Abstract

We demonstrate the spectral accumulation of large spontaneous emission (SE) for nanocavities with different sizes in the coupled Ag nanorod and epsilon-near-zero (ENZ) film system. This effect originates from the slowing down of the spectral shift of resonant nanocavities at the wavelength where the permittivity of the substrate vanishes, i.e., the resonance “pinning” near the ENZ frequency. In addition, most far field radiation of the emitter is concentrated in the forward field with small solid angle due to the impedance mismatch between the ENZ film and the free space. This kind of size-relaxed nanocavity for directional SE has potential applications in the bright single photon sources, plasmon-based nanolasers, and on-chip nanodevices.

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

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References

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    [Crossref]
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    [Crossref] [PubMed]
  3. B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
    [Crossref]
  4. A. R. Davoyan, A. M. Mahmoud, and N. Engheta, “Optical isolation with epsilon-near-zero metamaterials,” Opt. Express 21, 3279–3286 (2013).
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    [Crossref]
  7. J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
    [Crossref]
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  9. K.-H. Kim, Y.-S. No, S. Chang, J.-H. Choi, and H.-G. Park, “Invisible hyperbolic metamaterial nanotube at visible frequency,” Sci. Reports 5, 16027 (2015).
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  11. C. Díaz-Aviñò, M. Naserpour, and C. J. Zapata-Rodríguez, “Tunable scattering cancellation of light using anisotropic cylindrical cavities,” Plasmonics 12, 675–683 (2017).
    [Crossref]
  12. J. Kim, A. Dutta, G. V. Naik, A. J. Giles, F. J. Bezares, C. T. Ellis, J. G. Tischler, A. M. Mahmoud, H. Caglayan, O. J. Glembocki, A. V. Kildishev, J. D. Caldwell, A. Boltasseva, and N. Engheta, “Role of epsilon-near-zero substrates in the optical response of plasmonic antennas,” Optica 3, 339–346 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  21. S. A. Biehs and G. S. Agarwal, “Qubit entanglement across epsilon-near-zero media,” Phys. Rev. A 96, 022308 (2017).
    [Crossref]
  22. K. Kelly, E. Coronado, L. Zhao, and G. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  28. R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104, 026802 (2010).
    [Crossref] [PubMed]
  29. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J. P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J. J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013).
    [Crossref] [PubMed]
  30. P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
    [Crossref] [PubMed]
  31. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [Crossref] [PubMed]
  32. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
    [Crossref] [PubMed]
  33. M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
    [Crossref]
  34. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  35. R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
    [Crossref]
  36. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
    [Crossref] [PubMed]
  37. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
    [Crossref] [PubMed]
  38. A. Huck, S. Kumar, A. Shakoor, and U. L. Anderson, “Controlled coupling of a single Nitrogen-Vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
    [Crossref] [PubMed]
  39. M. H. Javani and M. I. Stockman, “Real and imaginary properties of epsilon-near-zero materials,” Phys. Rev. Lett. 117, 107404 (2016).
    [Crossref] [PubMed]
  40. W. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [Crossref] [PubMed]
  41. D. Singh, A. Dasgupta, V. G. Aswathy, R. P. N. Tripathi, and G. V. P. Kumar, “Directional out-coupling of light from a plasmonic nanowire-nanoparticle junction,” Opt. Lett. 40, 1006–1009 (2015).
    [Crossref] [PubMed]
  42. J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
    [Crossref] [PubMed]
  43. R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
    [Crossref] [PubMed]

2018 (4)

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-near-zero photonics: a new platform for integrated devices,” Adv. Opt. Mater. 6, 1701292 (2018).
[Crossref]

M. R. Forouzeshfard, M. Mohebbi, and A. Mollaei, “Scattering cross section in a cylindrical anisotropic layered metamaterial,” Opt. Commun. 407, 193–198 (2018).
[Crossref]

C. T. Devault, V. A. Zenin, A. Pors, K. Chaudhuri, J. Kim, A. Boltasseva, V. M. Shalaev, and S. I. Bozhevolnyi, “Suppression of near-field coupling in plasmonic antennas on epsilon-near-zero substrates,” Optica 5, 1557–1563 (2018).
[Crossref]

X. Duan, J. Ren, F. Zhang, H. Hao, G. Lu, Q. Gong, and Y. Gu, “Large Purcell enhancement with efficient one-dimensional collection via coupled nanowire-nanorod system,” Nanotechnology 29, 045203 (2018).
[Crossref]

