Abstract

Surface phonon polaritons (SPhPs) in polar dielectrics are potential candidates for infrared nanophotonics due to their low optical loss and long phonon life-time. However, the small confinement factors of bulk SPhPs, limits their applications that require small footprint and strong light-matter interaction. Here, we report that ultrathin van der Waals dielectrics (e.g., MoS2 and h-BN) on Silicon Carbide enable ultra-confined dielectric tailored surface phonon polaritons (d-SPhPs) where the confinement factor can exceed 100. By creating a heterostructure of these vdW dielectrics with graphene, the d-SPhPs can hybridize with graphene plasmons which can be electrically tuned. By subwavelength patterning of the vdW dielectrics, these hybrid polaritons can be localized into ultra-small antenna volumes (λ03/vantenna3~1003) with high-quality factor resonances (Q~85). Further, electric gating of graphene enables active tunability of these localized resonances which results in an electro-optic modulator with modulation depth exceeding 95%. Our report of manipulating and controlling ultra-confined SPhPs in van der Waals heterostructures, serves as a possible route for non-plasmonic platforms for infrared photodetectors, modulators and sensors.

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

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2019 (2)

H. Sumikura, T. Wang, P. Li, A. U. Michel, A. Heßler, L. Jung, M. Lewin, M. Wuttig, D. N. Chigrin, and T. Taubner, “Highly Confined and Switchable Mid-Infrared Surface Phonon Polariton Resonances of Planar Circular Cavities with a Phase Change Material,” Nano Lett. 19(4), 2549–2554 (2019).
[Crossref] [PubMed]

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref] [PubMed]

2018 (17)

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(7), 423–429 (2018).
[Crossref]

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]

Z. Zheng, J. Chen, Y. Wang, X. Wang, X. Chen, P. Liu, J. Xu, W. Xie, H. Chen, S. Deng, and N. Xu, “Highly Confined and Tunable Hyperbolic Phonon Polaritons in Van Der Waals Semiconducting Transition Metal Oxides,” Adv. Mater. 30(13), 1705318 (2018).
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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).
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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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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 Photonics. 5(6), 2106–2112 (2018).
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Y. Zhu, Z. Li, Z. Hao, C. DiMarco, P. Maturavongsadit, Y. Hao, M. Lu, A. Stein, Q. Wang, J. Hone, N. Yu, and Q. Lin, “Optical conductivity-based ultrasensitive mid-infrared biosensing on a hybrid metasurface,” Light Sci. Appl. 7(1), 67 (2018).
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A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
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M. Tamagnone, A. Ambrosio, K. Chaudhary, L. A. Jauregui, P. Kim, W. L. Wilson, and F. Capasso, “Ultra-confined mid-infrared resonant phonon polaritons in van der Waals nanostructures,” Sci.Adv. 4(6), eaat7189 (2018).

A. D. Dunkelberger, C. T. Ellis, D. C. Ratchford, A. J. Giles, M. Kim, C. S. Kim, B. T. Spann, I. Vurgaftman, J. G. Tischler, J. P. Long, O. J. Glembocki, J. C. Owrutsky, and J. D. Caldwell, “Active tuning of surface phonon polariton resonances via carrier photoinjection,” Nat. Photonics 12(1), 50–56 (2018).
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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).
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M. S. Jang, S. Kim, V. W. Brar, S. G. Menabde, and H. A. Atwater, “Modulated Resonant Transmission of Graphene Plasmons Across a λ/50 Plasmonic Waveguide Gap,” Phys. Rev. Appl. 10(5), 054053 (2018).
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S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically tunable perfect absorption in graphene,” Nano Lett. 18(2), 971–979 (2018).
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X. Xiao, X. Li, J. D. Caldwell, S. A. Maier, and V. Giannini, “Theoretical analysis of graphene plasmon cavities,” Appl. Mater. Today 12, 283–293 (2018).
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A. Keerthi, A. K. Geim, A. Janardanan, A. P. Rooney, A. Esfandiar, S. Hu, S. A. Dar, I. V. Grigorieva, S. J. Haigh, F. C. Wang, and B. Radha, “Ballistic molecular transport through two-dimensional channels,” Nature 558(7710), 420–424 (2018).
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2017 (8)

M. C. Sherrott, P. W. C. Hon, K. T. Fountaine, J. C. Garcia, S. M. Ponti, V. W. Brar, L. A. Sweatlock, and H. A. Atwater, “Experimental demonstration of >230◦ phase modulation in gate-tunable graphene–gold reconfigurable mid-infrared metasurfaces,” Nano Lett. 17(5), 3027–3034 (2017).
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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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F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
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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).
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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).
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P. Alonso-González, A. Y. Nikitin, Y. Gao, A. Woessner, M. B. Lundeberg, A. Principi, N. Forcellini, W. Yan, S. Vélez, and A. J. Huber, “Acoustic terahertz graphene plasmons revealed by photocurrent nanoscopy,” Nat. nanotech. 12(1), 31 (2017).

