Abstract

In this article, we have theoretically demonstrated that the perfect absorption at infrared frequencies can be achieved and controlled by using a graphene-hexagonal Boron Nitride (hBN) hyper crystal. hBN, the latest natural hyperbolic material, can be regarded as an excellent substrate to form a hyper crystal with graphene. Although the perfect absorption by a half-space of hBN crystal can be achieved due to its high optical anisotropy, but the perfect absorption can only appear at certain fixed wavenumber and incidence angle. By introducing a graphene-hBN hyper crystal, we can get perfect absorption at different wavenumbers and incidence angles by varying the Fermi energy level of graphene sheets via electrostatic biasing. We show that the perfect absorption can be realized at different Fermi energies for TM waves.

© 2016 Optical Society of America

Corrections

27 July 2016: A correction was made to the title.

1. Introduction

Over the past several years, perfect absorption (PA) at infrared frequencies has been widely investigated [1–3]. Since it is very vital in many promising applications, such as solar cells [4], plasmonic sensors [5], molecular dectors [6], and selective thermal emitters [7]. Most of the studies on PA are focused on broadband and wide-angle. For example, Deng et al. studied the broadband perfect absorber in the visible and near-infrared range by using a ultrathin layer of the refractory metal chromium (Cr) embedded between two silica (SiO2) layers [8]. Pu et al. proposed an approach for designing a wide-angle perfect absorber at infrared frequencies based on plasmonic structure [9]. Although the broadband and wide-angle perfect absorbers can be applied in the field of solar power harvesting [10] and electromagnetic wave spatial filter [11], the flexible control of PA is also very important for applications in optical devices. It is desired to tune PA by using an external bias voltage. For this purpose, introducing graphene into the perfect absorber seems to be a good approach for controlling PA. Up to now, a lot of researches on controlling the PA by varing the Fermi energy of graphene have been investigated [12–15]. Recently, Baranov et al. firstly predicted the interferenceless perfect absorption by a strongly anisotropic metamaterial [16], Baranov et al. demonstrated both theoretically and experimentally that PA at infrared frequencies can be realized by using a half-space of hexagonal Boron Nitride (hBN) crystal [17]. It is interesting to investigate the interferenceless perfect absorber based on the graphene-hBN hyper crystal.

hBN, an interesting optical material has attracted considerable interest in infrared ranges in photonics due to its high optical anisotropy [18,19]. Graphene, on the other hand, has found significant applications in both photonics and plasmonics in a broad frequency (visible to mid infrared to THz) range due to its unique and tunable optical properties [20–23]. hBN is widely used as an excellent substrate material to form a hyper crystal with graphene as it can provide an amazing clean environment [24–28]. So when constructing a graphene-hBN hyper crystal, it will have both hyperbolic and tunable characteristics.

In this article, we theoretically analyze the condition of total absorption at infrared frequencies by a graphene-hBN hyper crystal. It has been found that PA can be realized for TM waves. While PA by a half-space of hBN crystal can be achieved at certain fixed wavenumber and incidence angle. But using a graphene-hBN crystal, we are able to control PA that it can be realized at different wavenumbers and incidence angles by varing the Fermi energy of graphene. We believe this work will be very useful for future investigations on applications of graphene-hBN based hyper crystals and could find practical applications in optical devices and bio-sensor devices.

2. Theory

The graphene’s surface conductivity can be determined by using the Kubo formalisms [29–31]. Without considering the external magnetic field, the isotropic surface conductivity of graphene can be written as the sum of the intra-band and the inter-band terms. But when working in the infrared ranges, we can neglect the inter-band term, so the conductivity of graphene in the infrared ranges can be written as

σ=ie2EFπ2(ω+iτ1),
where ω is the frequency of the incident light, EF is the Fermi energy, τ is the relaxation time. e and are the universal constants related to the electron charge and Boltzmann constant, respectively. As we know that the relaxation time τ=μEf/evf2, in which μ=104cm2V-1s-1 and vf=106m/s are the mobility and Fermi velocity. We can use a conservative value (τ=1013 at Ef = 0.1 eV) extracted from the measured, impurity-limited dc mobility [32,33]. In this article, we choose τ=5×1013 for simplify at different Fermi energies.

