Abstract

Polaritons in polar-dielectrics and van der Waals (vdW) materials provide a channel for strong photon confinement. Precise control of their propagation could lead to deep sub-wavelength photonic devices. Here, we report negative refraction of hybrid surface phonon-hyperbolic polaritons (SPh-HP) at the interface of two-dimensional (2D) van der Waals layers such as hexagonal boron nitride (h-BN) and 3D semiconductors such as germanium and silicon carbide. These hybrid polariton modes have naturally negative group velocity arising from the intrinsic Type-I hyperbolicity of h-BN resulting in negative refraction at interfaces with positive group velocity. Using this phenomenon, we demonstrate an in-plane superlensing effect in an ultrathin (~10 nm) slab with spatial confinement of long Infrared wavelengths to below 200 nm focal spots. We further demonstrate electrical tunability of the superlens by controlling the Fermi level of graphene, thereby offering potential for miniaturized infrared to THz modulators, photodetectors as well as logic switches.

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

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2018 (10)

A. J. Giles, S. Dai, I. Vurgaftman, T. Hoffman, S. Liu, L. Lindsay, C. T. Ellis, N. Assefa, I. Chatzakis, T. L. Reinecke, J. G. Tischler, M. M. Fogler, J. H. Edgar, D. N. Basov, and J. D. Caldwell, “Ultralow-loss polaritons in isotopically pure boron nitride,” Nat. Mater. 17(2), 134–139 (2018).
[Crossref] [PubMed]

A. M. Dubrovkin, B. Qiang, H. N. S. Krishnamoorthy, N. I. Zheludev, and Q. J. Wang, “Ultra-confined surface phonon polaritons in molecular layers of van der Waals dielectrics,” Nat. Commun. 9(1), 1762 (2018).
[Crossref] [PubMed]

W. Ma, P. Alonso-González, S. Li, A. Y. Nikitin, J. Yuan, J. Martín-Sánchez, J. Taboada-Gutiérrez, I. Amenabar, P. Li, S. Vélez, C. Tollan, Z. Dai, Y. Zhang, S. Sriram, K. Kalantar-Zadeh, S. T. Lee, R. Hillenbrand, and Q. Bao, “In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal,” Nature 562(7728), 557–562 (2018).
[Crossref] [PubMed]

V. E. Babicheva, S. Gamage, L. Zhen, S. B. Cronin, V. S. Yakovlev, and Y. Abate, “Near-field Surface Waves in Few-Layer MoS2,” Acs Photon. 5(6), 2106–2112 (2018).
[Crossref]

B. Yao, Y. Liu, S. W. Huang, C. Choi, Z. Xie, J. F. Flores, Y. Wu, M. Yu, D. L. Kwong, and Y. Huang, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Y. Kurman, N. Rivera, T. Christensen, S. Tsesses, M. Orenstein, M. Soljačić, J. D. Joannopoulos, and I. Kaminer, “Control of semiconductor emitter frequency by increasing polariton momenta,” Nat. Photonics 12(8), 495 (2018).
[Crossref]

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

P. Li, I. Dolado, F. J. Alfaro-Mozaz, F. Casanova, L. E. Hueso, S. Liu, J. H. Edgar, A. Y. Nikitin, S. Vélez, and R. Hillenbrand, “Infrared hyperbolic metasurface based on nanostructured van der Waals materials,” Science 359(6378), 892–896 (2018).
[Crossref] [PubMed]

Y. Jiang, X. Lin, T. Low, B. Zhang, and H. Chen, “Group-velocity-controlled and gate-tunable directional excitation of polaritons in graphene-boron nitride heterostructures,” Laser Photonics Rev. 12(5), 1800049 (2018).
[Crossref]

D. Alcaraz Iranzo, S. Nanot, E. J. C. Dias, I. Epstein, C. Peng, D. K. Efetov, M. B. Lundeberg, R. Parret, J. Osmond, J.-Y. Hong, J. Kong, D. R. Englund, N. M. R. Peres, and F. H. L. Koppens, “Probing the ultimate plasmon confinement limits with a van der Waals heterostructure,” Science 360(6386), 291–295 (2018).
[Crossref] [PubMed]

