Graphene patterns supported terahertz tunable plasmon induced

Vol. 26, No. 8 | 16 Apr 2018 | OPTICS EXPRESS 9931

Graphene patterns supported terahertz tunable plasmon induced transparency XIAOYONG HE,1,2,* FENG LIU,1 FANGTING LIN,1 AND WANGZHOU SHI1 1

Department of Physics, Mathematics & Science College, Shanghai Normal University, No. 100 Guilin Road, Shanghai, 200234, China 2 Shanghai Key Lab for Astrophysics, No. 100 Guilin Road, Shanghai, 200234, China * [email protected]

Abstract: The tunable plasmonic induced transparency has been theoretically investigated based on graphene patterns/SiO2/Si/polymer multilayer structure in the terahertz regime, including the effects of graphene Fermi level, structural parameters and operation frequency. The results manifest that obvious Fano peak can be observed and efficiently modulated because of the strong coupling between incident light and graphene pattern structures. As Fermi level increases, the peak amplitude of Fano resonance increases, and the resonant peak position shifts to high frequency. The amplitude modulation depth of Fano curves is about 40% on condition that the Fermi level changes in the scope of 0.2-1.0 eV. With the distance between cut wire and double semi-circular patterns increases, the peak amplitude and figure of merit increases. The results are very helpful to develop novel graphene plasmonic devices (e.g. sensors, modulators, and antenna) and find potential applications in the fields of biomedical sensing and wireless communications. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (250.5403) Plasmonics; (240.6680) Surface plasmons; (260.3090) Infrared, far; (300.6495) Spectroscopy, terahertz; (310.6628) Subwavelength structures, nanostructures.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013). C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017). W. J. Wan, H. Li, and J. C. Cao, “Homogeneous spectral broadening of pulsed terahertz quantum cascade lasers by radio frequency modulation,” Opt. Express 26(2), 980–989 (2018). S. Zhang, Z. Jin, X. Liu, W. Zhao, X. Lin, C. Jing, and G. Ma, “Photoinduced terahertz radiation and negative conductivity dynamics in Heusler alloy Co2MnSn film,” Opt. Lett. 42(16), 3080–3083 (2017). T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10(6), 371–379 (2016). Z. L. Fu, L. L. Gu, X. G. Guo, Z. Y. Tan, W. J. Wan, T. Zhou, D. X. Shao, R. Zhang, and J. C. Cao, “Frequency up-conversion photon-type terahertz imager,” Sci. Rep. 6(1), 25383 (2016). N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014). N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). C. Argyropoulos, P. Y. Chen, G. D’Aguanno, and A. Alù, “Temporal soliton excitation in an ε-near-zero plasmonic metamaterial,” Opt. Lett. 39(19), 5566–5569 (2014). X. Zheng, W. Smith, J. Jackson, B. Moran, H. Cui, D. Chen, J. Ye, N. Fang, N. Rodriguez, T. Weisgraber, and C. M. Spadaccini, “Multiscale metallic metamaterials,” Nat. Mater. 15(10), 1100–1106 (2016). N. I. Zheludev and E. Plum, “Reconfigurable nanomechanical photonic metamaterials,” Nat. Nanotechnol. 11(1), 16–22 (2016). X. Y. He, “Tunable terahertz graphene metamaterials,” Carbon 82(1), 229–237 (2015). P. Fan, Z. Yu, S. Fan, and M. L. Brongersma, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014). J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014). S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).

#322689 Journal © 2018

https://doi.org/10.1364/OE.26.009931 Received 7 Feb 2018; revised 22 Mar 2018; accepted 25 Mar 2018; published 6 Apr 2018


17. Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, A. K. Azad, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015). 18. P. Fan, Z. Yu, S. Fan, M. L. Brongersma, M. Fleischhauer, T. Pfau, and H. Giessen, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014). 19. Q. Xu, X. Su, C. Ouyang, N. Xu, W. Cao, Y. Zhang, Q. Li, C. Hu, J. Gu, Z. Tian, A. K. Azad, J. Han, and W. Zhang, “Frequency-agile electromagnetically induced transparency analogue in terahertz metamaterials,” Opt. Lett. 41(19), 4562–4565 (2016). 20. M. Manjappa, Y. K. Srivastava, L. Cong, I. Al-Naib, and R. Singh, “Active photo switching of sharp Fano resonances in THz metadevices,” Adv. Mater. 29(3), 1603355 (2017). 21. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). 22. S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. L. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80(15), 153103 (2009). 23. X. Liu, Z. Zhang, X. Lin, K. Zhang, Z. Jin, Z. Cheng, and G. Ma, “Terahertz broadband modulation in a biased BiFeO3/Si heterojunction,” Opt. Express 24(23), 26618–26628 (2016). 24. H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable phonon-induced transparency in bilayer graphene nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014). 25. M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008). 26. F. Shafiei, F. Monticone, K. Q. Le, X. X. Liu, T. Hartsfield, A. Alù, and X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nat. Nanotechnol. 8(2), 95–99 (2013). 27. C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011). 28. H. Y. Zhang, Y. Y. Cao, Y. Z. Liu, Y. Li, and Y. P. Zhang, “Electromagnetically induced transparency based on cascaded pi-shaped graphene nanostructure,” Plasmonics 12(6), 1833–1839 (2017). 29. P. C. Kuan, C. Huang, W. S. Chan, S. Kosen, and S. Y. Lan, “Large Fizeau’s light-dragging effect in a moving electromagnetically induced transparent medium,” Nat. Commun. 7, 13030 (2016). 30. W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013). 31. M. Manjappa, Y. K. Srivastava, L. Cong, I. Al-Naib, and R. Singh, “Active photoswitching of sharp Fano resonances in THz metadevices,” Adv. Mater. 29(3), 1603355 (2017). 32. L. Zhang, P. Tassin, T. Koschny, C. Kurter, S. M. Anlage, and C. M. Soukoulis, “Large group delay in a microwave metamaterial analog of electromagnetically induced transparency,” Appl. Phys. Lett. 97(24), 241904 (2010). 33. O. Limaj, F. Giorgianni, A. D. Gaspare, V. Giliberti, G. de Marzi, P. Roy, M. Ortolani, X. Xi, D. Cunnane, and S. Lupi, “Superconductivity induced transparency in terahertz metamaterials,” ACS Photonics 1(7), 570–575 (2014). 34. D. N. Basov, M. M. Fogler, and F. J. García de Abajo, “Polaritons in van der Waals materials,” Science 354(6309), aag1992 (2016). 35. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012). 36. X. Xing, L. T. Zhao, Z. Y. Zhang, X. K. Liu, K. L. Zhang, Y. Yu, X. Lin, H. Y. Chen, J. Q. Chen, Z. M. Jin, J. H. Xu, and G. H. Ma, “Role of photoinduced exciton in the transient terahertz conductivity of few-layer WS2 laminate,” J. Phys. Chem. C 121(37), 20451–20457 (2017). 37. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). 38. Y. Zhang, T. Li, Q. Chen, H. Zhang, J. F. O’Hara, E. Abele, A. J. Taylor, H. T. Chen, and A. K. Azad, “Independently tunable dual-band perfect absorber based on graphene at mid-infrared frequencies,” Sci. Rep. 5(1), 18463 (2015). 39. C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011). 40. A. Y. Nikitin, P. A. Gonzalez, S. Velez, S. Mastel, A. Centeno, A. Pesquera, A. Zurutuza, F. Casanova, L. E. Hueso, and F. H. L. Koppens, “Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators,” Nat. Photonics 10(4), 239–243 (2016). 41. A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009). 42. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). 43. A. R. Wright and C. Zhang, “Dynamic conductivity of graphene with electron-LO-phonon interaction,” Phys. Rev. B 81(16), 165413 (2010). 44. X. He, Z. Y. Zhao, and W. Shi, “Graphene-supported tunable near-IR metamaterials,” Opt. Lett. 40(2), 178–181 (2015).


45. N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014). 46. W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015). 47. D. A. Smirnova, A. E. Miroshnichenko, Y. S. Kivshar, and A. B. Khanikaev, “Tunable nonlinear graphene metasurfaces,” Phys. Rev. B 92(16), 161406 (2015). 48. Q. Li, L. Cong, R. Singh, N. Xu, W. Cao, X. Zhang, Z. Tian, L. Du, J. Han, and W. Zhang, “Monolayer graphene sensing enabled by the strong Fano-resonant metasurface,” Nanoscale 8(39), 17278–17284 (2016). 49. Z. Y. Tan, T. Zhou, J. C. Cao, and H. C. Liu, “Terahertz imaging with quantum-cascade laser and quantum-well photodetector,” IEEE Photonics Technol. Lett. 25(14), 1344–1346 (2013). 50. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007). 51. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr., L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985). 52. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83(23), 235427 (2011).

