circuit model with external series resistor removed) is f−3dB ≈ 2.6 GHz, shown as the purple curve in Fig. 3(b).(Appendix D)
Although our graphene metamaterial modulator achieves relatively good peak modulation depths, any detector or imaging device which spectrally integrates over a given band will observe a severely reduced modulation depth, since we achieve both positive and negative M(λ). We have therefore tailored the operational wavelength of our graphene metamaterial modulator to work in harmony with a thermal infrared camera. The wavelength dependence of the IR camera is shown as the inset to Fig. 3(c), and thus naturally acts as a filter which maximizes the modulation index of our graphene metamaterial modulator, i.e. the zero crossing of M(λ) occurs near 7.5 µm, where the camera’s response goes to zero. We thus calculate the effective modulation depth, shown in Fig. 3(c), as the product of the normalized IR power response and M(λ) from Fig. 3(a). Figure 3(d) displays the modulated irradiance of the graphene metamaterial modulator as a function of the gate voltage over a range of 5 µm to 14 µm (green diamond symbols) and for the IR camera spectral range of 7.5 µm to 14 µm, (gold diamond symbols). Thus we have increased the ME by over a factor of two by considering the specific application of modulation of thermal infrared radiation.
We next show the utility of our graphene metamaterial modulator by reconstructing a fast signal with a period 166 times faster than the inherent camera frame rate (30 Hz) using a boxcar averaging technique (BAT). Conventional real time sampling is able to capture a transient signal in a single shot, with the highest frequency component equal to twice the sampling rate, according to the Nyquist theorem. However, for high-speed signals that are repetitive and limited in bandwidth, BAT, and other equivalent time sampling techniques, can overcome the limits of detectors with slow time constants by acquiring over many repetitions of the signal, with one or more samples obtained on each cycle. It is worth noting that, compared to conventional methods, BAT also improves the signal-to-noise ratio at least by , where N is the number of samplings. 
Figure 4(a) depicts our optical setup - radiation from a blackbody source is focused onto the graphene metamaterial modulator (Pixel 1) and then imaged with an IR camera. In Fig. 4(a), an infrared image shows a linear array of four graphene metamaterial modulators and an area of the sample used as a reference point - denoted by “Ref”. In our equivalent time sampling experiment, the repetitive signal was first generated by chopping blackbody radiation (1200 K) at a frequency of f0 = 5 kHz, see Fig. 4(b). In order to estimate the time-dependent temperature change on the modulator, we stopped the chopper and measured the spatial distribution of the temperature profile along a straight line normal to the chopper blade as shown in Fig. 4(c). The repetitive signal was sampled by modulating the graphene metamaterial device using a 0–60 V square wave with duty cycle of 10%, at a frequency fm = 5.0001 kHz. We thus acquired the modulated signal over a period of τb = 10 s, corresponding to the difference between fm and f0, which was detected by the camera at a frame rate of fc = 30 Hz. The reconstructed signal measured with our time equivalent technique is shown as the blue curve in Fig. 4(d) and was obtained using a one-minute acquisition time, corresponding to only 3 averages of the complete two-cycle waveform. We find excellent agreement between the temperature profile obtained in the static measurement, red curve in Fig. 4(c), and the signal obtained with our graphene metamaterial modulator. The black curve of Fig. 4(c) shows the detected camera signal without use of the metamaterial modulator, thus verifying that the 30Hz frame rate of the camera is not able to resolve the fast 5kHz signal. We have thus achieved an effective sampling rate of f0 fc τb = 1.5 MHz, which is over four orders of magnitude improvement over the IR camera sampling rate.
In conclusion, we have experimentally demonstrated a graphene-based infrared metamaterial modulator with a new architecture which eliminates channel resistance, thus maximizing modulation speed. The operational wavelength range of the modulator was tailored to that of an IR camera allowing a doubling of the irradiance modulation depth, and a peak filtered modulation depth of nearly 80% at a wavelength of 8 µm. Our device realized a modulation speed of f−3dB ≈ 2.6 GHz, but this modulation speed can be further increased via decreasing the pixel size to minimize device capacitance, lowering the contact resistance between metal and graphene, and improving the quality of graphene. We also successfully utilized our device for reconstructing signals in the time-domain with a repetitive rate two orders higher than the maximum integration time of the IR camera, achieving an effective sampling rate four orders greater than that of the camera. The design presented is scalable to large pixel arrays for high resolution applications and to other bands of the electromagnetic spectrum. Our work demonstrates a path forward for constructing frequency selective and high speed electronic devices for numerous scientific and technological applications in sensing, imaging and communications.
