Abstract

We study the optical properties of subwavelength metallic waveguides made of nanoscale apertures in a metal. We develop analytical expressions for the fundamental optical modes in apertures. The results are in excellent agreement with finite element calculations. This model provides a physical understanding of the role of non-perfect metallic walls, and of the shape and size of the apertures. They reveal the effect of the skin depth and of the surface plasmon polariton coupling on the waveguide modes. The nanoscopic origin of the increase of the cut-off wavelength due to the electromagnetic penetration depth in the metal is described. Simple expressions and universal curves for the effective index and the cut-off wavelength of the fundamental guided mode of any rectangular metallic waveguide are presented. The results provide an efficient tool for the design of nanoscale waveguides with real metal.

© 2007 Optical Society of America

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2006 (10)

F. J. Garcia-Vidal, L. Martin-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74,153411 (2006).
[CrossRef]

N. M. Arslanov, “The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture,” J. Opt. A 8,338 (2006).
[CrossRef]

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

P. Lalanne and J.-P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Mater. 2,509 (2006).

K. J. Webb and J. Li “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73,033401 (2006).
[CrossRef]

Jirun Luo and Chongqing Jiao “Effect of the lossy layer thickness of metal cylindrical waveguide wall on the propagation constant of electromagnetic modes,” Appl. Phys. Lett. 88,061115 (2006).
[CrossRef]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74,205419 (2006).
[CrossRef]

K. J. Webb and J. Li “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73,033401 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,508 (2006)
[CrossRef] [PubMed]

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14,9467 (2006).
[CrossRef] [PubMed]

2005 (10)

Reuven Gordon and Alexandre G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13,1933 (2005).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005).
[CrossRef] [PubMed]

Hocheol Shin, Peter B. Catrysse, and Shanhui Fan “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72,085436 (2005).
[CrossRef]

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamate-rials,” J. Opt. A 7,S97 (2005).
[CrossRef]

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A 7,S90 (2005).
[CrossRef]

F. J. Garcia-Vidal, Esteban Moreno, J. A. Porto, and L. Martin-Moreno “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95,103901 (2005).
[CrossRef] [PubMed]

Evgeny Popov, Michel Nevière, Philippe Boyer, and Nicolas Bonod, “Light transmission through a subwave-length hole,” Opt. Commun. 255,338 (2005).
[CrossRef]

P. Lalanne, J.-C. Rodier, and J.-P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A 7,422 (2005).
[CrossRef]

2004 (6)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305,847 (2004).
[CrossRef] [PubMed]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92,183901 (2004).
[CrossRef] [PubMed]

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85,4316 (2004).
[CrossRef]

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, “Optical transmission properties of a single subwave-length aperture in a real metal,” Opt. Commun. 239,61 (2004).
[CrossRef]

L. Martin-Moreno and F. J. Garcia-Vidal, “Optical transmission through circular hole arrays in optically thick metal films”, Opt. Express 12,3619 (2004).
[CrossRef]

2003 (2)

William L. Barnes, Alain Dereux, and Thomas W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 824,424 (2003).

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

2002 (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

Francisco Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10,,1475 (2002).

2001 (2)

Tineke Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972 (2001).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

1999 (2)

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen “Beyond the Bethe Limit : Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mat. 11,860 (1999).
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits”, Phys. Rev. Lett. 83,2845 (1999).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 667,391 (1998).

1994 (1)

L. Novotny and C. Hafner “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50,4094 (1994).
[CrossRef]

Abajo, Francisco Garcia de

Arslanov, N. M.

N. M. Arslanov, “The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture,” J. Opt. A 8,338 (2006).
[CrossRef]

Baida, F. I.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74,205419 (2006).
[CrossRef]

Baida, F.I.

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

Barnes, William L.

William L. Barnes, Alain Dereux, and Thomas W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 824,424 (2003).

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74,205419 (2006).
[CrossRef]

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

Bonod, Nicolas

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Evgeny Popov, Michel Nevière, Philippe Boyer, and Nicolas Bonod, “Light transmission through a subwave-length hole,” Opt. Commun. 255,338 (2005).
[CrossRef]

Boyer, Philippe

Evgeny Popov, Michel Nevière, Philippe Boyer, and Nicolas Bonod, “Light transmission through a subwave-length hole,” Opt. Commun. 255,338 (2005).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14,9467 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,508 (2006)
[CrossRef] [PubMed]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005).
[CrossRef] [PubMed]

Brolo, Alexandre G.