2017 (7)

X. Lin, Y. Yang, N. Rivera, J. J. López, Y. Shen, I. Kaminer, H. Chen, B. Zhang, J. D. Joannopoulos, and M. Soljačić, “All-angle negative refraction of highly squeezed plasmon and phonon polaritons in graphene-boron nitride heterostructures,” Proc. Natl. Acad. Sci. U.S.A. 114(26), 6717–6721 (2017).
[Crossref] [PubMed]

A. Woessner, Y. Gao, I. Torre, M. B. Lundeberg, C. Tan, K. Watanabe, T. Taniguchi, R. Hillenbrand, J. Hone, M. Polini, and F. H. L. Koppens, “Electrical 2π phase control of infrared light in a 350-nm footprint using graphene plasmons,” Nat. Photonics 11(7), 421–424 (2017).
[Crossref]

S. C. Dhanabalan, J. S. Ponraj, Z. Guo, S. Li, Q. Bao, and H. Zhang, “Emerging trends in phosphorene fabrication towards next generation devices,” Adv. Sci. (Weinh.) 4(6), 1600305 (2017).
[Crossref] [PubMed]

D. Jariwala, T. J. Marks, and M. C. Hersam, “Mixed-dimensional van der Waals heterostructures,” Nat. Mater. 16(2), 170–181 (2017).
[Crossref] [PubMed]

M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12(3), 207–211 (2017).
[Crossref] [PubMed]

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017).
[Crossref] [PubMed]

F. Hu, Y. Luan, M. Scott, J. Yan, D. Mandrus, X. Xu, and Z. Fei, “Imaging exciton–polariton transport in MoSe 2 waveguides,” Nat. Photonics 11(6), 356–360 (2017).
[Crossref]

2016 (7)

D. N. Basov, M. M. Fogler, and F. J. García de Abajo, “Polaritons in van der Waals materials,” Science 354(6309), aag1992 (2016).
[Crossref] [PubMed]

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. Mcleod, M. K. Liu, F. Keilmann, B. Özyilmaz, and A. H. C. Neto, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

J. S. Ponraj, Z.-Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

S. C. Dhanabalan, J. S. Ponraj, H. Zhang, and Q. Bao, “Present perspectives of broadband photodetectors based on nanobelts, nanoribbons, nanosheets and the emerging 2D materials,” Nanoscale 8(12), 6410–6434 (2016).
[Crossref] [PubMed]

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

J. D. Caldwell, I. Vurgaftman, J. G. Tischler, O. J. Glembocki, J. C. Owrutsky, and T. L. Reinecke, “Atomic-scale photonic hybrids for mid-infrared and terahertz nanophotonics,” Nat. Nanotechnol. 11(1), 9–15 (2016).
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B. Zhu, G. Ren, B. Wu, Y. Gao, H. Li, and S. Jian, “Nanofocusing of hybrid plasmons-phonons-polaritons in a graphene-hexagonal boron nitride heterostructure,” Opt. Lett. 41(19), 4578–4581 (2016).
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2015 (10)

