Abstract

A metamaterial perfect absorber composed of a black phosphorus (BP) monolayer, a photonic crystal, and a metallic mirror is designed and investigated to enhance light absorption at terahertz frequencies. Numerical results reveal that the absorption is enhanced greatly with narrow spectra due to critical coupling, which is enabled by guided resonances. Intriguingly, the structure manifests the unusual polarization-dependent feature attributable to the anisotropy of black phosphorus. The quality factor of the absorber can be as high as 95.1 for one polarization while 63.5 for another polarization, which is consistent with the coupled wave theory. The absorption is tunable by varying key parameters, such as period, radius, slab thickness, incident angle, and polarization angle. Furthermore, the state of the system (i.e., critical coupling, over coupling, and under coupling) can be tuned by changing the electron doping of BP, thus achieving various applications. This work offers a paradigm to enhance the light-matter interaction in monolayer BP without plasmonic response, and this easy-to-fabricate structure will provide potential applications in BP-based devices.

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

1. Introduction

Metamaterials, which do not exist in nature, have attracted considerable attentions due to its distinctive features, such as negative refraction [1], invisible cloaking [2], perfect lens [3], and perfect absorbers [4], etc. So far, various functional metamaterials have been put forward to satisfy practical requirements from the visible to microwave regions [5–11]. Especially for the metamaterial absorbers, they play an important role in many applications (e.g., sensors, detectors, and thermal emitters), which have been extensively investigated.

Recently, high-efficiency optoelectronic devices based on two-dimensional (2D) materials have attracted broad attention. The high optical absorption of 2D materials is of great significance for enhancing the light-matter interaction. However, due to the ultra-thin thickness of 2D materials, their inherent optical absorption is very low, which greatly limits their related applications, hence many mechanisms have been proposed to achieve optical absorption enhancement for 2D materials, such as surface plasmon polaritons [12], localized plasmons [13], magnetic polaritons [14], Tamm plasmon polaritons [15], critical coupling [16–18], Fabry-Perot resonance [19–21], Fano resonance [22], and photon localization [23], etc.

As a newly emerging 2D anisotropic material, black phosphorus (BP) has received extensive attention due to its unique optical and electrical properties [24–29]. To enhance the light-BP interaction in the structure, many BP-based devices have been extensively studied at terahertz (THz) frequencies. Specifically, Low et al. studied the excitation of plasmons in BP [30]. By placing a BP nanoribbon array on top of a thick spacer and a metallic mirror, Liu et al. theoretically investigated localized surface plasmons in periodic monolayer BP nanoribbons with a maximum absorption of near 40% [31]. Similarly, Ni et al. demonstrated that the excitation of anisotropic plasmons can be achieved by depositing a square array of few-layer BP on top of a dielectric substrate, which results in a maximum absorption enhancement of about 30% [32]. Lu et al. investigated the plasmonic responses between BP pairs theoretically [33]. Nong et al. theoretically studied the strong coupling between BP localized surface plasmons and graphene surface plasmons in a composite configuration, and the maximum absorption is about 20% [34]. Lee et al. studied acoustic plasmons excited in a BP layer placed above a conducting plate [35]. Qing et al. theoretically realized the strong hybridization between surface plasmons and magnetic plasmons in a BP-based hybrid system [36]. Hong et al. numerically studied the plasmonic properties in a graphene-BP bilayer [37], etc. Based on the above research works, plasmons in BP exhibits the strong field confinement, resulting in enhanced light-matter interaction. However, the weak light absorption and low sensitivity limit applications of BP-based devices. Another way of increasing the absorption relies on the introduction of multilayered BP into the design [38, 39], which directly complicates the fabrication.

Here, we propose an easy-to-fabricate structure consisting of a BP sheet, a 2D photonic crystal (PC) slab, and a perfect electric conductor (PEC) to achieve the near-unity absorption at terahertz frequencies. Unlike BP-based plasmonic devices, the absorption of BP monolayer is significantly enhanced due to the critical coupling with guided resonances. Because of the anisotropic properties of BP, an absorption peak reaching 99.9% at 4.31 THz is observed under TE incidence, while 87.1% at 4.332 THz under TM incidence is observed. In addition, the absorber exhibits distinct absorption characteristics under oblique incidence for both TE and TM polarizations. The influence of structural parameters (e.g., period, radius, and slab thickness) on the absorption spectra indicates that the critical coupling can be easily tuned. Furthermore, by changing the electron doping of BP, the state of the system can be changed to under coupling, critical coupling or over coupling. This simple structure greatly enhances the absorption of BP monolayer and improves light-matter interaction, providing potential applications for BP-based devices.

