Abstract

Dual plasmon-induced transparency (PIT) and plasmon-induced absorption (PIA) are simultaneously achieved in an integrated metamaterial composed of single layer of graphene. Electric field distribution and coupled mode theory (CMT) are used to demonstrate the physical mechanism of dual PIT and PIA, and the theoretical result of CMT is highly consistent with the finite-difference time-domain (FDTD) method simulation result. Further research shows that both the dual PIT and PIA phenomenon can be effectively modulated by the Fermi level, the carrier mobility of the graphene and the refractive index of the surrounding environment. It is meaningful that the absorption of the dual PIA spectrum can be abruptly increased to 93.5% when the carrier mobility of graphene is 0.8m2/Vs. In addition, the group index can be as high as 328. Thus, our work can pave new way for developing excellent slow-light and light absorption functional devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Electromagnetically induced transparency (EIT) is a quantum interference effect in the atomic system, which is produced by the interaction between the atomic layer and the external light field [1]. In general, the EIT effect can significantly slow the light velocity through the medium and thus has significant applications in the slow-light field [2]. Of course, it also has great application value in nonlinear optics [3] and biochemical sensing [4]. However, EIT is hindered by difficult experimental conditions in practical applications, such as very low experimental temperatures and stable gas lasers [5]. Therefore, plasmon-induced transparent (PIT) and plasmon-induced absorption (PIA) emerge as the times require, which are a phenomenon that is superimposed by interference between a broad-band bright mode and a narrow-band dark mode in metamaterials [6,7]. The bright mode and the excitation light field have a strong coupling, yet the dark mode can only be excited by the localized field which is formed by the coupling of the bright mode and the excitation light field. The PIT and PIA phenomena have potential value in many fields due to anomalous dispersion and narrower transparent peaks, such as light absorbers [8], light switch [9], optical filters [10] and optical sensors [11].

So far, many plasmonic devices have been proposed, and metal-dielectric-metal (MDM) plasmonic waveguides stand out due to support the acceptable length and high order wavelengths for surface plasmon polaritions (SPPs). Moreover, the coupling of MDM waveguides with double U-cavity [12], double-circular resonators and multi-ring resonators [13] have potential applications in the field of slow-light. However, the group index of the slow-light effect is only a few tens at most of these plasmonic waveguides. Moreover, it is hard to modulate the slow-light effect at a specific wavelength. Later, graphene composed of a single layer of carbon atoms as a novel two-dimensional material has been widely concerned by researchers because it can also support the propagation of SPPs in the terahertz and infrared band [14]. In addition, graphene has the advantages of dynamic adjustability, strong locality and low loss. Most importantly, the conductivity of graphene can be modulated by Fermi level or chemical potential, which has unparalleled advantages over other metamaterials. Therefore, it has important application in slow-light device [15,16], modulator [17], absorber [18], photon detector [19] and sensor [20]. However, many devices of light-graphene coupling can only realize one function, and multi-function graphene-based devices are rarely reported.

In our paper, a dynamically tunable plasmon-induced slow-light and light absorption multi-functional graphene-based metamaterial is proposed because the dual PIT and PIA phenomena, which are explained in detail by electric field distribution, electromagnetically induced transparency (EIT) and coupled mode theory (CMT). The slow-light and absorption effects can be effectively modulated by changing the Fermi level, the carrier mobility of the graphene and the surrounding medium environment. Generally, the proposed structure also has such merits. Firstly, the proposed structure base on a single-layer patterned graphene array, which is simpler than other two-layer [21], three-layer [22], and four-layer [20] graphene structures. Secondly, its slow-light characteristics are outstanding, and the group index can be as high as 328. Finally, the absorption rate can be as high as 93.5%, which shows excellent absorption property comparing with other single-layer graphene-based absorbers [21,23]. Based on the above advantages, our proposed structure opens a new door for achieving excellent slow-light and absorption multi-function metamaterial.

2. Structural design and theoretical analysis

Slow-light and light absorption integrated metamaterial is shown in Fig. 1(a). Each patterned graphene unit composed of four graphene blocks and three graphene ribbons is on the top of silicon substrate, and its top view is shown in Fig. 1(b). The specific structural parameters are given in the caption of Fig. 1, where l1, l2, l3, l4, l5 are no longer changed in this paper. A linear polarized plane wave is incident perpendicularly along the positive direction of the z-axis.

 

Fig. 1 (a) Schematic diagram of slow-light and light absorption integrated periodic metamaterials. Patterned periodic single-layer planar graphene is sandwiched in dielectric silicon, and the thickness of the upper medium and the lower substrate are 0.1μm and 0.25μm, respectively. (b) Top view of structural unit in metamaterial, and geometric parameters:l1 = 3.2µm, l2 = 0.5µm, l3 = 0.3µm, l4 = 1.5µm, l5 = 0.5µm, l6 = 0.5µm, L = 4µm.