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).
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E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nat. Photonics 9(10), 674–678 (2015).
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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. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
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P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6(1), 6963 (2015).
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H. Mu, Z. Wang, J. Yuan, S. Xiao, C. Chen, Y. Chen, Y. Chen, J. Song, Y. Wang, Y. Xue, H. Zhang, and Q. Bao, “Graphene–Bi2Te3 heterostructure as saturable absorber for short pulse generation,” Acs Photon. 2(7), 832–841 (2015).
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A. C. Ferrari, F. Bonaccorso, V. Fal’ko, K. S. Novoselov, S. Roche, P. Bøggild, S. Borini, F. H. Koppens, V. Palermo, N. Pugno, J. A. Garrido, R. Sordan, A. Bianco, L. Ballerini, M. Prato, E. Lidorikis, J. Kivioja, C. Marinelli, T. Ryhänen, A. Morpurgo, J. N. Coleman, V. Nicolosi, L. Colombo, A. Fert, M. Garcia-Hernandez, A. Bachtold, G. F. Schneider, F. Guinea, C. Dekker, M. Barbone, Z. Sun, C. Galiotis, A. N. Grigorenko, G. Konstantatos, A. Kis, M. Katsnelson, L. Vandersypen, A. Loiseau, V. Morandi, D. Neumaier, E. Treossi, V. Pellegrini, M. Polini, A. Tredicucci, G. M. Williams, B. H. Hong, J. H. Ahn, J. M. Kim, H. Zirath, B. J. van Wees, H. van der Zant, L. Occhipinti, A. Di Matteo, I. A. Kinloch, T. Seyller, E. Quesnel, X. Feng, K. Teo, N. Rupesinghe, P. Hakonen, S. R. Neil, Q. Tannock, T. Löfwander, and J. Kinaret, “Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems,” Nanoscale 7(11), 4598–4810 (2015).
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D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “APPLIED PHYSICS. Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
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J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
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J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nanotechnol. 10(1), 2–6 (2015).
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2014 (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).
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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(1), 5221 (2014).
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F. J. Garcia de Abajo, “Graphene plasmonics: challenges and opportunities,” Acs Photon. 1(3), 135–152 (2014).
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2012 (2)

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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2011 (1)

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
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2007 (1)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
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2006 (2)

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
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2005 (2)

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
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2004 (1)

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
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2003 (1)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: Negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
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2002 (1)

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
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2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
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2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
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V. E. Babicheva, S. Gamage, L. Zhen, S. B. Cronin, V. S. Yakovlev, and Y. Abate, “Near-field Surface Waves in Few-Layer MoS2,” Acs Photon. 5(6), 2106–2112 (2018).
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Ahn, J. H.

A. C. Ferrari, F. Bonaccorso, V. Fal’ko, K. S. Novoselov, S. Roche, P. Bøggild, S. Borini, F. H. Koppens, V. Palermo, N. Pugno, J. A. Garrido, R. Sordan, A. Bianco, L. Ballerini, M. Prato, E. Lidorikis, J. Kivioja, C. Marinelli, T. Ryhänen, A. Morpurgo, J. N. Coleman, V. Nicolosi, L. Colombo, A. Fert, M. Garcia-Hernandez, A. Bachtold, G. F. Schneider, F. Guinea, C. Dekker, M. Barbone, Z. Sun, C. Galiotis, A. N. Grigorenko, G. Konstantatos, A. Kis, M. Katsnelson, L. Vandersypen, A. Loiseau, V. Morandi, D. Neumaier, E. Treossi, V. Pellegrini, M. Polini, A. Tredicucci, G. M. Williams, B. H. Hong, J. H. Ahn, J. M. Kim, H. Zirath, B. J. van Wees, H. van der Zant, L. Occhipinti, A. Di Matteo, I. A. Kinloch, T. Seyller, E. Quesnel, X. Feng, K. Teo, N. Rupesinghe, P. Hakonen, S. R. Neil, Q. Tannock, T. Löfwander, and J. Kinaret, “Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems,” Nanoscale 7(11), 4598–4810 (2015).
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Alcaraz Iranzo, D.

D. Alcaraz Iranzo, S. Nanot, E. J. C. Dias, I. Epstein, C. Peng, D. K. Efetov, M. B. Lundeberg, R. Parret, J. Osmond, J.-Y. Hong, J. Kong, D. R. Englund, N. M. R. Peres, and F. H. L. Koppens, “Probing the ultimate plasmon confinement limits with a van der Waals heterostructure,” Science 360(6386), 291–295 (2018).
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P. Li, I. Dolado, F. J. Alfaro-Mozaz, F. Casanova, L. E. Hueso, S. Liu, J. H. Edgar, A. Y. Nikitin, S. Vélez, and R. Hillenbrand, “Infrared hyperbolic metasurface based on nanostructured van der Waals materials,” Science 359(6378), 892–896 (2018).
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Alonso-González, P.

W. Ma, P. Alonso-González, S. Li, A. Y. Nikitin, J. Yuan, J. Martín-Sánchez, J. Taboada-Gutiérrez, I. Amenabar, P. Li, S. Vélez, C. Tollan, Z. Dai, Y. Zhang, S. Sriram, K. Kalantar-Zadeh, S. T. Lee, R. Hillenbrand, and Q. Bao, “In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal,” Nature 562(7728), 557–562 (2018).
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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. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “APPLIED PHYSICS. Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
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Amenabar, I.