2. Structure and theory

The schematic diagram of the proposed absorber is shown in Fig. 1(a), which consists of three functional layers: a monolayer BP on the top acting as a lossy material, a silicon layer decorated with a periodic array of circular air holes acting as a 2D PC, and a thick PEC slab acting as a metallic mirror to suppress the transmission. The lattice periods of the silicon PC slab in both x- and y-directions are Px and Py, respectively. The thickness of the silicon PC slab is h and radius of the air hole is R. The structural parameters in designed absorber are set as: Px = Py = 30 μm, R = 6 μm, h = 13 μm. The refractive index of silicon is 3.42. The monolayer BP is modeled with anisotropic conductivity (σii) described by a semiclassical Drude model, where ii = x or y represents the direction concerned [31], as shown in Fig. 1(b). Here we choose the electron doping to be ns = 3 × 1013 cm−2. Figures 1(d) and 1(e) show the surface conductivity of BP in a broad spectrum for different ns. Due to the existence of PEC, this BP-based absorber can be well described by the single port resonator model, as shown in Fig. 1(c).

 

Fig. 1 (a) Schematic of the proposed structure. (b) Schematic of monolayer BP. (c) The single port resonator model in coupled mode theory. Frequency dependent surface conductivity along (d) the x-direction and (e) the y-direction. Solid lines and dashed lines denote the real part and imaginary part, respectively.

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According to the coupled mode theory (CMT) [16, 40], the system can be described by the following equations:

dadt=(jω0δγ)a+2γS+
S=S++2γa
Here, a is the resonant amplitude, S+ and S denote as the amplitudes of input and outgoing wave, δ and γ are described as intrinsic loss and external leakage rate, and ω0 is the resonant frequency. The reflection coefficient of the model is:
r=SS+=j(ωω0)+δγj(ωω0)+δ+γ
and the absorption coefficient is:
A=1|r|2=4δγ(ωω0)2+(δ+γ)2
As can be seen from Eq. (4), when δ = γ at resonance frequency (ω = ω0), the critical coupling is satisfied and perfect absorption can be achieved. In addition, the impedance of the absorber should match to that of the free space (Z = Z0 = 1) under the critical coupling condition. The effective impedance of the absorber is described as [41]:
Z=(1+S11)2S212(1S11)2S212
where S11 and S21 denote as the scattering parameters relevant to reflectance and transmittance coefficient. Here, the numerical simulations are performed with the finite-difference time-domain (FDTD) method. In the simulation, periodic boundary conditions are applied in the x direction and y direction, and the perfectly matched layer absorbing boundary conditions are employed along the z direction. The spatial mesh size of the structure is set to Δx = Δy = Δz = 0.2 μm. The surface conductivity model is utilized to represent the BP monolayer.

3. Results and analysis

Figures 2(a) and 2(b) illustrate the absorption spectra of the proposed metamaterial absorber. Since BP is the only lossy material in the system, the absorption of the system can be attributed entirely to BP. Once BP is removed, there is no absorption in the system, as depicted by green curves in Figs. 2(a) and 2(b). For the case of a TE-polarized wave (electric field is parallel to y-axis), the absorption spectrum is characterized by a peak with 99.9% at f0 = 4.31 THz, as depicted in Fig. 2(a) by the blue curve. Undoubtedly, the critical coupling can be achieved by the guided resonance in the THz range. The full width at half maximum (FWHM) is only Δf = 0.0453 THz, indicating that the linewidth of spectral absorption is very narrow. The total quality factor can be expressed as Q = f0f, which reaches about 95.1. Meanwhile, the absorption spectrum from CMT gives a comparison with the FDTD method, as depicted in Fig. 2(a) by the red triangles. The fitted δ = γ = 7.16 × 1010 Hz. According to CMT, the intrinsic loss and external leakage of the resonant mode can be defined as Qδ = ω0/2δ and Qγ = ω0/2γ, respectively. The theoretical quality factor can be obtained by QCMT = Qδ·Qγ/(Qδ + Qγ), and the value of QCMT is 94.6. The Q and QCMT are nearly identical, indicating that the total absorption of the absorber can be attributed to critical coupling. As depicted in the inset (i) of Fig. 2(a), one can clearly see that the resonance mode undergoes an abrupt π-phase jump across the resonance wavelength when the critical coupling is achieved [42]. In addition, we calculate the effective impedance of the system, as shown in the inset (ii) of Fig. 2(a). According to Eq. (5), the effective impedance is Z = 0.951 + 0.014i at resonance frequency, which is almost the same as the impedance of the free space. For the case of a TM-polarized wave (magnetic field is parallel to y-axis), one can clearly see a high absorption peak (87.1%) at the frequency of f0 = 4.332 THz, as shown in Fig. 2(b). Obviously, the absorption spectrum exhibits significant polarization dependent characteristics due to the anisotropic properties of BP. As the TE wave is converted to the TM wave, the resonance frequency increases from 4.31 THz to 4.332 THz, and the corresponding resonance position shift is 353.5nm. Furthermore, we observe the reflection phase under the TM wave, which occupies only a small range of less than π-phase, as shown in the inset (i) of Fig. 2(b). This also indicates that the system changes from a critical coupling to an under coupling, which is characterized by δ > γ [42]. The parameters of CMT used for fitting are δ = 15.01 × 1010 Hz and γ = 7.16 × 1010 Hz, respectively. The FWHM of this case is Δf = 0.0694 THz, and the quality factor is 62.4. Accordingly, the value of quality factor in theory is 61.4. Moreover, the effective impedance at the resonant frequency is Z = 1.157 – 0.813i, which no longer matches the impedance in the air, so the resonator cannot completely absorb the incident light. The absorption obtained from the FDTD method is almost the same as that of the CMT, which indicates that the CMT is valid for the single port system. It is noted that there is a slight deviation between the CMT model and the FDTD simulation at a position away from the wavelength of the resonance, because the CMT assumes that there is no loss away from the resonance [43]. To obtain further insight into the physical mechanism of the enhanced light absorption effect, Figs. 2(c) and 2(d) illustrate the simulated magnetic field |Hz|2 distributions of the proposed metamaterial absorber at the resonance frequency of 4.31 THz under TE-polarized wave. One can clearly see that the guided resonance with field confinement is mainly distributed in the lossless PC slab. The PEC can completely suppress transmission, so when the system satisfies the critical coupling, the localized incident energy at resonance can be fully absorbed by the system.

