Abstract

A rigorous theoretical formulation based on electromagnetic plane waves is utilized to construct a unified framework and identification of all possible surface-plasmon polariton solutions at an absorptive slab in a symmetric, lossless dielectric surrounding. In addition to the modes reported in literature, sets of entirely new mode solutions are presented. The corresponding fields are classified into different categories and examined in terms of bound and leaky modes, as well as forward-and backward-propagating modes, both outside and inside the slab. The results could benefit plasmon based applications in thin-film nanophotonics.

© 2014 Optical Society of America

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    [CrossRef]

2013 (1)

2011 (3)

2010 (2)

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

M. Fukuda, T. Aihara, K. Yamaguchi, Y. Y. Ling, K. Miyaji, M. Tohyama, “Light detection enhanced by surface plasmon resonance in metal film,” Appl. Phys. Lett. 96, 153107 (2010).
[CrossRef]

2009 (4)

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

E. Verhagen, M. Spacenovic, A. Polman, L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

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

2008 (2)

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[CrossRef] [PubMed]

2007 (4)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

S. Lal, S. Link, N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature Photon. 1, 641–648 (2007).
[CrossRef]

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

A. R. Zakharian, J. V. Moloney, M. Mansuripur, “Surface plasmon polaritons on metallic surfaces,” Opt. Express 15, 183–197 (2007).
[CrossRef] [PubMed]

2006 (1)

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

2005 (2)

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[CrossRef]

2003 (1)

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

1991 (1)

F. Yang, J. R. Sambles, G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

1983 (1)

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

1957 (1)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

Aihara, T.

M. Fukuda, T. Aihara, K. Yamaguchi, Y. Y. Ling, K. Miyaji, M. Tohyama, “Light detection enhanced by surface plasmon resonance in metal film,” Appl. Phys. Lett. 96, 153107 (2010).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[CrossRef]

Aussenegg, F. R.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Bakker, R.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Barnes, W. L.

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

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Belgrave, A. M.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Berini, P.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
[CrossRef]

Bozhevolnyi, S. I.

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

Bradberry, G. W.

F. Yang, J. R. Sambles, G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Dereux, A.

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

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[CrossRef]

Ditlbacher, H.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Ebbesen, T. W.

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

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

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Friberg, A. T.

Fukuda, M.

M. Fukuda, T. Aihara, K. Yamaguchi, Y. Y. Ling, K. Miyaji, M. Tohyama, “Light detection enhanced by surface plasmon resonance in metal film,” Appl. Phys. Lett. 96, 153107 (2010).
[CrossRef]

Galler, N.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Genet, C.

C. Genet, T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[CrossRef] [PubMed]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Gramotnev, D. K.

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

Halas, N. J.

S. Lal, S. Link, N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature Photon. 1, 641–648 (2007).
[CrossRef]

Hecht, B.

L. Novotny, B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).
[CrossRef]

Herz, E.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Hohenau, A.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Kato, J.-I.

M. Ozaki, J.-I. Kato, S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).
[CrossRef] [PubMed]

Kawata, S.

M. Ozaki, J.-I. Kato, S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).
[CrossRef] [PubMed]

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).
[CrossRef]

Koller, D. M.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Krenn, J. R.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Kuipers, L. K.

E. Verhagen, M. Spacenovic, A. Polman, L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Lal, S.

S. Lal, S. Link, N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature Photon. 1, 641–648 (2007).
[CrossRef]

Leitner, A.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Ling, Y. Y.

M. Fukuda, T. Aihara, K. Yamaguchi, Y. Y. Ling, K. Miyaji, M. Tohyama, “Light detection enhanced by surface plasmon resonance in metal film,” Appl. Phys. Lett. 96, 153107 (2010).
[CrossRef]

Link, S.

S. Lal, S. Link, N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature Photon. 1, 641–648 (2007).
[CrossRef]

List, E. J. W.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[CrossRef] [PubMed]

Ma, R.-M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

MacDonald, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

Mansuripur, M.

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Miyaji, K.

M. Fukuda, T. Aihara, K. Yamaguchi, Y. Y. Ling, K. Miyaji, M. Tohyama, “Light detection enhanced by surface plasmon resonance in metal film,” Appl. Phys. Lett. 96, 153107 (2010).
[CrossRef]

Moloney, J. V.

