Abstract

We study plasmonic waveguides with dielectric cores and hyperbolic multilayer claddings. The proposed design provides better performance in terms of propagation length and mode confinement in comparison to conventional designs, such as metal-insulator-metal and insulator-metal-insulator plasmonic waveguides. We show that the proposed structures support long-range surface plasmon modes, which exist when the permittivity of the core matches the transverse effective permittivity component of the metamaterial cladding. In this regime, the surface plasmon polaritons of each cladding layer are strongly coupled, and the propagation length can be on the order of a millimeter.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]

2015 (4)

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4(1), 165–185 (2015).
[Crossref]

E. E. Narimanov and A. V. Kildishev, “Naturally hyperbolic,” Nat. Photonics 9(4), 214–216 (2015).
[Crossref]

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]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (4)

V. E. Babicheva, R. Malureanu, and A. V. Lavrinenko, “Plasmonic finite-thickness metal-semiconductor-metal waveguide as ultra-compact modulator,” Photon. Nanostructures 11(4), 323–334 (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]

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

S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013).
[Crossref] [PubMed]

2012 (4)

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(08), 728–738 (2012).
[Crossref]

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]

Y. He, S. He, and X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907–2909 (2012).
[Crossref] [PubMed]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

2011 (2)

M. Yan, L. Thylén, and M. Qiu, “Layered metal-dielectric waveguide: subwavelength guidance, leveraged modulation sensitivity in mode index, and reversed mode ordering,” Opt. Express 19(4), 3818–3824 (2011).
[Crossref] [PubMed]

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

2010 (2)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

2009 (1)

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1, 484–588 (2009).

2008 (2)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

J. Chen, G. A. Smolyakov, S. R. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express 16(19), 14902–14909 (2008).
[Crossref] [PubMed]

2007 (2)

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]

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[Crossref]

2006 (1)

2000 (1)

D. A. B. Miller, “Rationale and Challenges for Optical Interconnects to Electronic Chips,” Proc. IEEE 88(6), 728–749 (2000).
[Crossref]

1992 (1)

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

1984 (1)

Akimov, A. V.

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]

Alekseyev, L. V.

Al-Jumaily, G. A.

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

Avrutsky, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[Crossref]

Babicheva, V. E.

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4(1), 165–185 (2015).
[Crossref]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
[Crossref] [PubMed]

V. E. Babicheva, R. Malureanu, and A. V. Lavrinenko, “Plasmonic finite-thickness metal-semiconductor-metal waveguide as ultra-compact modulator,” Photon. Nanostructures 11(4), 323–334 (2013).
[Crossref]

Baca, A. J.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Belov, P.

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

Berini, P.

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1, 484–588 (2009).

Bogart, G. R.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Boltasseva, A.

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]

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4(1), 165–185 (2015).
[Crossref]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Braun, P.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Brueck, S. R.

Cain, T.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Carlson, A.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Chanda, D.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Chen, J.

Cortes, C. L.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Dodge, M. J.

Drachev, V. P.

Elser, J.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[Crossref]

Ferrera, M.

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]

Gagliardi, F. J.

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Gupta, S.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

He, S.

He, Y.

Iorsh, I.

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

Irudayaraj, J.

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]

Ishii, S.

Jacob, Z.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

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]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

Kidwai, O.

Kildishev, A. V.

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (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]

E. E. Narimanov and A. V. Kildishev, “Naturally hyperbolic,” Nat. Photonics 9(4), 214–216 (2015).
[Crossref]

S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
[Crossref] [PubMed]

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]

Kivshar, Y.

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

Klimov, V. V.

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]

Kretzschmar, I.

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]

Krishnamoorthy, H. N. S.

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]

Lagutchev, A.

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]

Lavrinenko, A. V.

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4(1), 165–185 (2015).
[Crossref]

V. E. Babicheva, R. Malureanu, and A. V. Lavrinenko, “Plasmonic finite-thickness metal-semiconductor-metal waveguide as ultra-compact modulator,” Photon. Nanostructures 11(4), 323–334 (2013).
[Crossref]

Lee, H.

