Abstract

We simulate the early dynamics of enhanced light transmission through a subwavelength metallic slit and find that the amplitude of the transmitted light can be modulated. To understand this novel phenomenon and underlying physics, we develop a new analytical model. The field of each light period is considered as an individual unit. Each field is partially transmitted through the slit as the first subunit. The portion reflected from the exit interface travels a round trip in the slit and then partially exits again as the second subunit. There may be a gap in time between these two subunits. This process repeats so as to produce a subunit train, which is verified by the simulation of an incident sinusoidal pulse of one light period. When the wave units are continuous, the superposition of the trains produces the observed light. While the round-trip time is an integer multiple of the light period, the modulation period is the same. Besides academic importance, this study may be applicable to photonics with short laser pulses.

© 2015 Optical Society of America

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Near-field diffraction by a slit: implications for superresolution microscopy

Eric Betzig, A. Harootunian, A. Lewis, and M. Isaacson
Appl. Opt. 25(12) 1890-1900 (1986)

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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. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nature Photon. 3, 55–58 (2009).
    [Crossref]
  3. W. Zhang, L. Huang, C. Santschi, and O. J. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10, 1006–1011 (2010).
    [Crossref] [PubMed]
  4. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
    [Crossref]
  5. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
    [Crossref]
  6. L. Novotny and N. van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011).
    [Crossref]
  7. T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
    [Crossref] [PubMed]
  8. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
    [Crossref] [PubMed]
  9. F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Phys. 2, 551–556 (2006).
    [Crossref]
  14. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
    [Crossref] [PubMed]
  15. F. L. Neerhoff and G. Mur, “Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media,” Appl. Sci. Res. 28, 73–88 (1973).
  16. E. Betzig, A. Harootunian, A. Lewis, and M. Isaacson, “Near-field diffraction by a slit - implications for super-resolution microscopy,” Appl. Opt. 25, 1890–1900 (1986).
    [Crossref]
  17. R. F. Harrington and D. T. Auckland, “Electromagnetic transmission through narrow slots in thick conducting screens,” IEEE Trans. Antennas Propag. AP-28, 616–622 (1980).
    [Crossref]
  18. S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
    [Crossref]
  19. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
    [Crossref] [PubMed]
  20. J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
    [Crossref]
  21. R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
    [Crossref]
  22. M. Mechler, O. Samek, and S. V. Kukhlevsky, “Enhanced transmission and reflection of few-cycle pulses by a single slit,” Phys. Rev. Lett. 98, 163901 (2007).
    [Crossref] [PubMed]
  23. S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
    [Crossref]
  24. J. Wuenschell and H. K. Kim, “Excitation and propagation of surface plasmons in a metallic nanoslit structure,” IEEE Trans. Nanotechnol. 7, 229–236 (2008).
    [Crossref]
  25. X. Wang, X. G. Zhang, Q. Yu, and B. N. Harmon, “Multiple-scattering theory for electromagnetic waves,” Phys. Rev. B 47, 4161–4167 (1993).
    [Crossref]
  26. K. Y. Kim, Y. K. Cho, H.-S. Tae, and J.-H. Lee, “Light transmission along dispersive plasmonic gap and its subwavelength guidance characteristics,” Opt. Express 14, 320–330 (2006).
    [Crossref] [PubMed]

2011 (2)

2010 (4)

K. R. Chen, “Focusing of light beyond the diffraction limit of half the wavelength,” Opt. Lett. 35, 3763–3765 (2010).
[Crossref] [PubMed]

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
[Crossref]

W. Zhang, L. Huang, C. Santschi, and O. J. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10, 1006–1011 (2010).
[Crossref] [PubMed]

2009 (1)

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nature Photon. 3, 55–58 (2009).
[Crossref]

2008 (2)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
[Crossref]

J. Wuenschell and H. K. Kim, “Excitation and propagation of surface plasmons in a metallic nanoslit structure,” IEEE Trans. Nanotechnol. 7, 229–236 (2008).
[Crossref]

2007 (1)

M. Mechler, O. Samek, and S. V. Kukhlevsky, “Enhanced transmission and reflection of few-cycle pulses by a single slit,” Phys. Rev. Lett. 98, 163901 (2007).
[Crossref] [PubMed]

2006 (3)

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
[Crossref]

K. Y. Kim, Y. K. Cho, H.-S. Tae, and J.-H. Lee, “Light transmission along dispersive plasmonic gap and its subwavelength guidance characteristics,” Opt. Express 14, 320–330 (2006).
[Crossref] [PubMed]

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

2004 (2)

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

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[Crossref]

2003 (3)

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

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

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[Crossref]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[Crossref] [PubMed]

