Abstract

As a direct band gap two-dimensional (2D) semiconductor material, black phosphorus (BP) bridges the characteristics of graphene, with a zero or near-zero band gap, and transition metal dichalcogenides, with a wide band gap. In the infrared (IR) regime, 2D BP materials can harvest electromagnetic energy due to losses derived from its surface conductivity. In this paper, we propose an IR absorber design comprising 2D BP metamaterials sandwiched between dielectric layers. The multilayered sandwich-like absorber structure is mounted on a full reflective gold mirror, which forms a Fabry-Perot resonator to strengthen light-matter interactions. Harvested surface plasmons are excited around the 2D BP metamaterial edges, and the incident IR light can be efficiently dissipated by increasing the number of layers of the sandwich-like structure (NLSS). The physical absorption mechanism can be attributed to the destructive interference from the metamaterials, which can be enhanced with increasing NLSS. Here, a phase difference of about 180° is obtained between the directly reflected wave from the first interface and the emergent wave derived from the superposition of the multiple reflections among the resonator, and the amplitude of the emergent wave is steadily reduced to a value close to that of the directly reflected wave with increasing NLSS for incident transverse-magnetic polarized IR illumination.

© 2017 Optical Society of America

1. Introduction

As key components in biosensing, imaging, and communications systems, electromagnetic wave absorbers have been attracting increasing attention in the infrared (IR) regime [1]. Over the past few years, two-dimensional (2D) materials, such as graphene, transition metal dichalcogenides (TMDs), and black phosphorus (BP), with atomic-scale thicknesses, have shown great promise for use in applications such as photonics, optoelectronics, imaging, and telecommunications [2–5]. Despite the inherently ultra-compact size of such materials, they can still significantly respond to incident illumination due to strong light-matter interactions at a wavelength or subwavelength scale, and therefore can be regarded as suitable candidates in the design of IR absorbers [6–15].

As a 2D semiconductor material, graphene is characterized by a zero or near-zero band gap and low absorption co-efficiency, which limits its applications under conditions where high on-off ratio and strong light-matter interaction are required [11]. Despite some solutions such as silicon doping [16] have been applied to open the band gap, some other unexpected limitations were also accompanied together with these treatments [15]. In contrast, TMDs, like MoTe2, MoSe2, and MoS2, posses large intrinsic band gaps ranging from 1.0 eV to 2.0 eV, and electromagnetic properties that mainly depend on various factors such as temperature [4], train level [17], illumination intensity [18], and thickness [19]. With confirmed low electronic mobility, TMDs have been limited in many applications such as field-effect transistors (FET) and IR optoelectronics. Although TDMs with suitable defects can be developed to increase mobility, the preparation process is extremely difficult [11].

Similar to graphene, the atoms in 2D BP materials are strongly bonded to form in-plane layers with weak interaction between layers through van der Waals forces [20]. 2D BP materials can then be exfoliated from bulk BP by mechanical or chemical method [21–23]. Unlike other 2D materials, the atoms in 2D BP are arranged to form a puckered hexagonal honeycomb structure with ridges due to sp3 hybridization, which leads to strong in-plane anisotropic electrical and optical properties [24–27]. Therefore, the in-plane anisotropy of BP can be expressed in terms of Cartesian coordinates, i.e., the x-direction (or armchair direction) and y-direction (or zigzag direction) [26, 27], which are respectively perpendicular and parallel to the ridges. Compared with graphene and TMDs, BP has a remarkable direct band gap that is ~0.3 eV for bulk BP, but for which 2D BP provides a thickness-dependent direct band gap ranging up to ~2 eV for monolayer BP [27–29]. It suggests that BP could possess broadband response from mid-IR to far-IR and even visible band [15]. As such, 2D BP bridges the gap between graphene and TMDs [30], and offers great potential for various applications such as high-performance thin-film electronics, mid-IR and far-IR optoelectronics, and for the development of other novel devices [31–33]. Therefore, 2D BP materials have been attracting increasing attention as a candidate in the design of IR absorbers. BP-based saturable absorbers, for example, those used in Q-switching and mode-locking to achieve pulse emission of lasers, have been developed [11–15]. However, the patterning of BP materials, in the form of BP metamaterials, has thus far not been included in the design process.

In this paper, we propose an IR absorber that utilizes a multilayered BP-metamaterial/dielectric sandwich-like structure on an optically thick gold mirror, which blocks all transmission, and forms a Fabry-Perot resonator to enhance the light-matter interaction. In addition, we demonstrate using simulations that the absorption rate (AR) of the proposed IR absorber is highly dependent on the number of layers in the sandwich-like structure (NLSS). We present an investigation of the electromagnetic response of 2D BP metamaterials in the sandwich-like structure, and elaborate upon the mechanism of its response using interference theory [9, 34].

2. Electrical model of a 2D BP layer

The permittivity of a 2D BP layer can be characterized as a diagonal tensor

ε¯¯=[ε1000ε2000ε3],
where ε1, ε2, and ε3 denote the dispersion elements along the x, y, and z directions, respectively. These elements can be expressed as
εi=εr+jσiε0ωd(i=1,2or3),
where εr is the relative permittivity, j = √−1, σi is the in-plane surface conductivity (σ3 ≅ 0), the permittivity of free space ε0 = 8.854 × 10−12 F·m−1, ω is the frequency of the incident light, and d represents the thickness of the BP layer. For 2D BP, εr = 5.76 [35, 36]. Equation (2) indicates that the in-plane anisotropy is mainly caused by σi. From the classical Drude model, the value of σi in the mid-IR and far-IR wavelength regimes can be approximately given as [26, 27, 35]
σi=jDiπ(ω+jη/)(i=1or2).
Here, is the reduced Planck constant, η (eV) is the parameter describing the electron doping, and the Drude weight Di is given as
Di=πe2nsmi,
where e is the electron charge, ns describes the relaxation rate, and mi denotes the in-plane electron effective masses near the Γ point within the Hamiltonian model, which can be written as follows:

m1=22γ2/Δ+ηc,m2=2νc.

