Progress of Terahertz Devices Based on Graphene

Mai-Xia Fu and Yan Zhang

Progress of Terahertz Devices Based on Graphene

Mai-Xia Fu and Yan Zhang

—Graphene is a one-atom-thick planar sheet of sp2-hybridized orbital bonded honeycomb carbon crystal. Its gapless and linear energy spectra of electrons and holes lead to the unique carrier transport and optical properties, such as giant carrier mobility and broadband flat optical response. As a novel material, graphene has been regarded to be extremely suitable and competent for the development of terahertz (THz) optical devices. In this paper, the fundamental electronic and optic properties of graphene are described. Based on the energy band structure and light transmittance properties of graphene, many novel graphene based THz devices have been proposed, including modulator, generator, detector, and imaging device. This progress has been reviewed. Future research directions of the graphene devices for THz applications are also proposed.

IndexTerms—Detector,generator,graphene, imaging, modulator, terahertz device.

1. Introduction

Lying between the radio frequency and infrared, terahertz (THz) electromagnetic wave was notoriously difficult to generate, modulate, and detect. Recent progress in sources and detectors are turning the ‘THz gap’ into one of the most rapidly growing technological fields[1],[2]. THz research becomes a spotlight of scientific interest driven by a vast amount of new applications in the realms of security technology[3],[4], spectroscopy, biomedical imaging, astronomy, quality control, and sensing[5],[6]. Most of these applications benefit from the observation that a large number of materials are transparent for THz waves, which allows one to detect the properties of inclusions or materials behind dielectric obstacles. Moreover, the THz radiation has very low photon energy which is safer for living cell.

However, various applications require for high performance components such as wave plate, lens, and modulator, which are readily available for the optical, infrared, and microwave regions of the electromagnetic spectrum but not sufficient for the THz frequency regime. A promising approach for the implementation of THz devices is in urgent need. Metamaterial has been used to fabricate filter, wave plate, and lens for the THz radiation[7]?[9]. Graphene, a one-atom-thick planar sheet of a honeycomb carbon crystal, since its discovery in 2004, has become a spotlight of scientif i c interest due to its unique carrier transport and optical properties[10]. A whole range of experiments evidenced its exceptional physical properties. The observation of massless charge carriers in graphene has implied intriguing consequences. For example, it was possible to verify the principle of relativistic quantum mechanics and more specifically the quantum Hall effect in graphene[11]. Moreover, the grapherne provided some unique properties, such as uniform optical transparency, high fl exibility, high electron mobility. The conductivity[12]of the graphene can be tuned by electrochemical potential via electrostatic gating and magnetic fi eld or optical excitation. In recent years, it became evident that the graphene can play a signif i cant role in the THz region, with respect to its applications in optics. The graphene seems to provide some suitable properties that can be exploited for the design and implementation of one atomic layer thin THz optical devices.

In this paper, the optoelectronic prosperities of the graphene are summarized. Some recent advances in the graphene based THz devices are concluded and future research directions of the graphene device for THz applications are also proposed.

2. Optoelectronic Properties of the Graphene

The graphene shows some remarkable electronicproperties due to its unique energy band structure. Fig. 1 depicts the lattice and energy band structures of the graphene. The energy band structure of a single layer graphene (SLG) can be described using a tight-binding Hamiltonian model[13]. The conduction band and the valence band of the graphene take a symmetrical conical shape around theKandK′ points and contact each other at theKandK′ points. Electrons and holes in the graphene hold a linear dispersion relation with a zero band gap near theKandK′ points, resulting in some peculiar features, such as the specific integer and fractional quantum Hall effects, a ‘minimum’ conductivity of 4e2/heven when the carrier concentration tends to zero (eis the magnitude of the electric charge of the electron andhis the Planck constant), and Shubnikov de Haas oscillations with a π phase shift due to the Berry’s phase[13]. Mobility μ of up toare observed in suspended samples[14],[15]. Combined with the near-ballistic transport at the room temperature, these properties make the graphene be a potential material for nano-electronics, particularly for high-frequency applications[16].

