Abstract

We examine the modal characteristics of coupled metallic nanoscale rectangular apertures using a simple and accurate separation of variables method, recently proposed by us for a single aperture [Opt. Lett. 33, 333 (2008)]. The study shows that the coupling between the antisymmetric surface plasmon polariton (SPP) modes of the two rectangular apertures results in a coupled SPP mode with very large propagation length, larger than 1mm at the wavelength of 0.633μm, provided the aperture size and the separation are sufficiently large. The effective indices and the propagation lengths of various coupled SPP modes are presented.

© 2009 Optical Society of America

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  1. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface plasmon circuitry,” Phys. Today 61, 44-50 (2008).
    [CrossRef]
  2. M. L. Borngersma, R. Zia, and J. A. Schuller, “Plasmonics: the missing link between nanoelectronics and microphotonics,” Appl. Phys. A 89, 221-223 (2007).
    [CrossRef]
  3. W. L. Barnes, “Surface plasmon-polaritons length scales: a route to sub-wavelength optics,” J. Opt. A Pure Appl. Opt. 8, S87-S93 (2006).
    [CrossRef]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  5. 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]
  6. T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
    [CrossRef]
  7. 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, 820-822 (2002).
    [CrossRef] [PubMed]
  8. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
    [CrossRef]
  9. A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
    [CrossRef]
  10. M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
    [CrossRef]
  11. A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A Pure Appl. Opt. 7, S90-S96 (2005).
    [CrossRef]
  12. K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
    [CrossRef] [PubMed]
  13. 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, 4316-4318 (2004).
    [CrossRef]
  14. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
    [CrossRef] [PubMed]
  15. N. F. Van Hulst, “Sorting colours,” Nature Photon. 2, 139-140 (2008).
    [CrossRef]
  16. R. Gordan and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933-1938 (2005).
    [CrossRef]
  17. S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310-4320 (2007).
    [CrossRef] [PubMed]
  18. A. Kumar and T. Srivastava, “Modeling of a nanoscale rectangular hole in a real metal,” Opt. Lett. 33, 333-335 (2008).
    [CrossRef] [PubMed]
  19. A. Kumar and T. Srivastava, “Performance of effective index method in the modeling of a nanoscale rectangular apertures in a real metal,” Opt. Commun. 281, 4526-4529 (2008).
    [CrossRef]
  20. S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14, 9467-9476 (2006).
    [CrossRef] [PubMed]
  21. C. Themistos, B. M. A. Rahman, K. Thomas, and V. Grattan, “Finite element analysis of a lossy TE-TM modes in metal-clad optical waveguide,” Appl. Opt. 37, 5747-5754 (1998).
    [CrossRef]

2008

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface plasmon circuitry,” Phys. Today 61, 44-50 (2008).
[CrossRef]

N. F. Van Hulst, “Sorting colours,” Nature Photon. 2, 139-140 (2008).
[CrossRef]

A. Kumar and T. Srivastava, “Performance of effective index method in the modeling of a nanoscale rectangular apertures in a real metal,” Opt. Commun. 281, 4526-4529 (2008).
[CrossRef]

A. Kumar and T. Srivastava, “Modeling of a nanoscale rectangular hole in a real metal,” Opt. Lett. 33, 333-335 (2008).
[CrossRef] [PubMed]

2007

S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310-4320 (2007).
[CrossRef] [PubMed]

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

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

M. L. Borngersma, R. Zia, and J. A. Schuller, “Plasmonics: the missing link between nanoelectronics and microphotonics,” Appl. Phys. A 89, 221-223 (2007).
[CrossRef]

2006

W. L. Barnes, “Surface plasmon-polaritons length scales: a route to sub-wavelength optics,” J. Opt. A Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14, 9467-9476 (2006).
[CrossRef] [PubMed]

2005

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A Pure Appl. Opt. 7, S90-S96 (2005).
[CrossRef]

R. Gordan and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933-1938 (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]

2004

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “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, 4316-4318 (2004).
[CrossRef]

2003

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

2002

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, 820-822 (2002).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

1998

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

C. Themistos, B. M. A. Rahman, K. Thomas, and V. Grattan, “Finite element analysis of a lossy TE-TM modes in metal-clad optical waveguide,” Appl. Opt. 37, 5747-5754 (1998).
[CrossRef]

Barnes, W. L.

W. L. Barnes, “Surface plasmon-polaritons length scales: a route to sub-wavelength optics,” J. Opt. A Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

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

Borngersma, M. L.

M. L. Borngersma, R. Zia, and J. A. Schuller, “Plasmonics: the missing link between nanoelectronics and microphotonics,” Appl. Phys. A 89, 221-223 (2007).
[CrossRef]

Bozhevolnyi, S. I.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface plasmon circuitry,” Phys. Today 61, 44-50 (2008).
[CrossRef]

S. I. Bozhevolnyi, “Effective-index modeling of channel plasmon polaritons,” Opt. Express 14, 9467-9476 (2006).
[CrossRef] [PubMed]

Brolo, A. G.

Chang, H.-Y.