1. Introduction In recent years, terahertz (THz) technology has made great advance in the aspects of radiation sources and detectors, which propels its practical applications in the fields of biological samples analysis, THz image, high-speed wireless communication and so on [1–6]. For instance, based on the systems of THz quantum-well photo-detectors integrating with nearinfrared LED, the pixel-less imaging spatial resolution can reach the diffraction limitation and provides a new way to realize the high performance of THz imaging [6]. To the further development of THz technology, there is also a high demand for waveguide devices with fine performance, especially the tunable functional devices. Because of the scarcity of natural materials interacted with THz waves efficiently, the manipulation of THz waves is still a challenging task. Designed by tailoring the characters of unit cell (meta-molecule) [7], the emergence of metamaterials (MMs) may help to surmount this dilemma [8–12]. But due to Ohmic and radiation losses, the performances of meta-materials and surface plasmonic devices suffer from dissipation losses and low quality factor (Q-factor) [13–15]. This problem may also be overcome by Fano resonance, which is named after Italian physicist U. Fano [16–18] and arises from the destructive interference between bright continuum and dark discrete modes [19–21]. Among various Fano resonance phenomena, electromagnetically induced transparency (EIT) is generated in a three level atomic system and gives rise to a narrow transparency window in the spectrum of opaque medium. As a classical analogues of EIT, plasmon induced transparency (PIT) comes from the destructive interference between the bright and dark modes mimicked by metamaterials structures [22–24], where the bright mode exhibits a strong interacted and the dark mode only weakly couples to the incident field, respectively. PIT phenomenon possesses steep dispersion, large nonlinear properties and high spectral sensitivity to local dielectric environment, which is a key research focus and opens a new route in designing novel applicable devices, e.g. in optical filtering, sensing, and integrated functional components [25, 26]. Tunable PIT resonance, the central wavelength varies with external parameters, can find more flexible practical applications and is highly desirable [27– 29]. For current systems, usually the modulation of Fano resonant spectral curves can be realized by utilizing the thermal and electrical control of semiconductor or superconductors substrates, adjusting the geometrical structural parameters [30–33]. For example, by integrating implanted-Si with asymmetric metallic split ring resonator hybrid structure, the large modulation of resonant strength is achieved with the help of optical pump light, and the ultrasensitive Fano resonances can be switched by changing the pump light [31]. Based on the bright mode of high-temperature superconductive closed ring (Yttrium barium copper oxide, YBCO) and the dark mode of metallic split-ring resonators, the thermal controlled PIT curves have been experimentally achieved, manifesting that the transmission resonant peak enhances


and blue shifts with the decrease of temperature [32]. However, there are several important functionality limitations yet to be addressed in semiconductor or superconductor based active MMs devices, e.g. external equipment to provide pump light or changing temperature is needed, which is very inconveniently from the practical viewpoint. To maniputlate Fano resonance with electrical fields is much more preference and urgently required nowadays. Two-dimensional nano-materials are promising choice to fabricate reconfigurable devices, such as black phosphorus [34], MoS2 [35, 36] and graphene [37–40]. With the advantages of large carrier mobility, low cost, and excellent responses to incident waves when it is structurally patterned, and high tunability via gate voltage [41], graphene, a monolayer of hexagonally arranged carbon atoms has attracted increasing attention [42–44]. Much research work has carried out to explore the graphene PIT devices in recent years [45]. For instance, with the help of monolayer graphene, the absorption of Fano resonant asymmetric photonic crystal structure can reach 77% in the visible spectral range, and furthermore if MoS2 is adopted the absorption can reach more than 90% [46]. Based on the hybrid meta-surface of uniform graphene monolayer integrating with asymmetrical metal unit cell, the cascade Fano resonances exhibited in the THz regime, which displays that the tunability of graphene plasmons facilitates strong interaction between the sub-radiant modes, modifying the spectral position and lifetime of Fano resonances [47]. Based on the Fano resonances, Zhang et al. proposed a tunable ultrasensitive THz sensor by integrating a subwavelength graphene disk with metallic ring structures, which manifests that frequency sensitivity is more than 1.90 THz per refractive index unit and the value of figure of merit (FOM) is about 6.5 [17]. Li et al. investigate the strong Fano resonant phenomena in the THz regime on the base of monolayer graphene and asymmetrical metallic MMs structure, which shows that there exists tightly confined electric fields in the gap of Fano resonator, and thin analyte in the range of 10−6 can be detected [48]. The PIT phenomenon in bilayer graphene can be actively controlled by using the electrostatic grating method, and a strong distortion in light dispersion has been observed, the group index of is more than 500 [24]. The convenient manipulation of Fano resonance is highly expected for many applications, which is a significant importance and actively research topics nowadays [5,30]. For instance, representing broader bandwidths and implying high transmission rates of wireless communications (as high as 100 Gbit s−1), THz communications have made fast evolving development [49]. As the basic blocks, efficiently tunable devices, such as amplitude/phase modulators, broadband filters, and phase arrays, are the trend of THz technology [3–6]. While it should be noted that in the present research work the amplitude and frequency modulation of PIT resonances have been realized in the Mid-IR, near-IR and visible spectral ranges [46– 48]. The modulation depth and speed are also not very desirable due to the tunable range of active materials. It is still a tough work to modulate THz Fano resonances conveniently with fixed geometrical parameters or supporting substrate. With strong mode confinement and good tunability, graphene provides a good alternative method to steer the PIT resonant curves. Different from the dielectric properties in the optical and near-IR frequencies [30], graphene behaves strong plasmonic properties since intra-band contribution plays the major role in the THz regime, and its conductivity increases significantly with Fermi level, resulting into the large tunable range of functional devices. Therefore, by depositing cut wire (CW) and double semi-circular (DSC) graphene ribbons on the SiO2/Si/polymer substrate, the tunable Fano resonance has been theoretically investigated, including the effects of graphene Fermi levels, structural parameters, and operation frequency. Compared with the metal-based PIT systems, the major advantages of the proposed graphene patterns PIT devices is that the broad transparency window can be dynamically manipulated, which can operate as an efficient modulators. The results manifest that the Fano spectral curves of the proposed graphene CWDSC can be modulated by altering the Fermi level, the modulation depth of peak amplitude can achieve more than 40%.