For monolayer BP with a scale length α, the parameters in Eq. (5) can be set as γ = 4π/α, ηc = 2/(0.4m0), vc = 2/(0.7m0), and the band gap Δ = 2 eV, for a standard electron rest mass m0 = 9.10938 × 10−31 kg. Given a fixed η = 10 meV, Fig. 1 shows the real and imaginary part of σi (i = 1, 2) in a broad spectrum for different ns, where black and red lines refer to σ1 and σ2, and solid lines, dotted lines, and dashed lines are the conductivity for ns with 1013 cm−2, 5 × 1013 cm−2, and 1014 cm−2, respectively. It is clear that σi is approximately proportional to ns, σ1 is greater than σ2 for all ns, and only the real part of σi results in electromagnetic loss as expected.

 

Fig. 1 Frequency dependent surface conductivity: (a) real part; (b) imaginary part. Black lines and red lines denote the surface conductivity along the x-direction and y-direction, respectively; solid lines, dotted lines, and dashed lines are the conductivity values for electron doping parameter ns given as 1013 cm−2, 5 × 1013 cm−2, and 1014 cm−2, respectively.

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3. Results and discussion

A schematic diagram of the proposed sandwich-like structure absorber is shown in Fig. 2(a). The structure consists of 2D BP metamaterials comprising infinite length nano-ribbons sandwiched between dielectric layers with a refractive index n = 1.7, and is mounted on a full reflective gold mirror. The gold mirror does not allow the transmission of incident light, and forms a Fabry-Perot resonance with the BP metamaterials. Therefore, the reflected energy is suppressed through electromagnetic losses in the 2D BP, which leads to strong absorption. A front view of the absorber and its geometrical parameters are shown in Fig. 2(b). In the design, we employ the material parameter ns = 1013 cm−2, a 2D BP thickness d = 1 nm, and the following geometrical parameters: H = 8 μm, d0 = 10 nm, d1 = d2 = d3 = 0.5 μm, and d4 = 6.5 μm. In the analysis, the periodicity p and width w of the nano-ribbon are varied, obviously D = pw is the distance between neighboring nano-ribbons. In the far-IR and mid-IR regimes, the top dielectric layer has a negligible effect on the absorption performance because the wavelength is much greater than d0. Nevertheless, the top dielectric provides protection to the top BP metamaterials by preventing environmental-induced degradation [37, 38].

 

Fig. 2 (a) Schematic of the proposed sandwich-like structured absorber. (b) Front view of the proposed absorber with layer dimensions. Simulated absorption rate (AR) spectra for various BP monolayer nano-ribbon widths w, and for transverse-magnetic TM polarization and transverse-electric (TE) polarization with ridges perpendicular to the x-direction (c and d) and the y-direction (e and f). The inset of (c) shows the AR spectrum for w = 210 nm in the lower wavelength region. Simulated TM polarization AR spectra for various distances between two nano-ribbons (g) and for various thicknesses BP with monolayer, bilayer and trilayer atom (h) while ridges perpendicular to x-direction.

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The proposed absorber was investigated via simulations using CST Microwave Studio, where the 1 nm thick 2D BP were meshed using fine grids. Periodic boundary conditions were employed in the x and y directions, and the plane wave was incident downward on the top surface of the absorber with magnetic and electric fields Hy and Ey, respectively, perpendicular to the x-z plane [i.e., with either transverse-magnetic (TM) or transverse-electric (TE) polarizations]. The wavelength (λ) dependent AR can be obtained as A(λ) = 1 − R(λ) − T(λ) with reflection given by R(λ) = |S11(λ)|2 and transmission given by T(λ) = |S21(λ)|2. Because the gold mirror prevents the propagation of downward light, the transmission is regarded as zero over the entire wavelength range investigated. Therefore, A(λ) = 1 − R(λ).

When period p is fixed to 250 nm and BP metamaterials with monolayer thick, the wavelength dependent AR spectra for a pucker ridge alignment perpendicular to the x-direction and different values of w are shown in Figs. 2(c) and 2(d) for TM and TE polarizations, respectively. If we adjust the pucker ridge alignments and make them perpendicular to the y-direction [i.e., ε1 and ε2 are interchanged in Eq. (1)], the AR spectra obtained are shown in Figs. 2(e) and 2(f) for TM and TE polarizations, respectively. As shown in the figures, the AR of the proposed absorber is dependent on both the polarization and the pucker ridge alignment. This is because of the lack of fourfold rotational symmetry in the unit structure about the z-axis [39, 40] and the in-plane anisotropy [5, 24–27] of σi for themonolayer BP material. The resonance curves become broader with increasing w owing to the greater electromagnetic loss with increasing λ [i.e., the lower frequencies in Fig. 1(a)]. It is also obvious that the absorption peak position for TM polarization exhibits a red shift with increasing w, and the AR peak value firstly increases and then decreases. In contrast, the absorption peak position for TE polarization exhibits a slight blue shift, and the AR peak value increases consistently. From Fig. 2(c), we see that the value of w can be selected to maximize the absorption, where w = 210 nm provides peak absorption of ~98% at λ ≈54.3 μm, which satisfies the Fabry-Perot resonance condition [7] λ0 = 4nH/(2k − 1) for k = 1. Moreover, even for k ≥ 2, a series of weaker resonances are observed at around 18.1 μm, 10.9 μm, 7.8 μm, and so on, as shown in the inset of Fig. 2(c) for w = 210 nm. Similar Fabry-Perot resonance phenomena are also observable in Figs. 2(d)-2(f).

The distance of D between neighboring BP nano-ribbons affect the AR performance. We fixed the width of BP nano-ribbon with monolayer thick to 210 nm, and then the AR spectra under different D values are shown in Fig. 2(g) for TM polarization and ridges perpendicular to the x-direction. For D ≠ 0, the AR greater than 90% is achieved if D is less than 80nm. Additionally, the position of absorption peak exhibits a blue shift with increasing D. However when D = 0 nm (i.e. p = 210 nm), the performance of absorber is evidently reduced. Under this condition, metamaterials structure no longer exists, because all nano-ribbons are merged to a monolayer BP extending infinitely in xoy plane.