Graphene is an optically uni-axial anisotropic material due to its 2D nature, whose permittivity tensor can be given by,

εgraphene=[εg,t000εg,t000εg,],
Graphene’s tangential permittivity can be given by,
εg,t=εg=1+iσε0ωtg,
where ε0 is the free space permittivity and tg is the thickness of monolayer graphene. As graphene is a two dimensional material, the normal electric field cannot excite any current in the graphene sheet. So the normal component of the permittivity is given by εg,=1 [34].

hBN is a van der Waals crystal with two kinds of IR active phonon modes relevant to hyperbolicity: 1) out of plane A2u phonon modes which have ωTO=780cm1, ωLO=830cm1 and 2) in-plane E1u phonon modes which have ωTO=1370cm1, ωLO=1610cm1 [35–37]. These lead to two distinct Reststrahlen (RS) bands, which the lower frequency RS band corresponds to type I hyperbolicity (εx=εy>0, εz<0) and the upper RS band shows type II hyperbolicity (εx=εy<0,εz>0). The hBN permittivity is given by

εu=ε,u(1+(ωLO,u)2(ωTO,u)2(ωTO,u)2ω2iωγu)
where u=x,y represents the transverse (a, b crystal plane) and u=z represents the z (c crystal axis) axes. ε and γ represent the high-frequency dielectric permittivity and the damping constant respectively, ε,x=ε,y=4.87, γx=γy=5cm1 ,ε,z=2.95 , and γz=4cm1.

We plot the permittivities of monolayer graphene and hBN as a function of wavenumbers as shown in Fig. 1. Figures 1(a) and 1(b) show the real and imaginary parts of the permittivity of monolayer graphene at different Fermi energies. It is seen that the real part of the permittivity of graphene is negative and decreases with the increasing Fermi energy, while the imaginary part of the permittivity of graphene is positive and increases as increasing the Fermi energy. Figures 1(c) and 1(d) show the real and imaginary parts of the permittivity of hBN as a function of wavenumbers. It is abvious that the real part of εt>0 and εz<0 in type I, while the real part of εt<0 and εz>0 in type II. It is known from Fig. 1(d) that the imaginaty part εz is large positive in type I, while the imaginaty part εt is large positive in type II.

 figure: Fig. 1

Fig. 1 (a) and (b) are the real and imaginary parts of the permittivity of monolayer graphene as a function of the wavenumber for various chemical potential of graphene. (c) and (d) are the real and imaginary parts of the tangential and perpendicular permittivity of hBN.

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Our graphene-hBN hyper crystal is representatively shown in Fig. 2. It is a graphene multilayer structure in which separations between graphene sheets are assumed to be filled with the hBN crystal. Based on the effective medium theory [38,39], the permittivity of the graphene-hBN hyper crystal can be given by

εteff=εxeff=εyeff=fgεg,t+(1fg)εx,
εzeff=(fgεg,+1fgεz)1,
where fg=tg/t is the filling ratio of graphene sheet and t=tg+thBN. Here, we assume tg=N0.35nm, N = 1 and thBN=100nm.

 figure: Fig. 2

Fig. 2 The interferenceless perfect electromagnetic absorber based on the graphene-hBN hyper crystal.

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Figure 3 shows the real part of the permittivity of the graphene-hBN hyper crystal as a function of wavenumbers at different Fermi energies. It is seen that the real part of εteff can be positive at different Fermi energies, while it only can be negtive at Ef=1eV. And when increasing the Fermi energy, the real part εteff decreases. So if we want to get the negative real part of εteff, we should increase the Fermi energy at near 1 eV or optimizing other parameters, such as the filling ratio of graphene sheet. It is also seen that the real part of εzeff is fixed as varing the Fermi energy. It can be understand from Eq. (6) that the filling ratio of graphene sheet is very small and εg,=1, so εzeff is almost equal to the hBN’s permittivity εz. It means that the graphene has no influence on the real part of εzeff.

 figure: Fig. 3

Fig. 3 The real part of the tangential and perpendicular permittivities of the graphene-hBN hyper crystal.