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In this system, the temperature is T = 300K, and the conductivity of the monolayer graphene can be obtained by the Kubo formula. Since the direct interband electronic transitions are negligible in the terahertz frequency range, the main contribution comes from intraband electron photon scattering, whose expression can be expressed as [24]:

σg=ie2Efπ(ω+iτ1),
where e,Ef,ħ and ω represent the electron charge, the Fermi level of graphene, the Planck constant and the angular frequency of the incident light, respectively. Through the literature, we know that the Fermi level of graphene can be adjusted from 0.2eV to 1.2eV, using a gate voltage [25].The carrier relaxation time is τ = μEf / (evF2) [26], where vF = 106m/s and μ = 1m2/(V·s) are Fermi level of graphene and the carrier mobility of graphene, respectively. In addition, since the medium environment around the graphene is silicon, the propagation constant of the SPPs on the surface of the graphene is β = k0si – (2εsi / σgŋ0)2)1/2 [27,28]. Where k0, εsi, ŋ0 are the wave vector of the incident light, the dielectric constant of silicon and the inherent impedance, respectively. At the same time, effective refractive index can also be obtained as: neff = β / k0.

To demonstrate the physical mechanism of dual PIT and PIA clearly, we firstly investigate four metamaterials, as shown in Figs. 2(c)-2(f).The transmission and absorption spectra of the four metamaterials are shown in Figs. 2(a) and 2(b). For convenience of explanation, we have named the dips and peaks in the transmission spectrum of the whole structure from left to right as “dip1”, “peak1”, “dip2”, “peak2”, “dip3”. The black dual PIT line is generated by the metamaterial array of the whole structure in Fig. 2(c), which is composed of the monopole antenna, the quadrupole antenna and the octopole antenna, as shown in Figs. 2(d)-2(f). In general, patterned periodic graphene arrays can well support localized surface plasmons (LSPs). When a linearly polarized plane wave is incident, the monopole antenna is not directly excited due to the absence of electric fields component along the direction of the central axis of the monopole antenna, as indicated by the light blue line. However, the quadrupole antenna and the octopole antenna undergo LSPs resonance by the incident light field, and the classic Lorentz lines are formed at the position of f1 = 2.354THz and f2 = 4.038THz, respectively, as shown by the blue and red lines. In our proposed structure, the monopole antenna can’t be directly excited as a dark mode, while the quadrupole antenna and the octapole antenna are directly excited as two bright modes, and the destructive interference between the three modes forms a strong dual PIT effect and PIA effect, resulting in transparent windows at f3 = 2.093THz, f4 = 3.105THz, f5 = 4.188THz, respectively, wherein the coefficient of absorption transparent window is up to 48%.

 

Fig. 2 (a-b) Transmission and absorption spectra of slow-light and absorption integrated metamaterials, and Fermi level is set as 1.0eV. (c-f) Four metamaterial arrays, wherein graphene in (c) with the whole structure, four blocks graphene in (d) are monopole antenna, graphene ribbons in (e) are quadrupole antenna, and the two graphene ribbons in (f) are octapole antenna.

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In order to better analyze the dual PIT (PIA) phenomenon, we plot the electric field distributions at the resonance frequencies of the quadrupole antenna, the octapole antenna and the whole structure in the y direction, as shown in Fig. 3. Figure 3(a) shows very clearly that there are a pair of dipoles on the upper and lower sides of the graphene ribbon, and the charge polarity is opposite, which is the reason that we call it a quadrupole antenna (the same as the octapole antenna). In Fig. 3(b), the charge intensity of the dipole pair on the adjacent side is smaller than the outer side due to the coupling between the graphene pair. In the field distribution of the whole structure, Figs. 3(c)-3(e) clearly shows the monopole antenna is indirectly excited as a dark mode by two bright modes. The formation mechanism of dip1 is mainly the interaction between monopole antenna and quadrupole antenna, the formation mechanism of dip3 is mainly the interaction between monopole antenna and octupole antenna, and dip2 is caused by the interaction of three modes. Because the resonance dips of the two bright modes are basically the same, the resonance dips of the two single PITs obtained by their interaction with the dark mode are also basically the same. However, after the two single PITs are formed, the adjacent dips are superimposed to form dip2, and the two outer dips are keep the same as dip1 and dip3. The electric field distributions of dip1 and dip3 are basically the same, and the electric field distribution of dip2 also shows the interaction between the three modes, which is in perfect agreement with the above discussion.

 

Fig. 3 (a) The electric field distribution of the quadrupole antenna at f1 = 2.354THz. (b) The electric field distribution of the octupole antenna at f2 = 4.038THz. (c-e) Electric field distribution of dip1 (f3 = 2.093THz), dip2 (f4 = 3.105THz), dip3 (f5 = 4.188THz) for different resonance frequencies in the whole structure. These field distributions are all in the y direction.

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Then, the dual PIT (PIA) phenomenon can also be explained from the perspective of EIT. The three modes are assumed to be three photon states, and schematic diagram of their relationship to the Λ-shaped PIT [29] is shown in Fig. 4(a). The light source corresponds to the ground state, and the quadropole antenna and the octupole antenna can be directly excited by the light source to serve as the first excited state |2 and |3. However, the monopole antenna cannot be directly excited by light source but can be indirectly excited by the first excited state as the second excited state |1.There is a coupling field ΩC between |1 and |2, there is a detection field ΩP between |1 and |3, and the interference effect between the two fields produces a PIT (PIA) window.

 

Fig. 4 (a) Schematic diagram of a Λ-shaped PIT. (b) Schematic diagram of coupled mode theory.