2017 (4)

H. Hao, J. Ren, H. Chen, I. C. Khoo, Y. Gu, and Q. Gong, “Tunable enhanced spontaneous emission in plasmonic waveguide cladded with liquid crystal and low-index metamaterial,” Opt. Express 25, 3433–3444 (2017).
[Crossref] [PubMed]

S. A. Biehs and G. S. Agarwal, “Qubit entanglement across epsilon-near-zero media,” Phys. Rev. A 96, 022308 (2017).
[Crossref]

C. Díaz-Aviñò, M. Naserpour, and C. J. Zapata-Rodríguez, “Tunable scattering cancellation of light using anisotropic cylindrical cavities,” Plasmonics 12, 675–683 (2017).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

2016 (7)

J. Kim, A. Dutta, G. V. Naik, A. J. Giles, F. J. Bezares, C. T. Ellis, J. G. Tischler, A. M. Mahmoud, H. Caglayan, O. J. Glembocki, A. V. Kildishev, J. D. Caldwell, A. Boltasseva, and N. Engheta, “Role of epsilon-near-zero substrates in the optical response of plasmonic antennas,” Optica 3, 339–346 (2016).
[Crossref]

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

S. Campione, J. R. Wendt, G. A. Keeler, and T. S. Luk, “Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers,” ACS Photonics 3, 293–297 (2016).
[Crossref]

I. Liberal and N. Engheta, “Nonradiating and radiating modes excited by quantum emitters in open epsilon-near-zero cavities,” Sci. Adv. 2, e1600987 (2016).
[Crossref] [PubMed]

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

M. H. Javani and M. I. Stockman, “Real and imaginary properties of epsilon-near-zero materials,” Phys. Rev. Lett. 117, 107404 (2016).
[Crossref] [PubMed]

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref] [PubMed]

2015 (4)

D. Singh, A. Dasgupta, V. G. Aswathy, R. P. N. Tripathi, and G. V. P. Kumar, “Directional out-coupling of light from a plasmonic nanowire-nanoparticle junction,” Opt. Lett. 40, 1006–1009 (2015).
[Crossref] [PubMed]

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114, 193002 (2015).
[Crossref] [PubMed]

M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
[Crossref]

K.-H. Kim, Y.-S. No, S. Chang, J.-H. Choi, and H.-G. Park, “Invisible hyperbolic metamaterial nanotube at visible frequency,” Sci. Reports 5, 16027 (2015).
[Crossref]

2014 (1)

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
[Crossref]

2013 (5)

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
[Crossref]

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J. P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J. J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013).
[Crossref] [PubMed]

A. R. Davoyan, A. M. Mahmoud, and N. Engheta, “Optical isolation with epsilon-near-zero metamaterials,” Opt. Express 21, 3279–3286 (2013).
[Crossref] [PubMed]

R. Sokhoyan and H. A. Atwater, “Quantum optical properties of a dipole emitter coupled to an epsilon-near-zero nanoscale waveguide,” Opt. Express 21, 32279–32290 (2013).
[Crossref]

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87, 201101(R) (2013).
[Crossref]

2012 (1)

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

2011 (2)

F. Javier González and J. Alda, “Spectral response and far-field pattern of a dipole nano-antenna on metamaterial substrates having near-zero and negative indices of refraction,” Opt. Commun. 284, 1429–1434 (2011).
[Crossref]

A. Huck, S. Kumar, A. Shakoor, and U. L. Anderson, “Controlled coupling of a single Nitrogen-Vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
[Crossref] [PubMed]

2010 (1)

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[Crossref] [PubMed]

2009 (2)

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett. 103, 043902 (2009).
[Crossref] [PubMed]

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

2008 (1)

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[Crossref] [PubMed]

2007 (2)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

2006 (3)

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref] [PubMed]

2003 (2)

K. Kelly, E. Coronado, L. Zhao, and G. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[Crossref]

W. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

2002 (1)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

2000 (1)

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[Crossref] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Agarwal, G. S.

S. A. Biehs and G. S. Agarwal, “Qubit entanglement across epsilon-near-zero media,” Phys. Rev. A 96, 022308 (2017).
[Crossref]

Akimov, A. V.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Akselrod, G. M.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
[Crossref]

Alam, M. Z.