Appendix A Fabrication and experiments
The sample fabrication started from evaporating 10/150 nm Cr/Au on a silicon substrate. Then 300 nm aluminum oxide (AlOx) was deposited on the metal layer via atomic layer deposition (ALD) process. Next, a single layer graphene sheet grown on a 25 µm copper foil was transferred onto the AlOx layer using the typical PMMA transfer technique. After PMMA removal, the metamaterial layer was patterned on the graphene layer using electron beam lithography (EBL). The metal layer was evaporated on by an electron beam evaporator with thickness of 2/8/100 nm Ti/Pd/Au. Before patterning the electrodes, extra graphene surrounding the metamaterial was etched away using oxygen plasma. After patterning the electrodes, the sample was wire-bonded to a chip carrier for characterization. The total area of the metamaterial is 100 × 120 µm2.
The sample was mounted on a chip holder and characterized using an infrared microscope coupled to a Fourier transform infrared spectrometer. The chip holder was connected to a power supply so that the top metamaterial layer was connected to the ground of the source and the bottom metal layer was connected to the source output. Infrared light is generated from a globar source and focused on the device with a 15× Cassegrain objective (NA=0.4). The beam size is controlled to about 100 µm × 110 µm by a knife edge aperture. The reflected light from the absorber is refocused onto a mercury cadmium telluride (MCT) detector. The reflection spectra were measured under different voltage biases with frequency resolution of 4 cm−1, and every spectrum averaged over 60 seconds.
Appendix B Properties of transferred CVD graphene
Graphene was grown on both sides of a copper foil with chemical vapor deposition (CVD). The graphene was transferred to a 300 nm thick AlOx film.  First, 100 nm of PMMA was spin-coated onto the top side of the graphene coated copper foil and baked in a N2 box for 24 hours at room temperature. The graphene on the backside of the copper was removed with an O2 plasma etch. Then the copper foil was placed in the ammonium persulfate etchant (Transene Co., APS-100) for 2 hours to remove all of the copper. To ensure all the copper was removed from the graphene layer, the sample was also placed in diluted RCA2 solution for 15 mins. After a DI water rinse, the PMMA/graphene stack was wicked out of the water and onto an AlOx thin film. Additional water was removed by heating the samples on a hot plate at 70 °C for 5 min. The sample was then heated to 160 °C and baked for 5 min to increase the adhesion between the graphene and the substrate. The PMMA was dissolved in chloroform and degreased with methanol, acetone and IPA. The cleaned graphene was characterized by a Raman spectroscopy with a 633 nm excitation laser. Figure 5(a) shows the Raman spectroscopy of the transferred graphene.
The conductance of patterned graphene ribbons is measured using a cascade probe station with sweeping the back gate voltage from −40 V to 80 V. Figure 5(b) shows the measured conductance of the graphene ribbon with size of W = 20 µm and L = 33 µm. The voltage applied between the drain and the source is 10 mV as shown in the inset of Fig. 5(b). The graphene mobility is calculated from the measured conductance of the graphene given by µ = ∂σ/e∂n = L/(eVdsW)(∂Ids/∂Vg)(dVg/dn). The carrier density is given by , where α ≈ 1.34 × 1011cm−2V−1 is the gate capacitance in the unit of electron charges for graphene transferred on a 300 nm AlOx substrate, VCNP is the charge neutral gate voltage. Then the calculated graphene mobility near the charge neutral point (∼ 40 V) is about 830 cm2/V/s.Equation 1 is attributed to the interband transitions, the second term to the intraband transitions. The scattering time is estimated from an I–V measurement from transferred and patterned graphene ribbons at charge neutral point (CNP).  Here µ is the mobility calculated at the CNP, with a value of 830 cm2/V/s, vF ≈ 1 × 106 m/s is the Fermi velocity. The Fermi level is determined by the free carrier concentration, given by , where graphene carrier density n is directly controlled by the applied gating voltage Vg between the top metamaterial and the bottom gate. Due to process induced charge impurities residing within the dielectric, or at the graphene-substrate interface, there is an initial carrier doping which we estimate to be, (at the CNP), n0 ≈ σ0nimp h/20e2 = 6 × 1011cm−2,  where σ0 is the measured conductivity at the CNP and nimp ≈ 1 × 1012cm−2 for ALD grown on AlOx.  From Fig. 2(b), we found that the VCNP is around 100 V. However, our I–V transport measurements on graphene ribbons shows a smaller CNP voltage of about 40 V. We note that with applied positive voltage on the bottom gate, electrons gradually accumulate into the graphene-substrate interface trap centers, which may cause electrical screening thus shifting the VCNP to higher values. We thus attribute the discrepancy in CNP voltage values - transport compared to spectroscopic measurements - to be due to increased adsorbates on the surface of graphene underneath the patterned absorber structure as a result of post processing procedures necessary for development of the metamaterial graphene modulator.  Figure 6 shows the graphene sheet conductivity with various gate voltages. The imaginary part of conductivity σ2 as shown in Fig. 6(b) increases with the applied gate voltage from negative values to positive. Around 8 µm, the change of σ2 is over 3 times of the change of the real part of conductivity σ1, which indicates that the change of σ2 dominates the response tuning of the metamaterials.