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Finally, CMT [30,31] are used to analyze and calculate the dual PIT and PIA phenomena. A diagram of the CMT is shown in Fig. 4(b), where A, B, and C are three imaginary resonators respectively corresponding to one dark mode and two bright modes, whose composite amplitudes are denoted by a, b, c, respectively. A±in/out,B±in/out,C±in/out represent input or output waves propagating toward the positive or negative direction of the resonator, respectively. Moreover, μnm, γin, γon (n ≠ m, n = 1, 2, 3, m = 1, 2, 3) represent the coupling coefficients between the three resonators and their internal and external loss coefficients. The relationship between the three resonators is easily obtained [16]:

(γ1iμ12iμ13iμ21γ2iμ23iμ31iμ32γ3)(abc)=(γo11/2000γo21/2000γo31/2)(A+in+AinB+in+BinC+in+Cin),
where γn = iω − iωn − γin − γon. When a beam of light is emitted from A and finally from C, we can use energy conservation to get the relationship between them:
B+in=A+outeiφ1,Ain=Bouteiφ1,
C+in=B+outeiφ2,Bin=Couteiφ2,
A+out=A+inγo11/2a,Aout=Ainγo11/2a,
B+out=B+inγo21/2b,Bout=Binγo21/2b,
C+out=C+inγo31/2c,Cout=Cinγo31/2c,
where φ1 and φ2 refer to the phase difference of plasmonic wave between A and B, B and C, respectively. Since the three resonators are in the same plane, the phase difference between them is zero. Therefore, we can use the above relationship to get the transmission coefficient and reflection coefficient of the whole system:
t=C+outA+in=1γo11/2D1γo21/2D2γo31/2D3,
r=(γo1)1/2D1(γo2)1/2D2(γo3)1/2D3,
here,

D1=(γ2γ3γ23γ32)γo11/2+(γ12γ3+γ13γ32)γo21/2+(γ12γ23+γ13γ2)γo31/2γ1γ23γ32γ1γ2γ3+γ12γ21γ3+γ12γ23γ31+γ13γ21γ32+γ13γ2γ31,
D2=(γ21γ33+γ23γ31)γo11/2+(γ1γ3γ13γ31)γo21/2+(γ1γ23+γ13γ21)γo31/2γ1γ23γ32γ1γ2γ3+γ12γ21γ3+γ12γ23γ31+γ13γ21γ32+γ13γ2γ31,
D3=(γ21γ32+γ2γ31)γo11/2+(γ1γ32+γ12γ31)γo21/2+(γ1γ2γ12γ21)γo31/2γ1γ23γ32γ1γ2γ3+γ12γ21γ3+γ12γ23γ31+γ13γ21γ32+γ13γ2γ31,
γ12=iμ12+(γo1γo2)1/2,γ13=iμ13+(γo1γo3)1/2,γ21=iμ21+(γo1γo2)1/2,
γ23=iμ23+(γo2γo3)1/2,γ31=iμ31+(γo1γo3)1/2,γ32=iμ32+(γo2γo3)1/2,

Finally, we can use the CMT to obtain the transmittance of the dual PIT: T = t2, and the absorbance of the dual PIA: A = 1 − t2r2.

3. Regulation and discussion

Numerical simulations of dual PIT and PIA phenomena are shown in the blue solid line of Fig. 5, both the transmission and absorption spectra exhibit obvious blue-shift as the Fermi level increases from 0.9eV to 1.2eV. We also get results of the CMT theoretical calculation by coupling model formulas introduced earlier, as shown by the red dotted line in Fig. 5. As a result, the theoretical calculation of CMT is highly consistent with the finite-difference time-domain (FDTD) numerical simulation. The relationships between the resonant dips and peaks versus frequency at different Fermi levels are plotted in Fig. 6(a), which show a good linear relationship. Figure 6(b) shows the relationship between the internal loss quality factor and frequencies at different Fermi levels in the whole system, which can be obtained by: Qin = Re(neff) / Im(neff) [32]. Then, the quality factors of the transmission dips in the dual PIT line and the quality factors of the absorption peaks in the dual PIA line at different Fermi levels are shown in Figs. 6(c) and 6(d). In addition, the transmission and absorption evolution between Fermi levels and frequency are plotted in Figs. 6(e) and 6(f), and we can see the blue-shift of dual PIT and PIA lines and the approximate range of transmission and absorption coefficients as the increases of Fermi level.

 

Fig. 5 (a-d) and (e-i) are transmission and absorption spectra of FDTD numerical simulation and CMT theoretical calculation at different Fermi levels, respectively.

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Fig. 6 (a) Resonance dips and peaks versus frequency in transmission and absorption spectra. (b) Diagram of loss quality factor and frequency at different Fermi levels. (c-d) Quality factors of transmission dips and absorption peaks at different Fermi levels. (e-f) Evolution of transmission and absorbance among different Fermi levels and frequencies.

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The evolution of dual PIT and PIA are further explored by increasing the length l6 of monopole antenna from 0.20μm to 0.50μm with increments 0.06μm. Figures 7(a) and 7(b) show how the transmission (absorption) spectra evolve from a single PIT (PIA) to a dual PIT (PIA) as increases of l6. Interestingly, the first resonant dip (peak) of the dual PIT (PIA) is almost unchanged; however, the third resonant dip (peak) is changed rapidly with the decrease (increase). The above results highlight the importance of dark mode from the side-coupled, which has the greatest influence on the third resonance dip (peak) of dual PIT (PIA).

 

Fig. 7 (a-b) Evolution of dual PIT and PIA, and Fermi level is 1.0eV.