Capoulade, Jérémie

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Catrysse, Peter B.

Hocheol Shin, Peter B. Catrysse, and Shanhui Fan “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72,085436 (2005).
[CrossRef]

Craighead, H. G.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

Degiron, A.

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A 7,S90 (2005).
[CrossRef]

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, “Optical transmission properties of a single subwave-length aperture in a real metal,” Opt. Commun. 239,61 (2004).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

Dereux, Alain

William L. Barnes, Alain Dereux, and Thomas W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 824,424 (2003).

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,508 (2006)
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

Dintinger, José

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,508 (2006)
[CrossRef] [PubMed]

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A 7,S90 (2005).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

Tineke Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972 (2001).
[CrossRef]

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen “Beyond the Bethe Limit : Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mat. 11,860 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 667,391 (1998).

Ebbesen, T.W.

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, “Optical transmission properties of a single subwave-length aperture in a real metal,” Opt. Commun. 239,61 (2004).
[CrossRef]

Ebbesen, Thomas W.

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

William L. Barnes, Alain Dereux, and Thomas W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 824,424 (2003).

Enoch, S.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92,183901 (2004).
[CrossRef] [PubMed]

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005).
[CrossRef] [PubMed]

Fan, Shanhui

Hocheol Shin, Peter B. Catrysse, and Shanhui Fan “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72,085436 (2005).
[CrossRef]

Foquet, M.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74,153411 (2006).
[CrossRef]

F. J. Garcia-Vidal, Esteban Moreno, J. A. Porto, and L. Martin-Moreno “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95,103901 (2005).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamate-rials,” J. Opt. A 7,S97 (2005).
[CrossRef]

L. Martin-Moreno and F. J. Garcia-Vidal, “Optical transmission through circular hole arrays in optically thick metal films”, Opt. Express 12,3619 (2004).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305,847 (2004).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits”, Phys. Rev. Lett. 83,2845 (1999).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 667,391 (1998).

Gordon, R.

F. J. Garcia-Vidal, L. Martin-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74,153411 (2006).
[CrossRef]

Gordon, Reuven

Granet, G.

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

Grupp, D. E.

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen “Beyond the Bethe Limit : Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mat. 11,860 (1999).
[CrossRef]

Hafner, C.

L. Novotny and C. Hafner “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50,4094 (1994).
[CrossRef]

Harmsen, R. H.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

Hugonin, J.-P.

P. Lalanne and J.-P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Mater. 2,509 (2006).

P. Lalanne, J.-C. Rodier, and J.-P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A 7,422 (2005).
[CrossRef]

Hulst, N. F. van

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85,4316 (2004).
[CrossRef]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92,183901 (2004).
[CrossRef] [PubMed]

Hvam, J. M.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, Third Ed., sec. 8.6, (John Wiley & Sons, New York, 1998).

Jiao, Chongqing

Jirun Luo and Chongqing Jiao “Effect of the lossy layer thickness of metal cylindrical waveguide wall on the propagation constant of electromagnetic modes,” Appl. Phys. Lett. 88,061115 (2006).
[CrossRef]

Koerkamp, K. J. Klein

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92,183901 (2004).
[CrossRef] [PubMed]

Korlach, J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

Kuipers, L.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92,183901 (2004).
[CrossRef] [PubMed]

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85,4316 (2004).
[CrossRef]

Kumar, L. K. S.

F. J. Garcia-Vidal, L. Martin-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74,153411 (2006).
[CrossRef]

Labeke, D. Van

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74,205419 (2006).
[CrossRef]

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

Lalanne, P.

P. Lalanne and J.-P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Mater. 2,509 (2006).

P. Lalanne, J.-C. Rodier, and J.-P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A 7,422 (2005).
[CrossRef]

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,508 (2006)
[CrossRef] [PubMed]

Lamrous, O.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74,205419 (2006).
[CrossRef]

Lenne, Pierre-Franois

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Leosson, K.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005).
[CrossRef] [PubMed]

Levene, M. J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

Tineke Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972 (2001).
[CrossRef]

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen “Beyond the Bethe Limit : Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mat. 11,860 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 667,391 (1998).

Lezec, H.J.

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, “Optical transmission properties of a single subwave-length aperture in a real metal,” Opt. Commun. 239,61 (2004).
[CrossRef]

Li, J.