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Let us consider TM and TE waves incident from air to the surface of a half-space of graphene-hBN crystal, the reflection coefficients are given by

rTM=cos2θi(εzeffsin2θi)/(εzeffεxeff)cos2θi+(εzeffsin2θi)/(εzeffεxeff),
and
rTE=cos2θiεxeffsin2θicos2θi+εxeffsin2θi,
From Eq. (7), we can derive the condition for zero reflection for TM waves as
cos2θ0=εzeff1εzeffεxeff1,
where θ0 denotes the incidence angle at which the energy of the incident light are completely absorbed by the graphene-hBN crystal, meaning PA. When it meets 0<Re(cos2θ0)<1 and Im(cos2θ0)=0 at some wavenumbers, PA can be realized, where Re and Im represent the real and imaginary part. For TE waves, we also can know that when it meets εxeff=1, the reflection vanishes, however, this condition cannot be met with a lossy material at any frequency due to non-zero imaginary part of permittivity Im(εxeff). Although the imaginary part of in-plane permittivity εxeff can be very small far from phonon-polariton resonances of hBN, it is still finite and perfect absorption does not occur. Hence, we can obtain the nearly PA for the TE polarization.

3. Results and discussions

Firstly we discuss the absorption of our graphene-hBN hyper crystal based on both the effective medium theory and the transfer matrix method. In the transfer matrix method, we assume that graphene-hBN hyper-crystal has the periodic structure with (AB)N, where A is graphene and B is hBN thin film. In order to guarantee the accuracy of the numerical results, we have adopted enough periodic number N (N≥1000) due to the infinite thickness of graphene-hBN hypercrystal in the effective medium theory. In Fig. 4, we plot the absorption based on the effective medium theory and the transfer matrix method at the incidence angle 60° and 80°, respectively. Other parameters are τ=500fs and Ef = 0.25 eV. Figures 4(a) and 4(b) are the absorption based on the effective medium theory. Figures 4(c) and 4(d) show the absorption by using the transfer matrix method. It is obvious that Figs. 4(c) and 4(d) are in good agreement with Figs. 4(a) and 4(b). So the effective medium theory is credible in our model. Hence, in the following discussion, we will calculate the absorption by means of the effective medium theory.

 figure: Fig. 4

Fig. 4 (a) and (b) are the absorption as a function of the wavenumber based on the effective medium theory at the incidence angle 60°, 80°. (c) and (d) are the absorption as a function of the wavenumber by using the transfer matrix method with enough period at the incidence angle 60°, 80°, where Ef = 0.25 eV.

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In order to examine the possibility of PA for TM waves, we plot in Fig. 5(a) the real and imaginary parts of cos2θ0 deduced from Eq. (9) at Ef = 0.25 eV. It is clear that the condictions Im(cos2θ0)=0 and 0<Re(cos2θ0)<1 can be meet at some wavenumbers, so PA can be realized at those wavenumbers. Figures 5(b) and 5(c) show PA can be achieved at two points: point A and point B. It is seen in Fig. 5(b) that PA can be realized at point A which shows the wavenumber is at near 754 cm−1 and the corresponding θ0 is near 67°. Figure 5(c) shows that PA can be achieved at point B where the wavenumber is near 947 cm−1 and the corresponding θ0 is near 74°. Therefore, when a TM-polarized plane wave incident on a half-space of graphene-hBN hyper-crystal, the energy of the incident light can be totally absorbed at these two points.

 figure: Fig. 5

Fig. 5 (a) The real and imaginary parts of squared cosine of the perfect absorption angle θ0. (b) and (c) show that the perfect absorption of TM polarized wave can be achieved at point A and B according to the condition of perfect absorption.