W. Ma, P. Alonso-González, S. Li, A. Y. Nikitin, J. Yuan, J. Martín-Sánchez, J. Taboada-Gutiérrez, I. Amenabar, P. Li, S. Vélez, C. Tollan, Z. Dai, Y. Zhang, S. Sriram, K. Kalantar-Zadeh, S. T. Lee, R. Hillenbrand, and Q. Bao, “In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal,” Nature 562(7728), 557–562 (2018).
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S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6(1), 6963 (2015).
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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).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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J. S. Ponraj, Z.-Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
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A. J. Giles, S. Dai, I. Vurgaftman, T. Hoffman, S. Liu, L. Lindsay, C. T. Ellis, N. Assefa, I. Chatzakis, T. L. Reinecke, J. G. Tischler, M. M. Fogler, J. H. Edgar, D. N. Basov, and J. D. Caldwell, “Ultralow-loss polaritons in isotopically pure boron nitride,” Nat. Mater. 17(2), 134–139 (2018).
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H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
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T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017).
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Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: Negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
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V. E. Babicheva, S. Gamage, L. Zhen, S. B. Cronin, V. S. Yakovlev, and Y. Abate, “Near-field Surface Waves in Few-Layer MoS2,” Acs Photon. 5(6), 2106–2112 (2018).
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Bachtold, A.

A. C. Ferrari, F. Bonaccorso, V. Fal’ko, K. S. Novoselov, S. Roche, P. Bøggild, S. Borini, F. H. Koppens, V. Palermo, N. Pugno, J. A. Garrido, R. Sordan, A. Bianco, L. Ballerini, M. Prato, E. Lidorikis, J. Kivioja, C. Marinelli, T. Ryhänen, A. Morpurgo, J. N. Coleman, V. Nicolosi, L. Colombo, A. Fert, M. Garcia-Hernandez, A. Bachtold, G. F. Schneider, F. Guinea, C. Dekker, M. Barbone, Z. Sun, C. Galiotis, A. N. Grigorenko, G. Konstantatos, A. Kis, M. Katsnelson, L. Vandersypen, A. Loiseau, V. Morandi, D. Neumaier, E. Treossi, V. Pellegrini, M. Polini, A. Tredicucci, G. M. Williams, B. H. Hong, J. H. Ahn, J. M. Kim, H. Zirath, B. J. van Wees, H. van der Zant, L. Occhipinti, A. Di Matteo, I. A. Kinloch, T. Seyller, E. Quesnel, X. Feng, K. Teo, N. Rupesinghe, P. Hakonen, S. R. Neil, Q. Tannock, T. Löfwander, and J. Kinaret, “Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems,” Nanoscale 7(11), 4598–4810 (2015).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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A. C. Ferrari, F. Bonaccorso, V. Fal’ko, K. S. Novoselov, S. Roche, P. Bøggild, S. Borini, F. H. Koppens, V. Palermo, N. Pugno, J. A. Garrido, R. Sordan, A. Bianco, L. Ballerini, M. Prato, E. Lidorikis, J. Kivioja, C. Marinelli, T. Ryhänen, A. Morpurgo, J. N. Coleman, V. Nicolosi, L. Colombo, A. Fert, M. Garcia-Hernandez, A. Bachtold, G. F. Schneider, F. Guinea, C. Dekker, M. Barbone, Z. Sun, C. Galiotis, A. N. Grigorenko, G. Konstantatos, A. Kis, M. Katsnelson, L. Vandersypen, A. Loiseau, V. Morandi, D. Neumaier, E. Treossi, V. Pellegrini, M. Polini, A. Tredicucci, G. M. Williams, B. H. Hong, J. H. Ahn, J. M. Kim, H. Zirath, B. J. van Wees, H. van der Zant, L. Occhipinti, A. Di Matteo, I. A. Kinloch, T. Seyller, E. Quesnel, X. Feng, K. Teo, N. Rupesinghe, P. Hakonen, S. R. Neil, Q. Tannock, T. Löfwander, and J. Kinaret, “Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems,” Nanoscale 7(11), 4598–4810 (2015).
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W. Ma, P. Alonso-González, S. Li, A. Y. Nikitin, J. Yuan, J. Martín-Sánchez, J. Taboada-Gutiérrez, I. Amenabar, P. Li, S. Vélez, C. Tollan, Z. Dai, Y. Zhang, S. Sriram, K. Kalantar-Zadeh, S. T. Lee, R. Hillenbrand, and Q. Bao, “In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal,” Nature 562(7728), 557–562 (2018).
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S. C. Dhanabalan, J. S. Ponraj, H. Zhang, and Q. Bao, “Present perspectives of broadband photodetectors based on nanobelts, nanoribbons, nanosheets and the emerging 2D materials,” Nanoscale 8(12), 6410–6434 (2016).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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Acs Photon. (3)