The graphene also shows remarkable optical properties. Optical absorption in the graphene involves two processes: intraband transitions and interband transitions, which can be expressed using the optical conductivitywhere ω is the angular frequency of the photon. Calculations of the optical conductivity have shown that, for the infrared and visible range, the graphene optical conductivity is determined by interband transitions, whereas, for the THz range, it is dominated by intraband transitions[17],[18].

The transmittanceTof a freestanding SLG can be derived by applying the Fresnel equation in the thin film limit for a material with a fixed universal optical conductance, and be given as:

Fig. 1. Lattice and energy band structures of graphene[13]: (a) lattice and (b) energy band structures.

whereαis the fine structure constant. The optical absorption of the graphene layers is to be proportional to the number of layers, each absorbingAover the whole visible spectrum[19]is as following:

Fig. 2 (a) shows the transmittance of a single layer and double layers graphene. Inset is the sample design for the experiment, showing a thick metal support structure with several apertures, on top of which graphene fl akes are placed. Fig. 2 (b) shows the transmittance of different layers of graphene versus wavelength. The absorption spectrum of SLG is quite flat from 300 nm to 2500 nm with a peak in the ultraviolet region (～270 nm), due to the excition-shifted van Hove singularity in the few-layer graphene (FLG) sample. Each sheet can be seen as a 2D electron gas, with little perturbation from the adjacent layers, making it optically equivalent to a superposition of almost non-interacting SLG. The other absorption features can be seen at lower energies, associated with interband transitions.

3. Graphene Based THz Devices

The graphene has a unique band structure including a cone of linear dispersion with its apex at the Dirac point, which gives rise to the extraordinary transport properties of massless relativistic fermions. When a graphene sheet is deposited on a substrate, the symmetry breaking at the interface induces an intrinsic modif i cation of the electronic structure, opening up a band gap at the Dirac point. Most of the practical graphene devices are fabricated on a substrate providing a supporting structure[20]?[22]. More importantly, due to the advantage that the complex conductivity of graphene can be controlled with variations of chemical potential by external ways, the working frequency of the graphene can be continuously tuned into the range of IR and THz frequencies, effectively broadening the total working frequency range[23],[24]. These proprieties make the graphene be a good candidate for THz devices fabrication.

Fig. 2. Transmittance for different layers graphene[19]: (a) single layer and double layers and (b) transmittance of different layers versus wavelength.

In this section, recent progress of the graphene based THz devices is reviewed, some devices including modulator, generator, detector, and imaging device are described.

3.1 THz Modulator

At present, high performance elements to control and manipulate the THz electromagnetic wave, such as modulators and active filters, are in high demand to develop sophisticated communication and imaging systems. However, the THz wave modulators studied to date generally exhibit the compromised performance between the modulation depth, broadband operation, signal attenuation, polarization dependence, on chip integrability, and structural complexity[25],[26]. Research group of Berardi Sensale-Rodriguez demonstrates that the exceptionally efficient broadband modulation of THz waves at room temperature can be realized using the graphene with extremely low intrinsic signal attenuation in [27]. They experimentally achieved more than 2.5 times superior modulation than prior broadband intensity modulators, which is also the first demonstrated graphene-based device enabled solely by intraband transitions as shown in Fig. 3.

Fig. 3 (a) shows the conical band structure of the graphene and optical processes in the graphene. Interband transitions (green arrows) occurs from the valence to conduction band dominate in the infrared/visible range. However, under the THz illuminating where the photon energy is generally smaller than 12.4 meV (3 THz), intraband transitions (red arrows) will dominate. When tuning the Fermi levelEFin the graphene using a voltageVg, the density of states available for intraband transitions will be tuned, thus the THz transmission. Fig. 3 (b) shows the schematic of the proof-of-concept graphene THz modulator. The SLG was prepared on a SiO2/p-Si substrate. The top contacts were used to monitor the graphene conductivity, and the bottom ring-shaped gate was used to tune the graphene Fermi levelEF, that is, the conductivity of the graphene. The device size is about 1.5 cm×1.5 cm. The THz transmission spectra of the device is measured at 300 K for two voltageVg1AndVg2. The measured range is from 570 GHz to 630 GHz. Fig. 3 (c) shows the measured (symbols) and modeled (lines) intensity transmittance as a function of the frequency for back gate voltages of 0 V (dashed line) and 50 V (dotted line). The inset is the close-up of transmittance near 570 GHz showing a maximum modulation of 15±2% at 570 GHz.

