Abstract

We present a rigorous closed-form solution of the Sommerfeld integral for the optical scattering of a metal sub-wavelength slit. The two-dimensional (2D) field solution consists of the Surface Plasmon Polariton (SPP) mode at the metal surface and the 2D scattered field, which is the cylindrical harmonic of first order emitted by the electrical dipole and convolved with the 1D transient SPP along the interface. The creeping wave or quasi-cylindrical wave detected in the previous experiment is not an extra evanescent surface wave, but is the asymptotic behavior of the 2D scattered field at the proximity of the slit. Furthermore, our solution predicts a strong resonant enhancement of the scattered field at the proximity of the slit, depending on the materials and wavelength.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  23. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
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2009 (2)

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[CrossRef]

A. Y. Nikitin, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martín-Moreno, “In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region,” New J. Phys. 11(12), 123020 (2009).
[CrossRef]

2008 (3)

2007 (3)

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behaviour of surface plasmon polaritons scattered at a sub-wavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

B. Ung and Y. Sheng, “Interference of surface waves in a metallic nanoslit,” Opt. Express 15(3), 1182–1190 (2007).
[CrossRef] [PubMed]

2006 (3)

L. Chen, J. T. Robinson, and M. Lipson, “Role of radiation and surface plasmon polaritons in the optical interactions between a nano-slit and a nano-groove on a metal surface,” Opt. Express 14(26), 12629–12636 (2006).
[CrossRef] [PubMed]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

2005 (2)

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

2004 (3)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

R. E. Collin, “Hertzian dipole radiating over a lossy earth or sea: Some early and late 20th-century controversies,” IEEE Antennas Propagat. Mag. 46(2), 64–79 (2004).
[CrossRef]

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004).
[CrossRef] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2002 (1)

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403–057407 (2002).
[CrossRef] [PubMed]

2001 (1)

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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 391(6668), 667–669 (1998).
[CrossRef]

1995 (1)

1936 (1)

K. A. Norton, “The propagation of radio waves over the surface of the earth and in the upper atmosphere,” Proc. IRE 24(10), 1367–1387 (1936).
[CrossRef]

1909 (1)

A. N. Sommerfeld, “Propagation of waves in wireless telegraphy,” Ann. Phys. (Leipzig) 28, 665–737 (1909).

1907 (1)

J. Zenneck, “Propagation of plane EM waves along a plane conducting surface,” Ann. Phys. (Leipzig) 23, 846–866 (1907).

Alkemade, P. F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Alloschery, O.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Brown, D. E.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Cao, Q.

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403–057407 (2002).
[CrossRef] [PubMed]

Chen, L.

Collin, R. E.

R. E. Collin, “Hertzian dipole radiating over a lossy earth or sea: Some early and late 20th-century controversies,” IEEE Antennas Propagat. Mag. 46(2), 64–79 (2004).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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 391(6668), 667–669 (1998).
[CrossRef]

Eliel, E. R.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

A. Y. Nikitin, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martín-Moreno, “In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region,” New J. Phys. 11(12), 123020 (2009).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Gay, G.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

Gbur, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

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 391(6668), 667–669 (1998).
[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 391(6668), 667–669 (1998).
[CrossRef]

Gracia-Vidal, F. J.

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

Gravel, Y.

Hiller, J. M.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Hooft, G. W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Hua, J.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[CrossRef]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
[CrossRef]

Kimball, C. W.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Kowarz, M. W.

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Lalanne, P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[CrossRef]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
[CrossRef]

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403–057407 (2002).
[CrossRef] [PubMed]

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Lévêque, G.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behaviour of surface plasmon polaritons scattered at a sub-wavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

Lezec, H. J.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004).
[CrossRef] [PubMed]

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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 391(6668), 667–669 (1998).
[CrossRef]

Lipson, M.

Liu, H.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

Liu, H. T.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[CrossRef]

Martin, O. J. F.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behaviour of surface plasmon polaritons scattered at a sub-wavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

Martín-Moreno, L.

A. Y. Nikitin, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martín-Moreno, “In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region,” New J. Phys. 11(12), 123020 (2009).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Matrin-Moreno, L.