Narimanov, E. E.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Noginov, M. A.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Norrman, A.

Novotny, L.

L. Novotny, B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).
[CrossRef]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Ozaki, M.

M. Ozaki, J.-I. Kato, S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).
[CrossRef] [PubMed]

Ozbay, E.

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

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Polman, A.

E. Verhagen, M. Spacenovic, A. Polman, L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Reil, F.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

Sambles, J. R.

F. Yang, J. R. Sambles, G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[CrossRef]

Setälä, T.

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[CrossRef] [PubMed]

Shu, G.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

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J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Spacenovic, M.

E. Verhagen, M. Spacenovic, A. Polman, L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

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J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

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Stout, S.

M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

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M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, E. V. Stryland, Handbook of Optics, 3rd ed., Vol. 4. (McGraw-Hill, 2009).

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D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

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M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

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J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[CrossRef]

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[CrossRef]

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[CrossRef]

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E. Verhagen, M. Spacenovic, A. Polman, L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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M. A. Noginov, G. Shu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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F. Yang, J. R. Sambles, G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
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A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

M. Fukuda, T. Aihara, K. Yamaguchi, Y. Y. Ling, K. Miyaji, M. Tohyama, “Light detection enhanced by surface plasmon resonance in metal film,” Appl. Phys. Lett. 96, 153107 (2010).
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D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
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[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, J. R. Krenn, “Organic plasmon-emitting diode,” Nature Photon. 2, 684–687 (2008).
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A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
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Phys. Rev. B (4)

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

F. Yang, J. R. Sambles, G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855–5872 (1991).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[CrossRef] [PubMed]

E. Verhagen, M. Spacenovic, A. Polman, L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
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M. Ozaki, J.-I. Kato, S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).
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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Illustration of the geometry and notation related to electromagnetic plane waves at a lossy film of thickness d surrounded by non-absorptive dielectrics, possessing relative permittivities εr1 (complex) and εr2 (real), respectively. The quantities k ^ 1 ( 1 ), k ^ 1 ( 2 ), k ^ 2 ( 1 ), and k ^ 2 ( 2 ), and p ^ 1 ( 1 ), p ^ 1 ( 2 ), p ^ 2 ( 1 ), and p ^ 2 ( 2 ) in the xz plane are the unit wave and polarization vectors, respectively. The interfaces are at z = ±d/2.

Fig. 2
Fig. 2

Illustration of the possible directions of phase propagation (black arrows) and field attenuation (solid-red curves) for M1 decaying to the right. In the figure, (a) and (d) correspond to M1I [Eq. (34)], (b) and (e) to M1II [Eq. (35)], and (c) and (f) to M1III [Eq. (36)], respectively. The graphs in the bottom row are mirror images of those in the top row.

Fig. 3
Fig. 3

Illustration of the possible directions of phase propagation (black arrows) and field attenuation (solid-red curves) for M2 decaying to the right. Within the slab there are two fields whose wave-vector components perpendicular to the surfaces are purely real and opposite in sign. Graph (b) is a mirror image of graph (a).

Fig. 4
Fig. 4

Behavior of the real (left column) and imaginary (right column) parts of the tangential wave-vector component k x ( M 3 ) for symmetric (upper row) and antisymmetric (lower row) FMs at a silver slab in an air surrounding, as a function of the thickness d. The solid (blue), dashed (green), dash-dotted (orange), and dotted (red) lines correspond to the relative permittivities εr1 = −3.77+i0.67 (λ0 = 400 nm), εr1 = −8.50+i0.76 (λ0 = 500 nm), εr1 = −13.91 + i0.93 (λ0 = 600 nm), and εr1 = −20.44 + i1.29 (λ0 = 700 nm) of silver [27], with λ0 = 2π/k0 and k0 being the vacuum wavelength and wave number, respectively.