2. Research methods

Fig. 1. (a) The side view of the graphene MMs structure,the unit cell structure deposited on the SiO2/Si layers, the thickness of the dielectric layer is 30 nm, the doped Si layer is used to apply the gate voltage. The sol-gel layer deposits on graphene MMs to apply the bias voltage. The substrate is made from the polymer layer with the thickness of 2 μm. Figure 1(b) The top views of geometry and dimensions of graphene MMs unit cell structures. The periodic length along x and y directions are both 160 μm and 120 μm. The length and width of graphene ribbon are 108 μm and 30 μm, respectively.

Figures 1(a) and 1(b) show the side and top views of monolayer graphene CWDSC structure, depositing on the flexible polyimide substrate. The graphene pattern structures integrate with the SiO2/Si layers, the thicknesses of SiO2 and doped Si layers are 10 nm and 5 μm, respectively. The doping concentration of Si layer is 2.0 × 1014 cm−3. The refractive indices of SiO2 and polyimide layer are 1.98 and 1.80, respectively. The electrolyte gating made by the sol-gel ionic layer with the thickness of 0.2 μm situates on the graphene ribbons to apply the bias voltage. The graphene Fermi level can be modulated in a wide range by this sol-gel top gating method [39]. Figure 1(b) displays the top view of CW and DSC graphene ribbon pattern structure. The period lengths along x and y directions are px and py with the values of 160 μm and 120 μm, respectively. The incident waves normally transmit through the MMs structure along z direction. Graphene can be considered as a 2D material and described by a surface conductivity σg, which is related to the operation frequency ω, chemical potential μc, Fermi level Ef, the environmental temperature T, and the relaxation time τ. Under the random phase approximation (RPA), the graphene conductivity can be described as [50]:

σg =

μ  e 2 2k BT  j ln  2 cos h c  2 ω + j /τ π  2k BT   e2 + 2 4

  ω  4ω ∞ G (ξ ) − G ( ω / 2 )  dξ  G  + j 2 π 0   2   ( ω ) − 4ξ 2

G (ξ ) =

sin h (ξ / k BT )

cos h (ξ / k BT ) + cosh ( μc / k BT )

(1)

(2)

where j is the imaginary unit, ω is the operation frequency of incident light, kB is Boltzmann's constant,  is the reduced Planck's constant, μc is the chemical potential (Fermi level Ef), the value of scattering time τ is 0.5 ps. The first and second parts indicate the intra-band and inter-band contributions. The graphene permittivity is expressed as:


εg = 1+ j

σg ωε 0 Δ

(3)

where Δ is the graphene layer thickness with the value of 0.34 nm, ɛ0 is the permittivity of free space. The permittivity of metal in the THz regime can be written as [51]:

ε (ω ) = ε ∞ −

ω p2

ω (ω + iωτ

)

,

(4)

where ωp and ωτ are the plasma and damping frequencies, respectively. The resonance of THz transmission curves can be fitted with the Fano formula as [52]: T = Tbg + T0

( χ + q) 1+ χ 2

2

(5)

where Tbg and T0 are the slowly varying background transmittance and normalized transmission coefficients, q is the phenomenological shape parameter to describe the asymmetrical degree of line shape, i.e. the ratio of discrete resonance to the background resonance, χ = (ω-ωres)/(Γ/2) is the reduced frequency, ωres is the resonant frequency, Γ is the line-width of Fano spectral curves. The value of Q-factor is expressed as: Q=

f res FWHM

(6)

