Abstract

Plasmonics of two-dimensional materials have attracted increasing attention in the past few years. It provides a platform for strong light-matter interactions and enables a variety of novel applications in the infrared and terahertz ranges. In this paper, we study the plasmonic properties of a graphene-black phosphorus (G-BP) bilayer. It exhibits both strong and highly anisotropic plasmonic responses that performs beyond individual graphene and black phosphorus films. Polarization dependent, anisotropic perfect absorption can be realized in this type of two-dimensional plasmonic nanostructures with moderate doping levels. This type of hybrid architecture opens a new door for high performance two-dimensional material plasmonic devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Possessing charming optical and electric properties, graphene and graphene-like two-dimensional materials show promising prospect in the field of optics and optoelectronics [1]. Although one of the major challenges in the way is the relatively weak interaction between light and two-dimensional materials, the excitation of plasmons in graphene and graphene-like materials provides an effective way to overcome the difficulty [2]. In particular, theoretical and experimental researches prove that atomically thin patterned graphene supports both propagating [3,4] and localized [5] surface plasmon modes, leading to efficient confinement of light and strong enhancement of local fields [6, 7]. Basing on this property, many possible applications have been proposed such as graphene waveguides [3], polarizers [8,9], tunable metamaterials [10,11], photodetectors [12].

Similar to graphene, black phosphorus (BP), another layered material with puckered honeycomb structure [13], is reintroduced into the world from the perspective of two-dimensional materials, showing valuable properties like broadband tunable bandgap [14,15], strong light-interactions in the mid-IR range, high carrier mobility and intrinsic in-plane anisotropism. Based on these excellent properties, many potential applications have been explored, including field effect transistors [16,17], saturable absorbers [18], photodetectors [19], heterojunction p-n diodes [20] and others. Recently, it has been reported theoretically that mono [21,22] to few-layer [23–25] BP films support anisotropic plasmonic dispersion because of different effective electron masses along different crystal directions. However, the plasmon resonances of doped and patterned BP are relatively weak [26,27], which hinders its anisotropic applications.

By stacking different crystals together, van der Waals heterostructures of two-dimensional materials have been intensively studied to achieve novel properties and functionalities in optics, electronics and optoelectronics. Here we show that looking beyond the plasmons of single material, the isolated two-dimensional material could also be reassembled for plasmonics with enhanced properties. In this paper, we study the plasmonic properties of a graphene-black phosphorus bilayer. Combining the property of graphene plasmons and BP plasmons, it exhibits strong anisotropic plasmonic reponses that are not available in either individual graphene or black phosphorus films. Numerical simulation results show that polarization dependent, anisotropic perfect absorption can be realized in this type of two-dimensional plasmonic nanostructures with moderate doping levels.

2. Results and discussion

The optical conductivity of graphene can be expressed as [28]

σ(ω)=2e2kBTπ2iω+iτ1ln[2coshEf2kBT]+e28+e24[1πarctan(ω2Ef2kBT)i2πln(ω+2Ef)2(ω+2Ef)2+(2kBT)2]
It consists of contributions from intra-band transition and the inter-band transition. Here kB is the Boltzmann constant, ω is the frequency of the light, T is the temperature, τ is the carrier relaxation lifetime and Ef is the Fermi energy. We use a moderate measured mobility μ = 10 000 cm2/(V ·s) and choose concentration n = 1.9 × 1013 cm−2 (Ef ≈ 0.5eV) at the beginning. This assumption could be realized by chemical or electrostatic doping [29].

For BP, the conductivity can be described by employing a semi-classical Drude model as [23]

σj=ie2nmj(ω+iη)
Herein, j denotes the x- or y-direction and mj is the electron mass along the j-direction. For monolayer BP, mx ≈ 0.15m0, my ≈ 0.7m0. We choose η = 10 meV to describe the relaxation rate [23]. The concentration of electron doping n is set the same as graphene.