Fig. 5
Fig. 5

Behavior of the real (left column) and imaginary (right column) parts of the tangential wave-vector component k x ( M 3 ) for symmetric (upper row) and antisymmetric (lower row) FMs, as a function of the thickness d at a silver slab in different surroundings: gallium phosphide (solid lines), diamond (dashed lines), fused silica (dash-dotted lines), and air (dotted lines), having the relative permittivities εr2 = 11.01 [28], εr2 = 5.82 [29], εr2 = 2.12 [29], and εr2 = 1, respectively, at the vacuum wavelength λ0 = 2π/k0 = 632.8 nm (k0 is the free-space wave number). The relative permittivity of silver is εr1 = −15.87 + i1.07 [27].

Fig. 6
Fig. 6

Illustration of the possible directions of phase propagation (black arrows) and field attenuation (solid-red curves) for FMs, (a)–(c), and HOMIs, (c), decaying to the right. In the figure, (a) corresponds to Eq. (21), (b) to Eq. (22), and (c) to Eq. (23).

Fig. 7
Fig. 7

Behavior of the real (left column) and imaginary (right column) parts of the tangential wave-vector component k x ( M 3 ) for the four symmetric HOMIs (upper row) and HOMIIs (lower row) possessing the lowest k x ( M 3 ) at a silver slab in an air surrounding, as a function of the thickness d at the vacuum wavelength λ0 = 2π/k0 = 632.8 nm (k0 is the free-space wave number). The relative permittivity of silver is εr1 = −15.87 + i1.07 [27].

Fig. 8
Fig. 8

Behavior of the real (left column) and imaginary (right column) parts of the tangential wave-vector component k x ( M 3 ) for the symmetric HOMI (upper row) and HOMII (lower row) having the lowest k x ( M 3 ) , at a silver slab in an air surrounding as a function of the thickness d. The solid (blue), dashed (green), dash-dotted (orange), and dotted (red) lines correspond to the relative permittivities εr1 = −3.77 + i0.67 (λ0 = 400 nm), εr1 = −8.50 + i0.76 (λ0 = 500 nm), εr1 = −13.91 + i0.93 (λ0 = 600 nm), and εr1 = −20.44 + i1.29 (λ0 = 700 nm) of silver [27], with λ0 = 2π/k0 and k0 being the wavelength and wave number in vacuum, respectively.

Fig. 9
Fig. 9

Behavior of the real (left column) and imaginary (right column) parts of the tangential wave-vector component k x ( M 3 ) for the symmetric HOMI (upper row) and HOMII (lower row) having the lowest k x ( M 3 ) , as a function of the thickness d at a silver slab in different surroundings: gallium phosphide (solid lines), diamond (dashed lines), fused silica (dash-dotted lines), and air (dotted lines), possessing the relative permittivities εr2 = 11.01 [28], εr2 = 5.82 [29], εr2 = 2.12 [29], and εr2 = 1, respectively, at the vacuum wavelength λ0 = 2π/k0 = 632.8 nm (k0 is the free-space wave number). The relative permittivity of silver is εr1 = −15.87 + i1.07 [27].

Fig. 10
Fig. 10

Illustration of the possible directions of phase propagation (black arrows) and field attenuation (solid-red curves) for HOMIIs decaying to the right, when the slab thickness d is smaller than (left), equal to (middle), and larger than (right) the critical thickness dc.

Tables (1)

Tables Icon

Table 1 Summary of FPMs and BPMs for mode types M1–M3 inside the slab. The grey-shaded areas represent situations in which forward or backward propagation is not defined.

Equations (51)