Moreover, Δ is thickness-dependent. From monolayer to bulk BP, Δ monotonically decreases from ~2.0 eV to ~0.3 eV. For bilayer and trilayer BP, their band gaps are ~1.3 eV and ~1.07 eV, respectively [41]. The simulated wavelength dependent AR spectra for BP metamaterials with monolayer, bilayer and trilayer thick are shown in Fig. 2(h). In this simulation, ridges are perpendicular to the x-direction and the incident plane wave is TM polarization. It is obvious that the absorption peak position exhibits a blue shift with decreasing Δ. We also found that the proposed absorber achieves a perfect AR [i.e. A(λ) is very close to 100%] [42] for bilayer and trilayer BP metamaterials when w = 230 nm. From Eqs. (2)-(5), we can see that Δ determines the permittivity ε1 instead of ε2 (i.e. Δ only determines the permittivity along x-direction). For an incident wave with TE polarization, AR spectra for BP metamaterials with different thicknesses are consequently identical because the electric field of incident wave has only y-component.

Next, based on monolayer BP metamaterials, we investigate the relationship between the absorption performance and NLSS of the proposed absorber. To conduct a quantitative analysis, we assumed fixed values of w = 210 nm and p = 250 nm. Figure 3(a) presents the simulated averages of the electric field intensity Ez along the x-direction for TM polarization with λ = 54.3 μm, where the NLSS decreases from 4 to 1 [i.e., BP metamaterials have no 4th, 4th and 3rd, and 4th, 3rd, and 2nd layers for NLSS values of 3, 2, and 1 in Fig. 2(b), respectively]. The figure clearly shows that surface plasmons are mainly harvested around the edges of the BP nano-ribbon [26, 27, 35, 43]. Due to the electromagnetic loss in the BP material arising from the real part of σi [see Fig. 1(a)], the absorber is formed when the harvested electromagnetic field produces attenuation. In addition, the attenuation increases with increasing NLSS, and the AR performance of the proposed absorber is therefore improved accordingly. The AR spectra for various values of NLSS are shown in Figs. 3(b) and 3(c). For TM polarization, the AR peaks are about 55%, 80%, 93%, and 98% for NLSS values of 1, 2, 3, and 4, respectively. We can therefore predict that a perfect A(λ) [42] can be achieved by increasing the NLSS of the proposed absorber.

 

Fig. 3 (a) Simulated average electric field intensity values for monolayer BP metamaterials with two nano-ribbon periods aligned along the x-direction. The inset presents a sectional view at the in-plane across the 1st interface for NLSS value of 1. AR spectra for various NLSS with (b) TM polarization and (c) TE polarization. The open circles and lines denote results calculated from interference theory and simulation, respectively. The normalized AR spectra of (b) and (c) are presented in (d) and (e), respectively.

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The obtained spectra indicates that the absorption performance for NLSS = 4 is excellent, and an A(λ) ≥ 90% is obtained for a range of λ from 46.2 μm to 62.8 μm [see the shaded regions in Figs. 3(b)]. The absorption performance can be evaluated according to the relative absorption bandwidth (RABW), which is defined as RABW = 2(λ2 − λ1)/(λ2 + λ1) × 100%, where λ2 and λ1 are the respective upper and lower limits of the wavelength range for which A(λ) ≥ 90%. Compared with NLSS = 4, for which an RABW value of 30% is obtained, the RABW forNLSS = 3 is about 15%. As discussed above, AR peaks less than 90% were obtained for NLSS < 3, and RABW values are therefore not applicable. To investigate the NLSS-dependent bandwidth, we normalized the AR spectra in Figs. 3(b) and 3(c) according to their peak AR values Apeak [i.e., Anormalized(λ) = A(λ)/Apeak], and the results are respectively shown in Figs. 3(d) and 3(e). The RABWs of the normalized AR spectra with TM polarization were then obtained as 15%, 21%, 26%, and 33% for NLSS values of 1, 2, 3, and 4, respectively, and were almost uniformly 33% for TE polarization. Figure 3 obviously demonstrates the improved absorption performance with increasing NLSS. The improvement is mainly due to the increasing number of BP monolayers, resulting in increasing electromagnetic loss.

To reveal the physical mechanism behind the observed absorption phenomena, we employ interference theory [9, 10, 34] for the proposed sandwiched absorber with monolayer BP metamaterials. Figure 4(a) shows that the sandwich-like structure in Fig. 2(a) is assumed to be excited with an incident electromagnetic plane wave traveling in the –z direction. The destructive interference between the directly reflected wave and the following multiple emergent waves effectively traps the wave in the sandwiched absorber, resulting in the high absorption. The total reflection coefficients at the l-th interface can be expressed as

Γl=rl,l+1+tl+1,ltl,l+1Γl+1ei2ϕl1rl+1,lΓl+1ei2ϕl=rl,l+1+Tl+1,l,
where the number of interfaces l is 1–5, ϕl = knldl represents the k-th delayed phase across the dielectric substrates with thickness dl and refractive index nl, tl,l+1 and tl+1,l, and rl,l+1 and rl+1,l respectively denote the transmission and reflection coefficients across the l-th interface, and Tl+1,l is the following multiple emergent waves resulting from the superposition of the multiple reflections among the structure on the right side of the l-th interface in Fig. 4(a). The gold mirror acting as a ground does not allow waves to be transmitted, such that t56 = 0 and r56 = −1, and, therefore, Γ5 = r56 = −1 can be derived from Eq. (6). By reverse iteration, Γ1 can be obtained, and the AR can also be obtained as A(λ) = 1 − |Γ1|2. The AR spectra for the proposed absorber employing different NLSS values can be calculated by interference theory, as shown by the open circles in Figs. 3(b) and 3(c), and an excellent agreement is obtained between CST simulations and the results of interference theory.