The numerical simulations are conducted using a fully three-dimensional finite element technique (in COMSOL Multiphysics). In the simulations, both BP and graphene are set to be 0.5 nm thick. Gold is simulated by the Drude-Lorentz dispersion model. In the model, the plasma frequency and the damping constant are set as 1.37 × 1016 and 4.05 × 1013rad /s, respectively. We simulate graphene nanodisks, BP nanodisks and G-BP bilayer nanodisks with the same Fermi energy (0.5 eV) and geometric parameters (the period P and the diameter D). Figures 1(a)–1(c) show the schematic illustrations and geometric parameters of our design. The 2D periodical nanodisks are integrated on the semi-infinite substrate and excited by a plane wave at normal incidence. The substrate layer is assumed to be lossless with the refractive index of 2. The period of the nanodisks array is P = 250 nm and the diameter is D = 150 nm. Both the polarization of the electric field along x- (armchair) and y-direction (zigzag) are calculated in the structure. The absorption spectra are plotted in Figs. 1(d)–1(f) corresponding to the structure of Figs. 1(a)–1(c), respectively. Figure 1(d) shows that the resonances of monolayer BP with low doping is relatively weak for both x-polarization (6.99%) and y-polarization (1.37%). Figure 1(e) illustrates a strong resonance at 14.24 μm with the absorption of 26.50% while the optical response is independent of polarization because of the isotropic in-plane optical conductivity of graphene. To intensify the resonance of BP in this structure, the traditional way is increasing the diameter of the nanodisks in the same period or raising Fermi energy to influence the dielectric constant of BP. The improvement of the former is little. And considering the difficulty of raising Fermi energy in the experiment at present, the resonance enhancement for the latter method is strictly limited and at the price of its tunability. However, the G-BP bilayer structure, which successfully combines the advantage of graphene and BP, shows both strong and anisotropic plasmon resonances. As shown in Fig. 1(f), for y-polarization, there is a resonance at around 13.26 μm in the spectrum with strong light absorption (33.23%) while only 0.88% for x-polarization at the same wavelength. Similarly, at 11.36 μm, the absorption of x-polarization and y-polarization are 29.93% and 0.35%, respectively. This strong and anisotropic resonance makes it easier to take advantage of its unique optical properties towards applications like tunable polarizer in symmetrical structure.

 figure: Fig. 1

Fig. 1 Comparison of plasmon resonances between monolayer BP, graphene and G-BP bilayer structure. (a, b, c) Scheme of the proposed devices. The nanodisks array of two-dimensional material are placed on the semi-infinite substrate. The period is P = Px = Py = 250 nm and the diameter of the nanodisks is D = 150 nm. (d, e, f) simulated spectra of total absorption when the electric field polarizes along x- and y-direction with the doping concentration n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV).

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By inserting an insulator layer between G-BP bilayer, we study the plasmonic resonances of separated G-BP bilayer nanodisks to understand the interaction of these two materials. The refractive index of the insulator is 2 and its thickness is t. Figure 2 shows the absorption spectra of two polarization when t varies from 0 to 20 nm. As the thickness of the insulator layer is zero, the resonance peak of two polarization separates far away. With the increment of the thickness, the y-polarization resonance peak gets close to the x-polarization and almost overlaps each other at the thickness of 20 nm. The anisotropism becomes weaken due to a reduced proportion of confined field in the BP nanodisks (see the insets in Fig. 2). At the same time, the resonance wavelength blue-shifts from 11.36 μm to 10.74 μm for x-polarization and from 13.26 μm to 10.88 μm for y-polarization as the separation increases from 0 to 20 nm. As the separation between graphene and BP increases, the G-BP nanodisks become thicker and more exposed to air (particularly the graphene on the top), thus the effective refractive index of the surrounding media becomes lower and the resonance wavelength blue-shifts.

 figure: Fig. 2

Fig. 2 Simulated spectra of total absorption when the electric field polarizes along both x- and y-direction with different separations between the graphene nanodisk and the BP nanodisk. The separation ranges from t = 0 to 20 nm. The insets show the distributions of normalized electric fields at the resonance wavelength for y-polarized light.