Reference [24] proposed a centimeter size single layer graphene device with a gate electrode, which can modulate the transmission of THz and infrared waves. Fig. 4 (a) depicts the experimental sketch of the gated large area graphene device, together with the incident and transmitted THz/infrared beams. The cartoon on the right shows the band dispersions of the graphene with a gate-tuned Fermi energy. Fig. 4 (b) shows the gate voltage dependent coherent THz wave transmission through the graphene. AtVg= +30 V, the maximum THz transmission is observed, indicating that the Fermi energy at this gate voltage is closest to the Dirac point. At all other voltages above and below +30 V, the THz transmission decreases monotonically withVg, as shown in the up right and down left of Fig. 4 (b). The down right of Fig. 4 (b) shows the spectrally integrated power of the transmitted THz beam versusVg(circles), demonstrating thatVg= +30 V is indeed closest to the Dirac point, and the unbiased (0 V) point (dashed line) is on the p-side. The DC resistance measured in situ is also plotted in Fig. 4 (b) (smooth solid trace in the right down), showing the similar gate dependence to the transmitted THz power.

Fig. 3. Operating principle and structures of a graphene based THz modulator[27]: (a) band structure and optical processes in grapheme, (b) schematic of the graphene THz modulator, and (c) transmittance of the modulator.

Fig. 4. Sketch and performance of the modulator[24]: (a) sketch of gated large-area graphene device and (b) gate-voltage-dependent coherent THz wave transmission through graphene.

In [25], the Rusen Yan group proposed a new class of electrically tunable THz metamaterial modulators employing the metallic frequency selective surfaces (FSS) in conjunction with capacitive tunable layers of electrons, promising near 100% modulation depth and less than 15% attenuation. Fig. 5 (a) shows the proposed THz modulator structure. It consists of a square lattice of gold cross slot FSS and a pair of capacitive coupled graphene layers situated at a distanced. The dielectric separating the FSS and graphene pair and between the graphene layers is SiO2. Fig. 5 (b) shows the simulated behavior of the modulator. In this modulator, the transmission of the THz waves through the graphene can be controlled by electrically tuning the density of states available for the intraband transitions. An intensity modulation depth of 15%, an intrinsic insertion loss of 5%, and a modulation frequency of 20 kHz using a 570 GHz carrier at the room temperature can be achieved. This proposed method is applicable to all possible electrically tunable elements including the graphene, Si, MoS2, thus opening up myriad opportunities for realizing high performance switcher over an ultra-wide THz frequency range.

3.2 THz Generator and Detector

A THz laser with an optically pumped epitaxial multiple graphene layer structure was proposed by V. Ryzhii research group[26]. The schematic view of the laser is shown in Fig. 6 (a). The gain medium is the MGL. Fig. 6 (b) depicts the working principle of the proposed laser. Arrows show the transitions related to the interband emission and the intraband absorption of THz photons with energyhω. To achieve lasing in the MGL structures, the following condition should be satisfied.

Fig. 5. Proposed THz modulator[25]: (a) structure of the modulator and (b) simulated behavior of the modulator: transmittance (S21) amplitude, reflectance (S11) amplitude, associated absorption by the modulator and phase of transmittance.

In the regime sufficiently beyond the threshold of lasing, when the stimulated radiative recombination becomes dominant, the pumping efficiency (η) is determined just by the ratio of the energy of the emitted THz photonshω and the energy of optical photonshΩ, so /η ω Ω= , however, the nonradioactive recombination mechanisms will markedly decrease the η.

Reference [27] conducted time-domain spectroscopic studies using an optical pump/THz probe technique and showed that the graphene sheet can amplify an incoming THz radiation. The pump/probe geometry is shown in Fig. 7. The sample was placed on the stage and a 120 μm thick CdTe crystal was placed on the sample, acting as a THz probe pulse emitter and an electro-optic sensor. A single 80 fs, 1550 nm, 4 mW, 20 MHz fi ber laser beam is split into two: one for optical pumping and generating the THz probebeam in the CdTe, and the other for optical probing. The THz probe plus was double ref l ected to stimulate the THz emission in the graphene, which is detected as a THz photon echo signal.