 

Fig. 4 (a) A schematic diagram of the transmission and reflection for a four-layered sandwich-like structure. The amplitude and phase difference of direct reflection and multiple reflections for (b) TM polarization and (c) TE polarization for different NLSS of the proposed structure.

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At l = 1, r12 in Eq. (6) is the direct reflection from the first interface incorporating a BP metamaterial layer, and T21 is the multiple emergent wave resulting from the superposition of the multiple reflections among the sandwich-like structure and gold mirror. Under ideal conditions of amplitude (i.e., |r12| = |T21|) and phase difference [i.e., |arg(r12) − arg(T21)| = π], an ideal AR would be obtained, which satisfies the strongest destructive interference of the electromagnetic field. The amplitudes and phase differences for the proposed absorber structure with different NLSS are shown in Figs. 4(b) and 4(c), respectively. In the λ range of 46.2 μm and 62.8 μm, all of the phase differences are comparable, and are approximately 180°, while the amplitude of T21 approaches that of r12 with increasing NLSS. These results indicate that the phenomenon of destructive interference is increasingly strengthened, resulting in an increasing AR for the proposed sandwiched absorber. The results are substantially different for TE polarization, as shown in Fig. 4(c), where, despite phase differences that are also approximately 180° in an equivalent range of λ, the amplitudes of T21 are tremendously far from those of r12, which leads to very weak destructive interference and a lower AR. From these results, we can further conclude that 1) the NLSS has little effect on the phase difference, which is mainly determined by H, and 2) an increasing NLSS results in increasing electromagnetic loss in the sandwich-like absorber structure, which indicates that the decreasing amplitude of T21 is caused by electromagnetic losses in the BP metamaterial layers despite the fact that the variation is very small for TE polarization.

4. Conclusions

The present work proposed and investigated an absorber operating in the mid-IR regime based on 2D BP metamaterials comprising nano-ribbon arrays that are sandwiched between dielectric layers. The multilayered BP-metamaterial/dielectric sandwich-like structure, in conjunction with an optically thick gold mirror, forms a Fabry-Perot resonator. In this structure, the electromagnetic field is harvested around the edges of the BP nano-ribbons, which increases the attenuation through electromagnetic loss in the 2D BP material, and enhances the absorption performance of the proposed absorber. Simulations demonstrated that an increasing NLSS of the absorber not only significantly increased the AR, but also broadened the absorption bandwidth. An analysis of the physical mechanism based on interference theory showed that the destructive interference of the resonator increased with increasing NLSS. The sandwiched absorber includes a high degree of anisotropy, and its absorption performance is correspondingly dependent on both the polarization of the incident light and the alignment of the pucker ridge of the BP metamaterial layers due to a lack of the fourfold rotational symmetry in the unit structure and the in-plane anisotropy of the surface conductivity of 2D BP materials. Although the polarization-independent absorber can certainly be designed based on BP metamaterials, the intrinsic anisotropy of the presented absorber may in fact be useful for applications needing polarization-dependent absorption.

Funding

Natural Science Foundation of China (NSFC) (61661012); Natural Science Foundation of Guangxi (2015GXNSFBB139003, 2014GXNSFAA118283); Program for Innovation Research Team of Guilin University of Electromagnetic Technology; Dean Project of Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing.

Acknowledgments

A special acknowledgment should be shown to Prof. Qiang Cheng from Southeast University, for his revision. The reviewers are also acknowledged for the very valuable suggestions and comments.

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36. L. I. Berger, Semiconductor Materials (CRC, 1996).

37. J. D. Wood, S. A. Wells, D. Jariwala, K. S. Chen, E. Cho, V. K. Sangwan, X. Liu, L. J. Lauhon, T. J. Marks, and M. C. Hersam, “Effective passivation of exfoliated black phosphorus transistors against ambient degradation,” Nano Lett. 14(12), 6964–6970 (2014). [CrossRef]   [PubMed]  

38. J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (2015). [CrossRef]   [PubMed]  

39. N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009). [CrossRef]  

40. W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: theoretical and experimental investigations,” Phys. Rev. B 75(4), 041102 (2007). [CrossRef]  

41. L. Liang, J. Wang, W. Lin, B. G. Sumpter, V. Meunier, and M. Pan, “Electronic bandgap and edge reconstruction in phosphorene materials,” Nano Lett. 14(11), 6400–6406 (2014). [CrossRef]   [PubMed]  

42. 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]  