 

Fig. 2 Simulation results and CMT calculated results of absorption spectrum for (a) TE-polarized wave and (b) TM-polarized wave at normal incidence. Inset (i) shows the reflection phase of the absorber, and inset (ii) shows the effective impedance of the perfect absorption peak. Magnetic field |Hz|2 distributions of the guided resonance (c) in the xy plane and (d) in the xz plane at the resonance frequency of f = 4.31 THz for TE-polarized wave. The boundaries are indicated by the white lines.

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The absorption spectra at various parameters under TE polarizations are illustrated in Figs. 3(a)–3(c). Figure 3(a) illustrates the relation between the absorbance and the PC slab thickness (h). When h is increased from 12 μm to 15 μm, the absorption peak red-shifts from 4.42 THz to 4.14 THz, and the high absorptivity is maintained. Similarly, decreasing the radius pushes the resonance position to higher frequency, as shown in Fig. 3(b). Figure 3(c) exhibits the absorption spectra as a function of frequency and period (P). When P is increased from 28 μm to 34 μm, the resonance frequency is pushed down from 4.5 THz to 4 THz. In addition, a new absorption peak emerges when P is larger than 31.3 μm. The phenomenon that the absorption peak of the metamaterial absorber undergoes a significant red shift (i.e., the resonance frequency moves toward a lower frequency) may due to the increase of the effective refractive indices of the PC slab (i.e., increasing h, decreasing R, or increasing P). It should be noted that the tunable absorption based on structural parameters is necessary for some absorbers with specific requirements. In addition, the resonance position can also be adjusted by filling the air hole with the dielectric material. When the refractive index of the filled medium increases from 1 to 2, the resonance frequency is red-shifted from 4.31 THz to 4.185 THz, and the absorptivity is still above 95%, as shown in Fig. 3(d). These results indicate that the proposed BP-based structure has potential in terahertz sensing.

 

Fig. 3 Absorption response for the proposed absorber at different structural parameters under vertical illumination with TE-polarization: (a) h is allowed to change; (b) R is allowed to change; (c) P is allowed to change; (d) the filled medium with different refractive index is allowed to change. Except as indicated, the geometric parameters are fixed to the default values.

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Next, we study the absorption performance of the absorber under oblique incidence. For the TE-polarized case, when θ is smaller than 12° (θ denotes the angle between the incident wavevector and the z-axis), the intensity of the absorption peak slightly decreases as the incident angle increase, and the resonance peak undergoes a blue-shift. With θ increasing further, the intensity of the absorption peak sharply decreases, as shown in Fig. 4(a). In contrast, for TM polarization, the absorber exhibits better absorption stability. As θ increases from 0 to 60°, the absorbance decreases from 87.1% to 70.5%, as shown in Fig. 4(b). Furthermore, although the structure is centrally rotationally symmetric, this BP-based absorber exhibits polarization-dependent features due to the anisotropy of BP, as shown in Fig. 4(c). When φ (φ denotes the angle between the electric field and the y-axis) is varied from the 0 to 90°, the absorptivity decreases, the bandwidth increases, and the absorption peak blue-shifts from 4.31 THz to 4.332 THz. It is remarkable that the absorption tuning via incident angle or polarization angle can make the absorber with flexible tunability.