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The refractive index of the surrounding media and the carrier mobility of graphene are changed in order to achieve the purpose of effectively regulating the dual PIT and PIA phenomenon, the results are shown in Fig. 8. When only the refractive index of the medium around graphene increases from 2.92 to 3.52, the dual PIT (PIA) spectra are monotonically red-shifted. However, both the transmittance and reflectance of the proposed metamaterial are very low when only the carrier mobility of graphene is increased from 0.6m2/Vs to 0.8m2/Vs, so the absorption of the dual PIA line can suddenly increase to 93.5%. Therefore, we can fix the carrier mobility of graphene as μ = 0.8m2/Vs, and then change the surrounding medium environment to effectively modulate the absorption with excellent performance.

 

Fig. 8 (a-b) Evolution of dual PIT and PIA in different media environments. (c-d) Evolution of dual PIT and PIA at different carrier mobility. Here, Fermi level is 1.0eV.

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Slow-light effect is an important area in the application of PIT, so we analyzed the slow-light characteristics of the proposed metamaterial. In general, the slow-light effect is determined by the group index, the larger the group index, the better the slow-light characteristics. It can be obtained by: ng = c · dk / = c · dθ / (l · dω) [33], Where c, k, l are the light velocity, the wave vector in vacuum and the thickness of the substrate silicon, respectively, and transmission phase shift is θ = arg(t). Therefore, we plot the group index and phase shift at transparent windows from 0.9eV to 1.2eV in Fig. 9, the max group index of the metamaterials increases with increasing of the Fermi level. When the Fermi level is 1.2eV, the group index can be as high as 328, which is better than most of the slow-light equipment. Since the sharp change in the phase shift at the transmission dip (absorption peak), the group index drops sharply. Thence, large group index is produced around the transmission dip (absorption peak), which is caused by strong dispersion. Therefore, we can effectively modulate the dual PIT (PIA) phenomenon to seek the desired slow-light effect.

 

Fig. 9 (a-d) Group index and phase shifts of the proposed metamaterials at different Fermi levels.

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4. Conclusions

In summary, the dual PIT and PIA phenomena are numerically simulated and theoretically studied based on monolayer of periodically patterned graphene-based metamaterials, and the results of FDTD numerical simulation is highly consistent with CMT theoretical calculations. Dual PIT and PIA phenomena can be effectively modulated by the Fermi level, the carrier mobility of the graphene and the refractive index of the surrounding environment, which have potential applications in modulators. Interestingly, the absorption can be as high as 93.5% by changing the carrier mobility of graphene, which opens a new door for monolayer graphene to achieve excellent absorbers. In addition, the slow-light characteristics of the proposed structure are very outstanding, and the group index is as high as 328. Therefore, our work can pave new way for developing excellent slow-light and light absorption functional devices.

Funding

The National Natural Science Foundation of China (No. 11847026, 61764005 and 11804093); The Scientific Project of Jiangxi Education Department of China (No. GJJ160532); The Graduate Education Reform Project of Jiangxi Province of China (No. JXYJG-2017-080); The authors thank Professor Jicheng Zhao and Mary Anna Wildermuth of Ohio State University for discussions and revision of this paper.