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E ( r ) = { E 2 ( 1 ) e i k 2 ( 1 ) r p ^ 2 ( 1 ) , z d / 2 , E 1 ( 1 ) e i k 1 ( 1 ) r p ^ 1 ( 1 ) + E 1 ( 2 ) e i k 1 ( 2 ) r p ^ 1 ( 2 ) , | z | < d / 2 , E 2 ( 2 ) e i k 2 ( 2 ) r p ^ 2 ( 2 ) , z d / 2 ,
p ^ α ( β ) = k ^ α ( β ) × e ^ y , k ^ α ( β ) = k α ( β ) / | k α ( β ) | , α , β { 1 , 2 } ,
E 1 ( M 1 ) ( r ) = E 1 ( M 1 ) e i k 1 ( M 1 ) r p ^ 1 ( M 1 ) ,
{ ε r 2 k 1 z ( M 1 ) = ε r 1 k 2 z ( 1 ) , z = d / 2 , ε r 2 k 1 z ( M 1 ) = ε r 1 k 2 z ( 2 ) , z = d / 2 ,
k x ( M 1 ) = k 0 ε r 1 ε r 2 ε r 1 + ε r 2 , k α z ( M 1 ) = k 0 ε r α ε r 1 + ε r 2 , α { 1 , 2 } ,
r ( 1 ) e 2 i k 1 z ( 1 ) d = r ( 2 ) ,
r ( β ) ε r 2 k 1 z ( 1 ) ε r 1 k 2 z ( β ) ε r 2 k 1 z ( 1 ) + ε r 1 k 2 z ( β ) , β { 1 , 2 } .
e i k 1 z ( M 2 ) d = ± 1 ,
E 1 ± ( M 2 ) ( r ) = E 1 ( M 2 ) e i k 1 ( M 2 ) r | k 1 ( M 2 ) | { k 1 z ( M 2 ) [ 1 r e 2 i k 1 z ( M 2 ) z ] e ^ x + k x ( M 2 ) [ 1 ± r e 2 i k 1 z ( M 2 ) z ] e ^ z } ,
k x ( M 2 ) = k 0 ε r 1 ( m ± π k 0 d ) 2 , k 1 z ( M 2 ) = m ± ( π d ) , k 2 z ( M 2 ) = k 0 ε r 2 ε r 1 + ( m ± π k 0 d ) 2 ,
r ( 1 ) e i k 1 z ( M 3 ) d = ± 1 ,
E 1 ± ( M 3 ) ( r ) = E 1 ( M 3 ) e i k 1 ( M 3 ) r | k 1 ( M 3 ) | { k 1 z ( M 3 ) [ 1 e 2 i k 1 z ( M 3 ) z ] e ^ x + k x ( M 3 ) [ 1 ± e 2 i k 1 z ( M 3 ) z ] e ^ z } ,
Symmetric ( + ) : ε r 1 ε r 2 k 2 z ( M 3 ) k 1 z ( M 3 ) = tanh [ 1 2 i k 1 z ( M 3 ) d ] ,
Antisymmetric ( ) : ε r 1 ε r 2 k 2 z ( M 3 ) k 1 z ( M 3 ) = coth [ 1 2 i k 1 z ( M 3 ) d ] ,
k x ( M 3 ) k 0 ε r 1 ε r 2 ε r 1 + ε r 2 , k α z ( M 3 ) k 0 ε r α ε r 1 + ε r 2 , α { 1 , 2 } .
k x ( M 3 ) k 0 ε r 1 , k 1 z ( M 3 ) 0 , k 2 z ( M 3 ) k 0 ε r 2 ε r 1 .
k x ( M 3 ) k 0 ε r 2 , k 1 z ( M 3 ) k 0 ε r 1 ε r 2 , k 2 z ( M 3 ) 0 ,
e i k α ( β ) r = e [ k x x + k α z ( β ) z ] e i [ k x x + k α z ( β ) z ] , α , β { 1 , 2 } ,
k x k x = k 2 z ( β ) k 2 z ( β ) , β { 1 , 2 } ,
k x = 0 k 2 z ( β ) = 0 , k 2 z ( β ) = 0 k x = 0 , β { 1 , 2 } ,
k x k x < 1 2 k 0 2 ε r 1 k 1 z ( β ) k 1 z ( β ) > 0 , β { 1 , 2 } ,
k x k x = 1 2 k 0 2 ε r 1 k 1 z ( β ) k 1 z ( β ) = 0 , β { 1 , 2 } ,
k x k x > 1 2 k 0 2 ε r 1 k 1 z ( β ) k 1 z ( β ) < 0 , β { 1 , 2 } .