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We then study anisotropic perfect absorption based on nanostructured G-BP. Schematic illustration of the structure is depicted in Fig. 3(a). The design forms a typical Salisbury screen [30,31]. The optical responses of the structure rely on interplay of localized plasmonic resonances of the nanostructured G-BP and the F-P effect of the cavity (the thickness of the dielectric layer is generally designed to be around λ/4). Perfect absorption is achieved at the critical coupling condition. After numerical optimization, the absorption spectra are plotted in Fig. 3(b). Here, the thickness of the insulator layer and the dielectric layer are 2 nm and 1.65 μm. The refractive index of the insulator layer and the dielectric layer are 1.4 and 2, respectively. Other parameters are the same as the structure showed in Fig. 1. The absorption of x-polarization and y-polarization, in Fig. 3(b), are 99.98% and 9.17% at 11.08 μm, respectively. The device can work as a reflective polarizer. The polarizing extinction ratio, defined as 10lg(ratio of reflection power of y- and x-polarized light), is about 37 dB at 11.08 μm. As shown in Figs. 3(c) and 3(d), this resonance is attributed to the excitation of a dipolar plasmonic mode in G-BP bilayer nanodisks. Usually, the high doping concentration of monolayer BP or multi-layer structures are used to achieve perfect anisotropic absorption [32–34]. But the structure we proposed makes it possible to realize with relatively low doping concentration and has broader tunability.

 figure: Fig. 3

Fig. 3 Anisotropic perfect absorption in G-BP bilayer structure with reflecting mirror. (a) Scheme of the proposed structure. From top to bottom of the structures are array of G-insulator-BP nanodisks, dielectric layer, gold layer and semi-infinite substrate (not shown in the figure). The geometry parameters (period P and diameter D) are the same as the Fig. 1. (b) Simulated spectra of total absorption for both polarization with the doping concentration n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV). (c, d) Electric field in the z-direction for both polarization. c and d belong to x-polarization at the resonance wavelength of 11.08 μm and y-polarization at the resonance wavelength of 12.68 μm, respectively. The field is plotted in the x–y plane that is 4 nm above the G-insulator-BP nanodisks.

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Technically, the morphology of the edges of the nanodisks has an inevitable influence on the electronic properties [35]. And it still remains a challenge to achieve the precision required for a controllable manufacture of expected edges [36]. To make the polarizer easier to realize, the G-BP bilayer is kept as a whole and the gold nanoparticles array are added on the top of the structure to excite the plasmon resonances of the G-BP bilayer. The transfer process makes it feasible to create Au nanoparticles, keeping them nearly the same morphology [37]. Figure 4(a) is the schematic of the new structure. From top to bottom is gold nanoparticles, insulator layer, BP-insulator-graphene layer, dielectric layer and the gold mirror. Here, the insulator layer and the dielectric layer are assumed to be lossless with the refractive index of 1.4. The thickness of the insulator layer a, b and the dielectric layer are 2 nm, 2 nm and 1.7 μm, respectively. The period of the Au nanoparticle array is P = 500 nm and the diameter is D = 450 nm. The doping concentration is still n = 1.9 × 1013cm−2. In Fig. 4(b), the absorption of x- and y-polarization are 9.85% and 97.74% at 12.56 μm while 90.26% and 4.87% at 11 μm, exhibiting well anisotropic absorption property of improved structure. Figures 4(c) and 4(d) show the spectra of total absorption of the structure with different Fermi energy of the G-BP bilayer. For x-polarization, when Fermi energy is 0.4 eV, the resonance is at 12.8 μm (84.64%) and fail to reach perfect absorption. As the Fermi energy increases, the maximum absorption fluctuates slightly and still have around 10% away to 100% because the length of cavity is not the fittest for x-polarization. For y-polarization, the maximum absorption is 87.95% at 14.32 μm when Ef ≈ 0.4 eV and almost reaches 100% when Ef ≈ 0.7 eV, which is 99.4% at 10.42 μm. The figure tells us that for y-polarization, perfect absorption can be achieved when Ef ≥ 0.5 eV. The absorption spectra also suggest that the strong anisotropic absorption of the structure still exists and resonance shape becomes sharper with the increment of the Fermi energy. Furthermore, the resonance wavelength blue shifts from 12.8 μm to 8.82 μm for x-polarization and from 14.32 μm to 10.42 μm for y-polarization, respectively. Similar shifts of resonances have been observed for both graphene [38] and BP [34] plasmonic structures. Actually, it has been found that λL/n (where λ is the plasmonic resonance wavelength and n is the carrier density) [8,23]. It is worth mentioning that the range of Fermi energy we tune has been realized with electrostatic doping experimentally [5,38,39]. Finally, one may note that the order of graphene and BP is different in Fig. 3(a) and Fig. 4(a). Although there is a slight shift of the resonant wavelength and variation of peak absorption, changing the order of graphene and BP does not make a big difference on the performance of the devices.

 figure: Fig. 4

Fig. 4 Anisotropic absorption of metallic nanoparticles loaded G-BP bilayer. (a) Scheme of the new structure. From the top to the bottom are an array of gold nanoparticles, an insulator layer marked as a, monolayer BP, an insulator layer marked as b, the graphene layer, a dielectric layer, a gold mirror and a semi-infinite substrate. The period is Px = Py = P = 500 nm and the diameter of the gold nanoparticle is D = 450 nm. (b) Simulated spectra of total absorption for both polarization with the doping concentration n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV). (c,d) Spectra tunability of absorption with the variation of Fermi energy ranging from 0.4 eV to 0.7 eV.