 

Fig. 4 (a) and (b) depict the absorption with various incident angles from 0° to 60° for TE and TM polarizations. (c) Absorption spectra for different polarization angles. Except as indicated, the geometric parameters are fixed to the default values.

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Finally, we investigate the absorption performance at different electron doping (ns). It should be pointed out that ns can affect the absorption of electromagnetic energy because it directly determines the surface conductivity of BP. For TE polarization in Fig. 5(a), it is found that when ns increases, the resonance peak undergoes a blue-shift, and the intensity of the absorption peak is gradually increased until it reaches the perfect absorption, and then gradually decreases. Specifically, at ns = 1 × 1013 cm−2, an absorption peak reaching 73.5% at f = 4.298 THz can be observed. The corresponding reflection phase (ϕ) is depicted by red curve in the inset of Fig. 5(a). The phase difference Δϕ can cover the full 2π range without an abrupt π-phase jump, indicating that the state of the system is over coupling. It should be noted here that only ns of BP is changed, and other parameters remain unchanged, so it can be approximated that only the intrinsic loss (δ) and resonance frequency (f0) of the system change, while external leakage rate (γ) remains unchanged. The CMT fitted δ = 2.3 × 1010 Hz is smaller than γ = 7.16 × 1010 Hz, which also proves that the system is over coupling. As mentioned above, when ns = 3 × 1013 cm−2, the effective impedance of the system matches well with the free space at the resonance frequency, resulting in critical coupling. As ns continues to increase to 5 × 1013 cm−2, the effective impedance of absorber deviates from the free space, and the absorption decreases from nearly 100% to 94.6%. However, the state of the system transitions from critical coupling to under coupling. Unlike the cases of over coupling and critical coupling, the CMT fitted δ = 11.1 × 1010 Hz is larger than γ. Moreover, Δϕ can only cover less than π range. The above analysis results are also applicable to TM polarization, as shown in Fig. 5(b). When ns = 0.5 × 1013 cm−2, 1.3 × 1013 cm−2, and 3 × 1013 cm−2, the corresponding state of the system is over coupling, critical coupling, and under coupling, respectively. The competition between the δ and γ gives the BP-based structure many different physical properties, resulting in a variety of potential applications, such as phase-modulation-related devices (δ < γ), anisotropic perfect absorbers (δ = γ), and simple electric reflectors (δ > γ) [44,45].

 

Fig. 5 (a) FDTD simulated and CMT fitted absorption spectra at ns = 1 × 1013 cm−2 (red), 3 × 1013 cm−2 (blue), and 5 × 1013 cm−2 (green) under TE-polarized wave. (b) FDTD simulated and CMT fitted absorption spectra at ns = 0.5 × 1013 cm−2 (red), 1.3 × 1013 cm−2 (blue), and 3 × 1013 cm−2 (green) under TM-polarized wave. The insets show the reflection phase of the absorber.

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4. Conclusion

We have theoretically proposed a tunable BP-based absorber to enhance light absorption at terahertz frequencies. Unlike other plasmonic devices, the enhanced absorption of the absorber can be attributed to the critical coupling, which is enabled by the guided resonance in 2D PC. The results of FDTD are consistent with the results of CMT. Although the structure adopts central rotational symmetry, the absorber exhibits polarization-dependent features due to the anisotropy of BP. Furthermore, by varying the electron doping of BP, the resonance frequency could be tuned and the state of the system can be changed from critical coupling to over coupling or under coupling. This easy-to-fabricate structure may provide potential applications in many promising applications, such as detecting, sensing, and other BP-based optoelectronic devices.

Funding

National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, 2017YFA0700203); National Natural Science Foundation of China (NSFC) (61522106, 61571117, 61501117, 61501112, 61631007, 61701108, 61831006); and 111 Project (111-2-05).