Appendix C Extraction of dielectric properties of ALD AlOx thin film on gold
The dielectric properties of AlOx thin film in the infrared region was determined using our FTIR system based on a transfer matrix method. In the experiment, TM polarized light was incident onto the sample, which was mounted on a Harrick variable angle reflection stage so that the reflections from the sample at different angles were recorded. For a slab consisting of 300 nm AlOx thin film and 150 nm gold on a silicon substrate, the total reflectance is given by Fig. 7. klz, l = 1, 2, 3 are z-component wavenumbers for waves in different materials, determined by , and , l = 1, 2, 3, are the complex refractive indexes of air, AlOx and gold respectively. The dielectric properties of AlOx was based on the Brendel oscillator model, which includes m distributions of oscillators with a Gaussian distribution of the center frequencies , given by Figure 7(b) shows the extracted relative permittivity of 300 nm AlOx film deposited on gold.
Appendix D Modulation speed characterization
A signal generator was used to gate the modulator with a V = 10 V square wave and we utilized a silicon carbide Globar broadband infrared source and an MCT detector with an electronic bandwidth of approximately 16 MHz. The lock-in amplifier and signal generator realize electronic bandwidths of 200MHz and 2MHz and thus we added a series resistor to our circuit in order to characterize the modulation speed. In Fig. 3(c) we show the response of the MCT detector as a function of modulation frequency (red dots) for our graphene metamaterial with the series resistor attached. The frequency response of the graphene device is given by H(ωmod) = 1/[1 + iωmodRgCg + iωmodR0(CP + Cg + iiωmodRgCPCg)], where, the capacitance of the modulator Cg with area of 100 µm × 120 µm was determined through LCR measurements to be 3.6 pF; an extra capacitance because of a 150 µm × 150 µm electrode and parasitic capacitance was determined to be 12.6 pF, the measured series R0 resistor was 4.57 kΩ including the characteristic impedance of cables the electrode of our device is directly connected to the metamaterial layer, which is different from other field effect transistors (FETs) configuration, so the large graphene sheet resistance in the channel is minimized.  With typical contact resistivities of 1 ∼ 2 kΩ for Ti/Pd/Au on graphene, [36–38] the contact resistance Rg of our device with the contact length of over 120 m can be smaller than 17 Ω. We measured a 3dB roll-off frequency of about 2.1 MHz, with the external series resistor added, thus indicating our graphene metamaterial modulator realizes a modulation frequency of approximately 2.6 GHz.
Appendix E Blackbody radiation modulation through an IR camera
The demonstration of infrared light modulation in the transparency window was performed using a FLIR camera T640 as the detector and a cavity blackbody as the source. A 60 V gating voltage was applied on the device with a modulation rate of 1 Hz, which is smaller than the frame rate the camera of 30 Hz. Figure 8 shows the modulated differential irradiance detected at location ’Pixel’ with three different blackbody temperatures at 600 K, 800 K and 1200 K, respectively. The measured signals were referenced to the background at location ’Ref’ shown as the purple curve in Fig. 4(a) to remove the medium-time drift. As the temperature increases, the modulation amplitude accordingly increases, which implies modulated signals are from the reflectivity modulation rather than the local resistive heating induced by the applied voltage on the device. During illumination, since the sample was heated due to the absorption of IR radiation by the absorbers, substrates and chip carriers, there will be also modulated thermal emission directly from the device. Our calculations indicate that the reflected infrared light dominates the signal of the camera under high temperature blackbody radiation. The supplemental movie shows a modulation of thermal radiation from a 600 K blackbody with modulation rate of 4 Hz. ( Visualization 1)
Department of Energy (DOE) DE-SC0014372 (graphene theoretical, computational and experimental characterization); Office of Naval Research (ONR) N00014-15-1-0051 (metamaterial modulator and performance characterization). This work was performed in part at the Duke University Shared Materials Instrumentation Facility (SMIF), a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), which is supported by the National Science Foundation (NSF) (Grant ECCS-1542015) as part of the National Nanotechnology Coordinated Infrastructure (NNCI).
We would like to thank Dr. Wen-Chen Chen for useful discussions.