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]

Liu, J.

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]

Liu, Z.

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]

Ma, R.-M.

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(08), 728–738 (2012).
[Crossref]

Malloy, K. J.

Malureanu, R.

V. E. Babicheva, R. Malureanu, and A. V. Lavrinenko, “Plasmonic finite-thickness metal-semiconductor-metal waveguide as ultra-compact modulator,” Photon. Nanostructures 11(4), 323–334 (2013).
[Crossref]

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Menon, V. M.

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]

Mihi, A.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Miller, D. A. B.

D. A. B. Miller, “Rationale and Challenges for Optical Interconnects to Electronic Chips,” Proc. IEEE 88(6), 728–749 (2000).
[Crossref]

Molesky, S.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Narimanov, E.

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]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, “Naturally hyperbolic,” Nat. Photonics 9(4), 214–216 (2015).
[Crossref]

Newman, W.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Oulton, R. F.

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(08), 728–738 (2012).
[Crossref]

Poddubny, A.

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

Podolskiy, V.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[Crossref]

Podolskiy, V. A.

Qiu, M.

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Rogers, J. A.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Salakhutdinov, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[Crossref]

Shalaev, V. M.

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]

Shalaginov, M. Y.

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]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
[Crossref] [PubMed]

Shigeta, K.

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Sipe, J. E.

Smolyakov, G. A.

Smolyaninov, A. N.

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]

Snyder, P. G.

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

Sorger, V. J.

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(08), 728–738 (2012).
[Crossref]

Sun, C.

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]

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Thylén, L.

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Vorobyov, V. V.

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]

Woollam, J. A.

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

Xiong, Y.

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]

Xiong, Y.-M.

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

Yan, M.

Yang, X.

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Zhang, X.

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(08), 728–738 (2012).
[Crossref]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

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]

Zhukovsky, S. V.

Adv. Opt. Photonics (1)

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1, 484–588 (2009).

Appl. Opt. (1)

J. Opt. (1)

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

J. Vac. Sci. Technol. A (1)

P. G. Snyder, Y.-M. Xiong, J. A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10(4), 1462 (1992).
[Crossref]

Laser Photonics Rev. (1)

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]

MRS Bull. (1)

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(08), 728–738 (2012).
[Crossref]

Nanophotonics (1)

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4(1), 165–185 (2015).
[Crossref]

Nat. Nanotechnol. (1)

D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, and J. A. Rogers, “Large-area flexible 3D optical negative index metamaterial formed by nanotransfer printing,” Nat. Nanotechnol. 6(7), 402–407 (2011).
[Crossref] [PubMed]

Nat. Photonics (4)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

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

E. E. Narimanov and A. V. Kildishev, “Naturally hyperbolic,” Nat. Photonics 9(4), 214–216 (2015).
[Crossref]

Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Photon. Nanostructures (1)

V. E. Babicheva, R. Malureanu, and A. V. Lavrinenko, “Plasmonic finite-thickness metal-semiconductor-metal waveguide as ultra-compact modulator,” Photon. Nanostructures 11(4), 323–334 (2013).
[Crossref]

Phys. Rev. B (1)

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[Crossref]

Proc. IEEE (1)

D. A. B. Miller, “Rationale and Challenges for Optical Interconnects to Electronic Chips,” Proc. IEEE 88(6), 728–749 (2000).
[Crossref]

Science (2)

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]

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]

Other (2)

X. Ni, Z. Liu, and A. V. Kildishev, nanoHUB: Photonics DB (Optical Constants, 2010).

E. I. Lyashko and A. I. Maimistov, “Linear guided waves in hyperbolic slab waveguide. Dispersion relations,” arXiv preprint arXiv:1507.07253 (2015).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic view of the HIH waveguide: the dielectric core is cladded by the metal-dielectric multilayer structure. (b) Structure under investigation (transverse cross-section): the multilayer structure consists of Ag and MgF2 layers; core permittivity εc is varied. (c) Effective waveguide structure that corresponds to the HIH waveguide with the multilayer structure being replaced by an effective infinite medium with hyperbolic dispersion.