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The incident angle dependence of absorption has also been studied and the results are shown in Fig. 5. Here the doping concentration n and geometric parameters are the same as those in Fig. 4. When the incident angle is below 40 degrees, the dependence between absorption and incident angle for both polarization are quite weak and the resonance wavelength almost remains the same. For larger incident angle, the irrelevance of incident angle and absorption still exists in y-polarization. However, for x-polarization, the resonance wavelength red shifts and the maximum absorption declines seriously when the incident angle is larger than around 60 degrees. Interestingly, the anisotropic absorption still performs well with the increment of incident angle. This property of nearly omnidirectional anisotropic absorption is beneficial for practical applications.

 figure: Fig. 5

Fig. 5 Angular dispersions of the total absorption for (a) electric field along y-direction(TE) and (b) electric field along x-direction(TM). Here we use the structure in Fig. 4. The doping concentration is n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV).

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3. Conclusions

In conclusion, we propose G-BP bilayer for plasmonics and numerically demonstrate that it has both strong and anisotropic plasmon resonances which neither the monolayer graphene nor the BP possesses. The influence of the thickness of insulator layer between the G-BP bilayer is studied to analyze the G-BP bilayer interaction. And we show that anisotropic perfect absorption can be realized in both nanostructured G-BP bilayer and unstructured G-BP bilayer integrated with metallic nanoparticles. Electrical tunability of G-BP plasmon and the independence of incidence angle make it feasible for active spectral selectivity in an oblique incident light. This type of hybrid architecture opens a new door for high performance two-dimensional material plasmonic devices with potential applications ranging from polarization manipulation [40], photodetection [41–43] to sensing [44,45] and others. Although it still remains a challenge to obtain large monolayer BP for current research, the proposed structures provide the guidelines for further experimental research.

Funding

The Science and Technology Planning Project of Hunan Province (2017RS3039, 2018JJ1033); National Natural Science Foundation of China (11304389, 11674396).

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References

  • View by:

  1. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics,  4(9), 611–622(2010).
    [Crossref]
  2. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics,  6(11), 749–758(2012).
    [Crossref]
  3. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science,  332(6035), 1291–1294(2011).
    [Crossref] [PubMed]
  4. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano,  6(9), 7806–7813(2012).
    [Crossref] [PubMed]
  5. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature,  487(7405), 77–81(2012).
    [Crossref] [PubMed]
  6. V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.,  13(6), 2541–2547(2013).
    [Crossref] [PubMed]
  7. J. Zhang, Z. Zhu, W. Liu, X. Yuan, and S. Qin, “Towards photodetection with high efficiency and tunable spectral selectivity: graphene plasmonics for light trapping and absorption engineering,” Nanoscale,  7(32), 13530–13536(2015).
    [Crossref] [PubMed]
  8. Z. H. Zhu, C. C. Guo, K. Liu, J. F. Zhang, W. M. Ye, X. D. Yuan, and S. Q. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A,  114(4), 1017–1021(2014).
    [Crossref]
  9. Z. H. Zhu, C. C. Guo, K. Liu, J. F. Zhang, W. M. Ye, X. D. Yuan, and S. Q. Qin, “Electrically controlling the polarizing direction of a graphene polarizer,” J. Appl. Phys.,  116(10), 104304(2014).
    [Crossref]
  10. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics,  6(4), 259–264(2012).
    [Crossref]
  11. L. Wang, X. Chen, A. Yu, Y. Zhang, J. Ding, and W. Lu, “Highly sensitive and wide-band tunable terahertz response of plasma waves based on graphene field effect transistors,” Sci. Rep.,  4, 5470(2014).
    [Crossref] [PubMed]
  12. M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, and P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun.,  4, 1951(2013).
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  13. T. Low, A. S. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. H. C. Neto, “Tunable optical properties of multilayers black phosphorus thin films,” Phys. Rev. B,  90(7), 075434(2014).
    [Crossref]
  14. A. S. Rodin, A. Carvalho, and A. H. Castro Neto, “Strain-induced gap modification in black phosphorus,” Phys. Rev. Lett.,  112(17), 1–5(2014).
    [Crossref]
  15. V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B,  89(23), 1–6(2014).
    [Crossref]
  16. M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. Van Der Zant, A. Castellanos-Gomez, H. S. J. V. D. Zant, and A. Castellanos-Gomez, “Fast and Broadband Photoresponse of Few-Layer Black Phosphorus Field-Effect Transistors,” Nano Lett.,  14(6), 3347(2014).
    [Crossref] [PubMed]
  17. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol.,  9(5), 372–377(2014).
    [Crossref] [PubMed]
  18. Y. Chen, G. Jiang, S. Chen, Z. Guo, X. Yu, C. Zhao, H. Zhang, Q. Bao, S. Wen, D. Tang, and D. Fan, “Mechanically exfoliated black phosphorus as a new saturable absorber for both Q-switching and Mode-locking laser operation,” Opt. Express,  23(10), 12823(2015).
    [Crossref] [PubMed]
  19. M. Huang, M. Wang, C. Chen, Z. Ma, X. Li, J. Han, and Y. Wu, “Broadband Black-Phosphorus Photodetectors with High Responsivity,” Adv. Mater.,  28(18), 3481–3485(2016).
    [Crossref] [PubMed]
  20. J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus À Monolayer MoS 2 Diode,” ACS Nano,  8(8), 8292–8299(2014).
    [Crossref] [PubMed]
  21. D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: Anisotropic elliptical propagation and nonlocality-induced canalization,” J. Optics,  18(10), 1–10(2016).
    [Crossref]
  22. Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett.,  109(24), 241902(2016).
    [Crossref]
  23. T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett.,  113(10), 5–9(2014).
    [Crossref]
  24. D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, “Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit,” 2D Mater.,  4(2), 25064(2017).
    [Crossref]
  25. X. Ni, L. Wang, J. Zhu, X. Chen, and W. Lu, “Surface plasmons in a nanostructured black phosphorus flake,” Opt. Lett.,  42(13), 2659–2662(2017).
    [Crossref] [PubMed]
  26. Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett.,  16(6), 3457–3462(2016).
    [Crossref] [PubMed]
  27. J. P. Nong, W. Wei, W. Wang, and G. L. Lan, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express,  26(2), 1291–1294(2018).
    [Crossref]
  28. L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B,  56(4),281–284(2007).
    [Crossref]
  29. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science,  306(5696), 666–669(2004).
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  30. W. W. Salisbury, “Absorbent body for electromagnetic waves,” US Patent, 2599944 (1952).
  31. Y. Ra, C. R. Simovski, and S. A. Tretyakov, “Thin Perfect Absorbers for Electromagnetic Waves : Theory, Design, and Realizations,” Phys. Rev. Appl.,  3(3), 037001(2015).
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  32. J. Wang and Y. Jiang, “Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials,” Opt. Express,  25(5), 5206–5216(2017).
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  33. J. Wang, Y. Jiang, and Z. Hu, “Dual-band and polarization-independent infrared absorber based on two-dimensional black phosphorus metamaterials,” Opt. Express,  25(18), 22149–22157(2017).
    [Crossref] [PubMed]
  34. F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Optics,  19(7), 2–5(2017).
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  35. A. H. C. Neto, “The electronic properties of graphene,” Rev. mod. phys.,  81(1), 109 (2009).
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  36. J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: Equilibrium energetics versus dynamic effects,” ACS Nano,  6(1), 671–676(2012).
    [Crossref]
  37. Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun.,  2(1), 577–579(2011).
    [Crossref]
  38. Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. M. Ajayan, F. J. G. D. Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett.,  14(1), 299–304 (2013).
    [Crossref] [PubMed]
  39. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature,  487(7405), 82(2012).
    [Crossref] [PubMed]
  40. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol.,  7(5), 330–334(2012).
    [Crossref] [PubMed]
  41. T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun.,  2(1), 455–458(2011).
    [Crossref]
  42. W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials,  6(9), 155(2016).
    [Crossref]
  43. S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys.,  18(38), 26661–26669(2016).
    [Crossref] [PubMed]
  44. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García De Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science,  349(6244), 165–168(2015).
    [Crossref] [PubMed]
  45. Y. Yuan, X. Yu, Q. Ouyang, Y. Shao, J. Song, J. Qu, and K.-T. Yong, “Highly anisotropic black phosphorous-graphene hybrid architecture for ultrassensitive plasmonic biosensing: Theoretical insight,” 2D Mater.,  5(2), 025015(2018).
    [Crossref]