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References

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [Crossref] [PubMed]
  2. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
    [Crossref] [PubMed]
  3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref] [PubMed]
  4. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
    [Crossref] [PubMed]
  5. J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83(16), 165107 (2011).
    [Crossref]
  6. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
    [Crossref] [PubMed]
  7. T. J. Cui, S. Liu, and L. L. Li, “Information entropy of coding metasurface,” Light. Sci. Appl. 5(11), e16172 (2016).
    [Crossref] [PubMed]
  8. S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
    [Crossref] [PubMed]
  9. S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
    [Crossref]
  10. T. J. Cui, “Microwave metamaterials - From passive to digital and programmable controls of electromagnetic waves,” J. Opt. 19(8), 084004 (2017).
    [Crossref]
  11. T. J. Cui, “Microwave metamaterials,” Natl. Sci. Rev. 5(5), 134–136 (2018).
    [Crossref]
  12. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
  13. Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
    [Crossref] [PubMed]
  14. Y. Long, H. Deng, H. Xu, L. Shen, W. Guo, C. Liu, W. Huang, W. Peng, L. Li, H. Lin, and C. Guo, “Magnetic coupling metasurface for achieving broad-band and broad-angular absorption in the MoS2 monolayer,” Opt. Mater. Express 7(1), 100–110 (2017).
    [Crossref]
  15. H. Lu, X. Gan, D. Mao, Y. Fan, D. Yang, and J. Zhao, “Nearly perfect absorption of light in monolayer molybdenum disulfide supported by multilayer structures,” Opt. Express 25(18), 21630–21636 (2017).
    [Crossref] [PubMed]
  16. J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1(4), 347–353 (2014).
    [Crossref]
  17. H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
    [Crossref] [PubMed]
  18. Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014).
    [Crossref] [PubMed]
  19. H. Li, Y. Ren, J. Hu, M. Qin, and L. Wang, “Wavelength-selective wide-angle light absorption enhancement in monolayers of transition-metal dichalcogenides,” J. Light. Technol. 36(16), 3236–3241 (2018).
    [Crossref]
  20. Y. Jiang, W. Chen, and J. Wang, “Broadband MoS2-based absorber investigated by a generalized interference theory,” Opt. Express 26(19), 24403–24412 (2018).
    [Crossref]
  21. Y. Jiang, H. D. Zhang, J. Wang, C. N. Gao, J. Wang, and W. P. Cao, “Design and performance of a terahertz absorber based on patterned graphene,” Opt. Lett. 43(17), 4296–4299 (2018).
    [Crossref] [PubMed]
  22. W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
    [Crossref]
  23. J. T. Liu, N. H. Liu, J. Li, X. Jing Li, and J. H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
    [Crossref]
  24. X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618–655 (2016).
    [Crossref]
  25. F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5, 4458 (2014).
    [Crossref] [PubMed]
  26. G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
    [Crossref] [PubMed]
  27. X. Wang, Q. Ma, L. Wu, J. Guo, S. Lu, X. Dai, and Y. Xiang, “Tunable terahertz/infrared coherent perfect absorption in a monolayer black phosphorus,” Opt. Express 26(5), 5488–5496 (2018).
    [Crossref] [PubMed]
  28. X. Song, Z. Liu, Y. Xiang, and K. Aydin, “Biaxial hyperbolic metamaterials using anisotropic few-layer black phosphorus,” Opt. Express 26(5), 5469–5477 (2018).
    [Crossref] [PubMed]
  29. L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
    [Crossref]
  30. 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), 106802 (2014).
    [Crossref] [PubMed]
  31. Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
    [Crossref] [PubMed]
  32. 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]
  33. H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
    [Crossref] [PubMed]
  34. J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018).
    [Crossref] [PubMed]
  35. I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
    [Crossref]
  36. Y. M. Qing, H. F. Ma, and T. J. Cui, “Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system,” Opt. Lett. 43(20), 4985–4988 (2018).
    [Crossref] [PubMed]
  37. Q. Hong, F. Xiong, W. Xu, Z. Zhu, K. Liu, X. Yuan, J. Zhang, and S. Qin, “Towards high performance hybrid two-dimensional material plasmonic devices: strong and highly anisotropic plasmonic resonances in nanostructured graphene-black phosphorus bilayer,” Opt. Express 26(17), 22528–22535 (2018).
    [Crossref] [PubMed]
  38. J. Wang and Y. Jiang, “Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials,” Opt. Express 25(5), 5206–5216 (2017).
    [Crossref] [PubMed]
  39. 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]
  40. S. Fan and W. Suh, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
    [Crossref]
  41. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
    [Crossref]
  42. J. Yoon, K. H. Seol, and S. H. Song, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express 18(25), 25702–25711 (2010).
    [Crossref] [PubMed]
  43. Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
    [Crossref]
  44. X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012).
    [Crossref] [PubMed]
  45. C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
    [Crossref] [PubMed]

2019 (1)

Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
[Crossref]

2018 (11)

T. J. Cui, “Microwave metamaterials,” Natl. Sci. Rev. 5(5), 134–136 (2018).
[Crossref]

H. Li, Y. Ren, J. Hu, M. Qin, and L. Wang, “Wavelength-selective wide-angle light absorption enhancement in monolayers of transition-metal dichalcogenides,” J. Light. Technol. 36(16), 3236–3241 (2018).
[Crossref]