Fig. 6. Structure and working principle of the proposed device[26]: (a) schematic view of the MGL structure and (b) occupied and vacant states in different GLs under optical pumping.

Fig. 7. Observation of the amplif i ed stimulated THz emission from the optically pumped graphene[27]: (a) sketch of optically pumped graphene and (b) structure and working principle of optical pump and THz probe for observation of the amplif i ed stimulated THz emission.

Fig. 8 (a) shows the measured temporal response in [27]. The secondary pulse, the THz photon-echo signal, obtained with the graphene is more intense compared with that obtained without the graphene. This indicates that the graphene acts as an amplifying medium. As shown in Fig. 8 (b), the emission spectra show a threshold-like behavior as a function of the laser pumping intensity, testifying to the occurrence of negative conductivity and population inversion in the graphene[27]. A Lorentzian-like normal dispersion around the gain peak testif i es the occurrence of amplif i cation attributed to the stimulated emission of photocarriers in the inverted states.

Reference [28] conducted a similar experiment with a thinner (80 μm thick) CdTe crystal to shorten the terahertz probe delay time from the original 3.5 ps to 2.0 ps, which is the timing that gives the largest negative conductivity and hence wider gain spectral width, as seen in Fig. 9. The emission spectra exhibit a clear broadening (in particular, at higher cutoff frequencies) at 2 ps THz probe delay time. This tendency coincides with the simulated results in Fig. 8, giving a clear evidence of the nonequilibrium relaxation dynamics of the quasi-Fermi energy ref l ecting the population inversion. The obtained gain exceeds the maximal possible value of 2.3% which is limited by the absorbance of graphene.

3.3 THz Imaging Device

Fig. 8. Measured temporal responses and their gain spectra of the THz photon-echo probe pulse[27]: (a) temporal responses of the probe pulse and (b) gain spectra.

Fig. 9. Comparison of the measured gain spectra for two THz probe delays 2.0 ps (with a thin CdTe) and 3.5 ps (with a thick CdTe)[28].

Imaging with a resolution beyond the diffraction limit has been always one of the most important issues in the fi eld of optics, since Ernst Abbe discovered the fundamental barrier in 1873. The loss of subwavelength features of objects due to the fast decay of evanescent waves limits the resolution of a classical imaging system to about half of the illuminating wavelength λ. To overcome this limitation and recover the fi ne details of objects, one fundamental idea is to enhance and detect the evanescent waves in the near fi eld[29],[30]. Scanning near-f i eld optical microscopy (SNOM) uses a sharp tip to produce strong local fi eld enhancement and simultaneously collect the near fi eld information of samples[30]. However, the high spatial resolution in SNOM comes at the price of a pixel-by-pixel scanning of the tip close to the sample. This obvious time consuming characteristic restricts its application to small-area samples (typically 10 μm×10 μm or even less) for imaging within a reasonable time. For the demand of rapid and large-area sample detecting at high spatial resolution, other methods are needed. Superlens (SL) that is capable of imaging the samples at sub-wavelength resolution by using a thin slab of a material with negative permittivity is a good choice. However, a new emerging limitation in the SL is the narrow working frequency range.

Recently, it has been demonstrated that graphene sheets (GSs) can support and guide ultra-short effective wavelength for potential metamaterial and plasmonic applications[31],[32]. Peining Li research group verified that the well coupled GSs can also enable the enhancement of evanescent waves for subwavelength imaging[33]. Owing to the nonresonant nature of the imaging process, this enhancement is obviously weaker than the superlensing effect, but still a good subwavelength resolution of aroundcan be achieved for a bilayer case, and can be further improved to be better than around /10λ via multilayered conf i guration.