M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

Chuang, T.-H.

M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

Collin, S.

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 Pure Appl. Opt. 7, S90-S96 (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, 820-822 (2002).
[CrossRef] [PubMed]

Dereux, A.

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

Devaux, E.

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, 820-822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface plasmon circuitry,” Phys. Today 61, 44-50 (2008).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007).
[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 Pure Appl. Opt. 7, S90-S96 (2005).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[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, 820-822 (2002).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

Ebbessen, T. W.

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Enoch, S.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[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]

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, 820-822 (2002).
[CrossRef] [PubMed]

Genet, C.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface plasmon circuitry,” Phys. Today 61, 44-50 (2008).
[CrossRef]

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

Ghaemi, H. F.

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Gordan, R.

Grattan, V.

Koerkamp, K. J. K.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Kuipers, L.

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, 4316-4318 (2004).
[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Kumar, A.

A. Kumar and T. Srivastava, “Modeling of a nanoscale rectangular hole in a real metal,” Opt. Lett. 33, 333-335 (2008).
[CrossRef] [PubMed]

A. Kumar and T. Srivastava, “Performance of effective index method in the modeling of a nanoscale rectangular apertures in a real metal,” Opt. Commun. 281, 4526-4529 (2008).
[CrossRef]

Lee, S.-C.

M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

Lewen, G. D.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

Lezec, H. J.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[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, 820-822 (2002).
[CrossRef] [PubMed]

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[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, 820-822 (2002).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

Martin-Moreno, L.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[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, 820-822 (2002).
[CrossRef] [PubMed]

Mary, A.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Moreno, Esteban

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]

Moreno, L. Martin

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]

Nahata, A.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

Pardo, F.

Pellerin, K. M.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

Pelouard, J.-L.

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]

Rahman, B. M. A.

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Schuller, J. A.

M. L. Borngersma, R. Zia, and J. A. Schuller, “Plasmonics: the missing link between nanoelectronics and microphotonics,” Appl. Phys. A 89, 221-223 (2007).
[CrossRef]

Segerink, F. B.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “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, 4316-4318 (2004).
[CrossRef]

Srivastava, T.

A. Kumar and T. Srivastava, “Performance of effective index method in the modeling of a nanoscale rectangular apertures in a real metal,” Opt. Commun. 281, 4526-4529 (2008).
[CrossRef]

A. Kumar and T. Srivastava, “Modeling of a nanoscale rectangular hole in a real metal,” Opt. Lett. 33, 333-335 (2008).
[CrossRef] [PubMed]

Themistos, C.

Thio, T.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Thomas, K.

Tsai, M.-W.

M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

van der Molen, K. L.

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, 4316-4318 (2004).
[CrossRef]

Van Hulst, N. F.

N. F. Van Hulst, “Sorting colours,” Nature Photon. 2, 139-140 (2008).
[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, 4316-4318 (2004).
[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Zia, R.

M. L. Borngersma, R. Zia, and J. A. Schuller, “Plasmonics: the missing link between nanoelectronics and microphotonics,” Appl. Phys. A 89, 221-223 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys. A

M. L. Borngersma, R. Zia, and J. A. Schuller, “Plasmonics: the missing link between nanoelectronics and microphotonics,” Appl. Phys. A 89, 221-223 (2007).
[CrossRef]

Appl. Phys. Lett.

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, 4316-4318 (2004).
[CrossRef]

M.-W. Tsai, T.-H. Chuang, H.-Y. Chang, and S.-C. Lee, “Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice,” Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

J. Opt. A Pure Appl. Opt.

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A Pure Appl. Opt. 7, S90-S96 (2005).
[CrossRef]

W. L. Barnes, “Surface plasmon-polaritons length scales: a route to sub-wavelength optics,” J. Opt. A Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

Nanotechnology

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429-432 (2002).
[CrossRef]

Nature

T. W. Ebbessen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

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

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

Nature Photon.

N. F. Van Hulst, “Sorting colours,” Nature Photon. 2, 139-140 (2008).
[CrossRef]

Opt. Commun.

A. Kumar and T. Srivastava, “Performance of effective index method in the modeling of a nanoscale rectangular apertures in a real metal,” Opt. Commun. 281, 4526-4529 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414 (2007).
[CrossRef]

Phys. Rev. Lett.

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]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. KuipersI, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Phys. Today

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface plasmon circuitry,” Phys. Today 61, 44-50 (2008).
[CrossRef]

Science

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, 820-822 (2002).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic of (a) coupled metallic apertures, (b) pseudo coupled apertures considered by SVM, (c) dielectric constant profile ε ( x ) along the x direction, and (d)  ε ( y ) along the y direction.

Fig. 2
Fig. 2

Variation of the propagation length L and Re ( n eff ) (inset) with the normalized half-aperture length k 0 a ( b = 250 nm and d = 10 nm ) for the x-polarized modes.

Fig. 3
Fig. 3

Electric field distribution | E x | of the x-polarized SPP modes in coupled metallic apertures for d = 10 nm , a = 1 μm , and b = 250 nm . The x and y axes of the plot correspond to the coordinates along the x and y directions of the coupled apertures.