FWHM is the full width at a half maximum (FWHM) of the resonance peak, fres is the resonance frequency. 3. Results and discussion Figure 2(a) shows the transmission spectra of the proposed CWDSC structures. The length and width of graphene ribbon are 108 μm and 30 μm, and the outer and inner radii of the circular ribbons are 32 μm and 16 μm, respectively. The Fermi level is 1.0 eV. The distance between graphene CW and semi-circular ribbon is 15 μm. Evoked by a predominantly dipolar mode, single CW and DSC graphene ribbons manifest obvious transmission dip at the frequencies of 0.8486 THz and 1.405 THz, respectively. When the graphene CW and DSC ribbons put together, the strong interaction between them induces the counter-propagating currents, resulting into an obvious transmission Fano peak. By using the finite integration method, the simulation results have been acquired by using the CST Microwave Studio software. From the obtained S-parameters, the transmission (T(ω)) and reflection curves can be achieved by the formula, T(ω) = |S21|2, R(ω) = |S11|2, A(ω) = 1- T(ω)- R(ω). As shown in Fig. 2(b), a transmission peak situates between double transmission dips, i.e. a typical character of PIT transmission window. For the CWDSC graphene structures, the coupling strength between left and right semi-circular resonators enhances through magnetic field loops and the mirror symmetry of DSC avoids the magnetic dipole of the dark element. Compared with the single graphene CW and DSC patterns, the CWDSC structure gives rise to a slight red shift of low frequency dip and a blue shift of higher frequency. In addition, the effects of Fermi levels on resonant spectral curves can be found in Fig. 2(b).


Fig. 2. (a) Shows the transmission curves of the CW, DSC and CWDSC graphene MMs structures. Figure 2(b) depicts the transmission resonant curves of CWDSC graphene structure at different Fermi levels. Figures 2(c)-2(d) show the graphene permittivity versus frequency at different Fermi levels. The length and width of graphene ribbons are 108 μm and 30 μm, respectively. The period lengths along x and y directions are both 160 μm. The radii of circular graphene ribbon are 32 μm and 16 μm, respectively. The gap distance between graphene ribbon and circular is 15 μm.

The graphene permittivity versus frequency at different Fermi levels is shown in Figs. 2(c)-2(d). As Fermi level increases, the carrier concentration and permittivity increases, graphene layer shows much better plasmonic properties. For example, at 1.0 THz when the Femi levels are 0.3, 0.5, and 1.0 eV, the graphene permittivity are −7.080 × 105 + 7.319 × 105i, −1.766 × 106 + 1.107 × 106i, and −4.472 × 106 + 1.4126 × 106i, respectively. Consequently, the interaction between CW and DSC ribbons increases, and the resonance of graphene ribbon enhances at larger value of Fermi level. For example, when the Fermi levels are 0.3, 0.5, and 1.0 eV, the values of Fano peak amplitude are 0.3578, 0.4989, and 0.6553, respectively. The resonant frequency of PIT shifts upward with the increase of Ef, which results from the decrease of graphene kinetic inductance as the carrier concentration increase at larger Fermi level. The PIT spectral curves also broaden with increasing Fermi levels due to the increasing losses. Compared with conventional metallic system, the transmission curves of graphene CWDSC structure can be manipulated in a wide range. When the Fermi level of graphene layer change in the range of 0.2-1.0 eV, the resonant frequency of Fano curves shift from 0.9151 THz to 0.9816 THz, and the value of transmission peak changes in the scope of 0.3578-0.6553. Correspondingly, the modulation depth (MOD) of frequency is 6.77%, and the modulation depth of peak amplitude is 45.4%. The Q-factor is a good tool to measure the resonant quality of spectral curves, as shown in Eq. (5). As Fermi level increases, the carrier concentration of graphene layer increases, the transmission resonance sharpness reduces, leading into the Q-factor decreasing. For example, when the Fermi levels of graphene layers are 0.3, 0.5 and 1.0 eV, the Q-factors are 4.188, 3.572, and 3.280, respectively.


Fig. 3. The transmission curves of CWDSC graphene ribbon at different Fermi levels. The solid and dashed curves are for the simulation and fitting results. The Fermi levels are 0.3 eV, 0.5 eV, 0.8 eV, and 1.0 eV, respectively. The gap distance between graphene ribbon and circular is 15 μm. The period lengths along x and y directions are both 160 μm. The radii of circular graphene ribbon are 32 μm and 16 μm, respectively. The length and width of graphene ribbons are 108 μm and 30 μm, respectively.

