Abstract

One of the key challenges to move single-photon sources into practical applications is the ability to efficiently extract light from a single quantum emitter while maintaining efficient photon emission. Here, we propose to harness the optical topological transitions of graphene-hBN hyperstructure to engineer the emission from quantum emitters and achieve preferential power extraction. We have designed a hyperstructure, which possesses tunability of spontaneous emission and enhancement of extraction during optical topological transitions from the closed (ellipsoid) isofrequency surface to an open (hyperboloid) isofrequency surface by tuning the chemical potential of graphene. Such an interesting feature relies exclusively on the hyperbolic properties of hBN and tunable behavior of graphene, which is confirmed by detailed calculations and simulations. Remarkably, single-photon sources based on the hyperstructure do not require overmuch microfabrication and they are capable of working at tunable frequency.

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

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2018 (2)

L. Shen, L. Prokopeva, H. Chen, and A. Kildishev, “Designing optimal nanofoucsing with a gradient hyperlens,” Nanophotonics 7(2), 479–487 (2018).

S. Shah, X. Lin, L. Shen, M. Renuka, B. Zhang, and H. Chen, “Interferenceless polarization splitting through nanoscale van der Waals heterostructures,” Phys. Rev. Appl. 10(3), 034025 (2018).
[Crossref]

2017 (5)

L. Ferrari, J. S. T. Smalley, Y. Fainman, and Z. Liu, “Hyperbolic metamaterials for dispersion-assisted directional light emission,” Nanoscale 9(26), 9034–9048 (2017).
[Crossref] [PubMed]

H. Hajian, A. Ghobadi, S. A. Dereshgi, B. Butun, and E. Ozbay, “Hybrid plasmon-phonon polariton bands in graphene-hexagonal boron nitride metamaterials,” J. Opt. Soc. Am. B 34(7), D29–D35 (2017).
[Crossref]

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]

L. Shen, H. Wang, R. Li, Z. Xu, and H. Chen, “Hyperbolic-polaritons-enabled dark-field lens for sensitive detection,” Sci. Rep. 7(1), 6995 (2017).
[Crossref] [PubMed]

O. A. Makarova, M. Y. Shalaginov, S. Bogdanov, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Patterned multilayer metamaterial for fast and efficient photon collection from dipolar emitters,” Opt. Lett. 42(19), 3968–3971 (2017).
[Crossref] [PubMed]

2016 (2)

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16(8), 4940–4945 (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 hyperCrystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

2015 (8)

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 (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]

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

T. Galfsky, H. N. S. Krishnamoorthy, W. Newman, E. E. Narimanov, Z. Jacob, and V. M. Menon, “Active hyperbolic metamaterials: enhanced spontaneous emission and light extraction,” Optica 2(1), 62–65 (2015).
[Crossref]

P. R. West, N. Kinsey, M. Ferrera, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Adiabatically tapered hyperbolic metamaterials for dispersion control of high-k waves,” Nano Lett. 15(1), 498–505 (2015).
[Crossref] [PubMed]

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6(1), 7883 (2015).
[Crossref] [PubMed]

M. Y. Shalaginov, V. V. Vorobyov, J. Liu, M. Ferrera, A. V. Akimov, A. Lagutchev, A. N. Smolyaninov, V. V. Klimov, J. Irudayaraj, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Enhancement of single-photon emission from nitrogen-vacancy centers with TiN/(Al,Sc)N hyperbolic metamaterial,” Laser Photonics Rev. 9(1), 120–127 (2015).
[Crossref]

L. Shen, X. Lin, R. Zhang, X. Liu, S. Lin, and H. Chen, “Photonic transport in a graphene van der Waals homojunction,” J. Mater. Chem. C 3(41), 10879–10885 (2015).
[Crossref]

2014 (4)

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref] [PubMed]

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

M. Leifgen, T. Schröder, F. Gädeke, R. Riemann, V. Métillon, E. Neu, C. Hepp, C. Arend, C. Becher, K. Lauritsen, and O. Benson, “Evaluation of nitrogen-and silicon-vacancy defect centres as single photon sources in quantum key distribution,” New J. Phys. 16(2), 023021 (2014).
[Crossref]

X. Liu, R. Z. Zhang, and Z. Zhang, “Near-perfect photon tunneling by hybridizing graphene plasmons and hyperbolic Modes,” ACS Photonics 1(9), 785–789 (2014).
[Crossref]