Fig. 4
Fig. 4

Variation of the propagation length L and Re ( n eff ) (inset) with the normalized half-aperture separation k 0 d ( a = 1 μm and b = 250 nm ) for the x-polarized modes.

Fig. 5
Fig. 5

Variation of the propagation length L and Re ( n eff ) (inset) with normalized half-aperture width k 0 b ( a = 1 μm and d = 10 nm ) for S A 0 x and S A 1 x modes.

Fig. 6
Fig. 6

Variation of the propagation length L and Re ( n eff ) (inset) with the normalized half-aperture length k 0 a ( b = 250 nm and d = 10 nm ) for the y-polarized modes.

Fig. 7
Fig. 7

Variation of the propagation length L and Re ( n eff ) (inset) with the normalized half-aperture width k 0 b ( a = 1 μm and d = 10 nm ) for the y-polarized modes.

Tables (1)

Tables Icon

Table 1 Complex Mode Effective Index of x- and y-Polarized Modes of the Coupled Aperture Obtained by Finite Element Method and Semi-Volatile Metal

Equations (19)

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ε ( x , y ) = ε ( x ) + ε ( y ) ε d , ε ( x ) = { ε m ε d ε m | x | < d d < | x | < ( d + 2 a ) | x | > ( d + 2 a ) }    , ε ( y ) = { ε m ε d | y | < b | y | > b } ,
ψ ( x , y ) = X ( x ) Y ( y ) ,
β j 2 = β j 2 + β j 2 k 0 2 ε d ,
S S x ( S A x ) : X ( x ) = { A 1 cosh ( γ x m | x | ) | x | < d A 2 e γ x d ( | x | d ) + B 2 e γ x d ( | x | d ) d < | x | < ( d + 2 a ) A 3 e γ x m ( | x | ( d + 2 a ) ) | x | > ( d + 2 a ) } ,
A S x ( A A x ) : X ( x ) = { A 1 sinh ( γ x m | x | ) | x | < d A 2 e γ x d ( | x | d ) + B 2 e γ x d ( | x | d ) d < | x | < ( d + 2 a ) A 3 e γ x m ( | x | ( d + 2 a ) ) | x | > ( d + 2 a ) } ,
S S x ( S A x ) : tanh ( 2 γ x d a ) = ( γ x d ε m ) / ( γ x m ε d ) ( 1 + tanh ( γ x m d ) ) ( γ x d ε m ) 2 / ( γ x m ε d ) 2 + tanh ( γ x m d ) ,
A S x ( A A x ) : tanh ( 2 γ x d a ) = ( γ x m ε d ) / ( γ x d ε m ) ( 1 + tanh ( γ x m d ) ) ( γ x m ε d ) 2 / ( γ x d ε m ) 2 + tanh ( γ x m d ) .
Symmetric   TE : Y ( y ) = { C 1 cos ( κ x d | y | ) | y | < b C 2 e γ x m ( | y | b ) | y | > b } ,
Antisymmetric   TE : Y ( y ) = { C 1 sin ( κ x d | y | ) | y | < b C 2 e γ x m ( | y | b ) | y | > b } ,
Symmetric   TE : tan ( κ x d b ) = γ x m κ x d ,
Antisymmetric   TE : tan ( κ x d b ) = κ x d γ x m .
S S y ( S A y ) : X ( x ) = { A 1 cosh ( γ y m | x | ) | x | < d A 2 e i κ y d ( | x | d ) + B 2 e i κ y d ( | x | d ) d < | x | < ( d + 2 a ) A 3 e γ y m ( | x | ( d + 2 a ) ) | x | > ( d + 2 a ) } ,
A S y ( A A y ) : X ( x ) = { A 1 sinh ( γ y m | x | ) | x | < d A 2 e i κ y d ( | x | d ) + B 2 e i κ y d ( | x | d ) d < | x | < ( d + 2 a ) A 3 e γ y m ( | x | ( d + 2 a ) ) | x | > ( d + 2 a ) } ,
S S y ( S A y ) : ( γ y m κ y d ) tanh ( γ y m d ) = tan ( 2 κ y d a ) γ y m κ y d 1 + γ y m κ y d tan ( 2 κ y d a ) ,
A S y ( A A y ) : ( κ y d γ y m ) tanh ( γ y m d ) = 1 + γ y m κ y d tan ( 2 κ y d a ) tan ( 2 κ y d a ) γ y m κ y d .
Symmetric   SPP : Y ( y ) = { C 1 cosh ( γ y d | y | ) | y | < b C 2 e γ y m ( | y | b ) | y | > b } ,
Antisymmetric   SPP : Y ( y ) = { C 1 sinh ( γ y d | y | ) | y | < b C 2 e γ y m ( | y | b ) | y | > b } ,
Symmetric   SPP : tanh ( γ y d b ) = ε d γ y m ε m γ y d ,
Antisymmetric   SPP : tanh ( γ y d b ) = ε m γ y d ε d γ y m .

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