As shown in Fig. 3(a), the fitting curves of Fano resonance obtained from Eq. (4) and matches well with the simulation results in the PIT region. If the Fermi levels are about 0.3, 0.5, 0.8, and 1.0 eV, the values of asymmetrical parameters q are 2.629, 2.931, 3.256 and 3.331, respectively. The value of 1/q determines the departure of spectral curve from Lorentz line shape, which can be used as a measure degree of symmetric resonance. In the limit |q| →∞ the resonance is dominated by the line shape of discrete state (Lorentz resonance), whereas at values close to unity (q ∼1) the discrete state, which means that Fano resonances are most pronounced if two scattering pathways are of similar magnitudes. The absolute value of asymmetry parameter q increases as the coupling between the CW and DSC patterns increases. In addition, the modulation damping parameter b is defined as the ratios of the intrinsic loss to the transferred energy from a bright mode to a dark mode, i.e. b = γ i2 / ( γ i + γ c ) , in which γi and γc are the intrinsic damping and coupling to the 2

radiative loss, respectively. The parameter b is critical for achieving the PIT phenomenon. As Fermi level increases, the damping parameter decreases, when the Fermi level are 0.3, 0.5, 0.8, and 1.0 eV, the values of damping parameters are 0.2840, 0.2117, 0.1177, and 8.545 × 10−2, respectively. The smaller value of b at larger Fermi level means stronger interaction (γc>>γi) happens. The reasons are shown in the following. With the increase of Ef, the carrier concentration and dielectric constant of graphene increases, thus q and Q-factor decrease. But for the case of b, it is much more complex, which is affected by intrinsic losses and the coupling strength. At larger value of Fermi level, the mode coupling between the CW and DSC patters structures enhances the contribution of γc increases, leading to the intrinsic losses reducing and the ratio of coupling and radiative losses become larger.


Fig. 4. (a)-4(c) The transmission, reflection, and absorption of the graphene ribbon unit cell structure versus frequency at different distances. Figure 4(d) The Q-factor and FOM of transmission curve versus distance. The gap distances are 1, 2, 3, 5, 8, 10, 15, and 30 μm, respectively. The Fermi level of the graphene ribbon is 1.0 eV. The length and width of graphene ribbon are 108 μm and 30 μm, respectively. The period lengths along x and y directions are 160 μm and 120 μm. The radii of circular graphene ribbon are 32 μm and 16 μm, respectively.

The influences of different distances on the resonant curves of graphene CWDSC structure have been shown in Fig. 4. The Fermi level is 1.0 eV. The outer and inner radii of double semi-circular graphene ribbons are 32 μm and 16 μm, respectively. It can be found from Fig. 4 that the effects of distance are significant. As the distance increases, the peak amplitude of Fano curve increases, and the resonant peak position manifests blue shift. The resonant interaction improves further at larger gap distance, resulting into the broader transmission lines, as shown in Fig. 4(a). Additionally, Fig. 4(d) shows the Q-factor and FOM of transmission curves. As the distance between graphene CW and DSC increases, the transmission curves also become much broader, resulting into the value of Q-factor reducing, and the peak value of Fano resonance increasing. In order to quantize the trade-off between Q-factor and resonant strength, FOM has been defined as: FOM = Q × A, A is the peak amplitude of Fano curves. It can be found from Fig. 4(d) that as the distance increases, the value of FOM increases. When the distance is more than 10 μm, the value of FOM reaches a relatively saturated value about 2. The fitting curves obtained from Eq. (4) agree with the simulation results well. If the gap distances are 5, 10, 15, and 20 μm, the values of asymmetry q parameters are 3.022, 3.141, 3.355 and 3.602, respectively. This means that the asymmetry q parameter increases with gap distance, indicating that the PIT phenomenon deteriorates at larger distance.


Fig. 5. (a)-(c) Show the transmission, reflection, and absorption curves of the graphene-metal hybrid ribbon unit cell structure at different Fermi levels. Figure 5(d) The Q-factor and FOM of the graphene ribbon versus Fermi levels. The length and width of graphene ribbon are 108 μm and 30 μm, respectively. The period lengths along x and y directions are both 160 μm. The radii of circular graphene ribbon are 32 μm and 16 μm, respectively. The gap distance between graphene ribbon and circular is 15 μm.