Fig. 10 (a) shows the sketch of a 2-layered graphene under the gold double slits with the widthw= 800 nm and the separation of 2w=1.6 μm. The top and bottom dashed lines indicate the positions of object plane and image plane chosen for later numerical simulations. The up of Fig. 10 (b) shows the numerical simulations of the electric fi eld intensity distribution for the case at the frequency of 27.2 THz. The electric fields through each slit are effectively transferred (without obvious decreases) by the graphene, and thus the slits are also easily distinguished.Two well-separated peaks are clearly resolved for the case of the double slits on the graphene layer, showing an improved subwavelength resolution (λ/7) compared with the case without the graphene layer. Furthermore, the performance of this graphene layer at different frequencies is also shown in the down of Fig. 10 (b). Line profiles taken from the image plane at different frequencies from top to down are: the first line profiles is the case without the graphene layer, it is shown for comparison, the second shows the normalized intensity at frequency of 26 THz where the third is 27.2 THz and the last is 30 THz. The double slits can be resolved by the graphene layer in the range from 26 THz to 30 THz, suggesting an intrinsic operating frequency range of at least 4 THz. Obviously, the good performance of operation bandwidth of the graphene layer will provide more convenience in future practical applications, such as spectroscopic imaging or near-f i eld lithography without exactly matching the frequency. Line profiles taken from the image plane at different frequencies:f=26 THz (red), 27.2 THz (purple), and 30 THz (green). The case without the praphene layer (black) is shown for comparison.

The research group of Berardi Sensale-Rodriguez proposes and experimentally demonstrates an array of graphene electro absorption modulators as a electrically reconfigurable pattern for THz camera[34]. As shown in Fig. 11 (a), the pixel size of the array is 0.7 mm×0.7 mm. The electric field intensity at the active graphene was enhanced by 4 times when the substrate optical thickness is an odd multiple of the quarter wavelength of the incoming THz radiation, thus leading to the augmented modulation in reflectance compared with the transmission mode. The measured reflectance (blue circles) and associated conductivity (red circles) as functions of the voltage are shown in Fig. 11 (b). The radiation was focused onto the center of the modulator array and the frequency was set at 590 GHz.The estimated conductivity contribution of carriers in the Si substrate is shown in green squares. Fig. 11 (c) and Fig. 11 (d) show the map of “pixel related illumination” without and with an object. The two red crossed pixels did not show modulation due to the fabrication issues. The sketches of the objects made from the absorber material are shown in each map below. The close resemblance between the map and the object indicates that the graphene modulator array can be used for imaging.

The active element of these modulators consists of only single atom thick graphene, achieving a modulation of the THz wave reflectance more than 50% with a potential modulation depth approaching 100%. Although the prototype presented here only contains 4 4× pixels, it reveals the possibility of developing reliable low cost video rate THz imaging systems by employing a single detector.

Fig. 10. Sketch and imaging performance of the 2-layered graphene[33]: (a) sketch of a 2-layered graphene under the gold double slit and (b) imaging performance of the 2-layered graphene.

Fig. 11. Proposed imaging device[34]: (a) schematic of the graphene reflection modulator array, (b) measured reflectance (blue circles) and associated conductivity (red circles) versus voltage, (c) map of “pixel related illumination” without an object, and (d) map of “pixel related illumination” with an object.

4. Conclusions

Much unexplored territory still remains for the THz technology mainly owing to a lack of affordable and efficient sources, detectors, and modulator device. Graphene, as a new material, seems to provide suitable properties that can be exploited for the design and implementation of one atomic layer thin THz optical devices. Experimental observations of the THz emission and amplification in the optically pumped graphene have shown the feasibility of graphene based THz generation. By tuning the electronic and optical properties of grapheme through external means, the Fermi level of the graphene can be varied. Therefore, the SLG and few layers graphene arevery suitable for THz manipulation, including modulators, filter, switcher, beam splitter, and imaging device. In particular, the frequency of graphene plasma waves lies in the THz range, as well as the gap of graphene nanoribbons, and the bilayer graphene tunable band-gap, therefore, in the future, the combination of the graphene with plasmonics could lead to a wide range of advanced THz devices.

[1] G. P. Williams, “Filling the terahertz gap-high power sources and applications,”Rep. Prog. Phys., vol. 69, no. 2, pp. 301–326, 2006.

[2] M. Tonouchi, “Cutting-edge terahertz technology,”Nature Photon., 2007, doi: 10.1038/nphoton.2007.3.