43. D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016). [CrossRef]  

References

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  1. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98 (2012).
    [PubMed]
  2. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref] [PubMed]
  3. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [Crossref]
  4. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
    [Crossref] [PubMed]
  5. 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]
  6. J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
    [PubMed]
  7. B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
    [PubMed]
  8. S. He and T. Chen, “Broadband THz absorbers with graphene-based anisotropic metamaterial films,” IEEE Trans. THz Sci. Technol. 3, 757–763 (2013).
  9. M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express 21(24), 29938–29948 (2013).
    [Crossref] [PubMed]
  10. Y. N. Jiang, Y. Wang, D. B. Ge, S. M. Li, W. P. Cao, X. Gao, and X. H. Yu, “An ultra-wideband absorber based on graphene,” Wuli Xuebao 65, 054101 (2016).
  11. 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), 12823–12833 (2015).
    [Crossref] [PubMed]
  12. Z. C. Luo, M. Liu, Z. N. Guo, X. F. Jiang, A. P. Luo, C. J. Zhao, X. F. Yu, W. C. Xu, and H. Zhang, “Microfiber-based few-layer black phosphorus saturable absorber for ultra-fast fiber laser,” Opt. Express 23(15), 20030–20039 (2015).
    [Crossref] [PubMed]
  13. J. Sotor, G. Sobon, W. Macherzynski, P. Paletko, and K. M. Abramski, “Black phosphorus saturable absorber for ultrashort pulse generation,” Appl. Phys. Lett. 107(5), 051108 (2015).
    [Crossref]
  14. Z. Qin, G. Xie, H. Zhang, C. Zhao, P. Yuan, S. Wen, and L. Qian, “Black phosphorus as saturable absorber for the Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Express 23(19), 24713–24718 (2015).
    [Crossref] [PubMed]
  15. S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
    [Crossref] [PubMed]
  16. S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
    [Crossref] [PubMed]
  17. L. Chen, F. Xue, X. Li, X. Huang, L. Wang, J. Kou, and Z. L. Wang, “Strain-gated field effect transistor of a MoS2−ZnO 2D−1D hybrid structure,” ACS Nano 10(1), 1546–1551 (2016).
    [Crossref] [PubMed]
  18. H. Taghinejad, M. Taghinejad, A. Tarasov, M. Y. Tsai, A. H. Hosseinnia, H. Moradinejad, P. M. Campbell, A. A. Eftekhar, E. M. Vogel, and A. Adibi, “Resonant light-induced heating in hybrid cavity-coupled 2D transition-metal dichalcogenides,” ACS Photonics 3(4), 700–707 (2016).
    [Crossref]
  19. H. Zhang, S. B. Lu, J. Zheng, J. Du, S. C. Wen, D. Y. Tang, and K. P. Loh, “Molybdenum disulfide (MoS2) as a broadband saturable absorber for ultra-fast photonics,” Opt. Express 22(6), 7249–7260 (2014).
    [Crossref] [PubMed]
  20. H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
    [Crossref] [PubMed]
  21. Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
    [Crossref]
  22. P. Yasaei, B. Kumar, T. Foroozan, C. Wang, M. Asadi, D. Tuschel, J. E. Indacochea, R. F. Klie, and A. Salehi-Khojin, “High-quality black phosphorus atomic layers by liquid-phase exfoliation,” Adv. Mater. 27(11), 1887–1892 (2015).
    [Crossref] [PubMed]
  23. V. Sresht, A. A. H. Pádua, and D. Blankschtein, “Liquid-phase exfoliation of phosphorene: design rules from molecular dynamics simulations,” ACS Nano 9(8), 8255–8268 (2015).
    [Crossref] [PubMed]
  24. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014).
    [Crossref] [PubMed]
  25. A. S. Rodin, A. Carvalho, and A. H. Castro Neto, “Strain-induced gap modification in black phosphorus,” Phys. Rev. Lett. 112(17), 176801 (2014).
    [Crossref] [PubMed]
  26. 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]
  27. Z. W. Bao, H. W. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett. 109(24), 241902 (2016).
    [Crossref]
  28. 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), 235319 (2014).
    [Crossref]
  29. A. N. Rudenko and M. I. Katsnelson, “Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus,” Phys. Rev. B 89(20), 201408 (2014).
    [Crossref]
  30. A. Castellanos-Gomez, “Black phosphorus: narrow gap, wide applications,” J. Phys. Chem. Lett. 6(21), 4280–4291 (2015).
    [Crossref] [PubMed]
  31. 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]
  32. J. Qiao, X. Kong, Z. X. Hu, F. Yang, and W. Ji, “High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus,” Nat. Commun. 5, 4475 (2014).
    [Crossref] [PubMed]
  33. X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
    [Crossref] [PubMed]
  34. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012).
    [Crossref] [PubMed]
  35. Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
    [Crossref] [PubMed]
  36. L. I. Berger, Semiconductor Materials (CRC, 1996).
  37. J. D. Wood, S. A. Wells, D. Jariwala, K. S. Chen, E. Cho, V. K. Sangwan, X. Liu, L. J. Lauhon, T. J. Marks, and M. C. Hersam, “Effective passivation of exfoliated black phosphorus transistors against ambient degradation,” Nano Lett. 14(12), 6964–6970 (2014).
    [Crossref] [PubMed]
  38. J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (2015).
    [Crossref] [PubMed]
  39. N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
    [Crossref]
  40. W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: theoretical and experimental investigations,” Phys. Rev. B 75(4), 041102 (2007).
    [Crossref]
  41. L. Liang, J. Wang, W. Lin, B. G. Sumpter, V. Meunier, and M. Pan, “Electronic bandgap and edge reconstruction in phosphorene materials,” Nano Lett. 14(11), 6400–6406 (2014).
    [Crossref] [PubMed]
  42. 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]
  43. D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016).
    [Crossref]

2016 (7)

Y. N. Jiang, Y. Wang, D. B. Ge, S. M. Li, W. P. Cao, X. Gao, and X. H. Yu, “An ultra-wideband absorber based on graphene,” Wuli Xuebao 65, 054101 (2016).

S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
[Crossref] [PubMed]

L. Chen, F. Xue, X. Li, X. Huang, L. Wang, J. Kou, and Z. L. Wang, “Strain-gated field effect transistor of a MoS2−ZnO 2D−1D hybrid structure,” ACS Nano 10(1), 1546–1551 (2016).
[Crossref] [PubMed]

H. Taghinejad, M. Taghinejad, A. Tarasov, M. Y. Tsai, A. H. Hosseinnia, H. Moradinejad, P. M. Campbell, A. A. Eftekhar, E. M. Vogel, and A. Adibi, “Resonant light-induced heating in hybrid cavity-coupled 2D transition-metal dichalcogenides,” ACS Photonics 3(4), 700–707 (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]

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (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. Opt. 18(10), 104006 (2016).
[Crossref]

2015 (12)

X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
[Crossref] [PubMed]

J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (2015).
[Crossref] [PubMed]

A. Castellanos-Gomez, “Black phosphorus: narrow gap, wide applications,” J. Phys. Chem. Lett. 6(21), 4280–4291 (2015).
[Crossref] [PubMed]

H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
[Crossref] [PubMed]

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

P. Yasaei, B. Kumar, T. Foroozan, C. Wang, M. Asadi, D. Tuschel, J. E. Indacochea, R. F. Klie, and A. Salehi-Khojin, “High-quality black phosphorus atomic layers by liquid-phase exfoliation,” Adv. Mater. 27(11), 1887–1892 (2015).
[Crossref] [PubMed]