2001 (1)

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[Crossref] [PubMed]

2000 (1)

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[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 391, 667–669 (1998).
[Crossref]

1993 (1)

X. Wang, X. G. Zhang, Q. Yu, and B. N. Harmon, “Multiple-scattering theory for electromagnetic waves,” Phys. Rev. B 47, 4161–4167 (1993).
[Crossref]

1986 (1)

1980 (1)

R. F. Harrington and D. T. Auckland, “Electromagnetic transmission through narrow slots in thick conducting screens,” IEEE Trans. Antennas Propag. AP-28, 616–622 (1980).
[Crossref]

1973 (1)

F. L. Neerhoff and G. Mur, “Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media,” Appl. Sci. Res. 28, 73–88 (1973).

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
[Crossref]

Astilean, S.

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[Crossref]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
[Crossref]

Auckland, D. T.

R. F. Harrington and D. T. Auckland, “Electromagnetic transmission through narrow slots in thick conducting screens,” IEEE Trans. Antennas Propag. AP-28, 616–622 (1980).
[Crossref]

Barnes, W. L.

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

Betzig, E.

Bravo-Abad, J.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[Crossref]

Chen, K. R.

Cho, Y. K.

Chu, W. H.

Chuang, C. H.

Chui, H. C.

Csapo, L.

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-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. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[Crossref] [PubMed]

Ebbesen, T. W.

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

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[Crossref]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[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]

Fang, H. C.

Fuh, A. Y. G.

García-Vidal, F. J.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[Crossref]

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

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[Crossref]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[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]

Gordon, R.

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
[Crossref]

Guo, L. J.

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
[Crossref] [PubMed]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
[Crossref]

Harmon, B. N.

X. Wang, X. G. Zhang, Q. Yu, and B. N. Harmon, “Multiple-scattering theory for electromagnetic waves,” Phys. Rev. B 47, 4161–4167 (1993).
[Crossref]

Harootunian, A.

Harrington, R. F.

R. F. Harrington and D. T. Auckland, “Electromagnetic transmission through narrow slots in thick conducting screens,” IEEE Trans. Antennas Propag. AP-28, 616–622 (1980).
[Crossref]

Huang, C. H.

Huang, L.

W. Zhang, L. Huang, C. Santschi, and O. J. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10, 1006–1011 (2010).
[Crossref] [PubMed]

Hugonin, J. P.

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

Hwung, H. H.

Isaacson, M.

Janssens, K.

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Kim, H. K.

J. Wuenschell and H. K. Kim, “Excitation and propagation of surface plasmons in a metallic nanoslit structure,” IEEE Trans. Nanotechnol. 7, 229–236 (2008).
[Crossref]

Kim, K. Y.

Kukhlevsky, S. V.

M. Mechler, O. Samek, and S. V. Kukhlevsky, “Enhanced transmission and reflection of few-cycle pulses by a single slit,” Phys. Rev. Lett. 98, 163901 (2007).
[Crossref] [PubMed]

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Lalanne, P.

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

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[Crossref]

Lee, J.-H.

Lewis, A.

Lezec, H. J.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[Crossref]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[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]

Lin, C. Y.

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[Crossref] [PubMed]

Liu, C. P.

Lo, Y. L.

Luo, X.

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
[Crossref] [PubMed]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
[Crossref]

MacDonald, K. F.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nature Photon. 3, 55–58 (2009).
[Crossref]

Martin, O. J.

W. Zhang, L. Huang, C. Santschi, and O. J. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10, 1006–1011 (2010).
[Crossref] [PubMed]

Martín-Moreno, L.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[Crossref]

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

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[Crossref]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[Crossref] [PubMed]

Mechler, M.

M. Mechler, O. Samek, and S. V. Kukhlevsky, “Enhanced transmission and reflection of few-cycle pulses by a single slit,” Phys. Rev. Lett. 98, 163901 (2007).
[Crossref] [PubMed]

S. V. Kukhlevsky, M. Mechler, L. Csapo, and K. Janssens, “Near-field diffraction of fs and sub-fs pulses: super resolution of nsom in space and time,” Phys. Lett. A 319, 439–447 (2003).
[Crossref]

Mur, G.

F. L. Neerhoff and G. Mur, “Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media,” Appl. Sci. Res. 28, 73–88 (1973).

Neerhoff, F. L.

F. L. Neerhoff and G. Mur, “Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media,” Appl. Sci. Res. 28, 73–88 (1973).

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011).
[Crossref]

Palamaru, M.

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[Crossref]

Pendry, J. B.

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

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
[Crossref]

Samek, O.