V. E. Babicheva, S. Gamage, L. Zhen, S. B. Cronin, V. S. Yakovlev, and Y. Abate, “Near-field Surface Waves in Few-Layer MoS2,” Acs Photon. 5(6), 2106–2112 (2018).
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H. Mu, Z. Wang, J. Yuan, S. Xiao, C. Chen, Y. Chen, Y. Chen, J. Song, Y. Wang, Y. Xue, H. Zhang, and Q. Bao, “Graphene–Bi2Te3 heterostructure as saturable absorber for short pulse generation,” Acs Photon. 2(7), 832–841 (2015).
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Adv. Sci. (Weinh.) (1)

S. C. Dhanabalan, J. S. Ponraj, Z. Guo, S. Li, Q. Bao, and H. Zhang, “Emerging trends in phosphorene fabrication towards next generation devices,” Adv. Sci. (Weinh.) 4(6), 1600305 (2017).
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Laser Photonics Rev. (1)

Y. Jiang, X. Lin, T. Low, B. Zhang, and H. Chen, “Group-velocity-controlled and gate-tunable directional excitation of polaritons in graphene-boron nitride heterostructures,” Laser Photonics Rev. 12(5), 1800049 (2018).
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Nanophotonics (1)

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Nanoscale (2)

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of in-plane negative refraction between hybrid surface phonon-hyperbolic phonon polariton (SPh-HP) and tailored surface phonon polariton (SPhP). (b) Left part: the hybrid SPh-HP has negative group velocity, and the Ez distributions (mushroom pattern) inside and outside h-BN have opposite sign; Right part: tailored SPhP has positive group velocity, the Ez distributions inside and outside Ge have same sign. (c) Real permittivity for h-BN and SiC, the overlapping frequencies between h-BN’s first reststrahlen band (εx/y>0, εz<0) and SiC’s reststrahlen band (ε<0) from 797 to 835 cm−1. (d) Type-I hyperbolic responses (solutions for Eq. (1) at ω = 800 cm−1 (blue solid curve) and 820 cm−1 (blue dashed curve).
Fig. 2
Fig. 2 Theoretically calculated dispersions of the polariton modes, (a) hyperbolic phonon polaritons (HP) in the h-BN (400 nm)/SiO2 heterostructure, (b) surface phonon polariton (SPhP) on SiC substrate, (c) hybrid SPh-HP mode in the h-BN (500 nm)/ SiC heterostructure, and (d) tailored SPhP in the Ge (500 nm)/SiC heterostructure. Inset is the Ez field mode profile.
Fig. 3
Fig. 3 (a) 2D-view (y = 0 plane) of the complete heterostructure in Fig. 1(a). (b) Dependence of the real effective indices neff of the hybrid SPh-HP (blue curves) and the tailored SPhP (purple curves) modes on the wavenumber with different slab thicknesses, purple stars are intersection points. Mode profile of the magnetic Hy field for (c) hybrid SPh-HP mode within h-BN region and (d) tailored SPhP mode within Ge region at the neff matched intersection point (ω = 801cm−1, and neff = 1.98), the thicknesses of both h-BN and Ge slabs are 600 nm.
Fig. 4
