Abstract

We discuss how light can be efficiently bent by nanoscale-width slit waveguides in metals. The discussion is based on accurate numerical solutions of Maxwell’s equations. Our results, using a realistic model for silver at optical wavelengths, show that good right-angle bending transmission can be achieved for wavelengths λ > 600 nm. An approximate stop-band at lower wavelengths also occurs, which can be partly understood in terms of a dispersion curve analysis. The bending efficiency is shown to correlate with a focusing effect at the inner bend corner. Finally, we show that good bending transmission can even arise out of U-turn structures.

© 2005 Optical Society of America

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  1. W. L. Barnes , A. Dereux , and T. W. Ebbesen , “ Surface plasmon subwavelength optics ,” Nature (London)   424 , 824 – 830 ( 2003 ).
    [Crossref]
  2. A. V. Zayats and I. I. Smolyaninov , “ Near field photonics: surface plasmon polaritons and localized surface plasmons ,” J. Opt. A: Pure Appl. Opt.   5 , S16 – S50 ( 2003 ).
    [Crossref]
  3. T. W. Ebbesen , H. J. Lezec , H. F. Ghaemi , T. Thio , and P. Wolff , “ Extraordinary optical transmission through sub-wavelength hole arrays ,” Nature (London)   391 , 667 – 669 ( 1998 ).
    [Crossref]
  4. W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
    [Crossref] [PubMed]
  5. S.-H. Chang , S. K. Gray , and G. C. Schatz , “ Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes n thin metal films ,” Opt. Express   13 , 3150 – 3165 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3150 .
    [Crossref] [PubMed]
  6. S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
    [Crossref] [PubMed]
  7. E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
    [Crossref] [PubMed]
  8. K. Li , M. I. Stockman , and D. J. Bergman , “ Self-similar chain of metal nanospheres as an efficient nanolens ,” Phys. Rev. Lett.   91 , 227402 ( 2003 ).
    [Crossref] [PubMed]
  9. J. A. Porto , F. J. Garcia-Vidal , and J. B. Pendry , “ Transmission resonances on metallic gratings with very narrow slits ,” Phys. Rev. Lett.   83 , 2845 – 2848 ( 1999 ).
    [Crossref]
  10. S. Collin , F. Pardo , R. Teissier , and J. L. Pellouard , “ Strong discontinuities in complex photonic band structure of transmission metallic gratings ,” Phys. Rev. B   63 , 033107 ( 2001 ).
    [Crossref]
  11. J. Bravo-Abad , L. Martin-Moreno , and F. J. Garcia-Vidal , “ Transmission properties of a single metallic slit: From the subwavelength regime to the geometric-optics limit ,” Phys. Rev. E   69 , 026601 ( 2004 ).
    [Crossref]
  12. Y. Xie , A. R. Zakharian , J. V. Moloney , and M. Mansuripur , “ Transmission of light through slit apertures in metal films ,” Opt. Express   12 , 6106 – 6121 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6106 .
    [Crossref] [PubMed]
  13. D.-K. Qing and G. Chen , “ Nanoscale optical waveguides with negative dielectric claddings ,” Phys. Rev. B   71 , 153107 ( 2005 ).
    [Crossref]
  14. S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
    [Crossref] [PubMed]
  15. R. L. Espinola , R. U. Ahmad , F. Pizzuto , M. J. Steel , and R. M. Osgood , “ A study of high-index-contrast 90 degree waveguide bend structures ,” Opt. Express   8 , 517 – 528 ( 2001 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517 .
    [Crossref] [PubMed]
  16. G. Veronis and S. Fan , “ Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides ,” Appl. Phys. Lett.   87 , 131102 ( 2005 ).
    [Crossref]
  17. L. Liu , Z. Han , and S. He , “ Novel surface plasmon waveguide for high integration ,” Opt. Express   13 , 6645 – 6650 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6645 .
    [Crossref] [PubMed]
  18. A. Taflove and S. C. Hagness , Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. ( Artech House, Boston , 2000 ).
  19. P. B. Johnson and R. W. Christy , “ Optical constants of the noble metals ,” Phys. Rev. B   6 , 4370 – 4379 ( 1972 ).
    [Crossref]
  20. S. K. Gray and T. Kupka , “ Propagation of light in metallic nanowire arrays: Finite-difference time-domain results for silver cylinders ,” Phys. Rev. B   68 , 045415 ( 2003 ).
    [Crossref]
  21. T. O. Körner and W. Fichtner , “ Auxiliary differential equation: efficient implementation in the finite-difference time-domain method ,” Opt. Lett.   22 , 1586 ( 1997 ).
    [Crossref]
  22. N. Marcuvitz , Waveguide Handbook ( Peter Peregrinus Ltd., London , 1986 ). First published in MIT Radiation Laboratory Series ( McGraw-Hill, New York , 1951 ).
    [Crossref]
  23. J. J. Campbell and W. R. Jones , “ Symmetrically truncated right-angle corners in parallel plate and rectangular wavegudies ,” IEEE Trans. Microwave Theory and Tech. ,   MTT-16 , 517 ( 1968 ).
    [Crossref]
  24. C. A. Balanis , Advanced Engineering Electromagnetics ( John Wiley & Sons, New York , 1989 ).
  25. E. T. Arakawa , M. W. Williams , R. N. Hamm , and R. H. Ritchie , “ Effect of damping on surface plasmon dispersion ,” Phys. Rev. Lett.   31 , 1127 – 1129 ( 1973 ).
    [Crossref]
  26. P. M. Morse and H. Feshbach , Methods of Theoretical Physics , Part II, 1250 – 1251 ( McGraw-Hill, New York , 1953 )
  27. F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
    [Crossref]
  28. S. S. Akarca-Biyikli , I. Bulu , and E. Ozbay , “ Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture ,” Appl. Phys. Lett   85 , 1098 ( 2004 ).
    [Crossref]