Y. Jiang, W. Chen, and J. Wang, “Broadband MoS2-based absorber investigated by a generalized interference theory,” Opt. Express 26(19), 24403–24412 (2018).
[Crossref]

Y. Jiang, H. D. Zhang, J. Wang, C. N. Gao, J. Wang, and W. P. Cao, “Design and performance of a terahertz absorber based on patterned graphene,” Opt. Lett. 43(17), 4296–4299 (2018).
[Crossref] [PubMed]

X. Wang, Q. Ma, L. Wu, J. Guo, S. Lu, X. Dai, and Y. Xiang, “Tunable terahertz/infrared coherent perfect absorption in a monolayer black phosphorus,” Opt. Express 26(5), 5488–5496 (2018).
[Crossref] [PubMed]

X. Song, Z. Liu, Y. Xiang, and K. Aydin, “Biaxial hyperbolic metamaterials using anisotropic few-layer black phosphorus,” Opt. Express 26(5), 5469–5477 (2018).
[Crossref] [PubMed]

L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
[Crossref]

J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018).
[Crossref] [PubMed]

I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
[Crossref]

Y. M. Qing, H. F. Ma, and T. J. Cui, “Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system,” Opt. Lett. 43(20), 4985–4988 (2018).
[Crossref] [PubMed]

Q. Hong, F. Xiong, W. Xu, Z. Zhu, K. Liu, X. Yuan, J. Zhang, and S. Qin, “Towards high performance hybrid two-dimensional material plasmonic devices: strong and highly anisotropic plasmonic resonances in nanostructured graphene-black phosphorus bilayer,” Opt. Express 26(17), 22528–22535 (2018).
[Crossref] [PubMed]

2017 (8)

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]

T. J. Cui, “Microwave metamaterials - From passive to digital and programmable controls of electromagnetic waves,” J. Opt. 19(8), 084004 (2017).
[Crossref]

Y. Long, H. Deng, H. Xu, L. Shen, W. Guo, C. Liu, W. Huang, W. Peng, L. Li, H. Lin, and C. Guo, “Magnetic coupling metasurface for achieving broad-band and broad-angular absorption in the MoS2 monolayer,” Opt. Mater. Express 7(1), 100–110 (2017).
[Crossref]

H. Lu, X. Gan, D. Mao, Y. Fan, D. Yang, and J. Zhao, “Nearly perfect absorption of light in monolayer molybdenum disulfide supported by multilayer structures,” Opt. Express 25(18), 21630–21636 (2017).
[Crossref] [PubMed]

H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
[Crossref] [PubMed]

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]

H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
[Crossref] [PubMed]

2016 (6)

T. J. Cui, S. Liu, and L. L. Li, “Information entropy of coding metasurface,” Light. Sci. Appl. 5(11), e16172 (2016).
[Crossref] [PubMed]

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
[Crossref]

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618–655 (2016).
[Crossref]

G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
[Crossref] [PubMed]

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

2015 (2)

W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
[Crossref]

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

2014 (4)

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), 106802 (2014).
[Crossref] [PubMed]

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5, 4458 (2014).
[Crossref] [PubMed]

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014).
[Crossref] [PubMed]

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1(4), 347–353 (2014).
[Crossref]

2013 (1)

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

2012 (2)

J. T. Liu, N. H. Liu, J. Li, X. Jing Li, and J. H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
[Crossref]

X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012).
[Crossref] [PubMed]

2011 (3)

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

J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83(16), 165107 (2011).
[Crossref]

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

2010 (2)

2008 (1)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

2005 (1)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

2003 (1)

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Ajayan, P. M.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (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), 106802 (2014).
[Crossref] [PubMed]

Aydin, K.

X. Song, Z. Liu, Y. Xiang, and K. Aydin, “Biaxial hyperbolic metamaterials using anisotropic few-layer black phosphorus,” Opt. Express 26(5), 5469–5477 (2018).
[Crossref] [PubMed]

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

Bao, D.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

Bao, L.

G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
[Crossref] [PubMed]

Bolotin, K. I.

W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
[Crossref]

Briggs, D. P.

W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
[Crossref]

Cai, B.

Cao, W. P.

Chen, W.

Chen, X.

Cheng, Q.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
[Crossref]

Cui, T. J.

Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
[Crossref]

Y. M. Qing, H. F. Ma, and T. J. Cui, “Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system,” Opt. Lett. 43(20), 4985–4988 (2018).
[Crossref] [PubMed]

T. J. Cui, “Microwave metamaterials,” Natl. Sci. Rev. 5(5), 134–136 (2018).
[Crossref]

T. J. Cui, “Microwave metamaterials - From passive to digital and programmable controls of electromagnetic waves,” J. Opt. 19(8), 084004 (2017).
[Crossref]

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
[Crossref]

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

T. J. Cui, S. Liu, and L. L. Li, “Information entropy of coding metasurface,” Light. Sci. Appl. 5(11), e16172 (2016).
[Crossref] [PubMed]

X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[Crossref] [PubMed]

Dai, N.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Dai, X.

L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
[Crossref]

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G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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J. T. Liu, N. H. Liu, J. Li, X. Jing Li, and J. H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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Liu, N. H.

J. T. Liu, N. H. Liu, J. Li, X. Jing Li, and J. H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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Low, T.

I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
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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), 106802 (2014).
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Lu, S.

Lu, W.

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Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
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Ma, R.

G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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Martin-Moreno, L.

I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
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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), 106802 (2014).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
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I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
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X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
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G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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H. Li, Y. Ren, J. Hu, M. Qin, and L. Wang, “Wavelength-selective wide-angle light absorption enhancement in monolayers of transition-metal dichalcogenides,” J. Light. Technol. 36(16), 3236–3241 (2018).
[Crossref]

H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
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Qing, Y. M.

Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
[Crossref]

Y. M. Qing, H. F. Ma, and T. J. Cui, “Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system,” Opt. Lett. 43(20), 4985–4988 (2018).
[Crossref] [PubMed]

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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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Ren, Y.

H. Li, Y. Ren, J. Hu, M. Qin, and L. Wang, “Wavelength-selective wide-angle light absorption enhancement in monolayers of transition-metal dichalcogenides,” J. Light. Technol. 36(16), 3236–3241 (2018).
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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), 106802 (2014).
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L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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Song, X.

Soukoulis, C. M.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
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D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
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S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5, 4458 (2014).
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J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018).
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Wei, W.

Wen, S.

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014).
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X. Wang, Q. Ma, L. Wu, J. Guo, S. Lu, X. Dai, and Y. Xiang, “Tunable terahertz/infrared coherent perfect absorption in a monolayer black phosphorus,” Opt. Express 26(5), 5488–5496 (2018).
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L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
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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), 106802 (2014).
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L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
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X. Song, Z. Liu, Y. Xiang, and K. Aydin, “Biaxial hyperbolic metamaterials using anisotropic few-layer black phosphorus,” Opt. Express 26(5), 5469–5477 (2018).
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X. Wang, Q. Ma, L. Wu, J. Guo, S. Lu, X. Dai, and Y. Xiang, “Tunable terahertz/infrared coherent perfect absorption in a monolayer black phosphorus,” Opt. Express 26(5), 5488–5496 (2018).
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Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014).
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C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
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X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012).
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Xiong, F.

Xu, H.

Xu, Q.

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
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Yang, D.

Yang, H.

G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
[Crossref]

Yi, J.

Yoon, J.

You, Q.

L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
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Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
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Yuan, H.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
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Yuan, X.

Zhai, X.

Zhang, G.

G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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Zhang, H.

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014).
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Zhang, H. D.

Zhang, J.

Zhang, L.

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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Zhang, W.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
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Zhang, W. L.

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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Zhang, Y. Y.

G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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Zhao, J.

Zhou, L.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012).
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J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83(16), 165107 (2011).
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Zhou, X. Y.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
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Zhu, J.

L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
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ACS Nano (1)

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
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ACS Photon. (2)

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1(4), 347–353 (2014).
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I. H. Lee, L. Martin-Moreno, D. A. Mohr, K. Khaliji, T. Low, and S. H. Oh, “Anisotropic acoustic plasmons in black phosphorus,” ACS Photon. 5(6), 2208–2216 (2018).
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Adv. Opt. Mater. (1)

S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016).
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Adv. Opt. Photonics (1)

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618–655 (2016).
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Appl. Phys. Lett. (2)

W. Wang, A. Klots, Y. Yang, W. Li, I. I. Kravchenko, D. P. Briggs, K. I. Bolotin, and J. Valentine, “Enhanced absorption in two-dimensional materials via Fano-resonant photonic crystals,” Appl. Phys. Lett. 106(18), 181104 (2015).
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J. Light. Technol. (1)

H. Li, Y. Ren, J. Hu, M. Qin, and L. Wang, “Wavelength-selective wide-angle light absorption enhancement in monolayers of transition-metal dichalcogenides,” J. Light. Technol. 36(16), 3236–3241 (2018).
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J. Opt. (1)