Fig. 4 (a) Schematic of the in-plan negative refraction in lateral h-BN/Ge heterostructure above SiC substrate, the hybrid SPh-HP is launched by a mode source from h-BN side with incident angle 30°. Cross sectional view of (b) Ez field distribution and (c) Poynting vectors at xz plane. Top view of in-plan Ez field distributions (d and f) and Poynting vectors (e and g) outside (300 nm above top surface) in air and inside (300 nm below top surface) in h-BN/Ge, respectively. The power flow (wavevector) directions are marked by the red (green) arrows.
Fig. 5
Fig. 5 (a) Schematic of the superlens hybrid structure. (b) The dispersions of two type polaritons, g-SPhPs are electric tunable by controlling graphene’s Fermi level, both the thickness of h-BN and Gap is 10nm. Mode profiles of the magnetic Hy field for (c) hybrid SPh-HP mode within h-BN region and (d) g-SPhP mode within graphene region at the frequency of ω = 817 cm−1, the graphene Fermi level is μc = 0.16 ev, corresponds to a momentum matched neff = 80. (e) The figure of merit (γ−1) for graphene polaritons on different substrates, μc = 0.3 ev.
Fig. 6
Fig. 6 (a, b) The distributions of in-plan |E|2 and Hy field (5nm above SiC substrate) to illustrate the superlens effects, at the frequency of ω = 817 cm−1, the graphene Fermi level is μc = 0.16 ev, corresponds to a momentum matched neff = 80 for both polaritons. (c) The normalized Hy field at the image plane (black dashed line in (d)), the full width at half maximum (FWHM) is 125 nm. (d, e) The distributions of in-plan |E|2 and Hy field, and f) the normalized Hy field at the image plane, ω = 817 cm−1and μc = 0.41 ev.
Fig. 7
Fig. 7 The distributions of in-plan |E|2 and Hy field to illustrate the electrical tunability of the superlens. (a) ω = 824cm−1, μc = 0.41ev, corresponds to a momentum matched neff = 45 for both polaritons, the full width at half maximum (FWHM) is 200 nm. (b) ω = 817 cm−1, μc = 0.16 ev, neff = 80 and FWHM = 125 nm. (c) ω = 811 cm−1, μc = 0.11ev, neff = 105 and FWHM = 102 nm.
Fig. 8
Fig. 8 The schematic of three-layer heterostructure, layer 1 (z>d, air), layer 2 (0 <z<d, h-BN, Ge or air Gap), and layer 3 (z<0, SiC substrate), where d is the thickness of layer-2 slabs. The following derivations give the dispersions of hybrid SPh-HP, tailored-SPhP and g-SPhP, respectively.

Equations (9)

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ε(ω)= ε (1+ ω LO 2 ω TO 2 ω TO 2 ω 2 iωγ )
k z 2 / ε x +( k x 2 + k y 2 )/ ε z = (ω/c) 2
M=[ M aa M ab M ba M bb ]= R 1,2 T 2 R 2,3
R 1,2 = 1 t 1,2 [ 1 r 1,2 r 1,2 1 ], R 2,3 = 1 t 2,3 [ 1 r 2,3 r 2,3 1 ], T 2 =[ e i k z2 d 0 0 e i k z2 d ]
k z1 = ω 2 c 2 ε 1 k x 2 , k z2 = ω 2 c 2 ε 2x k x 2 ε 2x ε 2z , k z3 = ω 2 c 2 ε 3 k x 2
r i,j = ε xj k zi ε xi k zj ε xj k zi + ε xi k zj , t i,j = 2 ε xj k zi ε xj k zi + ε xi k zj
r p = M ba M aa
r 1,2 = ε x2 k z1 ε x1 k z2 +σ k z1 k z2 /ω ε 0 ε x2 k z1 + ε x1 k z2 +σ k z1 k z2 /ω ε 0 , t 1,2 = 2 ε x2 k z1 ε x2 k z1 + ε x1 k z2 +σ k z1 k z2 /ω ε 0
σ(ω)= e 2 E F π 2 i ω+i T 1 + e 2 4 2 ( θ(ω2 E F )+ i π log( | ω2 E F ω+2 E F | ) )

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