K. J. Webb and J. Li “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73,033401 (2006).
[CrossRef]

K. J. Webb and J. Li “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73,033401 (2006).
[CrossRef]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

Tineke Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972 (2001).
[CrossRef]

Luo, Jirun

Jirun Luo and Chongqing Jiao “Effect of the lossy layer thickness of metal cylindrical waveguide wall on the propagation constant of electromagnetic modes,” Appl. Phys. Lett. 88,061115 (2006).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74,153411 (2006).
[CrossRef]

F. J. Garcia-Vidal, Esteban Moreno, J. A. Porto, and L. Martin-Moreno “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95,103901 (2005).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamate-rials,” J. Opt. A 7,S97 (2005).
[CrossRef]

L. Martin-Moreno and F. J. Garcia-Vidal, “Optical transmission through circular hole arrays in optically thick metal films”, Opt. Express 12,3619 (2004).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305,847 (2004).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297,820 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

Molen, K. L. van der

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85,4316 (2004).
[CrossRef]

Moreau, A.

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

Moreno, Esteban

F. J. Garcia-Vidal, L. Martin-Moreno, Esteban Moreno, L. K. S. Kumar, and R. Gordon “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74,153411 (2006).
[CrossRef]

F. J. Garcia-Vidal, Esteban Moreno, J. A. Porto, and L. Martin-Moreno “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95,103901 (2005).
[CrossRef] [PubMed]

Nevière, Michel

Evgeny Popov, Michel Nevière, Philippe Boyer, and Nicolas Bonod, “Light transmission through a subwave-length hole,” Opt. Commun. 255,338 (2005).
[CrossRef]

Nieuwstadt, J. A. H. van

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

Novotny, L.

L. Novotny and C. Hafner “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50,4094 (1994).
[CrossRef]

Palik, E. D.

E. D. Palik “Handbook of Optical Constants of Solids,” New York: Academic, 1985.

Pellerin, K. M.

Tineke Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26,1972 (2001).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamate-rials,” J. Opt. A 7,S97 (2005).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305,847 (2004).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits”, Phys. Rev. Lett. 83,2845 (1999).
[CrossRef]

Popov, Evgeni

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Popov, Evgeny

Evgeny Popov, Michel Nevière, Philippe Boyer, and Nicolas Bonod, “Light transmission through a subwave-length hole,” Opt. Commun. 255,338 (2005).
[CrossRef]

Porto, J. A.

F. J. Garcia-Vidal, Esteban Moreno, J. A. Porto, and L. Martin-Moreno “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95,103901 (2005).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits”, Phys. Rev. Lett. 83,2845 (1999).
[CrossRef]

Prangsma, J. C.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

Rigneault, Hervé

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Rodier, J.-C.

P. Lalanne, J.-C. Rodier, and J.-P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A 7,422 (2005).
[CrossRef]

Sandtke, M.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

Segerink, F. B.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97,146102 (2006).
[CrossRef] [PubMed]

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72,045421 (2005).
[CrossRef]

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85,4316 (2004).
[CrossRef]

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92,183901 (2004).
[CrossRef] [PubMed]

Shin, Hocheol

Hocheol Shin, Peter B. Catrysse, and Shanhui Fan “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72,085436 (2005).
[CrossRef]

Skovgaard, P. M. W.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam “Channel Plasmon-Polariton Guiding by Subwavelength Metal Grooves,” Phys. Rev. Lett. 95,046802 (2005).
[CrossRef] [PubMed]

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86,1114 (2001).
[CrossRef] [PubMed]

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen “Beyond the Bethe Limit : Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mat. 11,860 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 667,391 (1998).

Thio, Tineke

Turner, S. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440,508 (2006)
[CrossRef] [PubMed]

Webb, K. J.

K. J. Webb and J. Li “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73,033401 (2006).
[CrossRef]

K. J. Webb and J. Li “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73,033401 (2006).
[CrossRef]

Webb, W. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-Mode Waveguides for Single-Molecule Analysis at High Concentrations,” Science 299,682 (2003).
[CrossRef] [PubMed]

Wenger, Jérôme

Hervé Rigneault, Jérémie Capoulade, José Dintinger, Jérôme Wenger, Nicolas Bonod, Evgeni Popov, Thomas W. Ebbesen, and Pierre-Franois Lenne “Enhancement of Single-Molecule Fluorescence Detection in Subwavelength Apertures,” Phys. Rev. Lett. 95,117401 (2005).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 667,391 (1998).

Yamamoto, N.