2018 (2)

J. P. Nong, W. Wei, W. Wang, and G. L. Lan, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express,  26(2), 1291–1294(2018).
[Crossref]

Y. Yuan, X. Yu, Q. Ouyang, Y. Shao, J. Song, J. Qu, and K.-T. Yong, “Highly anisotropic black phosphorous-graphene hybrid architecture for ultrassensitive plasmonic biosensing: Theoretical insight,” 2D Mater.,  5(2), 025015(2018).
[Crossref]

2017 (5)

D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, “Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit,” 2D Mater.,  4(2), 25064(2017).
[Crossref]

X. Ni, L. Wang, J. Zhu, X. Chen, and W. Lu, “Surface plasmons in a nanostructured black phosphorus flake,” Opt. Lett.,  42(13), 2659–2662(2017).
[Crossref] [PubMed]

J. Wang and Y. Jiang, “Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials,” Opt. Express,  25(5), 5206–5216(2017).
[Crossref] [PubMed]

J. Wang, Y. Jiang, and Z. Hu, “Dual-band and polarization-independent infrared absorber based on two-dimensional black phosphorus metamaterials,” Opt. Express,  25(18), 22149–22157(2017).
[Crossref] [PubMed]

F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Optics,  19(7), 2–5(2017).
[Crossref]

2016 (6)

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett.,  16(6), 3457–3462(2016).
[Crossref] [PubMed]

M. Huang, M. Wang, C. Chen, Z. Ma, X. Li, J. Han, and Y. Wu, “Broadband Black-Phosphorus Photodetectors with High Responsivity,” Adv. Mater.,  28(18), 3481–3485(2016).
[Crossref] [PubMed]

D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: Anisotropic elliptical propagation and nonlocality-induced canalization,” J. Optics,  18(10), 1–10(2016).
[Crossref]

Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett.,  109(24), 241902(2016).
[Crossref]

W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials,  6(9), 155(2016).
[Crossref]

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys.,  18(38), 26661–26669(2016).
[Crossref] [PubMed]

2015 (4)

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García De Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science,  349(6244), 165–168(2015).
[Crossref] [PubMed]

Y. Chen, G. Jiang, S. Chen, Z. Guo, X. Yu, C. Zhao, H. Zhang, Q. Bao, S. Wen, D. Tang, and D. Fan, “Mechanically exfoliated black phosphorus as a new saturable absorber for both Q-switching and Mode-locking laser operation,” Opt. Express,  23(10), 12823(2015).
[Crossref] [PubMed]

Y. Ra, C. R. Simovski, and S. A. Tretyakov, “Thin Perfect Absorbers for Electromagnetic Waves : Theory, Design, and Realizations,” Phys. Rev. Appl.,  3(3), 037001(2015).
[Crossref]

J. Zhang, Z. Zhu, W. Liu, X. Yuan, and S. Qin, “Towards photodetection with high efficiency and tunable spectral selectivity: graphene plasmonics for light trapping and absorption engineering,” Nanoscale,  7(32), 13530–13536(2015).
[Crossref] [PubMed]

2014 (10)

Z. H. Zhu, C. C. Guo, K. Liu, J. F. Zhang, W. M. Ye, X. D. Yuan, and S. Q. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A,  114(4), 1017–1021(2014).
[Crossref]

Z. H. Zhu, C. C. Guo, K. Liu, J. F. Zhang, W. M. Ye, X. D. Yuan, and S. Q. Qin, “Electrically controlling the polarizing direction of a graphene polarizer,” J. Appl. Phys.,  116(10), 104304(2014).
[Crossref]

L. Wang, X. Chen, A. Yu, Y. Zhang, J. Ding, and W. Lu, “Highly sensitive and wide-band tunable terahertz response of plasma waves based on graphene field effect transistors,” Sci. Rep.,  4, 5470(2014).
[Crossref] [PubMed]