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

Nikitin, A. Y.

A. Y. Nikitin, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martín-Moreno, “In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region,” New J. Phys. 11(12), 123020 (2009).
[CrossRef]

Norton, K. A.

K. A. Norton, “The propagation of radio waves over the surface of the earth and in the upper atmosphere,” Proc. IRE 24(10), 1367–1387 (1936).
[CrossRef]

O’Dwyer, C.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

O'Dwyer, C.

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

Pearson, J.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

Robinson, J. T.

Rodrigo, S. G.

A. Y. Nikitin, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martín-Moreno, “In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region,” New J. Phys. 11(12), 123020 (2009).
[CrossRef]

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Seideman, T.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

Sheng, Y.

Sommerfeld, A. N.

A. N. Sommerfeld, “Propagation of waves in wireless telegraphy,” Ann. Phys. (Leipzig) 28, 665–737 (1909).

Sukharev, M.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

Thio, T.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004).
[CrossRef] [PubMed]

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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 391(6668), 667–669 (1998).
[CrossRef]

Ung, B.

Viaris De Lesegno, B.

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

Visser, T. D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

Vlasko-Vlasov, V. K.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[CrossRef]

Weiner, J.

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behaviour of surface plasmon polaritons scattered at a sub-wavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

Welp, U.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (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 391(6668), 667–669 (1998).
[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 391(6668), 667–669 (1998).
[CrossRef]

Yin, L.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Zenneck, J.

J. Zenneck, “Propagation of plane EM waves along a plane conducting surface,” Ann. Phys. (Leipzig) 23, 846–866 (1907).

Ann. Phys. (Leipzig) (2)

A. N. Sommerfeld, “Propagation of waves in wireless telegraphy,” Ann. Phys. (Leipzig) 28, 665–737 (1909).

J. Zenneck, “Propagation of plane EM waves along a plane conducting surface,” Ann. Phys. (Leipzig) 23, 846–866 (1907).

Appl. Opt. (1)

IEEE Antennas Propagat. Mag. (1)

R. E. Collin, “Hertzian dipole radiating over a lossy earth or sea: Some early and late 20th-century controversies,” IEEE Antennas Propagat. Mag. 46(2), 64–79 (2004).
[CrossRef]

Nano Lett. (1)

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005).
[CrossRef] [PubMed]

Nat. Phys. (2)

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris De Lesegno, C. O'Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006).
[CrossRef]

Nature (4)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

New J. Phys. (1)

A. Y. Nikitin, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martín-Moreno, “In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region,” New J. Phys. 11(12), 123020 (2009).
[CrossRef]

Opt. Express (5)

Phys. Rev. B (1)

G. Lévêque, O. J. F. Martin, and J. Weiner, “Transient behaviour of surface plasmon polaritons scattered at a sub-wavelength groove,” Phys. Rev. B 76(15), 155418 (2007).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, “Surface quality and surface waves on subwavelength-structured silver films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016612 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403–057407 (2002).
[CrossRef] [PubMed]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94(5), 053901 (2005).
[CrossRef] [PubMed]

L. Matrin-Moreno, F. J. Gracia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through sub-wavelength hole arrays,” Phys. Rev. Lett. 86, 1112–1117 (2001).

Proc. IRE (1)

K. A. Norton, “The propagation of radio waves over the surface of the earth and in the upper atmosphere,” Proc. IRE 24(10), 1367–1387 (1936).
[CrossRef]

Science (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Surf. Sci. Rep. (1)

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[CrossRef]

Other (4)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007).

I. S. Gradshteyn and I. m. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic, 2007).

R. W. P. King, M. Owens, and T. T. Wu, Lateral Electromagnetic Waves: Theory and Applications to Communications, Geophysical Exploration and Remote Sensing (Springer-Verlag, New York, 1992).

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).

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Figures (6)

Fig. 1
Fig. 1

Geometry of model for the diffraction of a metal sub-wavelength slit.