V. Sresht, A. A. H. Pádua, and D. Blankschtein, “Liquid-phase exfoliation of phosphorene: design rules from molecular dynamics simulations,” ACS Nano 9(8), 8255–8268 (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), 12823–12833 (2015).
[Crossref] [PubMed]

Z. C. Luo, M. Liu, Z. N. Guo, X. F. Jiang, A. P. Luo, C. J. Zhao, X. F. Yu, W. C. Xu, and H. Zhang, “Microfiber-based few-layer black phosphorus saturable absorber for ultra-fast fiber laser,” Opt. Express 23(15), 20030–20039 (2015).
[Crossref] [PubMed]

J. Sotor, G. Sobon, W. Macherzynski, P. Paletko, and K. M. Abramski, “Black phosphorus saturable absorber for ultrashort pulse generation,” Appl. Phys. Lett. 107(5), 051108 (2015).
[Crossref]

Z. Qin, G. Xie, H. Zhang, C. Zhao, P. Yuan, S. Wen, and L. Qian, “Black phosphorus as saturable absorber for the Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Express 23(19), 24713–24718 (2015).
[Crossref] [PubMed]

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref] [PubMed]

2014 (13)

H. Zhang, S. B. Lu, J. Zheng, J. Du, S. C. Wen, D. Y. Tang, and K. P. Loh, “Molybdenum disulfide (MoS2) as a broadband saturable absorber for ultra-fast photonics,” Opt. Express 22(6), 7249–7260 (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]

J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
[PubMed]

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
[PubMed]

H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014).
[Crossref] [PubMed]

A. S. Rodin, A. Carvalho, and A. H. Castro Neto, “Strain-induced gap modification in black phosphorus,” Phys. Rev. Lett. 112(17), 176801 (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), 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]

J. Qiao, X. Kong, Z. X. Hu, F. Yang, and W. Ji, “High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus,” Nat. Commun. 5, 4475 (2014).
[Crossref] [PubMed]

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), 235319 (2014).
[Crossref]

A. N. Rudenko and M. I. Katsnelson, “Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus,” Phys. Rev. B 89(20), 201408 (2014).
[Crossref]

L. Liang, J. Wang, W. Lin, B. G. Sumpter, V. Meunier, and M. Pan, “Electronic bandgap and edge reconstruction in phosphorene materials,” Nano Lett. 14(11), 6400–6406 (2014).
[Crossref] [PubMed]

J. D. Wood, S. A. Wells, D. Jariwala, K. S. Chen, E. Cho, V. K. Sangwan, X. Liu, L. J. Lauhon, T. J. Marks, and M. C. Hersam, “Effective passivation of exfoliated black phosphorus transistors against ambient degradation,” Nano Lett. 14(12), 6964–6970 (2014).
[Crossref] [PubMed]

2013 (2)

S. He and T. Chen, “Broadband THz absorbers with graphene-based anisotropic metamaterial films,” IEEE Trans. THz Sci. Technol. 3, 757–763 (2013).

M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express 21(24), 29938–29948 (2013).
[Crossref] [PubMed]

2012 (3)

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98 (2012).
[PubMed]

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
[Crossref] [PubMed]

H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012).
[Crossref] [PubMed]

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)

N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009).
[Crossref]

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]

2007 (2)

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: theoretical and experimental investigations,” Phys. Rev. B 75(4), 041102 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Abramski, K. M.

J. Sotor, G. Sobon, W. Macherzynski, P. Paletko, and K. M. Abramski, “Black phosphorus saturable absorber for ultrashort pulse generation,” Appl. Phys. Lett. 107(5), 051108 (2015).
[Crossref]

Adibi, A.

H. Taghinejad, M. Taghinejad, A. Tarasov, M. Y. Tsai, A. H. Hosseinnia, H. Moradinejad, P. M. Campbell, A. A. Eftekhar, E. M. Vogel, and A. Adibi, “Resonant light-induced heating in hybrid cavity-coupled 2D transition-metal dichalcogenides,” ACS Photonics 3(4), 700–707 (2016).
[Crossref]

Akinwande, D.

J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (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. Opt. 18(10), 104006 (2016).
[Crossref]

Amin, M.

Aronsson, M. T.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: theoretical and experimental investigations,” Phys. Rev. B 75(4), 041102 (2007).
[Crossref]

Asadi, M.

P. Yasaei, B. Kumar, T. Foroozan, C. Wang, M. Asadi, D. Tuschel, J. E. Indacochea, R. F. Klie, and A. Salehi-Khojin, “High-quality black phosphorus atomic layers by liquid-phase exfoliation,” Adv. Mater. 27(11), 1887–1892 (2015).
[Crossref] [PubMed]

Averitt, R. D.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: theoretical and experimental investigations,” Phys. Rev. B 75(4), 041102 (2007).
[Crossref]

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.

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L. Liang, J. Wang, W. Lin, B. G. Sumpter, V. Meunier, and M. Pan, “Electronic bandgap and edge reconstruction in phosphorene materials,” Nano Lett. 14(11), 6400–6406 (2014).
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L. Chen, F. Xue, X. Li, X. Huang, L. Wang, J. Kou, and Z. L. Wang, “Strain-gated field effect transistor of a MoS2−ZnO 2D−1D hybrid structure,” ACS Nano 10(1), 1546–1551 (2016).
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J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (2015).
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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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S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
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Xia, F.

X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
[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]

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. Qin, G. Xie, H. Zhang, C. Zhao, P. Yuan, S. Wen, and L. Qian, “Black phosphorus as saturable absorber for the Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Express 23(19), 24713–24718 (2015).
[Crossref] [PubMed]

J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
[PubMed]

Xie, H.

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

Xu, W. C.

Xu, W. L.

S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
[Crossref] [PubMed]

Xu, X.