T. Low, A. S. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. H. C. Neto, “Tunable optical properties of multilayers black phosphorus thin films,” Phys. Rev. B,  90(7), 075434(2014).
[Crossref]

A. S. Rodin, A. Carvalho, and A. H. Castro Neto, “Strain-induced gap modification in black phosphorus,” Phys. Rev. Lett.,  112(17), 1–5(2014).
[Crossref]

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B,  89(23), 1–6(2014).
[Crossref]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. Van Der Zant, A. Castellanos-Gomez, H. S. J. V. D. Zant, and A. Castellanos-Gomez, “Fast and Broadband Photoresponse of Few-Layer Black Phosphorus Field-Effect Transistors,” Nano Lett.,  14(6), 3347(2014).
[Crossref] [PubMed]

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol.,  9(5), 372–377(2014).
[Crossref] [PubMed]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett.,  113(10), 5–9(2014).
[Crossref]

J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus À Monolayer MoS 2 Diode,” ACS Nano,  8(8), 8292–8299(2014).
[Crossref] [PubMed]

2013 (3)

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, and P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun.,  4, 1951(2013).
[Crossref] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.,  13(6), 2541–2547(2013).
[Crossref] [PubMed]

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. M. Ajayan, F. J. G. D. Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett.,  14(1), 299–304 (2013).
[Crossref] [PubMed]

2012 (7)

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature,  487(7405), 82(2012).
[Crossref] [PubMed]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol.,  7(5), 330–334(2012).
[Crossref] [PubMed]

P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics,  6(4), 259–264(2012).
[Crossref]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics,  6(11), 749–758(2012).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano,  6(9), 7806–7813(2012).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature,  487(7405), 77–81(2012).
[Crossref] [PubMed]

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: Equilibrium energetics versus dynamic effects,” ACS Nano,  6(1), 671–676(2012).
[Crossref]

2011 (3)

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun.,  2(1), 577–579(2011).
[Crossref]

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

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun.,  2(1), 455–458(2011).
[Crossref]

2010 (1)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics,  4(9), 611–622(2010).
[Crossref]

2009 (1)

A. H. C. Neto, “The electronic properties of graphene,” Rev. mod. phys.,  81(1), 109 (2009).
[Crossref]

2007 (1)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B,  56(4),281–284(2007).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science,  306(5696), 666–669(2004).
[Crossref] [PubMed]

Abajo, F. J. G. D.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. M. Ajayan, F. J. G. D. Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett.,  14(1), 299–304 (2013).
[Crossref] [PubMed]

Ajayan, P. M.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. M. Ajayan, F. J. G. D. Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett.,  14(1), 299–304 (2013).
[Crossref] [PubMed]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature,  487(7405), 77–81(2012).
[Crossref] [PubMed]

Altug, H.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García De Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science,  349(6244), 165–168(2015).
[Crossref] [PubMed]

Alù, A.

D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: Anisotropic elliptical propagation and nonlocality-induced canalization,” J. Optics,  18(10), 1–10(2016).
[Crossref]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature,  487(7405), 82(2012).
[Crossref] [PubMed]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett.,  13(6), 2541–2547(2013).
[Crossref] [PubMed]

Avouris, P.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett.,  113(10), 5–9(2014).
[Crossref]

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, and P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun.,  4, 1951(2013).
[Crossref] [PubMed]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol.,  7(5), 330–334(2012).
[Crossref] [PubMed]

Aydin, K.

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett.,  16(6), 3457–3462(2016).
[Crossref] [PubMed]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature,  487(7405), 77–81(2012).
[Crossref] [PubMed]

Bai, J.

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun.,  2(1), 577–579(2011).
[Crossref]

Bao, Q.

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature,  487(7405), 82(2012).
[Crossref] [PubMed]

Bao, Z. W.

Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett.,  109(24), 241902(2016).
[Crossref]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature,  487(7405), 82(2012).
[Crossref] [PubMed]

Blanter, S. I.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. Van Der Zant, A. Castellanos-Gomez, H. S. J. V. D. Zant, and A. Castellanos-Gomez, “Fast and Broadband Photoresponse of Few-Layer Black Phosphorus Field-Effect Transistors,” Nano Lett.,  14(6), 3347(2014).
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Bonaccorso, F.