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Alda, J.

F. Javier González and J. Alda, “Spectral response and far-field pattern of a dipole nano-antenna on metamaterial substrates having near-zero and negative indices of refraction,” Opt. Commun. 284, 1429–1434 (2011).
[Crossref]

Alù, A.

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87, 201101(R) (2013).
[Crossref]

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett. 103, 043902 (2009).
[Crossref] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Anderson, U. L.

A. Huck, S. Kumar, A. Shakoor, and U. L. Anderson, “Controlled coupling of a single Nitrogen-Vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
[Crossref] [PubMed]

Argyropoulos, C.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
[Crossref]

Aswathy, V. G.

Atwater, H. A.

Barnes, W.

W. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Barrow, S. J.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref] [PubMed]

Baumberg, J. J.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref] [PubMed]

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[Crossref] [PubMed]

Belacel, C.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J. P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J. J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013).
[Crossref] [PubMed]

Benz, F.

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G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
[Crossref]

Mizrahi, A.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Mock, J. J.

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[Crossref] [PubMed]

Mohebbi, M.

M. R. Forouzeshfard, M. Mohebbi, and A. Mollaei, “Scattering cross section in a cylindrical anisotropic layered metamaterial,” Opt. Commun. 407, 193–198 (2018).
[Crossref]

Mollaei, A.

M. R. Forouzeshfard, M. Mohebbi, and A. Mollaei, “Scattering cross section in a cylindrical anisotropic layered metamaterial,” Opt. Commun. 407, 193–198 (2018).
[Crossref]

Mukherjee, A.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Naik, G. V.

Naserpour, M.

C. Díaz-Aviñò, M. Naserpour, and C. J. Zapata-Rodríguez, “Tunable scattering cancellation of light using anisotropic cylindrical cavities,” Plasmonics 12, 675–683 (2017).
[Crossref]

Niu, X.

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-near-zero photonics: a new platform for integrated devices,” Adv. Opt. Mater. 6, 1701292 (2018).
[Crossref]

No, Y.-S.

K.-H. Kim, Y.-S. No, S. Chang, J.-H. Choi, and H.-G. Park, “Invisible hyperbolic metamaterial nanotube at visible frequency,” Sci. Reports 5, 16027 (2015).
[Crossref]

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

Park, H.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Park, H.-G.

K.-H. Kim, Y.-S. No, S. Chang, J.-H. Choi, and H.-G. Park, “Invisible hyperbolic metamaterial nanotube at visible frequency,” Sci. Reports 5, 16027 (2015).
[Crossref]

Parsons, J.

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
[Crossref]

Pelton, M.

M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
[Crossref]

Petroff, P.

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[Crossref] [PubMed]

Polman, A.

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
[Crossref]

Pors, A.

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Ren, J.

X. Duan, J. Ren, F. Zhang, H. Hao, G. Lu, Q. Gong, and Y. Gu, “Large Purcell enhancement with efficient one-dimensional collection via coupled nanowire-nanorod system,” Nanotechnology 29, 045203 (2018).
[Crossref]

H. Hao, J. Ren, H. Chen, I. C. Khoo, Y. Gu, and Q. Gong, “Tunable enhanced spontaneous emission in plasmonic waveguide cladded with liquid crystal and low-index metamaterial,” Opt. Express 25, 3433–3444 (2017).
[Crossref] [PubMed]

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114, 193002 (2015).
[Crossref] [PubMed]

Rogobete, L.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

Rosta, E.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref] [PubMed]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Sandoghdar, V.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

Schatz, G.

K. Kelly, E. Coronado, L. Zhao, and G. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[Crossref]

Scherman, O. A.

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref] [PubMed]

Schoenfeld, W.

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[Crossref] [PubMed]

Schulz, S. A.

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Schwob, C.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J. P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J. J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013).
[Crossref] [PubMed]

Senellart, P.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J. P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J. J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013).
[Crossref] [PubMed]

Shakoor, A.

A. Huck, S. Kumar, A. Shakoor, and U. L. Anderson, “Controlled coupling of a single Nitrogen-Vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
[Crossref] [PubMed]

Shalaev, V. M.

Silveirinha, M.

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref] [PubMed]

Silveirinha, M. G.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Simic, A.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Singh, D.

