Abstract

The asymptotic closed-form solution to the fundamental diffraction problem of a linear horizontal Hertzian dipole radiating over the metallo-dielectric interface is provided. For observation points just above the interface, we confirm that the total surface near-field is the sum of two components: a long-range surface plasmon polariton and a short-range radiative cylindrical wave. The relative phases, amplitudes and damping functions of each component are quantitatively elucidated through simple analytic expressions for the entire range of propagation: near and asymptotic. Validation of the analytic solution is performed by comparing the predictions of a dipolar model with recently published data.

© 2008 Optical Society of America

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  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 391, 667-669 (1998).
    [CrossRef]
  2. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
    [CrossRef] [PubMed]
  3. 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," Nat. Physics 2, 262-267 (2006).
    [CrossRef]
  4. G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
    [CrossRef] [PubMed]
  5. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
    [CrossRef] [PubMed]
  6. P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Physics 2, 551-556 (2006).
    [CrossRef]
  7. L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. 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, 1399-1402 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. M. Born and E. Wolf, Principles of optics 7th ed, (Cambridge University Press, Oxford, 1999), Chap. 8.9.
  16. M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
    [CrossRef]
  17. P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
    [CrossRef]

2007

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

G. Lévêque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B. 76, 155418 (2007).
[CrossRef]

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

2006

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Physics 2, 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," Nat. Physics 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

2005

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 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, 1399-1402 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

2004

1998

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, 667-669 (1998).
[CrossRef]

1950

P. C. Clemmow, "A note on the diffraction of a cylindrical wave by a perfectly conducting half-plane," Q. J. Mech. Appl. Math. 3, 377-384 (1950).
[CrossRef]

???t Hooft, G. W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Aigouy, L.

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

Alkemade, P. F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Alloschery, O.

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," Nat. Physics 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

Baida, F. I.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Besbes, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Bientsman, P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 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, 1399-1402 (2005).
[CrossRef]

Clemmow, P. C.

P. C. Clemmow, "A note on the diffraction of a cylindrical wave by a perfectly conducting half-plane," Q. J. Mech. Appl. Math. 3, 377-384 (1950).
[CrossRef]

Collin, R. E.

R. E. Collin, "Hertzian dipole radiating over a lossy earth or sea: some early and late 20th-century controversies," IEEE Antennas Propag. Mag. 46, 64-79 (2004).
[CrossRef]

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

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, 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. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Gay, G.

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[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," Nat. Physics 2, 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. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 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, 667-669 (1998).
[CrossRef]

Granet, G.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Guizal, B.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Helfert, S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

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, 1399-1402 (2005).
[CrossRef]

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, 1399-1402 (2005).
[CrossRef]

Hugonin, J. P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Physics 2, 551-556 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Janssen, O. T. A.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Julié, G.

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

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, 1399-1402 (2005).
[CrossRef]

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lalanne, P.

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Physics 2, 551-556 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lévêque, G.

G. Lévêque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B. 76, 155418 (2007).
[CrossRef]

Lezec, H. J.

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," Nat. Physics 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
[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, 667-669 (1998).
[CrossRef]

Mansuripur, M.

Martin, O. J. F.

G. Lévêque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B. 76, 155418 (2007).
[CrossRef]

Mathet, V.

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

Moloney, J. V.

Moreau, A.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Mortier, M.

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

Nugrowati, A. M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

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," Nat. Physics 2, 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, 1399-1402 (2005).
[CrossRef]

Pereira, S. F.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Seideman, T.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Sheng, Y.

Sukharev, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

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, 3629-3651 (2004).
[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, 667-669 (1998).
[CrossRef]

Ung, B.

Urbach, H. P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

van de Nes, A. S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

van Haver, S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Van Labeke, D.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

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," Nat. Physics 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

Visser, T. D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 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, 1399-1402 (2005).
[CrossRef]

Weiner, J.

G. Lévêque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B. 76, 155418 (2007).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[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," Nat. Physics 2, 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, 1399-1402 (2005).
[CrossRef]

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, 667-669 (1998).
[CrossRef]

Xie, Y.

Xu, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[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, 1399-1402 (2005).
[CrossRef]

Zakharian, A. R.

IEEE Antennas Propag. Mag.

R. E. Collin, "Hertzian dipole radiating over a lossy earth or sea: some early and late 20th-century controversies," IEEE Antennas Propag. Mag. 46, 64-79 (2004).
[CrossRef]

J. Eur. Opt. Soc.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bientsman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 2, 07022 (2007).
[CrossRef]

Nano. Lett.

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, 1399-1402 (2005).
[CrossRef]

Nat. Physics

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," Nat. Physics 2, 262-267 (2006).
[CrossRef]

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Physics 2, 551-556 (2006).
[CrossRef]

Nature

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, 667-669 (1998).
[CrossRef]

Opt. Express

Phys. Rev. B.

G. Lévêque, O. J. F. Martin, and J. Weiner, "Transient behavior of surface plasmon polaritons scattered at a subwavelength groove," Phys. Rev. B. 76, 155418 (2007).
[CrossRef]

Phys. Rev. Lett.