References and links
4. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008). [CrossRef] [PubMed]
8. S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11, 936–941 (2012). [CrossRef] [PubMed]
9. H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photon. 2, 295–298 (2008). [CrossRef]
10. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. 10, 4222–4227 (2010). [CrossRef] [PubMed]
11. K. Fan, A. C. Strikwerda, X. Zhang, and R. D. Averitt, “Three-dimensional broadband tunable terahertz metamaterials,” Phys. Rev. B 87, 161104 (2013). [CrossRef]
12. H. T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photon. 3, 148–151 (2009). [CrossRef]
13. Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5, 041027 (2015).
14. B. Zhu, Y. Feng, J. Zhao, C. Huang, Z. Wang, and T. Jiang, “Polarization modulation by tunable electromagnetic metamaterial reflector/absorber,” Opt. Express 18, 23196–23203 (2010). [CrossRef] [PubMed]
15. S. Zhang, J. Zhou, Y.-S. Park, J. Rho, R. Singh, S. Nam, A. K. Azad, H.-T. Chen, X. Yin, A. J. Taylor, and X. Zhang, “Photoinduced handedness switching in terahertz chiral metamolecules,” Nat. Commun. 3, 942 (2012). [CrossRef] [PubMed]
16. K. Fan, X. Zhao, J. Zhang, K. Geng, G. R. Keiser, H. R. Seren, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically tunable terahertz metamaterials on highly flexible substrates,” IEEE Trans. Terahertz. Sci. Technol. 3, 702–708 (2013). [CrossRef]
17. T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325, 1518–1521 (2009). [CrossRef] [PubMed]
19. W. M. Zhu, A. Q. Liu, W. Zhang, J. F. Tao, T. Bourouina, J. H. Teng, X. H. Zhang, Q. Y. Wu, H. Tanoto, H. C. Guo, G. Q. Lo, and D. L. Kwong, “Polarization dependent state to polarization independent state change in THz metamaterials,” Appl. Phys. Lett. 99, 221102 (2011). [CrossRef]
20. X. Liu and W. J. Padilla, “Dynamic manipulation of infrared radiation with MEMS metamaterials,” Adv. Opt. Mater. 1, 559–562 (2013). [CrossRef]
22. D. Shrekenhamer, S. Rout, A. C. Strikwerda, C. Bingham, R. D. Averitt, S. Sonkusale, and W. J. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express 19, 9968–9975 (2011). [CrossRef] [PubMed]
24. M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Tunable meta-liquid crystals,” Adv. Mater. 28, 1553–1558 (2016). [CrossRef]
25. L. Falkovsky and S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007). [CrossRef]
26. G. M. Hieftje, “Signal-to-noise enhancement through instrumental techniques. II. Signal averaging, boxcar integration, and correlation techniques,” Anal. Chem. 44, 69A–78a (1972).
27. X. Liang, B. A. Sperling, I. Calizo, G. Cheng, C. A. Hacker, Q. Zhang, Y. Obeng, K. Yan, H. Peng, Q. Li, X. Zhu, H. Yuan, A. R. H. Walker, Z. Liu, L.-M. Peng, and C. A. Richter, “Toward clean and crackless transfer of graphene,” ACS Nano 5, 9144–9153 (2011). [CrossRef] [PubMed]
28. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
29. J. Horng, C.-F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83, 165113 (2011). [CrossRef]
31. S. Kim, J. Nah, I. Jo, D. Shahrjerdi, L. Colombo, Z. Yao, E. Tutuc, and S. K. Banerjee, “Realization of a high mobility dual-gated graphene field-effect transistor with Al2O3 dielectric,” Appl. Phys. Lett. 94, 062107 (2009). [CrossRef]
33. C. M. Soukoulis and P. Markos, Wave Propagation: From Electrons to Photonic Crystals and Left-handed Materials (Princeton University, 2008).
34. J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. T. Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51, 6789–6798 (2012). [CrossRef] [PubMed]
35. K. Nagashio, T. Nishimura, K. Kita, and A. Toriumi, “Contact resistivity and current flow path at metal/graphene contact,” Appl. Phys. Lett. 97, 143514 (2010). [CrossRef]
36. B.-C. Huang, M. Zhang, Y. Wang, and J. Woo, “Contact resistance in top-gated graphene field-effect transistors,” Appl. Phys. Lett. 99, 032107 (2011). [CrossRef]
37. E. Watanabe, A. Conwill, D. Tsuya, and Y. Koide, “Low contact resistance metals for graphene based devices,” Diamond Relat. Mater. 24, 171–174 (2012). [CrossRef]
38. A. Hsu, H. Wang, K. K. Kim, J. Kong, and T. Palacios, “Impact of graphene interface quality on contact resistance and RF device performance,” IEEE Electron. Dev. Lett. 32, 1008–1010 (2011). [CrossRef]