Slutsky, B.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Smith, D. R.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
[Crossref]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[Crossref] [PubMed]

Sokhoyan, R.

Song, G.

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

Stockman, M. I.

M. H. Javani and M. I. Stockman, “Real and imaginary properties of epsilon-near-zero materials,” Phys. Rev. Lett. 117, 107404 (2016).
[Crossref] [PubMed]

Tahir, A. A.

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

Teperik, T. V.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[Crossref] [PubMed]

Tischler, J. G.

Tripathi, R. P. N.

Upham, J.

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

Wang, L.

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114, 193002 (2015).
[Crossref] [PubMed]

Wendt, J. R.

S. Campione, J. R. Wendt, G. A. Keeler, and T. S. Luk, “Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers,” ACS Photonics 3, 293–297 (2016).
[Crossref]

Xu, J.

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

Yang, Y.

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

Yu, C. L.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Zapata-Rodríguez, C. J.

C. Díaz-Aviñò, M. Naserpour, and C. J. Zapata-Rodríguez, “Tunable scattering cancellation of light using anisotropic cylindrical cavities,” Plasmonics 12, 675–683 (2017).
[Crossref]

Zauscher, S.

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[Crossref] [PubMed]

Zenin, V. A.

Zhang, F.

X. Duan, J. Ren, F. Zhang, H. Hao, G. Lu, Q. Gong, and Y. Gu, “Large Purcell enhancement with efficient one-dimensional collection via coupled nanowire-nanorod system,” Nanotechnology 29, 045203 (2018).
[Crossref]

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114, 193002 (2015).
[Crossref] [PubMed]

Zhang, L.

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[Crossref] [PubMed]

Zhang, Z.

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

Zhao, L.

K. Kelly, E. Coronado, L. Zhao, and G. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[Crossref]

Zhu, S.

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

Zibrov, A. S.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Zubairy, M. S.

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

ACS Photonics (1)

S. Campione, J. R. Wendt, G. A. Keeler, and T. S. Luk, “Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers,” ACS Photonics 3, 293–297 (2016).
[Crossref]

Adv. Opt. Mater. (1)

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-near-zero photonics: a new platform for integrated devices,” Adv. Opt. Mater. 6, 1701292 (2018).
[Crossref]

J. Appl. Phys. (1)

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

J. Phys. Chem. B (1)

K. Kelly, E. Coronado, L. Zhao, and G. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[Crossref]

Nano Lett. (2)

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J. P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J. J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516–1521 (2013).
[Crossref] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245–2252 (2008).
[Crossref] [PubMed]

Nanotechnology (1)

X. Duan, J. Ren, F. Zhang, H. Hao, G. Lu, Q. Gong, and Y. Gu, “Large Purcell enhancement with efficient one-dimensional collection via coupled nanowire-nanorod system,” Nanotechnology 29, 045203 (2018).
[Crossref]

Nat. Photonics (4)

M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
[Crossref]

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
[Crossref]

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

Nature (4)

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

W. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref] [PubMed]

Opt. Commun. (2)

M. R. Forouzeshfard, M. Mohebbi, and A. Mollaei, “Scattering cross section in a cylindrical anisotropic layered metamaterial,” Opt. Commun. 407, 193–198 (2018).
[Crossref]

F. Javier González and J. Alda, “Spectral response and far-field pattern of a dipole nano-antenna on metamaterial substrates having near-zero and negative indices of refraction,” Opt. Commun. 284, 1429–1434 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optica (2)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (2)

S. A. Biehs and G. S. Agarwal, “Qubit entanglement across epsilon-near-zero media,” Phys. Rev. A 96, 022308 (2017).
[Crossref]

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Phys. Rev. B (4)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

J. Xu, G. Song, Z. Zhang, Y. Yang, H. Chen, M. S. Zubairy, and S. Zhu, “Unidirectional single-photon generation via matched zero-index metamaterials,” Phys. Rev. B 94, 220103(R) (2016).
[Crossref]

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87, 201101(R) (2013).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (8)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[Crossref] [PubMed]

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

A. Huck, S. Kumar, A. Shakoor, and U. L. Anderson, “Controlled coupling of a single Nitrogen-Vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
[Crossref] [PubMed]

M. H. Javani and M. I. Stockman, “Real and imaginary properties of epsilon-near-zero materials,” Phys. Rev. Lett. 117, 107404 (2016).
[Crossref] [PubMed]