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M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, and P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun.,  4, 1951(2013).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol.,  7(5), 330–334(2012).
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Xiao, S.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys.,  18(38), 26661–26669(2016).
[Crossref] [PubMed]

Xiong, F.

F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Optics,  19(7), 2–5(2017).
[Crossref]

Xu, C.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys.,  18(38), 26661–26669(2016).
[Crossref] [PubMed]

Xu, Q.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano,  6(9), 7806–7813(2012).
[Crossref] [PubMed]

Xu, X.

J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus À Monolayer MoS 2 Diode,” ACS Nano,  8(8), 8292–8299(2014).
[Crossref] [PubMed]

Yan, H.

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, and P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun.,  4, 1951(2013).
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S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys.,  18(38), 26661–26669(2016).
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V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B,  89(23), 1–6(2014).
[Crossref]

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L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol.,  9(5), 372–377(2014).
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J. Lou, X. Xu, and P. D. Ye, “Black Phosphorus À Monolayer MoS 2 Diode,” ACS Nano,  8(8), 8292–8299(2014).
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L. Wang, X. Chen, A. Yu, Y. Zhang, J. Ding, and W. Lu, “Highly sensitive and wide-band tunable terahertz response of plasma waves based on graphene field effect transistors,” Sci. Rep.,  4, 5470(2014).
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Zhang, J.

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Figures (5)

Fig. 1
Fig. 1 Comparison of plasmon resonances between monolayer BP, graphene and G-BP bilayer structure. (a, b, c) Scheme of the proposed devices. The nanodisks array of two-dimensional material are placed on the semi-infinite substrate. The period is P = Px = Py = 250 nm and the diameter of the nanodisks is D = 150 nm. (d, e, f) simulated spectra of total absorption when the electric field polarizes along x- and y-direction with the doping concentration n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV).
Fig. 2
Fig. 2 Simulated spectra of total absorption when the electric field polarizes along both x- and y-direction with different separations between the graphene nanodisk and the BP nanodisk. The separation ranges from t = 0 to 20 nm. The insets show the distributions of normalized electric fields at the resonance wavelength for y-polarized light.
Fig. 3
Fig. 3 Anisotropic perfect absorption in G-BP bilayer structure with reflecting mirror. (a) Scheme of the proposed structure. From top to bottom of the structures are array of G-insulator-BP nanodisks, dielectric layer, gold layer and semi-infinite substrate (not shown in the figure). The geometry parameters (period P and diameter D) are the same as the Fig. 1. (b) Simulated spectra of total absorption for both polarization with the doping concentration n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV). (c, d) Electric field in the z-direction for both polarization. c and d belong to x-polarization at the resonance wavelength of 11.08 μm and y-polarization at the resonance wavelength of 12.68 μm, respectively. The field is plotted in the x–y plane that is 4 nm above the G-insulator-BP nanodisks.
Fig. 4
Fig. 4 Anisotropic absorption of metallic nanoparticles loaded G-BP bilayer. (a) Scheme of the new structure. From the top to the bottom are an array of gold nanoparticles, an insulator layer marked as a, monolayer BP, an insulator layer marked as b, the graphene layer, a dielectric layer, a gold mirror and a semi-infinite substrate. The period is Px = Py = P = 500 nm and the diameter of the gold nanoparticle is D = 450 nm. (b) Simulated spectra of total absorption for both polarization with the doping concentration n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV). (c,d) Spectra tunability of absorption with the variation of Fermi energy ranging from 0.4 eV to 0.7 eV.
Fig. 5
Fig. 5 Angular dispersions of the total absorption for (a) electric field along y-direction(TE) and (b) electric field along x-direction(TM). Here we use the structure in Fig. 4. The doping concentration is n = 1.9 × 1013cm−2 (Ef ≈ 0.5 eV).

Equations (2)

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σ ( ω ) = 2 e 2 k B T π 2 i ω + i τ 1 ln [ 2 cosh E f 2 k B T ] + e 2 8 + e 2 4 [ 1 π arctan ( ω 2 E f 2 k B T ) i 2 π ln ( ω + 2 E f ) 2 ( ω + 2 E f ) 2 + ( 2 k B T ) 2 ]
σ j = i e 2 n m j ( ω + i η )

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