2005 (6)

W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
[Crossref] [PubMed]

S.-H. Chang , S. K. Gray , and G. C. Schatz , “ Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes n thin metal films ,” Opt. Express   13 , 3150 – 3165 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3150 .
[Crossref] [PubMed]

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

D.-K. Qing and G. Chen , “ Nanoscale optical waveguides with negative dielectric claddings ,” Phys. Rev. B   71 , 153107 ( 2005 ).
[Crossref]

G. Veronis and S. Fan , “ Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides ,” Appl. Phys. Lett.   87 , 131102 ( 2005 ).
[Crossref]

L. Liu , Z. Han , and S. He , “ Novel surface plasmon waveguide for high integration ,” Opt. Express   13 , 6645 – 6650 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6645 .
[Crossref] [PubMed]

2004 (3)

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

Y. Xie , A. R. Zakharian , J. V. Moloney , and M. Mansuripur , “ Transmission of light through slit apertures in metal films ,” Opt. Express   12 , 6106 – 6121 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6106 .
[Crossref] [PubMed]

S. S. Akarca-Biyikli , I. Bulu , and E. Ozbay , “ Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture ,” Appl. Phys. Lett   85 , 1098 ( 2004 ).
[Crossref]

2003 (6)

F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
[Crossref]

K. Li , M. I. Stockman , and D. J. Bergman , “ Self-similar chain of metal nanospheres as an efficient nanolens ,” Phys. Rev. Lett.   91 , 227402 ( 2003 ).
[Crossref] [PubMed]

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

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

A. V. Zayats and I. I. Smolyaninov , “ Near field photonics: surface plasmon polaritons and localized surface plasmons ,” J. Opt. A: Pure Appl. Opt.   5 , S16 – S50 ( 2003 ).
[Crossref]

S. K. Gray and T. Kupka , “ Propagation of light in metallic nanowire arrays: Finite-difference time-domain results for silver cylinders ,” Phys. Rev. B   68 , 045415 ( 2003 ).
[Crossref]

2001 (2)

S. Collin , F. Pardo , R. Teissier , and J. L. Pellouard , “ Strong discontinuities in complex photonic band structure of transmission metallic gratings ,” Phys. Rev. B   63 , 033107 ( 2001 ).
[Crossref]