2013 (4)

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and V. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B. 87(7), 075416 (2013).
[Crossref]

J. T. Choy, I. Bulu, B. J. M. Hausmann, E. Janitz, I. C. Huang, and M. Lončar, “Spontaneous emission and collection efficiency enhancement of single emitters in diamond via plasmonic cavities and gratings,” Appl. Phys. Lett. 103(16), 161101 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013).
[Crossref] [PubMed]

2012 (3)

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B. 86(3), 035148 (2012).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109(6), 063602 (2012).
[Crossref] [PubMed]

2011 (4)

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J.-M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011).
[Crossref] [PubMed]

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107(19), 193903 (2011).
[Crossref] [PubMed]

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One- and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7(1), 69–74 (2011).
[Crossref] [PubMed]

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

2010 (4)

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10(10), 3922–3926 (2010).
[Crossref] [PubMed]

J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Grard, “A highly efficient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
[Crossref]

J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J. M. Grard, “A highly effiecient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
[Crossref]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

2008 (1)

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[Crossref] [PubMed]

2007 (3)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
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2006 (2)

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
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Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
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2004 (2)

V. V. Klimov and M. Ducloy, “Spontaneous emission rate of an exited atom placed near a nanofiber,” Phys. Rev. A 69(1), 013812 (2004).
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P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004).
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2002 (2)

M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002).
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C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002).
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M. S. Yeung and T. K. Gustafson, “Spontaneous emission near an absorbing dielectric surface,” Phys. Rev. A 54(6), 5227–5242 (1996).
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E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
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E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6(1), 7883 (2015).
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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 (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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A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (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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J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J. M. Grard, “A highly effiecient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
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M. Leifgen, T. Schröder, F. Gädeke, R. Riemann, V. Métillon, E. Neu, C. Hepp, C. Arend, C. Becher, K. Lauritsen, and O. Benson, “Evaluation of nitrogen-and silicon-vacancy defect centres as single photon sources in quantum key distribution,” New J. Phys. 16(2), 023021 (2014).
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J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One- and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7(1), 69–74 (2011).
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P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
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I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and V. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B. 87(7), 075416 (2013).
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A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B. 86(3), 035148 (2012).
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M. Leifgen, T. Schröder, F. Gädeke, R. Riemann, V. Métillon, E. Neu, C. Hepp, C. Arend, C. Becher, K. Lauritsen, and O. Benson, “Evaluation of nitrogen-and silicon-vacancy defect centres as single photon sources in quantum key distribution,” New J. Phys. 16(2), 023021 (2014).
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E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6(1), 7883 (2015).
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J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J.-M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011).
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J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Grard, “A highly efficient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
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J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J. M. Grard, “A highly effiecient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
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M. Y. Shalaginov, V. V. Vorobyov, J. Liu, M. Ferrera, A. V. Akimov, A. Lagutchev, A. N. Smolyaninov, V. V. Klimov, J. Irudayaraj, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Enhancement of single-photon emission from nitrogen-vacancy centers with TiN/(Al,Sc)N hyperbolic metamaterial,” Laser Photonics Rev. 9(1), 120–127 (2015).
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P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
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E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6(1), 7883 (2015).
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W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
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W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
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L. Shen, L. Prokopeva, H. Chen, and A. Kildishev, “Designing optimal nanofoucsing with a gradient hyperlens,” Nanophotonics 7(2), 479–487 (2018).

S. Shah, X. Lin, L. Shen, M. Renuka, B. Zhang, and H. Chen, “Interferenceless polarization splitting through nanoscale van der Waals heterostructures,” Phys. Rev. Appl. 10(3), 034025 (2018).
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L. Shen, H. Wang, R. Li, Z. Xu, and H. Chen, “Hyperbolic-polaritons-enabled dark-field lens for sensitive detection,” Sci. Rep. 7(1), 6995 (2017).
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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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L. Shen, X. Lin, R. Zhang, X. Liu, S. Lin, and H. Chen, “Photonic transport in a graphene van der Waals homojunction,” J. Mater. Chem. C 3(41), 10879–10885 (2015).
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Chen, W. Y.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
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Chou, C. T.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16(8), 4940–4945 (2016).
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Choy, J. T.

J. T. Choy, I. Bulu, B. J. M. Hausmann, E. Janitz, I. C. Huang, and M. Lončar, “Spontaneous emission and collection efficiency enhancement of single emitters in diamond via plasmonic cavities and gratings,” Appl. Phys. Lett. 103(16), 161101 (2013).
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Chyi, J. I.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006).
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Claudon, J.

