Abstract

We theoretically demonstrate that a single bare subwavelength metal slit without any surrounding corrugations can have a capability to steer the incident light into focusing patterns by introducing a high index in the transmission half-space. The focusing properties are identified to depend on both the slit width and the output permittivity. The underlying physics lies in the interference of quasi-cylindrical waves scattered from the slit, and our proposed model agrees well with the simulation results. This finding is believed to inspire some novel ideas for the nano-optics design.

© 2013 OSA

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
    [CrossRef]
  2. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
    [CrossRef] [PubMed]
  3. 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,” Science297(5582), 820–822 (2002).
    [CrossRef] [PubMed]
  4. S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
    [CrossRef]
  5. H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett.34(17), 2569–2571 (2009).
    [CrossRef] [PubMed]
  6. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (2003).
    [CrossRef] [PubMed]
  7. L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
    [CrossRef]
  8. Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
    [CrossRef]
  9. X. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett.31(9), 1322–1324 (2006).
    [CrossRef] [PubMed]
  10. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
    [CrossRef] [PubMed]
  11. G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B79(20), 201103 (2009).
    [CrossRef]
  12. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B69(12), 121402 (2004).
    [CrossRef]
  13. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
    [CrossRef] [PubMed]
  14. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
    [CrossRef]
  15. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
    [CrossRef] [PubMed]
  16. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature452(7188), 728–731 (2008).
    [CrossRef] [PubMed]
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
  18. H. Liu and P. Lalanne, “Light scattering by metallic surface with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
    [CrossRef]
  19. P. Lalanne, J. Hugonin, H. 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]
  20. C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
    [CrossRef]
  21. S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B26(12), B28–B33 (2009).
    [CrossRef]
  22. H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
    [CrossRef] [PubMed]
  23. For a lineup arrangement of N point sources with a between spacing of d, the constructive interference of their emitted waves requires that the maximum phase difference among them should satisfy the relationship of k(Nd)2+f2−k f=(2n+1)π2, where k is the wavevector of the propagating wave, f is the distance along the central perpendicular of the source plane, n is an integer. From the above mentioned formula, we can derive f expression to represent the spatial position of the focal spot.
  24. S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
    [CrossRef] [PubMed]
  25. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
    [CrossRef] [PubMed]
  26. A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
    [CrossRef] [PubMed]
  27. N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317(5845), 1698–1702 (2007).
    [CrossRef] [PubMed]

2011 (1)

C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
[CrossRef]

2010 (2)

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

H. Liu and P. Lalanne, “Light scattering by metallic surface with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

2009 (5)

P. Lalanne, J. Hugonin, H. 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]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B79(20), 201103 (2009).
[CrossRef]

S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B26(12), B28–B33 (2009).
[CrossRef]

H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett.34(17), 2569–2571 (2009).
[CrossRef] [PubMed]

2008 (2)

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature452(7188), 728–731 (2008).
[CrossRef] [PubMed]

2007 (3)

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
[CrossRef]

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (3)

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

2004 (4)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B69(12), 121402 (2004).
[CrossRef]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

2003 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (2003).
[CrossRef] [PubMed]

2002 (1)

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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

1997 (1)

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Aigouy, L.

C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
[CrossRef]

Aussenegg, F. R.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Bartal, G.

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B79(20), 201103 (2009).
[CrossRef]

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Chang, Y.-C.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Chen, Y.-C.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Deng, Y.

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Dong, X.

Drezet, A.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Du, C.

Ea Kim, B.

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Emory, S. R.

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Fan, X.

Gan, C. H.

C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
[CrossRef]

Gao, H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B69(12), 121402 (2004).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (2003).
[CrossRef] [PubMed]

Ghaem, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Gösele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Hohenau, A.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Huang, K.-T.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Hugonin, J.

P. Lalanne, J. Hugonin, H. 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]

Hugonin, J. P.

S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B26(12), B28–B33 (2009).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

Hyun, J. K.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Jacubowiez, L.

Jiao, X.

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

Kim, H.

H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett.34(17), 2569–2571 (2009).
[CrossRef] [PubMed]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

Kim, S.

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
[CrossRef]

Koller, D.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Krenn, J. R.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Lalanne, P.

C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
[CrossRef]

H. Liu and P. Lalanne, “Light scattering by metallic surface with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

P. Lalanne, J. Hugonin, H. 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]

S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B26(12), B28–B33 (2009).
[CrossRef]

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature452(7188), 728–731 (2008).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

Lalouat, L.

C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
[CrossRef]

Lauhon, L. J.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Lee, B.

H. Kim, J. Park, and B. Lee, “Tunable directional beaming from subwavelength metal slits with metal-dielectric composite surface gratings,” Opt. Lett.34(17), 2569–2571 (2009).
[CrossRef] [PubMed]

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
[CrossRef]

Lee, C.-K.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Lee, M. H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Leitner, A.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Lerosey, G.

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B79(20), 201103 (2009).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Liaw, J.-W.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Lim, Y.

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
[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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Liu, D.-Z.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Liu, H.

H. Liu and P. Lalanne, “Light scattering by metallic surface with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

P. Lalanne, J. Hugonin, H. 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,” Nature452(7188), 728–731 (2008).
[CrossRef] [PubMed]

Liu, J.-M.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Luo, X.

Martin-Moreno, L.

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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B69(12), 121402 (2004).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (2003).
[CrossRef] [PubMed]

Min, C.

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

Ming, H.

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

Moreno, E.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B69(12), 121402 (2004).
[CrossRef]

Müller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Nie, S. M.