To compare with the graphene CWDSC structure, the resonant curves of metal-graphene hybrid structure have also been shown in Fig. 5. The dispersion properties of metal permittivity have been taken into account and obtained from Eq. (4). The influence of Fermi level on transmission curves can be found in Fig. 5(a). As Fermi level increases, the Fano resonance becomes stronger. When the Fermi level changes in the range of 0.2-1.0 eV, the value of transmission peak varies in the scope of 0.6248-0.7368 and correspondingly the modulation depth of peak amplitude is 15.2%. Compared with graphene CWDSC structure, the tunable range of metal-graphene hybrid structure is roughly small. This can be explained by the fact that the graphene conductivity changes with Fermi level, resulting into resonant dip decreasing, as shown in Fig. 5(a). While for the high frequency dip resulting from the resonance of metal meta-surface, it changes little. For instance, when the Fermi level varies in the range of 0.2-1.0 eV, the value of resonant frequency of CW can be manipulated from 0.6719 THz to 0.7992 THz, and the value of transmission peak varies in the scope of 0.35590.0393. Correspondingly, the modulation depth of frequency is 15.93%, and the modulation depth of peak amplitude is 88.95%. In addition, the influence of Ef on reflection and absorption curves can also be shown in Figs. 5(c) and 5(d), respectively. Compared with transmission spectra, the reflection and absorption curves become very sharper. In addition, as Fermi level increases, the conductivity of graphene ribbon increases, leading to the reflection peak increasing at low frequency. For instance, when the Fermi level changes in the range of 0.2-1.0 eV, the value of resonant frequency of CW can be modulated from 0.5978 THz to 0.7745 THz, and the value of transmission peak changes in the scope of 0.21170.6650. Correspondingly, the modulation depth of frequency is 22.81%, and the MOD of reflection peak amplitude is 68.17%. As for the case of absorption curves, due to the coupling between graphene CW and metal DSC increases, the transmission and reflection curves increase with Fermi level, resulting into the value of absorption reducing, as shown in Fig. 6(c). This can also be confirmed by the damping parameter b from the fitting Eq. (4). For


example, when the Fermi levels are 0.3, 0.5, 0.8, and 1.0 eV, the value of b are 6.990 × 10−2, 5.237 × 10−2, 4.447 × 10−2, and 4.249 × 10−2, respectively. The Q-factor and FOM can be found in Fig. 6(d). As Fermi level increases, the amplitude of Fano resonance increases, the value of FOM increases.

Fig. 6. (a)-(c) Show the transmission, reflection, and absorption curves of the graphene CWDSC patter structures at different period number. The inset in Fig. 6(b) shows the sketch of stacked graphene-dielectrics super-lattice structure in the active region. Figure 6(d) The Qfactor and FOM of the graphene ribbon versus different number. The length and width of graphene ribbon are 108 μm and 30 μm, respectively. The period lengths along x and y directions are both 160 μm. The radii of circular graphene ribbons are 32 μm and 16 μm, respectively.

To improve the tunable properties of the proposed graphene CWDSC structure, the stacked graphene-dielectrics structure have been adopted in the active region, consisting of graphene patterns separated by dielectric spacer layer (Al2O3) along propagation direction, as shown in Fig. 6(a). The Fermi level is 0.3 eV. The polarization is along y direction. The influences of stack number on transmission curves can be found in Fig. 6(a). As the period number increases, the conductive property of active region increases, the resonant strength becomes stronger. Consequently, the peak value of transmission curve increases. As the periodic stack number increases, the carrier concentration increases, and the kinetic inductance reduces, and the peak position moves to higher frequency. For example, if the periodic numbers are 1, 2, 5, and 10, the peak values are 0.6553, 0.6967, 0.7282 and 0.7420, and peak resonance frequencies are 09816 THz, 1.0006 THz, 1.0006 THz and 1.0006 THz, respectively. Correspondingly, the values of Q-factors are 3.280, 3.172, 3.153, and 3.135, respectively. But it should be noted that if the periodic number is large, e.g. >5, the influences of stack number on transmission curves are not obvious. In addition, when the Fermi level changes in the range of 0.3-1.0 eV, if the period number are 3, 5 and 10, the peak value of Fano resonance modulates in the scope of 0.3468-0.7130, 0.4275-0.7282, 0.5459-0.7420, and the peak position can be modulated in the range of 0.9322-0.9968, 0.9721-1.0006, 0.9931.0006, respectively. The corresponding modulation depths of amplitude are 51.36%, 41.29%, 26.43%, and the frequency MOD is 6.48%, 2.85%, and 0.76%, respectively. Figure


6(b) illustrates that the reflection curve becomes stronger with the increase of period number; the dip position manifests blue shift. If the stack periodic numbers are 2, 5, and 10, the peak values are 0.19759, 0.02598, and 0.02311, respectively. When the period number is more than 5, the dip value of reflection curve is nearly zero. As the period number increases, the graphene stack multilayer structure displays better conductive properties, the transmission and reflection curves become stronger, resulting into the absorption curves decreasing as well, as shown in the Fig. 6(c). Furthermore, compared with transmission and reflection curves, the absorption curves are much sharper. The influence of period number on the Q-factor and FOM has been shown in Fig. 6(d). As period number increases, the value of Q-factor increases, but due to the amplitude of Fano resonance increases, the FOM increases.