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J.-M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011).
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J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Grard, “A highly efficient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
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J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J. M. Grard, “A highly effiecient single-photon source based on quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010).
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Considine, C. R.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16(8), 4940–4945 (2016).
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J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J.-M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106(10), 103601 (2011).
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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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Dowling, J. P.

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Ducloy, M.

V. V. Klimov and M. Ducloy, “Spontaneous emission rate of an exited atom placed near a nanofiber,” Phys. Rev. A 69(1), 013812 (2004).
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Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
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D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10(10), 3922–3926 (2010).
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L. Ferrari, J. S. T. Smalley, Y. Fainman, and Z. Liu, “Hyperbolic metamaterials for dispersion-assisted directional light emission,” Nanoscale 9(26), 9034–9048 (2017).
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L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
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Fang, N. X.

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

C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002).
[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).
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L. Ferrari, J. S. T. Smalley, Y. Fainman, and Z. Liu, “Hyperbolic metamaterials for dispersion-assisted directional light emission,” Nanoscale 9(26), 9034–9048 (2017).
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P. R. West, N. Kinsey, M. Ferrera, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Adiabatically tapered hyperbolic metamaterials for dispersion control of high-k waves,” Nano Lett. 15(1), 498–505 (2015).
[Crossref] [PubMed]

M. Y. Shalaginov, V. V. Vorobyov, J. Liu, M. Ferrera, A. V. Akimov, A. Lagutchev, A. N. Smolyaninov, V. V. Klimov, J. Irudayaraj, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Enhancement of single-photon emission from nitrogen-vacancy centers with TiN/(Al,Sc)N hyperbolic metamaterial,” Laser Photonics Rev. 9(1), 120–127 (2015).
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P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
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J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “One- and two-dimensional photonic crystal microcavities in single crystal diamond,” Nat. Nanotechnol. 7(1), 69–74 (2011).
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[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).
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D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
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A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Gädeke, F.

M. Leifgen, T. Schröder, F. Gädeke, R. Riemann, V. Métillon, E. Neu, C. Hepp, C. Arend, C. Becher, K. Lauritsen, and O. Benson, “Evaluation of nitrogen-and silicon-vacancy defect centres as single photon sources in quantum key distribution,” New J. Phys. 16(2), 023021 (2014).
[Crossref]

Galfsky, T.

T. Galfsky, Z. Sun, C. R. Considine, C. T. Chou, W. C. Ko, Y. H. Lee, E. E. Narimanov, and V. M. Menon, “Broadband enhancement of spontaneous emission in two-dimensional semiconductors using photonic hypercrystals,” Nano Lett. 16(8), 4940–4945 (2016).
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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. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
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García-Vidal, F. J.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6(1), 7883 (2015).
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Geiselmann, M.

E. Bermúdez-Ureña, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. García-Vidal, S. I. Bozhevolnyi, and R. Quidant, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6(1), 7883 (2015).
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Figures (9)