X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
[Crossref] [PubMed]

H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014).
[Crossref] [PubMed]

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S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
[Crossref] [PubMed]

Xue, F.

L. Chen, F. Xue, X. Li, X. Huang, L. Wang, J. Kou, and Z. L. Wang, “Strain-gated field effect transistor of a MoS2−ZnO 2D−1D hybrid structure,” ACS Nano 10(1), 1546–1551 (2016).
[Crossref] [PubMed]

Yang, B.

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
[PubMed]

Yang, F.

J. Qiao, X. Kong, Z. X. Hu, F. Yang, and W. Ji, “High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus,” Nat. Commun. 5, 4475 (2014).
[Crossref] [PubMed]

Yang, L.

X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
[Crossref] [PubMed]

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), 235319 (2014).
[Crossref]

Yasaei, P.

P. Yasaei, B. Kumar, T. Foroozan, C. Wang, M. Asadi, D. Tuschel, J. E. Indacochea, R. F. Klie, and A. Salehi-Khojin, “High-quality black phosphorus atomic layers by liquid-phase exfoliation,” Adv. Mater. 27(11), 1887–1892 (2015).
[Crossref] [PubMed]

Ye, G. J.

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]

Ye, P. D.

H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
[Crossref] [PubMed]

H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014).
[Crossref] [PubMed]

Yu, H.

J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
[PubMed]

Yu, X.

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), 12823–12833 (2015).
[Crossref] [PubMed]

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

Yu, X. F.

Yu, X. H.

Y. N. Jiang, Y. Wang, D. B. Ge, S. M. Li, W. P. Cao, X. Gao, and X. H. Yu, “An ultra-wideband absorber based on graphene,” Wuli Xuebao 65, 054101 (2016).

Yu, Y.

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]

Yuan, P.

Z. Qin, G. Xie, H. Zhang, C. Zhao, P. Yuan, S. Wen, and L. Qian, “Black phosphorus as saturable absorber for the Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Express 23(19), 24713–24718 (2015).
[Crossref] [PubMed]

J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
[PubMed]

Zhang, H.

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), 12823–12833 (2015).
[Crossref] [PubMed]

Z. Qin, G. Xie, H. Zhang, C. Zhao, P. Yuan, S. Wen, and L. Qian, “Black phosphorus as saturable absorber for the Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Express 23(19), 24713–24718 (2015).
[Crossref] [PubMed]

Z. C. Luo, M. Liu, Z. N. Guo, X. F. Jiang, A. P. Luo, C. J. Zhao, X. F. Yu, W. C. Xu, and H. Zhang, “Microfiber-based few-layer black phosphorus saturable absorber for ultra-fast fiber laser,” Opt. Express 23(15), 20030–20039 (2015).
[Crossref] [PubMed]

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref] [PubMed]

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

H. Zhang, S. B. Lu, J. Zheng, J. Du, S. C. Wen, D. Y. Tang, and K. P. Loh, “Molybdenum disulfide (MoS2) as a broadband saturable absorber for ultra-fast photonics,” Opt. Express 22(6), 7249–7260 (2014).
[Crossref] [PubMed]

J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
[PubMed]

Zhang, S. J.

S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
[Crossref] [PubMed]

Zhang, Y.

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]

Zhao, C.

Zhao, C. J.

Zhao, H.

X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
[Crossref] [PubMed]

Zheng, J.

Zhong, H. K.

S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (2016).
[Crossref] [PubMed]

Zhou, Y.

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

Zhu, W.

J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (2015).
[Crossref] [PubMed]

Zhu, Z.

H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014).
[Crossref] [PubMed]

ACS Nano (3)

L. Chen, F. Xue, X. Li, X. Huang, L. Wang, J. Kou, and Z. L. Wang, “Strain-gated field effect transistor of a MoS2−ZnO 2D−1D hybrid structure,” ACS Nano 10(1), 1546–1551 (2016).
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V. Sresht, A. A. H. Pádua, and D. Blankschtein, “Liquid-phase exfoliation of phosphorene: design rules from molecular dynamics simulations,” ACS Nano 9(8), 8255–8268 (2015).
[Crossref] [PubMed]

H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014).
[Crossref] [PubMed]

ACS Photonics (1)

H. Taghinejad, M. Taghinejad, A. Tarasov, M. Y. Tsai, A. H. Hosseinnia, H. Moradinejad, P. M. Campbell, A. A. Eftekhar, E. M. Vogel, and A. Adibi, “Resonant light-induced heating in hybrid cavity-coupled 2D transition-metal dichalcogenides,” ACS Photonics 3(4), 700–707 (2016).
[Crossref]

Adv. Funct. Mater. (1)

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

Adv. Mater. (2)

P. Yasaei, B. Kumar, T. Foroozan, C. Wang, M. Asadi, D. Tuschel, J. E. Indacochea, R. F. Klie, and A. Salehi-Khojin, “High-quality black phosphorus atomic layers by liquid-phase exfoliation,” Adv. Mater. 27(11), 1887–1892 (2015).
[Crossref] [PubMed]

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98 (2012).
[PubMed]

Appl. Phys. Lett. (2)

J. Sotor, G. Sobon, W. Macherzynski, P. Paletko, and K. M. Abramski, “Black phosphorus saturable absorber for ultrashort pulse generation,” Appl. Phys. Lett. 107(5), 051108 (2015).
[Crossref]

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

Chem. Soc. Rev. (1)

H. Liu, Y. Du, Y. Deng, and P. D. Ye, “Semiconducting black phosphorus: synthesis, transport properties and electronic applications,” Chem. Soc. Rev. 44(9), 2732–2743 (2015).
[Crossref] [PubMed]

IEEE Trans. THz Sci. Technol. (1)

S. He and T. Chen, “Broadband THz absorbers with graphene-based anisotropic metamaterial films,” IEEE Trans. THz Sci. Technol. 3, 757–763 (2013).