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References

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  1. K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
    [Crossref] [PubMed]
  2. G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
    [Crossref] [PubMed]
  3. S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
    [Crossref] [PubMed]
  4. C. Sui, B. Han, T. Lang, X. Li, X. Jing, and Z. Hong, “Electromagnetically Induced Transparency in an All-Dielectric Metamaterial-Waveguide With Large Group Index,” IEEE P. J. 9(5), 1–8 (2017).
    [Crossref]
  5. L. Qi, Z. Xiang, L. L. Wang, B. X. Wang, G. D. Liu, and S. X. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” Epl 111(2015), 34004 (2015).
  6. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
    [Crossref] [PubMed]
  7. S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of Electromagnetically Induced Transparency in a Terahertz Metamaterial,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 153103 (2009).
    [Crossref]
  8. X. Luo, X. Zhai, L. Wang, and Q. Lin, “Enhanced dual-band absorption of molybdenum disulfide using a plasmonic perfect absorber,” Opt. Express 26(9), 11658–11666 (2018).
    [Crossref] [PubMed]
  9. A. Haddadpour, V. F. Nezhad, Z. Yu, and G. Veronis, “Highly compact magneto-optical switches for metal-dielectric-metal plasmonic waveguides,” Opt. Lett. 41(18), 4340–4343 (2016).
    [Crossref] [PubMed]
  10. Z. Q. Chen, H. J. Li, B. X. Li, Z. H. He, H. Xu, M. F. Zheng, and M. Z. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
    [Crossref]
  11. Z. He, H. Li, B. Li, Z. Chen, H. Xu, and M. Zheng, “Theoretical analysis of ultrahigh figure of merit sensing in plasmonic waveguides with a multimode stub,” Opt. Lett. 41(22), 5206–5209 (2016).
    [Crossref] [PubMed]
  12. S. P. Zhan, D. Kong, G. T. Cao, Z. H. He, Y. Wang, G. J. Xu, and H. J. Li, “Analogy of plasmon induced transparency in detuned U-resonators coupling to MDM plasmonic waveguide,” Solid State Commun. 174(11), 50–54 (2013).
    [Crossref]
  13. S. P. Zhan, H. J. Li, G. T. Cao, Z. H. He, B. X. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
    [Crossref]
  14. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
  15. H. Xu, M. Z. Zhao, M. F. Zheng, C. X. Xiong, B. H. Zhang, Y. Y. Peng, and H. J. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D Appl. Phys. 52(2), 025104 (2019).
    [Crossref]
  16. B. Zhang, H. Li, H. Xu, M. Zhao, C. Xiong, C. Liu, and K. Wu, “Absorption and slow-light analysis based on tunable plasmon-induced transparency in patterned graphene metamaterial,” Opt. Express 27(3), 3598–3608 (2019).
    [Crossref] [PubMed]
  17. H. Xu, C. X. Xiong, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, B. H. Zhang, and H. J. Li, “Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial,” J. Opt. Soc. Am. B 35(6), 1463 (2018).
    [Crossref]
  18. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B Condens. Matter Mater. Phys. 85(8), 081405 (2012).
    [Crossref]
  19. J. Hafner, “Imaging Art and Facts,” ACS Nano 10(7), 6417–6419 (2016).
    [Crossref] [PubMed]
  20. H. Xu, M. Z. Zhao, Z. Q. Chen, M. F. Zheng, C. X. Xiong, B. H. Zhang, and H. J. Li, “Sensing analysis based on tunable Fano resonance in terahertz graphene-layered metamaterials,” J. Appl. Phys. 123(20), 203103 (2018).
    [Crossref]
  21. H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
    [Crossref]
  22. H. Xu, H. Li, Z. He, Z. Chen, M. Zheng, and M. Zhao, “Dual tunable plasmon-induced transparency based on silicon-air grating coupled graphene structure in terahertz metamaterial,” Opt. Express 25(17), 20780–20790 (2017).
    [Crossref] [PubMed]
  23. T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
    [Crossref]
  24. N. Rouhi, S. Capdevila, D. Jain, K. Zand, Y. Y. Wang, E. Brown, L. Jofre, and P. Burke, “Terahertz graphene optics,” Nano Res. 5(10), 667–678 (2012).
    [Crossref]
  25. S. Balci, O. Balci, N. Kakenov, F. B. Atar, and C. Kocabas, “Dynamic tuning of plasmon resonance in the visible using graphene,” Opt. Lett. 41(6), 1241–1244 (2016).
    [Crossref] [PubMed]
  26. H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
    [Crossref]
  27. H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
    [Crossref]
  28. C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 85(12), 125431 (2012).
    [Crossref]
  29. Z. H. He, X. C. Ren, S. M. Bai, H. J. Li, D. M. Cao, and G. Li, “Λ-Type and V-Type plasmon-induced transparency in plasmonic waveguide systems,” Plasmonics 13(6), 2255 (2018).
    [Crossref]
  30. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
    [Crossref]
  31. K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
    [Crossref] [PubMed]
  32. X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
    [Crossref] [PubMed]
  33. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B Condens. Matter Mater. Phys. 80(19), 195415 (2009).
    [Crossref]

2019 (2)

H. Xu, M. Z. Zhao, M. F. Zheng, C. X. Xiong, B. H. Zhang, Y. Y. Peng, and H. J. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D Appl. Phys. 52(2), 025104 (2019).
[Crossref]

B. Zhang, H. Li, H. Xu, M. Zhao, C. Xiong, C. Liu, and K. Wu, “Absorption and slow-light analysis based on tunable plasmon-induced transparency in patterned graphene metamaterial,” Opt. Express 27(3), 3598–3608 (2019).
[Crossref] [PubMed]

2018 (6)

H. Xu, C. X. Xiong, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, B. H. Zhang, and H. J. Li, “Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial,” J. Opt. Soc. Am. B 35(6), 1463 (2018).
[Crossref]

X. Luo, X. Zhai, L. Wang, and Q. Lin, “Enhanced dual-band absorption of molybdenum disulfide using a plasmonic perfect absorber,” Opt. Express 26(9), 11658–11666 (2018).
[Crossref] [PubMed]

H. Xu, M. Z. Zhao, Z. Q. Chen, M. F. Zheng, C. X. Xiong, B. H. Zhang, and H. J. Li, “Sensing analysis based on tunable Fano resonance in terahertz graphene-layered metamaterials,” J. Appl. Phys. 123(20), 203103 (2018).
[Crossref]

H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
[Crossref]

T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
[Crossref]

Z. H. He, X. C. Ren, S. M. Bai, H. J. Li, D. M. Cao, and G. Li, “Λ-Type and V-Type plasmon-induced transparency in plasmonic waveguide systems,” Plasmonics 13(6), 2255 (2018).
[Crossref]

2017 (3)

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

H. Xu, H. Li, Z. He, Z. Chen, M. Zheng, and M. Zhao, “Dual tunable plasmon-induced transparency based on silicon-air grating coupled graphene structure in terahertz metamaterial,” Opt. Express 25(17), 20780–20790 (2017).
[Crossref] [PubMed]

C. Sui, B. Han, T. Lang, X. Li, X. Jing, and Z. Hong, “Electromagnetically Induced Transparency in an All-Dielectric Metamaterial-Waveguide With Large Group Index,” IEEE P. J. 9(5), 1–8 (2017).
[Crossref]

2016 (6)

2015 (2)

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

L. Qi, Z. Xiang, L. L. Wang, B. X. Wang, G. D. Liu, and S. X. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” Epl 111(2015), 34004 (2015).