H. Lian, Y. Gu, J. Ren, F. Zhang, L. Wang, and Q. Gong, “Efficient single photon emission and collection based on excitation of gap surface plasmons,” Phys. Rev. Lett. 114, 193002 (2015).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett. 103, 043902 (2009).
[Crossref] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref] [PubMed]

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104, 026802 (2010).
[Crossref] [PubMed]

Plasmonics (1)

C. Díaz-Aviñò, M. Naserpour, and C. J. Zapata-Rodríguez, “Tunable scattering cancellation of light using anisotropic cylindrical cavities,” Plasmonics 12, 675–683 (2017).
[Crossref]

Sci. Adv. (1)

I. Liberal and N. Engheta, “Nonradiating and radiating modes excited by quantum emitters in open epsilon-near-zero cavities,” Sci. Adv. 2, e1600987 (2016).
[Crossref] [PubMed]

Sci. Reports (1)

K.-H. Kim, Y.-S. No, S. Chang, J.-H. Choi, and H.-G. Park, “Invisible hyperbolic metamaterial nanotube at visible frequency,” Sci. Reports 5, 16027 (2015).
[Crossref]

Science (2)

P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[Crossref] [PubMed]

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of the coupled Ag nanorod and ENZ film system. The Ag nanorod is placed on the ENZ film with thickness of 100 nm. The length of the Ag nanorod is labled as a and the diameter is D. A quantum emitter (the red point) polarized along z axis is embedded at the left side of the Ag nanorod with distance of 5 nm. The surrounded medium is air with permittivity of 1. (b) Real and imaginary permittivity of the ENZ film. The complex permittivity can be described as the function =(−7/500 * λ + 46/5) + 0.1 * i and the real part is zero at 657 nm. (c) Normalized decay rates of the emitter in the coupled system for a = 85 nm and D = 16 nm. The Ag nanorod is resonant with the emitter when λ = 657 nm, where γtotal/γ0 = 3445, γnr/γ0 = 2932, γr/γ0 = 506, and γfr/γ0 = 408, respectively.
Fig. 2
Fig. 2 The SE enhancement of the emitter near Ag nanorods with different lengths placed (a) on the ENZ film and (b) in the vacuum. The diameter D is 16 nm in both figures. Compared with in vacuum, the spectral shift of the Ag nanorods on the film slows down and the “pinning” effect of large SE enhancement forms at the ENZ wavelength. The SE enhancement of the emitter near Ag nanorods with different diameters placed (c) on the ENZ film and (d) in the vacuum. The length is 85 nm in both figures. Compared with in vacuum, the spectral shift of the Ag nanorods on the film also slows down but just weak “pinning” effect of large SE enhancement forms at the ENZ wavelength.
Fig. 3
Fig. 3 The SE enhancement changing with (a) the length a and (b) the diameter D of the Ag nanorod for emitters with different frequencies. Due to the “pinning” effect of SE enhancement, the curve is the widest when the frequency of the emitter is at the ENZ point of the film. Besides, 1/e of the maximum SE enhancement can be maintained even if a is changed in the range of 16 nm or D is changed within the scope of 4 nm. The diameter D is 16 nm in (a).
Fig. 4
Fig. 4 (a) Normalized radiative decay rate γr/γ0 and normalized forward radiative decay rate γfr/γ0 for emitter with different frequencies. The diameter D of the nanorod is 16 nm. The ratio of γfr and γr is the largest with the value of 80.3% when the emitter works under ENZ wavelength. (b) The far field radiation patterns of emitters with λ = 550 nm (black curve), λ = 600 nm (blue curve) and λ = 657 nm (red curve). It is seen that the far field radiation is concentrated in the front field with small solid angle when at the ENZ wavelength of λ = 657 nm.
Fig. 5
Fig. 5 (a) Normalized total decay rate γtotal/γ0, (b) normalized radiative decay rate γr/γ0, and normalized forward radiative decay rate γfr/γ0 for emitters with different working wavelength when the imaginary part of permittivity of the ENZ film is 0.05. With smaller imaginary value, the SE enhancement and radiative part are both increased. More than 1/e of the maximum SE enhancement can be maintained within the length scope of 12 nm at the ENZ frequency and about 81.5% of the far field radiation is reflected forward.

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