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).
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D. Jariwala, T. J. Marks, and M. C. Hersam, “Mixed-dimensional van der Waals heterostructures,” Nat. Mater. 16(2), 170–181 (2017).
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2016 (11)

C. R. Gubbin, F. Martini, A. Politi, S. A. Maier, and S. De Liberato, “Strong and Coherent Coupling between Localized and Propagating Phonon Polaritons,” Phys. Rev. Lett. 116(24), 246402 (2016).
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I. Razdolski, Y. Chen, A. J. Giles, S. Gewinner, W. Schöllkopf, M. Hong, M. Wolf, V. Giannini, J. D. Caldwell, S. A. Maier, and A. Paarmann, “Resonant Enhancement of Second-Harmonic Generation in the Mid-Infrared Using Localized Surface Phonon Polaritons in Subdiffractional Nanostructures,” Nano Lett. 16(11), 6954–6959 (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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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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Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
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D. N. Basov, M. M. Fogler, and F. J. García de Abajo, “Polaritons in van der Waals materials,” Science 354(6309), aag1992 (2016).
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P. Li, X. Yang, T. W. Maß, J. Hanss, M. Lewin, A. K. Michel, M. Wuttig, and T. Taubner, “Reversible optical switching of highly confined phonon-polaritons with an ultrathin phase-change material,” Nat. Mater. 15(8), 870–875 (2016).
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S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7(1), 12323 (2016).
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Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro‐absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
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B. Radha, A. Esfandiar, F. C. Wang, A. P. Rooney, K. Gopinadhan, A. Keerthi, A. Mishchenko, A. Janardanan, P. Blake, L. Fumagalli, M. Lozada-Hidalgo, S. Garaj, S. J. Haigh, I. V. Grigorieva, H. A. Wu, and A. K. Geim, “Molecular transport through capillaries made with atomic-scale precision,” Nature 538(7624), 222–225 (2016).
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Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
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2015 (9)

M. M. Jadidi, A. B. Sushkov, R. L. Myers-Ward, A. K. Boyd, K. M. Daniels, D. K. Gaskill, M. S. Fuhrer, H. D. Drew, and T. E. Murphy, “Tunable Terahertz Hybrid Metal-Graphene Plasmons,” Nano Lett. 15(10), 7099–7104 (2015).
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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).
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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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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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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. Hee Hong, J. H. Ahn, J. Min 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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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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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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D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
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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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2014 (5)

Y. Chen, Y. Francescato, J. D. Caldwell, V. Giannini, T. W. W. Maß, O. J. Glembocki, F. J. Bezares, T. Taubner, R. Kasica, and M. Hong, “Spectral Tuning of Localized Surface Phonon Polariton Resonators for Low-Loss Mid-IR Applications,” Acs Photonics. 1(8), 718–724 (2014).
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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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Y. Yao, M. A. Kats, R. Shankar, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Wide wavelength tuning of optical antennas on graphene with nanosecond response time,” Nano Lett. 14(1), 214–219 (2014).
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F. J. Garcia de Abajo, “Graphene plasmonics: challenges and opportunities,” Acs Photonics. 1(3), 135–152 (2014).
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2013 (1)

J. D. Caldwell, O. J. Glembocki, Y. Francescato, N. Sharac, V. Giannini, F. J. Bezares, J. P. Long, J. C. Owrutsky, I. Vurgaftman, J. G. Tischler, V. D. Wheeler, N. D. Bassim, L. M. Shirey, R. Kasica, and S. A. Maier, “Low-Loss, Extreme Subdiffraction Photon Confinement via Silicon Carbide Localized Surface Phonon Polariton Resonators,” Nano Lett. 13(8), 3690–3697 (2013).
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2012 (6)

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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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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C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
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K. Chen, R. Adato, and H. Altug, “Dual-Band Perfect Absorber for Multispectral Plasmon-Enhanced Infrared Spectroscopy,” ACS Nano 6(9), 7998–8006 (2012).
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M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotech. 7(5), 330 (2012).

2011 (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).
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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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2008 (2)

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
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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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2005 (2)

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (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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Abate, Y.

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 Photonics. 5(6), 2106–2112 (2018).
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Absil, P.

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 Gb/s operation of graphene electro‐absorption modulator on silicon,” Laser Photonics Rev. 10(2), 307–316 (2016).
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Adato, R.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
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K. Chen, R. Adato, and H. Altug, “Dual-Band Perfect Absorber for Multispectral Plasmon-Enhanced Infrared Spectroscopy,” ACS Nano 6(9), 7998–8006 (2012).
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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. Hee Hong, J. H. Ahn, J. Min 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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Alfaro-Mozaz, F. J.

F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
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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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P. Alonso-González, A. Y. Nikitin, Y. Gao, A. Woessner, M. B. Lundeberg, A. Principi, N. Forcellini, W. Yan, S. Vélez, and A. J. Huber, “Acoustic terahertz graphene plasmons revealed by photocurrent nanoscopy,” Nat. nanotech. 12(1), 31 (2017).