[3] H. Hoshina, Y. Sasaki, A. Hayashi, C. Otani, and K. Kawase,“Noninvasive mail inspection system with terahertz radiation,”Appl. Spectrosc., vol. 63, pp. 81–86, Apr. 2009.

[4] J. S. Melinger, S. S. Harsha, N. Laman, and D. Grischkowsky, “Temperature dependent characterization of terahertz vibrations of explosives and related threat materials,”O(jiān)pt. Express., vol. 18, pp. 27238–27250, Dec. 2010.

[5] S. Yoshida, K. Suizu, E. Kato, Y. Nakagomi, Y. Ogawa, and K. Kawase, “THz imaging techniques for nondestructive inspections,”J. Mol. Spectrosc., vol. 256, no. 7–8, pp. 146–151, 2009.

[6] M. Theuer, S. S. Harsha, D. Molter, G. Torosyan and R. Beigang, “Terahertz time-domain spectroscopy of gases, liquids, and solids,”Chem Phys Chem., vol. 12, no. 15, pp. 2695–2705, 2011.

[7] H. T. Chen, J. F. O'Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer,et al., “Experimental demonstration of frequency-agile terahertz metamaterials,”Nat. Photonics, vol. 2, pp. 295–298, Apr. 2008.

[8] P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm,“Strongly birefringent metamaterials as negative index terahertz wave plates,”Appl. Phys. Lett., vol. 95, no. 17, pp. 171104–171104-3, 2009.

[9] J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,”O(jiān)pt. Express., 2010, doi: 10.1364/OE.18.027748.

[10] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos,et al., “Electric field effect in atomically thin carbon films,”Science, vol. 306, no. 5696, pp. 666?669, 2004.

[11] Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim,“Experimental observation of the quantum Hall effect and Berry’s phase in grapheme,”Nature, vol. 438, pp. 201–204, Nov. 2005.

[12] A. Vakil and N. Engheta, “Transformation optics using graphene,”Science, vol. 332, no. 6035, pp. 1291–1294, 2011.

[13] P. R. Wallace, “The band theory of graphite,”Phys. Rev., vol. 71, no. 9, pp. 622–634, 1947.

[14] A. S. Mayorov, R. V. Gorbachev, S. V. Morozov, L. Britnell, R. Jalil, L. A. Ponomarenko,et al., “Micrometer-scale ballistic transport in encapsulated graphene at room temperature,”Nano Lett., vol. 11, no. 6, pp. 2396–2399, 2011.

[15] K. Bolotina, K. J. Sikesb, Z. Jianga, M. Klimac, G. Fudenberga, J. Honec,et al., “Ultrahigh electron mobility in suspended graphene,”Solid State Commun., vol. 146, no. 9–10, pp. 351–355, 2008.

[16] Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H. Y. Chiu, A. Grill,et al., “100-GHz transistors from wafer-scale epitaxial grapheme,”Science, vol. 327, no. 5966, pp. 662, 2010.

[17] J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana,et al., “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,”Appl. Phys. Lett., vol. 93, no. 13, pp. 131905, 2008.

[18] H. Choi, F. Borondics, D. A. Siegel, S. Y. Zhou, M. C. Martin, A. Lanzara,et al., “Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene,”Appl. Phys. Lett., vol. 94, no.17, pp. 172102, 2009.

[19] R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber,et al., “Fine structure constant deines transparency of grapheme,”Science, vol. 320, no. 5881, pp. 1308–1308, 2008.

[20] S. H. Lee, M. M. Choi, T. T. Kim, S. Lee, M. Liu, X. B. Yin,et al., “Switching terahertz waves with gate- ontrolled active graphene metamaterials,”Nature Mat., vol. 11, pp. 936–941, Sep. 2012.

[21] A. Andryieuski, A. Lavrinenko, and D. Chigrin, “Graphene hyperlens for terahertz radiation,”Phys. Rev. B., vol. 86, no. 12, pp. 121108, 2012.

[22] R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,”O(jiān)pt. Express., vol. 20, no. 27, pp. 28017–28024, 2012.

[23] K. F. Mak, L. Ju, F. Wang, and T. F. Heinz, “Optical spectroscopy of graphene: from the far infrared to the ultraviolet,”Solid State Comm., vol. 152, no. 15, pp. 1341–1349, 2012.