Fig. 2
Fig. 2

Exponential integral function E1(ikspx): (a): Real, imaginary parts and amplitude;(b): Phase. Constitutive parameters have been taken for an air-silver interface at λ=1 μm.

Fig. 3
Fig. 3

Spectrum of the transient SPP for an air-silver interface at λ=1 μm with the pole at ksp slightly higher than k0.

Fig. 4
Fig. 4

Field scattered by a metal nano-slit in the near-slit region at λ=1 μm. (a) and (b): Amplitude profile along respectively the x and y axis (solid lines) compared to a typical cylindrical wave (dashed line). (c): 2D plot of amplitude in arbitrary units and (d): the phase in radians. The black semicircle is the upper limit of the approximation (x2 + y2)1/2 << λ/(21/2π). For all figures, the complex permittivity of silver was calculated using the Lorentz-Drude dispersive model.

Fig. 5
Fig. 5

Amplitude of the coefficient hs of the scattered field in Eq. (9) in arbitrary units as a function of the incident wavelength for (a): Ag; and (b): Au. The index of refraction in the dielectric medium over the metal slit is n = 1 (black), 1.5 (blue), 2 (red), 2.5 (green), 3 (orange).

Fig. 6
Fig. 6

FDTD simulations (OptiwaveTM) for real part of the magnetic intensity at λ = 500 nm from a punctual magnetic line source located on a metallo-dielectric interface with (a): Perfect electric conductor and (b): Silver.

Equations (46)