S ( r ) 1 2 [ E ( r ) × H * ( r ) ] ,
S 2 ( β ) ( r ) = σ ε r 2 | E 2 ( β ) | 2 | k 2 | 2 e 2 k 2 ( β ) r k 2 ( β ) , β { 1 , 2 } ,
S 1 ( M 1 ) ( r ) = σ | E 1 ( M 1 ) | 2 | k 1 ( M 1 ) | 2 e 2 k 1 ( M 1 ) r { [ ε r 1 k x ( M 1 ) + ε r 1 k x ( M 1 ) ] e ^ x + [ ε r 1 k 1 z ( M 1 ) + ε r 1 k 1 z ( M 1 ) ] e ^ z } ,
S 1 ± ( M 2 ) ( r ) = σ | E 1 ( M 2 ) | 2 | k 1 ( M 2 ) | 2 e 2 k x ( M 2 ) x ( ε r 1 * { k x ( M 2 ) [ 1 + | r | 2 ± r * e 2 i k 1 z ( M 2 ) z ± r e 2 i k 1 z ( M 2 ) z ] e ^ x + k 1 z ( M 2 ) [ 1 | r | 2 ± r * e 2 i k 1 z ( M 2 ) z r e 2 i k 1 z ( M 2 ) z ] e ^ z } ) ,
S 1 ± ( M 3 ) ( r ) = 2 σ | E 1 ( M 3 ) | 2 | k 1 ( M 3 ) | 2 e 2 k x ( M 3 ) x [ ε r 1 * ( k x ( M 3 ) { cosh [ 2 k 1 z ( M 3 ) z ] ± cos [ 2 k 1 z ( M 3 ) z ] } e ^ x k 1 z ( M 3 ) { sinh [ 2 k 1 z ( M 3 ) z ] i sin [ 2 k 1 z ( M 3 ) z ] } e ^ z ) ] .
k x ( M 1 ) k x ( M 1 ) > 0 , k 2 z ( M 1 ) k 2 z ( M 1 ) < 0 ,
ε r 2 < ε r 1 k 1 z ( M 1 ) k 1 z ( M 1 ) > 0 ,
( ε r 1 + ε r 2 ) 2 > ε r 2 2 ε r 1 2 k 1 z ( M 1 ) k 1 z ( M 1 ) > 0 ,
( ε r 1 + ε r 2 ) 2 = ε r 2 2 ε r 2 k 1 z ( M 1 ) = 0 ,
( ε r 1 + ε r 2 ) 2 < ε r 2 2 ε r 1 2 k 1 z ( M 1 ) k 1 z ( M 1 ) < 0.
M1 I : = k 1 z ( M 1 ) k 1 z ( M 1 ) > 0 ,
M 1 II : = k 1 z ( M 1 ) = 0 ,
M 1 III : = k 1 z ( M 1 ) k 1 z ( M 1 ) < 0 ,
k 1 z ( M 1 ) k 2 z ( M 1 ) < 0 ,
k x ( M 2 ) k x ( M 2 ) > 0 , k 2 z ( M 2 ) k 2 z ( M 2 ) < 0.
k x ( M 3 ) k x ( M 3 ) > 0 , k 2 z ( M 3 ) < 0 ,
HOM I : = k 2 z ( M 3 ) > 0 , d ,
HOM II : = { k 2 z ( M 3 ) > 0 , d < d c , k 2 z ( M 3 ) = 0 , d = d c , k 2 z ( M 3 ) < 0 , d > d c ,
k x ( M 3 ) k x ( M 3 ) > 0 , k 2 z ( M 3 ) < 0 ,
d < d c [ k 2 z ( M 3 ) > 0 ] k x ( M 3 ) k x ( M 3 ) < 0 , k 2 z ( M 3 ) > 0 ,
d = d c [ k 2 z ( M 3 ) = 0 ] k x ( M 3 ) = 0 , k 2 z ( M 3 ) > 0 ,
d > d c [ k 2 z ( M 3 ) < 0 ] k x ( M 3 ) k x ( M 3 ) > 0 , k 2 z ( M 3 ) > 0.
ε r 1 > 1 2 ε r 2 S 1 x ( M 1 ) > 0 ,
ε r 1 = 1 2 ε r 2 S 1 x ( M 1 ) = 0 ,
ε r 1 < 1 2 ε r 2 S 1 x ( M 1 ) < 0.
k 1 z ( M 1 ) 0 S 1 z ( M 1 ) < 0 ,
sgn [ S 1 x ( M 2 ) ] = sgn [ ε r 1 k x ( M 2 ) + ε r 1 k x ( M 2 ) ] ,
sgn [ S 1 x ( M 3 ) ] = sgn [ ε r 1 k x ( M 3 ) + ε r 1 k x ( M 3 ) ] .

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