J. Opt. (1)

D. Correas-Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016).
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J. Phys. Chem. Lett. (1)

A. Castellanos-Gomez, “Black phosphorus: narrow gap, wide applications,” J. Phys. Chem. Lett. 6(21), 4280–4291 (2015).
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Nano Lett. (3)

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
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J. D. Wood, S. A. Wells, D. Jariwala, K. S. Chen, E. Cho, V. K. Sangwan, X. Liu, L. J. Lauhon, T. J. Marks, and M. C. Hersam, “Effective passivation of exfoliated black phosphorus transistors against ambient degradation,” Nano Lett. 14(12), 6964–6970 (2014).
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L. Liang, J. Wang, W. Lin, B. G. Sumpter, V. Meunier, and M. Pan, “Electronic bandgap and edge reconstruction in phosphorene materials,” Nano Lett. 14(11), 6400–6406 (2014).
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Nanoscale (1)

S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, “Opening the band gap of graphene through silicon doping for the improved performance of graphene/GaAs heterojunction solar cells,” Nanoscale 8(1), 226–232 (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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J. Qiao, X. Kong, Z. X. Hu, F. Yang, and W. Ji, “High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus,” Nat. Commun. 5, 4475 (2014).
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Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
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Nat. Nanotechnol. (3)

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
[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]

X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
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Opt. Express (7)

M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express 21(24), 29938–29948 (2013).
[Crossref] [PubMed]

H. Zhang, S. B. Lu, J. Zheng, J. Du, S. C. Wen, D. Y. Tang, and K. P. Loh, “Molybdenum disulfide (MoS2) as a broadband saturable absorber for ultra-fast photonics,” Opt. Express 22(6), 7249–7260 (2014).
[Crossref] [PubMed]

Z. Qin, G. Xie, H. Zhang, C. Zhao, P. Yuan, S. Wen, and L. Qian, “Black phosphorus as saturable absorber for the Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Express 23(19), 24713–24718 (2015).
[Crossref] [PubMed]

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (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), 12823–12833 (2015).
[Crossref] [PubMed]

Z. C. Luo, M. Liu, Z. N. Guo, X. F. Jiang, A. P. Luo, C. J. Zhao, X. F. Yu, W. C. Xu, and H. Zhang, “Microfiber-based few-layer black phosphorus saturable absorber for ultra-fast fiber laser,” Opt. Express 23(15), 20030–20039 (2015).
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H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012).
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Phys. Rev. B (4)

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), 235319 (2014).
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A. N. Rudenko and M. I. Katsnelson, “Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus,” Phys. Rev. B 89(20), 201408 (2014).
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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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Sci. Rep. (3)

J. S. Kim, Y. Liu, W. Zhu, S. Kim, D. Wu, L. Tao, A. Dodabalapur, K. Lai, and D. Akinwande, “Toward air-stable multilayer phosphorene thin-films and transistors,” Sci. Rep. 5, 8989 (2015).
[Crossref] [PubMed]

J. Ma, G. Xie, P. Lv, W. Gao, P. Yuan, L. Qian, U. Griebner, V. Petrov, H. Yu, H. Zhang, and J. Wang, “Wavelength-versatile graphene-gold film saturable absorber mirror for ultra-broadband mode-locking of bulk lasers,” Sci. Rep. 4, 5016 (2014).
[PubMed]

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Wuli Xuebao (1)

Y. N. Jiang, Y. Wang, D. B. Ge, S. M. Li, W. P. Cao, X. Gao, and X. H. Yu, “An ultra-wideband absorber based on graphene,” Wuli Xuebao 65, 054101 (2016).

Other (1)

L. I. Berger, Semiconductor Materials (CRC, 1996).

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Figures (4)

Fig. 1
Fig. 1 Frequency dependent surface conductivity: (a) real part; (b) imaginary part. Black lines and red lines denote the surface conductivity along the x-direction and y-direction, respectively; solid lines, dotted lines, and dashed lines are the conductivity values for electron doping parameter ns given as 1013 cm−2, 5 × 1013 cm−2, and 1014 cm−2, respectively.
Fig. 2
Fig. 2 (a) Schematic of the proposed sandwich-like structured absorber. (b) Front view of the proposed absorber with layer dimensions. Simulated absorption rate (AR) spectra for various BP monolayer nano-ribbon widths w, and for transverse-magnetic TM polarization and transverse-electric (TE) polarization with ridges perpendicular to the x-direction (c and d) and the y-direction (e and f). The inset of (c) shows the AR spectrum for w = 210 nm in the lower wavelength region. Simulated TM polarization AR spectra for various distances between two nano-ribbons (g) and for various thicknesses BP with monolayer, bilayer and trilayer atom (h) while ridges perpendicular to x-direction.
Fig. 3
Fig. 3 (a) Simulated average electric field intensity values for monolayer BP metamaterials with two nano-ribbon periods aligned along the x-direction. The inset presents a sectional view at the in-plane across the 1st interface for NLSS value of 1. AR spectra for various NLSS with (b) TM polarization and (c) TE polarization. The open circles and lines denote results calculated from interference theory and simulation, respectively. The normalized AR spectra of (b) and (c) are presented in (d) and (e), respectively.
Fig. 4
Fig. 4 (a) A schematic diagram of the transmission and reflection for a four-layered sandwich-like structure. The amplitude and phase difference of direct reflection and multiple reflections for (b) TM polarization and (c) TE polarization for different NLSS of the proposed structure.

Equations (6)

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

ε ¯ ¯ =[ ε 1 0 0 0 ε 2 0 0 0 ε 3 ],
ε i = ε r + j σ i ε 0 ωd ( i=1, 2 or 3 ),
σ i = j D i π( ω+ jη / ) ( i=1 or 2 ).
D i = π e 2 n s m i ,
m 1 = 2 2 γ 2 /Δ + η c , m 2 = 2 ν c .
Γ l = r l,l+1 + t l+1,l t l,l+1 Γ l+1 e i2 ϕ l 1 r l+1,l Γ l+1 e i2 ϕ l = r l,l+1 + T l+1,l ,

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