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The absorption of our graphene-hBN hyper-crystal as a function of wavenumbers depending on the incidence angle is shown in Fig. 6. It is seen in Fig. 6(a) that there is an absorption dip which the wavenumber is near 830 cm−1, while both sides have a relatively high absorption, but the absorption varies at different incidence angles. Note in Fig. 6(b) that PA can be realized at the wavenumber near 750 cm−1 and the incidence angle θ0 near 67°, which corresponds with point A in Fig. 5(b). It is also seen that when the incidence angle is near θ0, the absorption is relatively high. When we increase the incidence angle from 65° to θ0, the absorption increases. While from θ0 to 69°, the absorption decreases. Figure 6(c) shows PA can be achieved at the wavenumber near 950 cm−1 and the incidence angle θ0 near 74°, which corresponds with point B in Fig. 5(c).

 figure: Fig. 6

Fig. 6 (a) calculated absorption spectra for TM polarized wave at different incidence angles. (b) shows the perfect absorption occurs at the angle 67°. (c) shows the perfect absorption occurs at the angle 74°.

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Through the above discussions, we know that PA can be realized at two different wavenumbers and two different incidence angles. But the condition discussed above is all at Ef = 0.25 eV, next we will discuss PA at different Fermi energies. We plot the real and imaginary parts of cos2θ0 deduced from Eq. (9) at different Fermi energies, as shown in Fig. 7. It is seen from Fig. 7(a) that there are two parts that can meet the conditionIm(cos2θ0)=0. One part is at the wavenumber from 700 cm−1 to 830 cm−1 which we regard as part 1 and another part is at the wavenumber from 830 cm−1 to 1000 cm−1 which we regard as part 2. It is known that when we increase the Fermi energy in part 1, the position of PA is blue shift, while in part 2, the position of PA is red shift. Figure 7(b) shows that PA angle θ0 decreases as increasing the Fermi energy both in part 1 and part 2, but PA angle changes greater in part 1 than in part 2.

 figure: Fig. 7

Fig. 7 (a) and (b) show the perfect absorption condition for TM polarized wave as a function of the wavenumber at different Fermi energy Ef.

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For TE waves, we can know from Eq. (8) that the reflection vanishes when the in-plane permittivity component εxeff is equal to 1. We plot in Fig. 8(a) the reflection of our graphene-hBN hyper-crystal as a function of wavenumbers depending on the incidence angle at Ef = 0.25 eV and Fig. 8(b) the perfect transmittance condition at different Fermi energies. Figure 8(a) shows the reflection dip only occur at the wavenumber near 1700 cm−1, which corresponds to the condition εt=1 at Ef = 0.25 eV for TE waves as seen from Fig. 8(b), and it is therefore insensitive to the incidence angle. Figure 8(b) also shows that by tuning the Fermi energy, the wavenumber that meets εt=1 changes and the position of the reflection dip is blue shift as increasing the Fermi energy.

 figure: Fig. 8

Fig. 8 (a) calculated reflection spectra for TE polarized wave at different incidence angles for Ef = 0.25 ev. (b) the perfect transmittance condition for TE polarized wave at different Fermi energies Ef.

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4. Conclusions

In conclusion, we have studied PA in a half-space of graphene-hBN hyper-crystal. The permittivity of the hyper-crystal was approximated by the the effective medium theory. Through PA condition anlysis, we find that PA at infrared frequencies can be achieved and controlled. For TM waves, we can realize PA at two different wavenumbers and two different incidence angles, while for TE waves, we find that only the nearly PA can be realized due to non-zero imaginary part of permittivity of the graphene-hBN hyper-crystal. But both PA of TM polarization and nearly PA of TE polarization can be controlled by tuning the Fermi energy of graphene. We believe PA at infrared frequencies and the flexible control of PA is very interesting and will find potential applications in optical communications, photovoltaic and optical detectors.

Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61505111, 61575127 and 61490713), the Guangdong Natural Science Foundation (Grant No. 2015A030313549), the Science and Technology Planning Project of Guangdong Province (Grant No. 2016B050501005), the Science and Technology Project of Shenzhen (grant Nos.JCYJ20140828163633996 and JCYJ20150324141711667), and the Natural Science Foundation of SZU (Grant Nos. 201517, 201452, 827-000051, 827-000052, and 827-000059).

References and links

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]  

2. W. Zhu and X. Zhao, “Metamaterial absorber with dendritic cells at infrared frequencies,” J. Opt. Soc. Am. B 12(12), 2382–2385 (2009). [CrossRef]  

3. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009). [CrossRef]  

4. T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008). [CrossRef]  

5. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef]   [PubMed]  

6. V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013). [CrossRef]   [PubMed]  

7. 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]  

8. H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015). [CrossRef]   [PubMed]  

9. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011). [CrossRef]   [PubMed]  

10. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef]   [PubMed]  

11. B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010). [CrossRef]  

12. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012). [CrossRef]   [PubMed]  

13. 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]  

14. J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Phys. Opt. 1602, 01466 (2016).

15. G. Yao, F. Ling, J. Yue, C. Luo, J. Ji, and J. Yao, “Dual-band tunable perfect metamaterial absorber in the THz range,” Opt. Express 24(2), 1518–1527 (2016). [CrossRef]   [PubMed]  

16. D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012). [CrossRef]  

17. D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015). [CrossRef]  

18. J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014). [CrossRef]   [PubMed]  

19. S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014). [CrossRef]   [PubMed]  

20. Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015). [CrossRef]   [PubMed]  

21. B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012). [CrossRef]   [PubMed]  

22. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef]   [PubMed]  

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

24. C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012). [CrossRef]  

25. L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012). [CrossRef]   [PubMed]  

26. S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013). [CrossRef]   [PubMed]  

27. A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015). [CrossRef]   [PubMed]  

28. A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016). [CrossRef]   [PubMed]  

29. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011). [CrossRef]   [PubMed]  

30. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]  

31. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007). [CrossRef]  

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

33. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef]   [PubMed]  

34. B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013). [CrossRef]   [PubMed]  

35. Z. Jacob, “Nanophotonics: Hyperbolic phonon-polaritons,” Nat. Mater. 13(12), 1081–1083 (2014). [CrossRef]   [PubMed]  

36. S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015). [CrossRef]   [PubMed]  

37. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014). [CrossRef]   [PubMed]  

38. F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).

39. C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000). [CrossRef]  

References

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  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]
  2. W. Zhu and X. Zhao, “Metamaterial absorber with dendritic cells at infrared frequencies,” J. Opt. Soc. Am. B 12(12), 2382–2385 (2009).
    [Crossref]
  3. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
    [Crossref]
  4. T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
    [Crossref]
  5. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
    [Crossref] [PubMed]
  6. V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
    [Crossref] [PubMed]
  7. 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]
  8. H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015).
    [Crossref] [PubMed]
  9. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011).
    [Crossref] [PubMed]
  10. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
    [Crossref] [PubMed]
  11. B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
    [Crossref]
  12. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
    [Crossref] [PubMed]
  13. 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]
  14. J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Phys. Opt. 1602, 01466 (2016).
  15. G. Yao, F. Ling, J. Yue, C. Luo, J. Ji, and J. Yao, “Dual-band tunable perfect metamaterial absorber in the THz range,” Opt. Express 24(2), 1518–1527 (2016).
    [Crossref] [PubMed]
  16. D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012).
    [Crossref]
  17. D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
    [Crossref]
  18. J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
    [Crossref] [PubMed]
  19. S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
    [Crossref] [PubMed]
  20. Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
    [Crossref] [PubMed]
  21. B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
    [Crossref] [PubMed]
  22. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref] [PubMed]
  23. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
    [Crossref]
  24. C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
    [Crossref]
  25. L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
    [Crossref] [PubMed]
  26. S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
    [Crossref] [PubMed]
  27. A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
    [Crossref] [PubMed]
  28. A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
    [Crossref] [PubMed]
  29. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
    [Crossref] [PubMed]
  30. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
    [Crossref]
  31. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
    [Crossref]
  32. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
    [Crossref] [PubMed]
  33. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
    [Crossref] [PubMed]
  34. B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013).
    [Crossref] [PubMed]
  35. Z. Jacob, “Nanophotonics: Hyperbolic phonon-polaritons,” Nat. Mater. 13(12), 1081–1083 (2014).
    [Crossref] [PubMed]
  36. S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
    [Crossref] [PubMed]
  37. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
    [Crossref] [PubMed]
  38. F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).
  39. C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
    [Crossref]