M. Mechler, O. Samek, and S. V. Kukhlevsky, “Enhanced transmission and reflection of few-cycle pulses by a single slit,” Phys. Rev. Lett. 98, 163901 (2007).
[Crossref] [PubMed]

Samson, Z. L.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nature Photon. 3, 55–58 (2009).
[Crossref]

Santschi, C.

W. Zhang, L. Huang, C. Santschi, and O. J. Martin, “Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas,” Nano Lett. 10, 1006–1011 (2010).
[Crossref] [PubMed]

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
[Crossref]

Stockman, M. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nature Photon. 3, 55–58 (2009).
[Crossref]

Tae, H.-S.

Takakura, Y.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[Crossref] [PubMed]

Thio, T.

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]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater. 7, 442–453 (2008).
[Crossref]

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011).
[Crossref]

Wang, X.

X. Wang, X. G. Zhang, Q. Yu, and B. N. Harmon, “Multiple-scattering theory for electromagnetic waves,” Phys. Rev. B 47, 4161–4167 (1993).
[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]

Wu, Y.-K.

T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
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T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun. 1, 59 (2010).
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Figures (5)

Fig. 1
Fig. 1 Schematic of the simulated structure. A p-polarized wave with its wavelength of λ0 = 560 nm is generated at a distance of one λ0 away from the top of the PEC. The slit width 2s is 40 nm while the film thickness h will vary. In the model, the space is divided into three areas of a, b, and c.
Fig. 2
Fig. 2 Normalized energy flux as a function of the film thickness h (a), and as a function of wavelength when h = 205 nm (b), 470 nm (c), and 730 nm (d), respectively, where the blue solid curve is from the sinusoidal pulse of one light period, and the red dots are from the monochromatic sources.
Fig. 3
Fig. 3 The history of the electric fields at (0, λ0) from the simulation (solid blue curve) and the modeling result of M = 20 and N = 10(dashed red curve), where h = 205 nm (a), 470 nm (b), and 730 nm (c), respectively.
Fig. 4
Fig. 4 The history of the simulated electric field at the centers of the entrance (a) and the exit (b) from the simulation of h = 10 μm.
Fig. 5
Fig. 5 The history of the electric field at (0, −λ0) of the wave unit m = 1 obtained from the model, where N = 10, h = 205 nm (trt = T) (a), 470 nm (trt ≃ 2T) (b), and 730 nm (trt ≃ 3T) (c), respectively. The grey curves show the history of the electric field from the sinusoidal pulse of one light period, while the colored curves are from a continuous sinusoidal wave source.

Tables (1)

Tables Icon

Table 1 The time of first five peaks arriving at the centers of the entrance and the exit as well as their corresponding electric field amplitudes obtained from the simulation of h = 10 μm.

Equations (14)

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P ( ω 0 ) = π | y | s E 0 2 T t f T t f e x ( 0 , y , t ) h z ( 0 , y , t ) d t ,
e x i ( x , y , t ) = rect ( t 0.5 T T ) E 0 sin ( k 0 y + ω 0 t ) ,
P ( ω ) = π | y | 2 s Re { [ E x ( 0 , y , ω ) * H z ( 0 , y , ω ) ] } Re { [ E x i ( 0 , y , ω ) * H z i ( 0 , y , ω ) ] } ,
F ( ω ) = 0 t f f ( t ) exp i ω t d t
e x m ( t ) = E 0 rect ( t t m T ) sin ( ω 0 t ) ,
t m n = t m + d / c 0 + t s + ( n 1 ) t r t + | y | / c 0 ,
E m n ( y ) = α ( y ) E 0 | τ a b ρ a b c n 1 τ b c | .
e x m n ( y , t ) = rect ( t t m n T ) E m n ( y ) sin [ ω 0 ( t t m n + T / 2 ) ] .
e x ( y , t ) = m = 1 M n = 1 N e x m n ( y , t ) ,
S ( y ) = E 2 ( y ) | Z ( y ) | 1 T t f T t f sin ( ω 0 t ) sin { ω 0 t arg [ Z ( y ) ] } d t ,
2 s S ( 0 ) = π | y | S ( y ) .
α ( y ) E ( y ) E ( 0 ) = 2 s π | y | | Z ( y ) | | Z ( 0 ) | cos { arg [ Z ( 0 ) ] } cos { arg [ Z ( y ) ] } .
t r t = 2 h λ s + arg ( ρ a b c ) 2 π = 1 ,
e x ( 0 , t M 1 T / 4 ) = α ( 0 ) E 0 | τ a b τ b c | ( 1 + | ρ a b c 1 | + | ρ a b c 2 | + + | ρ a b c M 1 | ) ,

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