Fig. 1
Fig. 1 (a) Schematic configuration of a graphene-hBN hyperstructure; (b) Real and (c) imaginary parts of the effective permittivity of graphene-hBN hyperstructure at two different graphene chemical potentials ( μ c =0eV and μ c =0.3eV) when the temperature is set to 300 K. Colored regions indicate different optical topological transitions from the closed (ellipsoid, ϵ t >0, ϵ z >0) isofrequency surface to an open (hyperboloid, ϵ t <0, ϵ z >0)isofrequency surface.
Fig. 2
Fig. 2 Theoretical estimations of the Purcell factor for an emitter located at 10 nm above the graphene-hBN hyperstructure surface. The Purcell factors at different chemical potentials of graphene ( μ c =0eV to μ c =0.3eV) are shown here. Three different topological transitions (a), (b) and (c) are considered which correspond to region I, region II and region III respectively, as shown in Fig. 1.
Fig. 3
Fig. 3 Theoretical estimations of (a-c) side and (d-f) top extractions for an emitter located at 10 nm away from the side and top interfaces of the graphene-hBN hyperstructure surface, respectively. The extractions at different chemical potentials of graphene ( μ c =0eV to μ c =0.3eV) are shown here. Three different topological transitions (a,d), (b,e) and (c,f) are considered which correspond to region I, region II, and region IV, respectively, as shown in Fig. 1. The extraction power through the interface of hyperstructure is calculated as an integral through a circular area which mimics the emission collection using a commercially available objective lens with numerical aperture (NA) 1.49 (cross-section angle 79.6°).
Fig. 4
Fig. 4 Spatial power distributions (magnitude of the Poynting vector) of a dipole located at 10 nm above the hyperstructure in the air at  λ=6μm. a, b, c and d represent the power distributions of the dipole along x-direction (x-dipole) and z-direction (z-dipole), respectively, at two different graphene chemical potentials ( μ c ). When μ c changes from 0 to 0.3 eV, the topological transition from an ellipsoid ( ϵ t >0, ϵ z >0) to a hyperboloid ( ϵ t <0, ϵ z >0) happens respectively.
Fig. 5
Fig. 5 Theoretical estimations of the (a-c) Purcell factor and (d-f) top extractions for an emitter located at 10 nm away from the top interfaces of the graphene-hBN hyperstructure surface, respectively. Different chemical potentials of graphene (from μ c =0eV to μ c =0.3eV) are shown here. Three different topological transitions (a,d), (b,e) and (c,f) are considered which correspond to region I, region II, and region III as shown in Fig. 1 respectively.
Fig. 6
Fig. 6 Theoretical estimations of the Purcell factor versus different distances between the dipole and the hyperstructure h. The chemical potential of graphene here is μ c =0eV.
Fig. 7
Fig. 7 (a) Real and imaginary parts of the permittivity of hBN. (b) Real and imaginary parts of conductivity of graphene as a function of chemical potential. Colored regions indicate the two mid-infrared Reststrahlen bands.
Fig. 8
Fig. 8 Theoretical estimations of the (a-c) Purcell factor and (d-f) top extractions for an emitter located at 10 nm away from the top interfaces of the graphene-hBN heterostructure, respectively. Different chemical potentials of graphene (from μ c =0eV to μ c =0.3eV) are shown here.
Fig. 9
Fig. 9 Theoretical estimations of the (a-c) Purcell factor and (d-f) top extractions for an emitter located at 10 nm away from the top interfaces of the graphene-hBN-graphene heterostructure, respectively. Different chemical potentials of graphene (from μ c =0eV to μ c =0.3eV) are shown here.

Equations (12)

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ϵ t,eff = f gra ϵ t,gra +( 1 f gra ) ϵ t,hBN
ϵ z,eff 1 = f gra ϵ z,gra + ( 1 f gra ) ϵ z,hBN .
ϵ hBN = ϵ l ( )+ s v,l ω v,l 2 ω v,l 2 v,l ω ω 2 ,l=x,y,z
σ D = i ω+i/τ 2 e 2 k B T π 2 ln[ 2cosh( μ c 2 k B T ) ]
σ I = e 2 4 [ H( ω/2,T )+ 4 π 0 H( ζ,T )H( ω/2,T ) ω 2 4 ζ 2 ],
F P =1+ 3 4 1 ε sup 1/2 0 Re{ s s ,sup ( s ) [ r ˜ s ( s ) s ,sup 2 ( s ) ε sup r ˜ p ( s ) ] e 2i k 0 s ,sup ( s )h }ds
F P =1+ 3 2 1 ε sup 3/2 0 Re{ s 3 s ,sup ( s ) r ˜ p ( s ) e 2i k 0 s ,sup ( s )h   }ds
F P ave = 2 3 F P + 1 3 F P ,
f rad || = 3 8 0 θ max cos 2 θ | e i ε sup 1/2 k 0 hcosθ r ˜ p ( θ ) e i ε sup 1/2 k 0 hcosθ   | 2 +   | e i ε sup 1/2 k 0 hcosθ + r ˜ p ( θ ) e i ε sup 1/2 k 0 hcosθ   | 2 sinθdθ
f rad = 3 4 0 θ max sin 3 θ | e i ε sup 1/2 k 0 hcosθ + r ̃ p ( θ ) e i ε sup 1/2 k 0 hcosθ   | 2 dθ,
f rad ave = 2 3 f rad || + 1 3 f rad .
R ˜ l,l+1 t = R l,l+1 t T l,l+1 t R ˜ l+1,l+2 t T l+1,l t e 2i k l+1,z t d l+1 1 R l+1,l t R ˜ l+1,l+2 t e 2i k l+1,z t d l+1 ,

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