T. J. Cui, “Microwave metamaterials - From passive to digital and programmable controls of electromagnetic waves,” J. Opt. 19(8), 084004 (2017).
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J. Opt. Soc. Am. A (1)

J. Phys. Chem. C (1)

L. Wu, Q. Wang, B. Ruan, J. Zhu, Q. You, X. Dai, and Y. Xiang, “High-performance lossy-mode resonance sensor based on few-layer black phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018).
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J. Phys. D: Appl. Phys. (1)

Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Tunable dual-band perfect metamaterial absorber based on a graphene-SiC hybrid system by multiple resonance modes,” J. Phys. D: Appl. Phys. 52(1), 015104 (2019).
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Light. Sci. Appl. (2)

T. J. Cui, S. Liu, and L. L. Li, “Information entropy of coding metasurface,” Light. Sci. Appl. 5(11), e16172 (2016).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light. Sci. Appl. 5(5), e16076 (2016).
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Nano Lett. (2)

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
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G. Wang, L. Bao, T. Pei, R. Ma, Y. Y. Zhang, L. Sun, G. Zhang, H. Yang, J. Li, C. Gu, S. Du, S. T. Pantelides, R. D. Schrimpf, and H. Gao, “Introduction of interfacial charges to black phosphorus for a family of planar devices,” Nano Lett. 16(11), 6870–6878 (2016).
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Nat. Commun. (2)

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5, 4458 (2014).
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H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
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Natl. Sci. Rev. (1)

T. J. Cui, “Microwave metamaterials,” Natl. Sci. Rev. 5(5), 134–136 (2018).
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Opt. Express (11)

H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
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H. Lu, X. Gan, D. Mao, Y. Fan, D. Yang, and J. Zhao, “Nearly perfect absorption of light in monolayer molybdenum disulfide supported by multilayer structures,” Opt. Express 25(18), 21630–21636 (2017).
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X. Wang, Q. Ma, L. Wu, J. Guo, S. Lu, X. Dai, and Y. Xiang, “Tunable terahertz/infrared coherent perfect absorption in a monolayer black phosphorus,” Opt. Express 26(5), 5488–5496 (2018).
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X. Song, Z. Liu, Y. Xiang, and K. Aydin, “Biaxial hyperbolic metamaterials using anisotropic few-layer black phosphorus,” Opt. Express 26(5), 5469–5477 (2018).
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Y. Jiang, W. Chen, and J. Wang, “Broadband MoS2-based absorber investigated by a generalized interference theory,” Opt. Express 26(19), 24403–24412 (2018).
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H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
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J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the proposed structure. (b) Schematic of monolayer BP. (c) The single port resonator model in coupled mode theory. Frequency dependent surface conductivity along (d) the x-direction and (e) the y-direction. Solid lines and dashed lines denote the real part and imaginary part, respectively.
Fig. 2
Fig. 2 Simulation results and CMT calculated results of absorption spectrum for (a) TE-polarized wave and (b) TM-polarized wave at normal incidence. Inset (i) shows the reflection phase of the absorber, and inset (ii) shows the effective impedance of the perfect absorption peak. Magnetic field |Hz|2 distributions of the guided resonance (c) in the xy plane and (d) in the xz plane at the resonance frequency of f = 4.31 THz for TE-polarized wave. The boundaries are indicated by the white lines.
Fig. 3
Fig. 3 Absorption response for the proposed absorber at different structural parameters under vertical illumination with TE-polarization: (a) h is allowed to change; (b) R is allowed to change; (c) P is allowed to change; (d) the filled medium with different refractive index is allowed to change. Except as indicated, the geometric parameters are fixed to the default values.
Fig. 4
Fig. 4 (a) and (b) depict the absorption with various incident angles from 0° to 60° for TE and TM polarizations. (c) Absorption spectra for different polarization angles. Except as indicated, the geometric parameters are fixed to the default values.
Fig. 5
Fig. 5 (a) FDTD simulated and CMT fitted absorption spectra at ns = 1 × 1013 cm−2 (red), 3 × 1013 cm−2 (blue), and 5 × 1013 cm−2 (green) under TE-polarized wave. (b) FDTD simulated and CMT fitted absorption spectra at ns = 0.5 × 1013 cm−2 (red), 1.3 × 1013 cm−2 (blue), and 3 × 1013 cm−2 (green) under TM-polarized wave. The insets show the reflection phase of the absorber.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

d a d t = ( j ω 0 δ γ ) a + 2 γ S +
S = S + + 2 γ a
r = S S + = j ( ω ω 0 ) + δ γ j ( ω ω 0 ) + δ + γ
A = 1 | r | 2 = 4 δ γ ( ω ω 0 ) 2 + ( δ + γ ) 2
Z = ( 1 + S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2

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