F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
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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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Altug, H.

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
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D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
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Figures (8)

Fig. 1
Fig. 1 (a) Schematic, (b) dispersion, and (c) electric Ez field mode profile for SiC based bulk SPhP, inset (b) show the Ez fields of the propagating SPhP mode. (d-f) The results for vdW dielectric tailored d-SPhP in multilayer MoS2 (5nm) on SiC. (g-i) The results for electric tunable graphene plasmon hybridized g-SPhP in heterostructure of graphene/h-BN (5nm) on SiC, the Fermi level (μc) of graphene is 0.3ev.
Fig. 2
Fig. 2 Simulated dispersions of d-SPhP (green curves) and g-SPhP (red curves) for (a) different MoS2 and h-BN thicknesses, and (b) different dielectric index layers (5nm). (c) The figure of merit (γ−1) for different polaritons, the thickness of MoS2 (green curve) and h-BN (red curve) is 5nm. The Fermi level (μc) of graphene is 0.3ev.
Fig. 3
Fig. 3 (a) Schematic of the in-plane superlens, the thickness of MoS2 and h-BN is 10nm. (b) The dispersions of d-SPhP and g-SPhP, particularly g-SPhP is electric tunable by controlling graphene’s Fermi level. (c, d) The distributions of in-plan |E|2 and Hy field (5nm above SiC substrate) at ω = 883 cm−1 and μc = 0.3 ev, corresponds to a momentum matched neff = 80 for both polaritons. (e) The normalized Hy field at the image plane (white dashed line in (d)). (f-h) The corresponding results at ω = 883 cm−1and μc = 0.5 ev.
Fig. 4
Fig. 4 (a) Schematic of the optical modulator with graphene-hybrid localized surface phonon resonance (LSPh-SPR), the thickness, width and period of MoS2 grating are 40nm, 150nm and 300nm, respectively. (b) Simulated reflectance spectra for graphene nano-ribbons (w/p = 150/300nm) based g-LSPR (black line), non-graphene coved d-LSPhR (green line) hybrid LSPh-SPR (red line), and graphene on SiC gratings (d/w/p = 2/1.5/3μm) hybrid Fabry Pérot cavity-graphene plasmon model (FP-SPR), respectively. (c, e, g and i) Electric filed intensity enhancements |E/E0|2 and (d, f, h and j) the real part of Ez field distributions for four different types of localized polariton resonances. The Fermi level (μc) of graphene is 0.45ev.
Fig. 5
Fig. 5 (a) The modulation of d-LSPhR with the heights of MoS2 antenna (d/p = 40/300nm), each y-tick represents the reflectance from 0 to 1. (b) The modulation of graphene hybrid LSPh-SPRs with the widths of MoS2 antenna (w/p = 150/300nm). (c) The modulation of LSPh-SPRs with different graphene Fermi levels. The Ez electric distributions of g-LSPhR-1 with (d) weak coupling (μc = 0ev, light red circles in (c)) and (e) strong coupling (μc = 0.65ev, dark red circles in (c)). (f) The reflectance differences (△R) and (g) resonant frequencies ω as a function of graphene’s Fermi-levels μc for LSPh-SPR-1 and LSPh-SPR-2.
Fig. 6
Fig. 6 The Ez electric distribution and Poynting vector of the weak coupling resonance (a, b) and strong coupling resonance (c, d) for LSPh-SPR-1; the weak coupling resonance (e, f) and strong coupling resonance (g, h) for LSPh-SPR-2, d/w/p = 40/150/300nm. The corresponding reflectance spectra are shown in Fig. 5(c).
Fig. 7
Fig. 7 (a) Real part permittivity of h-BN and SiC. h-BN’s first reststrahlen band (εx/y>0, εz<0) is from 780 to 830 cm−1, and h-BN work as a hyperbolic dielectric at frequencies ω>830 cm−1; SiC’s reststrahlen band (ε<0) is from 797 to 973 cm−1. (b) In-plane real and imaginary permittivity of MoS2.
Fig. 8
Fig. 8 The schematic of three-layer heterostructure, layer 1 (z>d, air), layer 2 (0 <z<d, MoS2 or h-BN), and layer 3 (-H<z<0, SiC substrate), where d is the thickness of layer-2 slabs. The following derivations give the dispersions of bulk SPhP, d-SPhP and g-SPhP, respectively.

Equations (9)

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β iλψ 4πd ln[ 1iψ( ε 2x / ε 1 )+iβ( Z 0 σ/ ε 1 ) 1+iψ( ε 2x / ε 1 )+iβ( Z 0 σ/ ε 1 ) 1iψ( ε 2x / ε 3 ) 1+iψ( ε 2x / ε 3 ) ],ψ= ε 2z i ε 2x
ε(ω)= ε (1+ ω LO 2 ω TO 2 ω TO 2 ω 2 iωγ )
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 | ) )
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