Fig. 7. Shows the surface current density and magnetic fields of Hz for the graphene CWDSC structures. The according resonant frequencies are 0.7935, 0.9816, and 1.5022 THz. The polarization direction of incident light is along y direction. The Fermi level of graphene is 1.0 eV. The length and width of graphene ribbons are 108 μm and 30 μm, respectively. The period lengths along x and y directions are both 160 μm. The radii of circular graphene ribbon are 32 μm and 16 μm, respectively. The gap distance between graphene ribbon and circular is 15 μm.

The 2D field plot is a good means to comprehend the mechanisms of Fano spectral curves. Figure 7 shows that the surface current density and magnetic components for the graphene CWDSC structure. The polarization direction is along y direction. The graphene Fermi level is 1.0 eV. The resonant frequencies are 0.7935 THz, 0.9816 THz, and 1.502 THz, respectively. At the low frequency of 0.7935 THz, the electric dipolar mode of CW stripe is excited and behaves the bright mode, which can be found from Fig. 7(a) that the surface current distributions are much stronger than that in the DSC. While at the frequency of 1.502 THz, the dark modes in the DSC have been excited, the surface current distributions are obvious and flow in opposite directions. At the Fano frequency of 0.9816 THz, the energy transfer from the CW to the DSC patters, resulting into the transmission peak in Fig. 2. But due to the thin thickness of graphene layer, the bright mode in CW is not completed suppressed.


Fig. 8. The surface current density and magnetic fields of Hz for the graphene ring structures. The according resonant frequencies are 0.9152, 0.9569, and 0.9816 THz. The polarization direction of the incident light is along y direction. The Fermi levels of graphene are 0.3, 0.5, and 1.0 eV, respectively. The length and width of graphene ribbons are 108 μm and 30 μm, respectively. The period lengths along x and y directions are both 160 μm. The radii of circular graphene ribbon are 32 μm and 16 μm, respectively. The gap distance between graphene ribbon and circular is 15 μm.

Figure 8 manifests that the surface current density and magnetic components for the graphene CWDSC structure at different Fermi levels. The polarization direction is along y direction. The graphene Fermi levels are 0.3, 0.5, and 1.0 eV. The resonant Fano frequencies are 0.9152 THz, 0.9596 THz, and 0.9816 THz, respectively. It can be found from Fig. 8 that the currents in the left and right semi-circular ribbons are in anti-clockwise and clockwise, respectively. They are the symmetric hybridization of magnetic dipole resonances. At resonant frequencies both the CW and DSC graphene patterns structure have been excited. The induced currents oscillate with the same amplitude and phase, resulting into an electromagnetically trapped mode. The destructive interference of scattered fields between graphene CW and DSC leads to obvious transparency peak window. In addition, as Fermi level increases, the magnetic fields increases, which means that the resonant strength increase with the Fermi level, this is accords with the Fano amplitude in Fig. 2(a). For instance, when the Fermi levels are 0.3, 0.5, and 1.0 eV, the values of Hz are 3388, 5250, and 6938 A/m, respectively. 4. Conclusion Based on the graphene CWDSC patterns structure, the tunable Fano phenomenon are investigated in the THz regime, including the influences of Fermi levels of graphene layer, operation frequency, and structural parameters. The results manifest that the obvious Fano peak can be observed and efficient modulated because of the strong coupling between graphene CW and DSC ribbons structures. As the Fermi level of graphene layer increases, the peak amplitude of Fano curve increases, and the resonant position shifts to high frequency. If Fermi level changes in the range of 0.2-1.0 eV, the frequency modulation depth of Fano resonant curves can reach more than 10%, and the amplitude MOD is about 45%. In addition, as the distance between graphene CW and DSC structure increases, the peak amplitude and FOM of Fano resonance increases, but the Q-factor of Fano curves decreases. The results are


very helpful to understand the tunable mechanisms of graphene based Fano systems and design high sensitivity functional devices, e.g. sensors, modulators, and antenna. Funding National Natural Science Foundation of China (Grant Nos. 61674106 and U1531109); Shanghai Pujiang Program (Grant Nos. 15PJ1406500); Natural Science Foundation of Shanghai (Grant No. 16ZR1424300).