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

( y 2 + γ 2 ) H ˜ ( k x ,y)=iω ε d J m * δ(y)
H(x,y)= ω J m * 2π e i k x x e iγy 1 ε d ε d k 0 2 k x 2 + 1 ε m ε m k 0 2 k x 2 d k x
k x = k 0 ε d ε m ε d + ε m k sp
H a (x)=H(x,y=0) =iω J m * ε d ε m [ ( ε d ε m ) 1 2 ε d 2 + ε m 2 e i k sp x + 1 2π( ε d + ε m ) e i k sp x E 1 ( i k sp x ) ]
E n (z)= 1 e zt t n dt
H b ( x,y )= i 2 k d y x 2 + y 2 H 1 (1) ( k d x 2 + y 2 )= i k d 2 sin( θ ) H 1 (1) ( k d r )
H sp (x,y)= 2 h sp i k d e i k sp xi k d 2 k sp 2 y
h sp = ω k d J m * ( ε d ε m ) 3/2 2( ε d 2 + ε m 2 )
H s (x,y) h s y ( xx' ) 2 + y 2 H 1 (1) ( k d ( xx' ) 2 + y 2 ) e i k sp x' E 1 ( i k sp x' )dx'
h s = ω k d J m * ε d ε m 4π( ε d + ε m )
e i k sp x E 1 ( i k sp x )= 0 e ikx k k sp dk
H 1 (1) ( k d r )= 2 iπ k d r
E 1 ( z )=γln( z )+ n=1 ( 1 ) n+1 z n nn!
H s ( x,y ) 2 h s i k d e i k sp ( xiy ) E 1 ( i k sp ( xiy ) )
H s ( x,y ) h s 2π k sp y x 2 + y 2 H 1 (1) ( k d x 2 + y 2 )
H s ( x,y ) h s 2π k sp y x H 1 (1) ( k d x )
H b ( x,y )= 1 2π e i ε d k 0 2 k 2 y e ikx dk
H b ( x,y )= 1 2π e i ε d k 0 2 k 2 y ( cos( kx )+isin( kx ) )dk
H b ( x,y )= 1 π 0 cos( kx ) e k 2 ε d k 0 2 y dk
0 cos( bx ) e β γ 2 + x 2 dx = βγ β 2 + b 2 K 1 ( γ β 2 + b 2 )
H b ( x,y )= 1 π y( ±i k 0 ε d ) x 2 + y 2 K 1 ( ±i ε d k 0 x 2 + y 2 )
H b ( x,y )= i 2 k d y x 2 + y 2 H 1 (1) ( k d x 2 + y 2 )
H(x,y)= 1 2π H ˜ a (k) H ˜ b (k,y) e ikx dk
H ˜ a ( k )=ω J m * 1 1 ε d ε d k 0 2 k 2 + 1 ε m ε m k 0 2 k 2
H ˜ b ( k,y )= e i ε d k 0 2 k 2 y
H(x,y)= H a (x) H b (x,y)
H( x,y )= h sp y ( xx' ) 2 + y 2 H 1 (1) ( k d ( xx' ) 2 + y 2 ) e i k sp x' dx' + h s y ( xx' ) 2 + y 2 H 1 (1) ( k d ( xx' ) 2 + y 2 ) e i k sp x' E 1 ( i k sp x' )dx'
h sp = ω k d J m * ( ε d ε m ) 3 2 2( ε d 2 + ε m 2 )
h s = ω k d J m * ε d ε m 4π( ε d + ε m )
H( x,y )= h sp y ( x' ) 2 + y 2 H 1 (1) ( k d ( x' ) 2 + y 2 ) e i k sp (xx') dx' + h s y ( x' ) 2 + y 2 H 1 (1) ( k d ( x' ) 2 + y 2 ) e i k sp (xx') E 1 ( i k sp ( xx' ) )dx'
H( x,y )= H sp ( x,y )+ H s ( x,y )
H sp ( x,y )= h sp y ( x' ) 2 + y 2 H 1 (1) ( k d ( x' ) 2 + y 2 ) e i k sp (xx') dx'
H sp ( x,y )= h sp y e i k sp x 1 x ' 2 + y 2 H 1 (1) ( k d x ' 2 + y 2 )( cos( k sp x' )isin( k sp x' ) ) dx'
H sp ( x,y )=2 h sp y e i k sp x [ 0 J 1 ( k d x ' 2 + y 2 ) x ' 2 + y 2 cos( k sp x' ) dx'+i 0 Y 1 ( k d x ' 2 + y 2 ) x ' 2 + y 2 cos( k sp x' ) dx' ]
0 ( x 2 + b 2 ) ν 2 J ν ( a x 2 + b 2 )cos( cx )dx = π 2 a ν b ν+ 1 2 ( a 2 c 2 ) ν 2 1 4 J ν 1 2 ( b a 2 c 2 )
0 ( x 2 + b 2 ) ν 2 Y ν ( a x 2 + b 2 )cos( cx )dx = π 2 a ν b ν+ 1 2 ( a 2 c 2 ) ν 2 1 4 Y ν 1 2 ( b a 2 c 2 )
H sp ( x,y )=2 h sp y e i k sp x [ π 2 ( k d 2 k sp 2 ) 1 4 k d y J 1 2 ( ±y k d 2 k sp 2 )+i π 2 ( k d 2 k sp 2 ) 1 4 k d y Y 1 2 ( ±y k d 2 k sp 2 ) ]
H sp ( x,y )= h sp e i k sp x 2π ( k d 2 k sp 2 ) 1 4 k d y H 1 2 (1) ( ±y k d 2 k s 2 )
H 1 2 (1) (z)= 2 πz e iz i
H sp ( x,y )= h sp 2i k d e i k sp x e ±iy k d 2 k sp 2
H( x,y )= h s y ( x' ) 2 + y 2 H 1 (1) ( k d ( x' ) 2 + y 2 ) e i k sp (xx') E 1 ( i k sp ( xx' ) )dx'
H 1 (1) ( z ) 2 iπz
E 1 ( z )=γln( z )+ n=1 ( 1 ) n+1 z n nn!
H s ( x,y ) 2 h s y iπ k d e i k sp x 1 ( x' ) 2 + y 2 e i k sp x' [ γln( i k sp ( xx' ) ) + n=1 ( 1 ) n+1 ( i k sp ( xx' ) ) n nn! ]dx'
H s ( x,y ) 2 h s i k d e i k sp ( xiy ) [ γln( i k sp ( xiy ) )+ n=1 ( 1 ) n+1 ( i k sp ( xiy ) ) n nn! ]
H s ( x,y ) 2 h s i k d e i k sp ( xiy ) E 1 ( i k sp ( xiy ) )

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