2016 (3)

J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Phys. Opt. 1602, 01466 (2016).

G. Yao, F. Ling, J. Yue, C. Luo, J. Ji, and J. Yao, “Dual-band tunable perfect metamaterial absorber in the THz range,” Opt. Express 24(2), 1518–1527 (2016).
[Crossref] [PubMed]

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

2015 (5)

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015).
[Crossref] [PubMed]

2014 (5)

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (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]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Z. Jacob, “Nanophotonics: Hyperbolic phonon-polaritons,” Nat. Mater. 13(12), 1081–1083 (2014).
[Crossref] [PubMed]

2013 (3)

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

2012 (6)

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

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

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

2011 (4)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

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]

M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011).
[Crossref] [PubMed]

2010 (3)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

2009 (2)

W. Zhu and X. Zhao, “Metamaterial absorber with dendritic cells at infrared frequencies,” J. Opt. Soc. Am. B 12(12), 2382–2385 (2009).
[Crossref]

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[Crossref]

2008 (3)

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

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]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

2007 (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

2004 (1)

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

2000 (1)

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

1997 (1)

F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).

Abdelsalam, M.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Andersen, T.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Ansell, D.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

Araujo, P. T.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Avouris, P.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Banerjee, K.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Baranov, D. G.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012).
[Crossref]

Bartlett, P. N.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Basov, D. N.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Bassim, N.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

Baumberg, J. J.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Belle, B. D.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Borisov, A. G.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Britnell, L.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Caldwell, J. D.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Carrega, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Castro Neto, A. H.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Chen, Y.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Chia, E. E.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Czaplewski, D.

Dai, S.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Dai, X.

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]

Dean, C.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Deng, H.

Deorani, P.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Diem, M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[Crossref]

Dominguez, G.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Dresselhaus, M.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Eaves, L.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Edgar, J. H.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

Ellis, C. T.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Fang, N. X.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Fang, T.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Fei, Z.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Feng, Q.

Feng, Y.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Fogler, M. M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Francescato, Y.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Fung, K. H.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Gannett, W.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Gao, J.

Gao, Y.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Garcia de Abajo, F. J.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

García de Abajo, F. J.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Garcia-Vidal, F.

F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).

Geim, A. K.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Georgiou, T.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Giannini, V.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Giles, A. J.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Goldflam, M. D.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Gorbachev, R. V.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Grigorenko, A. N.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

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

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Guo, J.

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]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Halterman, K.

J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Phys. Opt. 1602, 01466 (2016).

Hanson, G. W.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Hillenbrand, R.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Hoffman, T.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

Hone, J.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Hong, M.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Hsu, A.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Hu, C.

Huang, C.

M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011).
[Crossref] [PubMed]

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Hwang, W. S.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Idrobo, J. C.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Jacob, Z.

Z. Jacob, “Nanophotonics: Hyperbolic phonon-polaritons,” Nat. Mater. 13(12), 1081–1083 (2014).
[Crossref] [PubMed]

Jahangir, I.

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

Jalil, R.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Janssen, G. C. A. M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Jarillo-Herrero, P.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Jena, D.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Ji, J.

Jian, S.

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Jiang, T.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Jokerst, N. M.

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]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Kabashin, A. V.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

Katsnelson, M. I.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Keilmann, F.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Kelly, M. M.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Kim, K. K.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Kim, P.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Kim, S. M.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Kong, J.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Koppens, F. H. L.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Koschny, T.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[Crossref]

Kravets, V. G.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

Kretinin, A. V.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Kumar, A.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Landy, N. I.