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, “Optical transmission properties of a single subwave-length aperture in a real metal,” Opt. Commun. 239,61 (2004).
[CrossRef]

Adv. Mat. (1)

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen “Beyond the Bethe Limit : Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mat. 11,860 (1999).
[CrossRef]

Appl. Phys. B (1)

F.I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79,1 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

Jirun Luo and Chongqing Jiao “Effect of the lossy layer thickness of metal cylindrical waveguide wall on the propagation constant of electromagnetic modes,” Appl. Phys. Lett. 88,061115 (2006).
[CrossRef]

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85,4316 (2004).
[CrossRef]

J. Opt. A (4)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamate-rials,” J. Opt. A 7,S97 (2005).
[CrossRef]

N. M. Arslanov, “The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture,” J. Opt. A 8,338 (2006).
[CrossRef]

P. Lalanne, J.-C. Rodier, and J.-P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A 7,422 (2005).
[CrossRef]

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A 7,S90 (2005).
[CrossRef]

Nat. Mater. (1)

P. Lalanne and J.-P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Mater. 2,509 (2006).

Nature (1)

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Nature (London) (2)

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Phys. Rev. B (6)

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of 1D planar metallic waveguide (a) and 2D rectangular metallic waveguide (d). The fundamental TM mode of planar 1D waveguides is composed of two surface plasmons waves (red). They are weakly coupled in wide waveguides (wλ, (b)) and strongly coupled in narrow waveguides (wλ, (c))

Fig. 2.
Fig. 2.

Effective index of the fundamental TM mode of a planar metallic waveguide (εd = 1) as a function of the width w for εm = -50.

Fig. 3.
Fig. 3.

Skin depth of the metal δ = λ ( 2 π ε m ( λ ) ) (dark) as a function of the wavelength. The skin depth is nearly constant and equal to δ = c/ωp (red) between 0.5 and 20 μm.

Fig. 4.
Fig. 4.

Real (left) and imaginary (right) parts of the effective index of the fundamental TM mode of a planar metallic waveguide as a function of the wavelength λ. Dark solid line: effective index of a single metal/dielectric surface plasmon polariton. The metal permittivity is given by a Drude model: ε m = 1 ω p 2 ω 2 + iωγ , ω p = 1.2 × 10 16 s 1 , γ = 1.2 × 10 14 s 1 . The waveguide width is w = 100 nm.

Fig. 5.
Fig. 5.

Real (left) and imaginary (right) parts of the effective index of the fundamental TE10 mode of a rectangular metallic waveguide as a function of the wavelength λ. The widths of the waveguide is wx = 300 nm and wy = 200 nm. The results of the perfect metal (dark), finite element calculation (blue) and coupled SPP approximation (Eq. (7) and (8)) (red) are compared.

Fig. 6.
Fig. 6.

Cut-off wavelength of the fundamental guided mode TE10 as a function of wy , for a silver rectangular waveguide with wx = 270 nm. The approximated model from Eq. (11) (solid curve) is compared to reference [31] (red points), and to the perfect metal case (horizontal dashed line).

Fig. 7.
Fig. 7.

Universal curves for the real part of the effective index of the fundamental guided mode TE10 for three different wavelengths (λ/δ = 100, 200 and 500). Dimensions of the rectangular waveguide (wx ,wy ) are normalized to the metal skin depth δ.

Fig. 8.
Fig. 8.

Universal curves for the cut-off wavelength of the fundamental guided mode TE10 of rectangular metallic waveguides. Dimensions and wavelengths are normalized to the metal skin depth δ.

Equations (11)

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k xd ε d [ 1 e ik xd w 1 + e ik xd w ] + k xm ε m = 0
k xm ε m = k xd ε d ( ik xd w 2 ) .
k xd 2 [ 1 + k xd 2 ( ε m ε d ) 2 w 2 4 ] = ( ε d ε m ) k 0 2
n 1 D = κ k 0 = ε d ( 1 + λ πw ε m 1 + ε d ε m ) 1 2
n w = ε d ( 1 + 2 δ c w )
tan ( k xd w x 2 ) = i k xm k xd
n 2 D = κ k 0 = ε d ( λ 2 w x ) 2
w x = w x ( 1 + λ πw x ( ε d ε m ) + ( λ 2 w x ) 2 )
w x = w x + 2 δ
n 2 D = ε d ( 1 + 2 δ w y ) ( λ 2 ( w x + 2 δ ) ) 2
λ c = 2 ( w x + 2 δ ) ε d ( 1 + 2 δ w y )

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