2014 (1)

S. P. Zhan, H. J. Li, G. T. Cao, Z. H. He, B. X. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

2013 (3)

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

S. P. Zhan, D. Kong, G. T. Cao, Z. H. He, Y. Wang, G. J. Xu, and H. J. Li, “Analogy of plasmon induced transparency in detuned U-resonators coupling to MDM plasmonic waveguide,” Solid State Commun. 174(11), 50–54 (2013).
[Crossref]

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

2012 (3)

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 85(12), 125431 (2012).
[Crossref]

N. Rouhi, S. Capdevila, D. Jain, K. Zand, Y. Y. Wang, E. Brown, L. Jofre, and P. Burke, “Terahertz graphene optics,” Nano Res. 5(10), 667–678 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B Condens. Matter Mater. Phys. 85(8), 081405 (2012).
[Crossref]

2011 (1)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

2009 (2)

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of Electromagnetically Induced Transparency in a Terahertz Metamaterial,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 153103 (2009).
[Crossref]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B Condens. Matter Mater. Phys. 80(19), 195415 (2009).
[Crossref]

2008 (1)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

1991 (2)

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Altug, H.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Atar, F. B.

Bai, S. M.

Z. H. He, X. C. Ren, S. M. Bai, H. J. Li, D. M. Cao, and G. Li, “Λ-Type and V-Type plasmon-induced transparency in plasmonic waveguide systems,” Plasmonics 13(6), 2255 (2018).
[Crossref]

Balci, O.

Balci, S.

Bettiol, A. A.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of Electromagnetically Induced Transparency in a Terahertz Metamaterial,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 153103 (2009).
[Crossref]

Boller, K.-J.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

Boyd, R. W.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Brown, E.

N. Rouhi, S. Capdevila, D. Jain, K. Zand, Y. Y. Wang, E. Brown, L. Jofre, and P. Burke, “Terahertz graphene optics,” Nano Res. 5(10), 667–678 (2012).
[Crossref]

Burke, P.

N. Rouhi, S. Capdevila, D. Jain, K. Zand, Y. Y. Wang, E. Brown, L. Jofre, and P. Burke, “Terahertz graphene optics,” Nano Res. 5(10), 667–678 (2012).
[Crossref]

Cao, D. M.

Z. H. He, X. C. Ren, S. M. Bai, H. J. Li, D. M. Cao, and G. Li, “Λ-Type and V-Type plasmon-induced transparency in plasmonic waveguide systems,” Plasmonics 13(6), 2255 (2018).
[Crossref]

Cao, G. T.

S. P. Zhan, H. J. Li, G. T. Cao, Z. H. He, B. X. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

S. P. Zhan, D. Kong, G. T. Cao, Z. H. He, Y. Wang, G. J. Xu, and H. J. Li, “Analogy of plasmon induced transparency in detuned U-resonators coupling to MDM plasmonic waveguide,” Solid State Commun. 174(11), 50–54 (2013).
[Crossref]

Capdevila, S.

N. Rouhi, S. Capdevila, D. Jain, K. Zand, Y. Y. Wang, E. Brown, L. Jofre, and P. Burke, “Terahertz graphene optics,” Nano Res. 5(10), 667–678 (2012).
[Crossref]

Chen, S. Q.

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Chen, Z.

Chen, Z. Q.

H. Xu, C. X. Xiong, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, B. H. Zhang, and H. J. Li, “Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial,” J. Opt. Soc. Am. B 35(6), 1463 (2018).
[Crossref]

H. Xu, M. Z. Zhao, Z. Q. Chen, M. F. Zheng, C. X. Xiong, B. H. Zhang, and H. J. Li, “Sensing analysis based on tunable Fano resonance in terahertz graphene-layered metamaterials,” J. Appl. Phys. 123(20), 203103 (2018).
[Crossref]

H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
[Crossref]

Z. Q. Chen, H. J. Li, B. X. Li, Z. H. He, H. Xu, M. F. Zheng, and M. Z. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

Cheng, H.

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Chiam, S.-Y.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of Electromagnetically Induced Transparency in a Terahertz Metamaterial,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 153103 (2009).
[Crossref]

Chu, H. S.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 85(12), 125431 (2012).
[Crossref]

Dai, J.

T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
[Crossref]

Dai, Y. T.

T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
[Crossref]

Deng, X.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Duan, X. Y.

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Gan, C. H.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 85(12), 125431 (2012).
[Crossref]

Gao, P.

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

Garcia-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B Condens. Matter Mater. Phys. 85(8), 081405 (2012).
[Crossref]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Guinea, F.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B Condens. Matter Mater. Phys. 85(8), 081405 (2012).
[Crossref]

Haddadpour, A.

Hafner, J.

J. Hafner, “Imaging Art and Facts,” ACS Nano 10(7), 6417–6419 (2016).
[Crossref] [PubMed]

Halfmann, T.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Han, B.

C. Sui, B. Han, T. Lang, X. Li, X. Jing, and Z. Hong, “Electromagnetically Induced Transparency in an All-Dielectric Metamaterial-Waveguide With Large Group Index,” IEEE P. J. 9(5), 1–8 (2017).
[Crossref]

Han, X.

T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
[Crossref]

Harris, S. E.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Haus, H. A.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

He, X.

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

He, Z.

He, Z. H.