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet, and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures," Phys. Rev. Lett. 98, 153902 (2007).
[CrossRef] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. J. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry," Phys. Rev. Lett. 96, 213901 (2006).
[CrossRef] [PubMed]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ???t Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young???s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

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P. C. Clemmow, "A note on the diffraction of a cylindrical wave by a perfectly conducting half-plane," Q. J. Mech. Appl. Math. 3, 377-384 (1950).
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Other

M. Born and E. Wolf, Principles of optics 7th ed, (Cambridge University Press, Oxford, 1999), Chap. 8.9.

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[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Radiating horizontal electric dipole located in region 1 (air).

Fig. 2.
Fig. 2.

Integration contours and location of the single pole in the α-plane.

Fig. 3.
Fig. 3.

Amplitude moduli of the total field (solid line), SPP field (dotted line), boundary wave field (dashed line) and the envelope function U(x) (dashed-dotted line) for ε 1=1, ε 2=-33.22+i1.17 and λ=852nm. The successive peaks of U(x) are numbered x 1, x 2,…, xm .

Fig. 4.
Fig. 4.

Real components of the total field (solid line), boundary wave field(dashed line), SPP field (dotted line) and their moduli for λ/8≤x≤10λ

Fig. 5.
Fig. 5.

Schematic of the near-field interactions in the groove-slit setup

Fig. 6.
Fig. 6.

Normalized slit transmission as a function of groove-slit distance d. Comparison between experimental (circles) [3], numerical (dashed line) [16], and the analytical (solid line) results with λ=852nm and ε 2=-33.22+1.17i.

Fig. 7.
Fig. 7.

Near-field fringe pattern in the double-slit setup. Comparison between the experimental (circles) [7] and analytical (solid line) results with 2d=10.44µm, λ=974.3nm and ε 2=-44.05+3.24i

Equations (22)

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

E 1 z = ω μ 0 2 π k 0 2 + γ 2 e i γ 1 h ε 2 γ 1 + ε 1 γ 2 + sin ( γ 1 h ) i ε 1 e i γ 1 z k e i k x d k
I 1 = C sin α · cos α · ε 2 sin 2 α · e i k 0 R 2 cos ( α θ ) ( ε 2 cos α + ε 2 sin 2 α ) · d α
I 1 = e i k 0 R 2 + f ( τ ) · exp ( k 0 R 2 τ 2 2 ) · d τ
g ( τ ) = sin α · cos α ε 2 sin 2 α · d α d τ
h ( τ ) = ε 2 cos α + ε 2 sin 2 α
f ( τ ) = A τ τ p + f ( τ ) · ( τ τ p ) A τ τ p
  = f p ( τ ) + f A ( τ )
A = g ( τ ) τ h ( τ ) τ p = g ( τ p ) α h ( α ) . α τ τ p = ε p 2 ε 2 1
I A = e i k 0 R 2 + f A ( 0 ) · exp ( k 0 R 2 τ 2 2 ) · d τ
I A = [ e i π 4 sin θ cos θ · ε 2 sin 2 θ ( ε 2 cos θ + ε 2 sin 2 θ ) + A e i π 4 2 · sin ( ( α p θ ) 2 ) ] 2 π k 0 R 2 e i k 0 R 2
I P = e i k 0 R 2 + f P ( τ ) · exp ( k 0 R 2 τ 2 2 ) · d τ = A e i k 0 R 2 P ( τ )
I P = 2 π i · A · U ( R 2 , θ ) · exp [ i k 0 R 2 cos ( α p θ ) ]
U ( R 2 , θ ) = 1 1 2 e r f c [ ( 1 + i ) k 0 R 2 2 ( cos ( α p θ ) 1 ) ]
I I = sin θ cos θ · e i π 4 2 2 π k 0 R 2 exp ( i k 0 R 2 )
I D = + sin θ cos θ · e i π 4 2 2 π k 0 R 1 exp ( i k 0 R 1 )
E 1 z = ω μ 0 4 π sin θ cos θ · e i π 4 2 π k 0 R 1 e i k 0 R 1 Direct dipole field
+ ω μ 0 4 π sin θ cos θ · r T M · e i π 4 2 π k 0 R 2 e i k 0 R 2 Reflected field
+ ω μ 0 4 π A · e i π 4 4 π k 0 R 2 ( cos ( α p θ ) 1 ) e i k 0 R 2 Boundary wave field
+ ω μ 0 A · e i π 2 · U ( R 2 , θ ) · exp [ i k 0 R 2 cos ( α p θ ) ]   SPP field
E s w + ( x ) = U ( x ) · exp [ i ( k p x π 2 ) ] + 1 4 π · Δ k x x exp [ i ( k 0 x 3 π 4 ) ]
= E s p p + ( x ) +     E b w + ( x )
U ( x ) = 1 1 2 e r f c [ ( 1 + i ) Δ k · x 2 ]

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