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]

La-o-vorakiat, C.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Lee, G.-H.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Lee, Y.-H.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Leist, J.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Li, Z.

Lin, Z.

Linder, J.

J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Phys. Opt. 1602, 01466 (2016).

Ling, F.

Liu, J.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Liu, L.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Liu, M. K.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Liu, X.

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]

Low, T.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Lu, T.

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

Lundeberg, M. B.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Luo, C.

Luo, X.

Ma, Q.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Mahdy, M. R.

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

Maier, S. A.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

McLeod, A. S.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Meric, I.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Mishchenko, A.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Mock, J. J.

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]

Morozov, S. V.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Novoselov, K. S.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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

Padilla, W. J.

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]

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]

Palacios, T.

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

Pendry, J. B.

F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).

Peres, N. M. R.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Pitarke, J. M.

F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).

Polini, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

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

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Ponomarenko, L. A.

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Principi, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Pu, M.

Qiu, X.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Rahman, M. M.

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

Rahman, M. S.

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

Regan, W.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Ren, G.

Rodin, A. S.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Rosenmann, D.

Sajuyigbe, S.

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]

Sayem, A. A.

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

Schedin, F.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Sensale-Rodriguez, B.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Shepard, K.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Simovski, C. R.

D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012).
[Crossref]

Smith, D. R.

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]

Son, J.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Soukoulis, C. M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[Crossref]

Stan, L.

Starr, A. F.

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]

Starr, T.

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]

Su, W.

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

Sugawara, Y.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Tahy, K.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Tang, D.

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]

Taniguchi, T.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Teperik, T. V.

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Thackray, B.

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

Thiemens, M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Thongrattanasiri, S.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Tischler, J. G.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Tyler, T.

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]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Vignale, G.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Vinogradov, A. P.

D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012).
[Crossref]

Wagner, M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Wang, C.

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Wang, L.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Wang, M.

Wang, Z.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Watanabe, K.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Woessner, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Woods, C. R.

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Wu, X.

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

Wu, Y.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Xiang, Y.

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]

Xing, H. G.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Yan, R.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

Yang, B.

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

Yang, H.

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

Yang, X.

Yao, G.

Yao, J.

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Young, A. F.

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

Yue, J.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zettl, A.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Zhang, C.

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

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).
[Crossref] [PubMed]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhang, Y.

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

Zhao, J.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Zhao, X.

Zhao, Z.

Zheng, S.

Zheng, Y.

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

Zhu, B.

B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013).
[Crossref] [PubMed]

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Zhu, S. E.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Zhu, W.

ACS Nano (1)

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Adv. Mater. (1)

Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. Chia, and H. Yang, “Graphene terahertz modulators by ionic liquid gating,” Adv. Mater. 27(11), 1874–1879 (2015).
[Crossref] [PubMed]

J. Appl. Phys. (1)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Metamaterials (Amst.) (1)

D. G. Baranov, A. P. Vinogradov, and C. R. Simovski, “Perfect absorption at Zenneck wave to plane wave transition,” Metamaterials (Amst.) 6(1-2), 70–75 (2012).
[Crossref]

Nano Lett. (3)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

S. M. Kim, A. Hsu, P. T. Araujo, Y.-H. Lee, T. Palacios, M. Dresselhaus, J. C. Idrobo, K. K. Kim, and J. Kong, “Synthesis of patched or stacked graphene and hBN flakes: a route to hybrid structure discovery,” Nano Lett. 13(3), 933–941 (2013).
[Crossref] [PubMed]

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Nat. Commun. (2)

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5, 5221 (2014).
[Crossref] [PubMed]

Nat. Mater. (4)

Z. Jacob, “Nanophotonics: Hyperbolic phonon-polaritons,” Nat. Mater. 13(12), 1081–1083 (2014).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, R. Jalil, L. Britnell, R. V. Gorbachev, D. Ansell, B. Thackray, K. S. Novoselov, A. K. Geim, A. V. Kabashin, and A. N. Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Nat. Photonics (2)

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

T. V. Teperik, F. J. Garcia de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[Crossref]

Nature (2)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Opt. (1)

J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Phys. Opt. 1602, 01466 (2016).