Z. H. He, X. C. Ren, S. M. Bai, H. J. Li, D. M. Cao, and G. Li, “Λ-Type and V-Type plasmon-induced transparency in plasmonic waveguide systems,” Plasmonics 13(6), 2255 (2018).
[Crossref]

Z. Q. Chen, H. J. Li, B. X. Li, Z. H. He, H. Xu, M. F. Zheng, and M. Z. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
[Crossref]

S. P. Zhan, H. J. Li, G. T. Cao, Z. H. He, B. X. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

S. P. Zhan, D. Kong, G. T. Cao, Z. H. He, Y. Wang, G. J. Xu, and H. J. Li, “Analogy of plasmon induced transparency in detuned U-resonators coupling to MDM plasmonic waveguide,” Solid State Commun. 174(11), 50–54 (2013).
[Crossref]

Heinze, G.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Hong, Z.

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Z. H. He, X. C. Ren, S. M. Bai, H. J. Li, D. M. Cao, and G. Li, “Λ-Type and V-Type plasmon-induced transparency in plasmonic waveguide systems,” Plasmonics 13(6), 2255 (2018).
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H. Xu, M. Z. Zhao, Z. Q. Chen, M. F. Zheng, C. X. Xiong, B. H. Zhang, and H. J. Li, “Sensing analysis based on tunable Fano resonance in terahertz graphene-layered metamaterials,” J. Appl. Phys. 123(20), 203103 (2018).
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[Crossref]

Xu, K.

T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
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S. P. Zhan, H. J. Li, G. T. Cao, Z. H. He, B. X. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
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H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Yu, Z.

Zand, K.

N. Rouhi, S. Capdevila, D. Jain, K. Zand, Y. Y. Wang, E. Brown, L. Jofre, and P. Burke, “Terahertz graphene optics,” Nano Res. 5(10), 667–678 (2012).
[Crossref]

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T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B Condens. Matter Mater. Phys. 80(19), 195415 (2009).
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Zhan, S. P.

S. P. Zhan, H. J. Li, G. T. Cao, Z. H. He, B. X. Li, and H. Yang, “Slow light based on plasmon-induced transparency in dual-ring resonator-coupled MDM waveguide system,” J. Phys. D Appl. Phys. 47(20), 205101 (2014).
[Crossref]

S. P. Zhan, D. Kong, G. T. Cao, Z. H. He, Y. Wang, G. J. Xu, and H. J. Li, “Analogy of plasmon induced transparency in detuned U-resonators coupling to MDM plasmonic waveguide,” Solid State Commun. 174(11), 50–54 (2013).
[Crossref]

Zhang, B.

Zhang, B. H.

H. Xu, M. Z. Zhao, M. F. Zheng, C. X. Xiong, B. H. Zhang, Y. Y. Peng, and H. J. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D Appl. Phys. 52(2), 025104 (2019).
[Crossref]

H. Xu, C. X. Xiong, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, B. H. Zhang, and H. J. Li, “Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial,” J. Opt. Soc. Am. B 35(6), 1463 (2018).
[Crossref]

H. Xu, M. Z. Zhao, Z. Q. Chen, M. F. Zheng, C. X. Xiong, B. H. Zhang, and H. J. Li, “Sensing analysis based on tunable Fano resonance in terahertz graphene-layered metamaterials,” J. Appl. Phys. 123(20), 203103 (2018).
[Crossref]

H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
[Crossref]

Zhang, M.

H. Liang, S. Ruan, M. Zhang, H. Su, and I. L. Li, “Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces,” Appl. Phys. Lett. 107(9), 091602 (2015).
[Crossref]

Zhang, S.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B Condens. Matter Mater. Phys. 80(19), 195415 (2009).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Zhang, T.

T. Zhang, J. Z. Zhou, J. Dai, Y. T. Dai, X. Han, J. Q. Li, F. F. Yin, Y. Zhou, and K. Xu, “Plasmon induced absorption in a graphene-based nanoribbon waveguide system and its applications in logic gate and sensor,” J. Phys. D Appl. Phys. 51(5), 055103 (2018).
[Crossref]

Zhang, W.

S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of Electromagnetically Induced Transparency in a Terahertz Metamaterial,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 153103 (2009).
[Crossref]

Zhang, X.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B Condens. Matter Mater. Phys. 80(19), 195415 (2009).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Zhao, M.

Zhao, M. Z.

H. Xu, M. Z. Zhao, M. F. Zheng, C. X. Xiong, B. H. Zhang, Y. Y. Peng, and H. J. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D Appl. Phys. 52(2), 025104 (2019).
[Crossref]

H. Xu, C. X. Xiong, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, B. H. Zhang, and H. J. Li, “Dynamic plasmon-induced transparency modulator and excellent absorber-based terahertz planar graphene metamaterial,” J. Opt. Soc. Am. B 35(6), 1463 (2018).
[Crossref]

H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
[Crossref]

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H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
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K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
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Appl. Phys. Express (2)

H. Xu, H. J. Li, Z. Q. Chen, M. F. Zheng, M. Z. Zhao, C. X. Xiong, and B. H. Zhang, “Novel tunable terahertz graphene metamaterial with an ultrahigh group index over a broad bandwidth,” Appl. Phys. Express 11(4), 042003 (2018).
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Z. Q. Chen, H. J. Li, B. X. Li, Z. H. He, H. Xu, M. F. Zheng, and M. Z. Zhao, “Tunable ultra-wide band-stop filter based on single-stub plasmonic-waveguide system,” Appl. Phys. Express 9(10), 102002 (2016).
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Figures (9)