Fig. 2
Fig. 2

Schematic view of (a) HMM-dielectric and (b) metal-dielectric single interfaces. (c) Propagation length L and penetration depth δ of SPPs for the HMM-dielectric and metal-dielectric single interfaces with varied dielectric permittivity. For the calculations of metal-dielectric case, the metal is the same as for the HMM (Ag). (d) Schematic view of the HMM-dielectric interface and resonant coupling of bulk plasmon-polaritons (“Bulk PP”) inside HMM cladding to LR-SPP at the boundary.

Fig. 3
Fig. 3

(a) Propagation length L in the HIH waveguides in the case of semi-infinite EMT-approximated and 1-µm-thick multilayer cladding with different layer thicknesses. Core thickness d is 50 or 300 nm, and layer thicknesses dm = 2 nm, dd = 8 nm (“2/8 nm”) or dm = 8 nm, dd = 32 nm (“8/32 nm”). Increase in propagation length L is observed for ε c Re[ ε yy ]. Circle marks on the curves designate core permittivity chosen for further analysis (see Fig. 5). (b) Penetration depth δ y,HMM of plasmonic mode into waveguide cladding vs. permittivity of the core εc. Waveguide parameters are the same as for (a).

Fig. 4
Fig. 4

Mode profiles for the core thickness d = 300 nm and layer thicknesses dm = 8 nm and dd = 32 nm. (a) The mode profiles (Ey field) at ε c =2 (purple curve) and ε c =1.7 (black curve) demonstrate the mode expansion when ε c approaches Re[ ε yy ]=2.35 (long-range regime). Antisymmetric mode profile of the Ez field is shown by the blue curve. (b) Change of the mode profile for the case of small D. (c) Symmetric-symmetric (Ss) and symmetric-antisymmetric (Sa) modes can exist in the HIH waveguide with the claddings of smaller thickness D.

Fig. 5
Fig. 5

The dependence of propagation length L on cladding thickness D for the HIH waveguide with parameters specified in the legend. For each line, the core permittivity εc is fixed and corresponds to circle marks shown in Fig. 3(a). Solid lines correspond to the maximums of the propagation length Lmax.

Fig. 6
Fig. 6

Range of dielectric permittivities εc, where SPP mode propagating along HMM-dielectric interface can be considered as localized. Red and blue curves correspond to the HMM and dielectric semi-infinite media, respectively.

Fig. 7
Fig. 7

(a) Mode effective index and (b) propagation length L vs. dielectric core thickness d for different values of core permittivity εc.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

k z 2 ε yy + k y,HMM 2 ε zz = k 0 2 ,
k z 2 + k y,diel 2 = ε c k 0 2 ,
k z = k 0 ( ε c ( ε zz ε c ) ε zz ε c 2 / ε yy ) 1/2 .
k y,HMM 2 <0 and k y,diel 2 <0.
Im[ k y ]Re[ k y ].
k z = ( 1 2 ( [ p 2 + q 2 ] 1/2 +p ) ) 1/2 ,
k z = ( 1 2 ( [ p 2 + q 2 ] 1/2 p ) ) 1/2 ,
p= ε c k 0 2 a( ε zz ε c )+ ε zz a 2 + b 2 ,
q= ε c k 0 2 a ε zz b( ε zz ε c ) a 2 + b 2 ,
a= ε zz ε c 2 / ε yy ,b= ε zz + ε yy ε c 2 / ( ε yy ) 2 .
tanh( γ c ε c d 2 )= γ HMM γ c ,
γ HMM = ( ε yy ε zz ) 1/2 ( k z 2 ε yy k 0 2 ) 1/2 and γ c = ε c 1 ( k z 2 ε c k 0 2 ) 1/2 .
k z k 0 = { ε c + 1 2 [ k z (0) k 0 ] 2 + ( [ k z (0) k 0 ] 2 ( ε c ε yy + 1 4 [ k z (0) k 0 ] 2 ) ) 1/2 } 1/2 ,
k z (0) k 0 = 2 ε c ( ε zz ε yy ) 1/2 1 k 0 d

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