Phys. Rev. B (3)

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a van der Waals crystal,” Phys. Rev. B 92(20), 201405 (2015).
[Crossref]

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[Crossref]

F. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. B 78, 4289 (1997).

Phys. Rev. Lett. (3)

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]

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]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Physica B (1)

C. Zhang, B. Yang, X. Wu, T. Lu, Y. Zheng, and W. Su, “Calculation of the effective dielectric function of composites with periodic geometry,” Physica B 293(1-2), 16–32 (2000).
[Crossref]

Prog. Electromagnetics Res. (1)

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagnetics Res. 101, 231–239 (2010).
[Crossref]

Sci. Rep. (2)

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]

A. A. Sayem, M. M. Rahman, M. R. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref] [PubMed]

Science (3)

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

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

L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science 335(6071), 947–950 (2012).
[Crossref] [PubMed]

Solid State Commun. (1)

C. Dean, A. F. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 15(15), 1275–1282 (2012).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) and (b) are the real and imaginary parts of the permittivity of monolayer graphene as a function of the wavenumber for various chemical potential of graphene. (c) and (d) are the real and imaginary parts of the tangential and perpendicular permittivity of hBN.
Fig. 2
Fig. 2 The interferenceless perfect electromagnetic absorber based on the graphene-hBN hyper crystal.
Fig. 3
Fig. 3 The real part of the tangential and perpendicular permittivities of the graphene-hBN hyper crystal.
Fig. 4
Fig. 4 (a) and (b) are the absorption as a function of the wavenumber based on the effective medium theory at the incidence angle 60°, 80°. (c) and (d) are the absorption as a function of the wavenumber by using the transfer matrix method with enough period at the incidence angle 60°, 80°, where Ef = 0.25 eV.
Fig. 5
Fig. 5 (a) The real and imaginary parts of squared cosine of the perfect absorption angle θ 0 . (b) and (c) show that the perfect absorption of TM polarized wave can be achieved at point A and B according to the condition of perfect absorption.
Fig. 6
Fig. 6 (a) calculated absorption spectra for TM polarized wave at different incidence angles. (b) shows the perfect absorption occurs at the angle 67°. (c) shows the perfect absorption occurs at the angle 74°.
Fig. 7
Fig. 7 (a) and (b) show the perfect absorption condition for TM polarized wave as a function of the wavenumber at different Fermi energy Ef.
Fig. 8
Fig. 8 (a) calculated reflection spectra for TE polarized wave at different incidence angles for Ef = 0.25 ev. (b) the perfect transmittance condition for TE polarized wave at different Fermi energies Ef.

Equations (9)

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σ = i e 2 E F π 2 ( ω + i τ 1 ) ,
ε g r a p h e n e = [ ε g , t 0 0 0 ε g , t 0 0 0 ε g , ] ,
ε g , t = ε g = 1 + i σ ε 0 ω t g ,
ε u = ε , u ( 1 + ( ω L O , u ) 2 ( ω T O , u ) 2 ( ω T O , u ) 2 ω 2 i ω γ u )
ε t e f f = ε x e f f = ε y e f f = f g ε g , t + ( 1 f g ) ε x ,
ε z e f f = ( f g ε g , + 1 f g ε z ) 1 ,
r T M = cos 2 θ i ( ε z e f f sin 2 θ i ) / ( ε z e f f ε x e f f ) cos 2 θ i + ( ε z e f f sin 2 θ i ) / ( ε z e f f ε x e f f ) ,
r T E = cos 2 θ i ε x e f f sin 2 θ i cos 2 θ i + ε x e f f sin 2 θ i ,
cos 2 θ 0 = ε z e f f 1 ε z e f f ε x e f f 1 ,

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