Fig. 1
Fig. 1 (a) Schematic diagram of slow-light and light absorption integrated periodic metamaterials. Patterned periodic single-layer planar graphene is sandwiched in dielectric silicon, and the thickness of the upper medium and the lower substrate are 0.1μm and 0.25μm, respectively. (b) Top view of structural unit in metamaterial, and geometric parameters:l1 = 3.2µm, l2 = 0.5µm, l3 = 0.3µm, l4 = 1.5µm, l5 = 0.5µm, l6 = 0.5µm, L = 4µm.
Fig. 2
Fig. 2 (a-b) Transmission and absorption spectra of slow-light and absorption integrated metamaterials, and Fermi level is set as 1.0eV. (c-f) Four metamaterial arrays, wherein graphene in (c) with the whole structure, four blocks graphene in (d) are monopole antenna, graphene ribbons in (e) are quadrupole antenna, and the two graphene ribbons in (f) are octapole antenna.
Fig. 3
Fig. 3 (a) The electric field distribution of the quadrupole antenna at f1 = 2.354THz. (b) The electric field distribution of the octupole antenna at f2 = 4.038THz. (c-e) Electric field distribution of dip1 (f3 = 2.093THz), dip2 (f4 = 3.105THz), dip3 (f5 = 4.188THz) for different resonance frequencies in the whole structure. These field distributions are all in the y direction.
Fig. 4
Fig. 4 (a) Schematic diagram of a Λ-shaped PIT. (b) Schematic diagram of coupled mode theory.
Fig. 5
Fig. 5 (a-d) and (e-i) are transmission and absorption spectra of FDTD numerical simulation and CMT theoretical calculation at different Fermi levels, respectively.
Fig. 6
Fig. 6 (a) Resonance dips and peaks versus frequency in transmission and absorption spectra. (b) Diagram of loss quality factor and frequency at different Fermi levels. (c-d) Quality factors of transmission dips and absorption peaks at different Fermi levels. (e-f) Evolution of transmission and absorbance among different Fermi levels and frequencies.
Fig. 7
Fig. 7 (a-b) Evolution of dual PIT and PIA, and Fermi level is 1.0eV.
Fig. 8
Fig. 8 (a-b) Evolution of dual PIT and PIA in different media environments. (c-d) Evolution of dual PIT and PIA at different carrier mobility. Here, Fermi level is 1.0eV.
Fig. 9
Fig. 9 (a-d) Group index and phase shifts of the proposed metamaterials at different Fermi levels.

Equations (14)

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σ g = i e 2 E f π(ω+i τ 1 ) ,
( γ 1 i μ 12 i μ 13 i μ 21 γ 2 i μ 23 i μ 31 i μ 32 γ 3 )( a b c )=( γ o1 1/2 0 0 0 γ o2 1/2 0 0 0 γ o3 1/2 )( A + in + A in B + in + B in C + in + C in ),
B + in = A + out e i φ 1 , A in = B out e i φ 1 ,
C + in = B + out e i φ 2 , B in = C out e i φ 2 ,
A + out = A + in γ o1 1/2 a, A out = A in γ o1 1/2 a,
B + out = B + in γ o2 1/2 b, B out = B in γ o2 1/2 b,
C + out = C + in γ o3 1/2 c, C out = C in γ o3 1/2 c,
t= C + out A + in =1 γ o1 1/2 D 1 γ o2 1/2 D 2 γ o3 1/2 D 3 ,
r= ( γ o1 ) 1/2 D 1 ( γ o2 ) 1/2 D 2 ( γ o3 ) 1/2 D 3 ,
D 1 = ( γ 2 γ 3 γ 23 γ 32 ) γ o1 1/2 +( γ 12 γ 3 + γ 13 γ 32 ) γ o2 1/2 +( γ 12 γ 23 + γ 13 γ 2 ) γ o3 1/2 γ 1 γ 23 γ 32 γ 1 γ 2 γ 3 + γ 12 γ 21 γ 3 + γ 12 γ 23 γ 31 + γ 13 γ 21 γ 32 + γ 13 γ 2 γ 31 ,
D 2 = ( γ 21 γ 33 + γ 23 γ 31 ) γ o1 1/2 +( γ 1 γ 3 γ 13 γ 31 ) γ o2 1/2 +( γ 1 γ 23 + γ 13 γ 21 ) γ o3 1/2 γ 1 γ 23 γ 32 γ 1 γ 2 γ 3 + γ 12 γ 21 γ 3 + γ 12 γ 23 γ 31 + γ 13 γ 21 γ 32 + γ 13 γ 2 γ 31 ,
D 3 = ( γ 21 γ 32 + γ 2 γ 31 ) γ o1 1/2 +( γ 1 γ 32 + γ 12 γ 31 ) γ o2 1/2 +( γ 1 γ 2 γ 12 γ 21 ) γ o3 1/2 γ 1 γ 23 γ 32 γ 1 γ 2 γ 3 + γ 12 γ 21 γ 3 + γ 12 γ 23 γ 31 + γ 13 γ 21 γ 32 + γ 13 γ 2 γ 31 ,
γ 12 =i μ 12 + ( γ o1 γ o2 ) 1/2 , γ 13 =i μ 13 + ( γ o1 γ o3 ) 1/2 , γ 21 =i μ 21 + ( γ o1 γ o2 ) 1/2 ,
γ 23 =i μ 23 + ( γ o2 γ o3 ) 1/2 , γ 31 =i μ 31 + ( γ o1 γ o3 ) 1/2 , γ 32 =i μ 32 + ( γ o2 γ o3 ) 1/2 ,

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