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

Odom, T. W.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Park, J.

Ravets, S.

Rodier, J. C.

S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B26(12), B28–B33 (2009).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Shi, H.

Soukoulis, C. M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Wang, B.

P. Lalanne, J. Hugonin, H. 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]

Wang, C.

Wang, G. P.

Wang, P.

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Yang, J.-C.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Yeh, C.-S.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Yeh, J.-T.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Yu, L.-B.

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

Zhang, X.

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B79(20), 201103 (2009).
[CrossRef]

Appl. Phys. B (1)

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam focusing by metallic nano-slit array containing nonlinear material,” Appl. Phys. B90(1), 97–99 (2008).
[CrossRef]

Appl. Phys. Lett. (2)

S. Kim, H. Kim, Y. Lim, and B. Lee, “Off-axis directional beaming of optical field diffracted by a single subwavelength metal slit with asymmetric dielectric surface gratings,” Appl. Phys. Lett.90(5), 051113 (2007).
[CrossRef]

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nano Lett. (3)

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett.7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009).
[CrossRef] [PubMed]

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett.10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Nature (2)

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature452(7188), 728–731 (2008).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaem, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (5)

G. Bartal, G. Lerosey, and X. Zhang, “Subwavelength dynamic focusing in plasmonic nanostructures using time reversal,” Phys. Rev. B79(20), 201103 (2009).
[CrossRef]

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B69(12), 121402 (2004).
[CrossRef]

H. Liu and P. Lalanne, “Light scattering by metallic surface with subwavelength patterns,” Phys. Rev. B82(11), 115418 (2010).
[CrossRef]

L.-B. Yu, D.-Z. Liu, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B71(4), 041405 (2005).
[CrossRef]

C. H. Gan, L. Lalouat, P. Lalanne, and L. Aigouy, “Optical quasicylindrical waves at dielectric interfaces,” Phys. Rev. B83(8), 085422 (2011).
[CrossRef]

Phys. Rev. Lett. (4)

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett.92(11), 113903 (2004).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett.95(26), 263902 (2005).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett.90(16), 167401 (2003).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

Science (3)

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface enhanced Raman scattering,” Science275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science317(5845), 1698–1702 (2007).
[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,” Science297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Surf. Sci. Rep. (1)

P. Lalanne, J. Hugonin, H. 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 (2)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

For a lineup arrangement of N point sources with a between spacing of d, the constructive interference of their emitted waves requires that the maximum phase difference among them should satisfy the relationship of k(Nd)2+f2−k f=(2n+1)π2, where k is the wavevector of the propagating wave, f is the distance along the central perpendicular of the source plane, n is an integer. From the above mentioned formula, we can derive f expression to represent the spatial position of the focal spot.

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Figures (6)

Fig. 1
Fig. 1

A schematic diagram of a single bare subwavelength metal slit with a high-index transmission half-space, where QCW (blue arrows) and SPP (red arrows) indicate optical quasi-cylindrical waves and surface plasmon polariton scattered by the slit edges, respectively. The direction and line thickness of arrows respectively indicate the propagation direction and intensity attenuation of these surface waves.

Fig. 2
Fig. 2

(a)-(c) Simulated real part of the magnetic field, Re(Hz), around the metal slit (w = 100 nm) for the output permittivity of Ɛd = 1, 6 and 10, respectively. Here the incident wavelength is λ = 1 μm.

Fig. 3
Fig. 3

Simulated beam focusing behaviors of the magnetic field intensity |Hz| around the single bare slit when the output permittivity is given by Ɛd = 14. (a)-(b) The single slit with two different widths of w = 200 nm and w = 300 nm, respectively, at the incident wavelength of λ = 1 μm. An inset curve in Fig. 3(a) indicates the spatial distribution of transmission intensity along the y direction at x = 0. (c) The single slit of w = 600 nm at the incident wavelength of λ = 2 μm. (d)-(e) The electric fields intensities |Ex| and |Ey| with the same parameters of (c), respectively. Here all field intensities are always normalized to the incidence.

Fig. 4
Fig. 4

Normalized (to the incident wavelength) beam focusing parameters versus the output permittivity. (a)-(b) Variations of FWHM of the focal spot and the focal length as a function of the output permittivity for several slit widths at the incident wavelength of λ = 1 μm. (c) Variations of the focal length with the output permittivity for several different wavelengths at the certain normalized slit width (w/λ = 0.3). Here the solid curves in both (b) and (c) are the results of Eq. (1) derived from the physical model proposed in the current study.

Fig. 5
Fig. 5

Simulated phase distributions of electromagnetic field around the single bare subwavelength slit. (a) Phase map of Hz field around the slit with the output permittivity of Ɛd = 14, wherein the situation of free transmission space (Ɛd = 1) is shown by the inset for comparison. (b) Phase map of Ey field around the slit exit interface with the output permittivity of Ɛd = 14, where the vertical white dashed line indicates the axis of x = 0. The incident wavelength is λ = 1 μm and the slit width is w = 300 nm.

Fig. 6
Fig. 6

Proposed physical model for the near-field beam focusing of the single bare subwavelength slit. (a) Retrieved nanograting-like intensity fringes (|Hz| component) formation on the slit-dielectric interface due to the interference of QCW components scattered from the slit edges. The parameters used for the simulations are the same as in Fig. 3(c). (b) Retrieved beam focusing pattern of the magnetic field intensity on the basis of our physical model.

Equations (1)

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f=a (Nd) 2 ε d λ b λ ε d .

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