[24] L. Ren, Q. Zhang, J. Yao, Z. Z. Sun, R. Kaneko, Z. Yan,et al., “Terahertz and infrared spectroscopy of gated large-area graphene,”Nano Lett., vol. 12, no. 7, pp. 3711–3715, 2012.

[25] C. W. Berry, J. Moore, and M. Jarrahi, “Design of reconfigurable metallic slits for terahertz beam modulation,”O(jiān)pt. Express., vol. 19, no. 2, pp. 1236–1245, 2011.

[26] T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room temperature operation of an electrically driven terahertz modulator,”Appl. Phys. Lett., vol. 84, no. 18, pp. 3555–3557, 2004.

[27] B. Sensale-Rodriguez, R. Yan, and M. Kelly, “Broadband graphene terahertz modulators enabled by intraband transitions,”Nature Comm., vol. 3, pp. 780–787, Apr. 2012.

[28] A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, T. Otsuji, and V.Ryzhii, “Terahertz surface plasmons in optically pumped grapheme structure,”J. Phys.: Condens. Matter.,vol. 23, no. 14, pp. 145302, 2011.

[29] A. Lewis, H. Taha, A. Strinkovski, A. Manevitch, A. Khatchatouriants, R. Dekhter,et al., “Near-field optics: from subwavelength illumination to nanometric shadowing,”Nat. Biotechnology, vol. 21, pp. 1378–1386, Oct. 2003.

[30] A. Hartschuh, “Tip-enhanced near-field optical microscopy,”Angew. Chem., vol. 47, no. 43, pp. 8178–8191, 2008.

[31] J. N. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond,et al., “Optical nano-imaging of gate-tunable graphene plasmons,”Nature, vol. 487, pp. 77–81, Jun. 2012.

[32] A. N. Grigorenko, M. Polini, and K. S. Novoselov,“Graphene plasmonics,”Nature Photonics, vol. 487, pp. 749–758, Nov. 2012.

[33] P. N. Li and T. Taubner, “Broadband subwavelength imaging using a tunable graphene-lens,”ACS Nano., vol. 6, no. 11, pp. 10107–10114, 2012.

[34] B. Sensale-Rodriguez, S. Rafique, R. Yan, M. D. Zhu, V. Protasenko, D. Jena,et al., “Terahertz imaging employing grapheme modulator arrays,”O(jiān)pt. Express., vol. 21, no. 2, pp. 2324–2330, 2013.

Mai-Xia Fuwas born in Henan, China in 1981. She received her B.S. degree from the University of information engineering of PLA of China, Zhengzhou in 2003 and the M.S. degree from the University of Zhengzhou in 2009, both in electronic and information engineering. She is currently pursuing her Ph.D. degree in optical engineering with Capital Normal University. Her research interests include spectrum analysis, signal processing, and information theory.

received his M. S. degree and Ph.D. degree from Harbin Institute of Technology and Institute of Physics, Chinese Academy of Science in 1996 and 1999, respectively. He is now a professor with the Department of Physics, Capital Normal University. He has published more than 150 journal papers. His research interests include optical information processing, surface plasmoic optics, and THz spectroscopy and imaging.

Manuscript received October 25, 2013; revised November 30, 2013. This work was supported by the 973 Program of China under Grant No. 2013CBA01702, the National Natural Science Foundation of China under Grant No. 11204188, 61205097, 91233202, 11374216, and 11174211, the National High Technology Research and Development Program of China under Grant No. 2012AA101608-6, the Beijing Natural Science Foundation under Grant No. KZ201110028035, the Program for New Century Excellent Talents in University under Grant No. NCET-12-0607, and the CAEP THz Science and Technology Foundation.

M.-X. Fu is with Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education and Department of Physics, Capital Normal University, Beijing 100048, China (e-mail: fumaixia@126.com).

Y. Zhang is with Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education and Department of Physics, Capital Normal University, Beijing 100048, China (Corresponding author e-mail: yzhang@mail.cnu.edu.cn).

Color versions of one or more of the figures in this paper are available online at http://www.intl-jest.com.

Digital Object Identifier: 10.3969/j.issn.1674-862X.2013.04.004