R. L. Espinola , R. U. Ahmad , F. Pizzuto , M. J. Steel , and R. M. Osgood , “ A study of high-index-contrast 90 degree waveguide bend structures ,” Opt. Express   8 , 517 – 528 ( 2001 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517 .
[Crossref] [PubMed]

1999 (1)

J. A. Porto , F. J. Garcia-Vidal , and J. B. Pendry , “ Transmission resonances on metallic gratings with very narrow slits ,” Phys. Rev. Lett.   83 , 2845 – 2848 ( 1999 ).
[Crossref]

1998 (2)

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

S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
[Crossref] [PubMed]

1997 (1)

1973 (1)

E. T. Arakawa , M. W. Williams , R. N. Hamm , and R. H. Ritchie , “ Effect of damping on surface plasmon dispersion ,” Phys. Rev. Lett.   31 , 1127 – 1129 ( 1973 ).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy , “ Optical constants of the noble metals ,” Phys. Rev. B   6 , 4370 – 4379 ( 1972 ).
[Crossref]

1968 (1)

J. J. Campbell and W. R. Jones , “ Symmetrically truncated right-angle corners in parallel plate and rectangular wavegudies ,” IEEE Trans. Microwave Theory and Tech. ,   MTT-16 , 517 ( 1968 ).
[Crossref]

Ahmad, R. U.

Akarca-Biyikli, S. S.

S. S. Akarca-Biyikli , I. Bulu , and E. Ozbay , “ Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture ,” Appl. Phys. Lett   85 , 1098 ( 2004 ).
[Crossref]

Arakawa, E. T.

E. T. Arakawa , M. W. Williams , R. N. Hamm , and R. H. Ritchie , “ Effect of damping on surface plasmon dispersion ,” Phys. Rev. Lett.   31 , 1127 – 1129 ( 1973 ).
[Crossref]

Atwater, H. A.

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

Balanis, C. A.

C. A. Balanis , Advanced Engineering Electromagnetics ( John Wiley & Sons, New York , 1989 ).

Barnes, W. L.

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

Bergman, D. J.

K. Li , M. I. Stockman , and D. J. Bergman , “ Self-similar chain of metal nanospheres as an efficient nanolens ,” Phys. Rev. Lett.   91 , 227402 ( 2003 ).
[Crossref] [PubMed]

Bravo-Abad, J.

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

Brueck, S. R. J.

W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
[Crossref] [PubMed]

Bulu, I.

S. S. Akarca-Biyikli , I. Bulu , and E. Ozbay , “ Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture ,” Appl. Phys. Lett   85 , 1098 ( 2004 ).
[Crossref]

Campbell, J. J.

J. J. Campbell and W. R. Jones , “ Symmetrically truncated right-angle corners in parallel plate and rectangular wavegudies ,” IEEE Trans. Microwave Theory and Tech. ,   MTT-16 , 517 ( 1968 ).
[Crossref]

Chang, S.-H.

Chen, G.

D.-K. Qing and G. Chen , “ Nanoscale optical waveguides with negative dielectric claddings ,” Phys. Rev. B   71 , 153107 ( 2005 ).
[Crossref]

Chow, E.

S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy , “ Optical constants of the noble metals ,” Phys. Rev. B   6 , 4370 – 4379 ( 1972 ).
[Crossref]

Collin, S.

S. Collin , F. Pardo , R. Teissier , and J. L. Pellouard , “ Strong discontinuities in complex photonic band structure of transmission metallic gratings ,” Phys. Rev. B   63 , 033107 ( 2001 ).
[Crossref]

Dereux, A.

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

Duyne, R. P. Van

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

Ebbesen, T. W.

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

F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
[Crossref]

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

Espinola, R. L.

Fan, S.

G. Veronis and S. Fan , “ Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides ,” Appl. Phys. Lett.   87 , 131102 ( 2005 ).
[Crossref]

Fan, W. J.

W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
[Crossref] [PubMed]

Feshbach, H.

P. M. Morse and H. Feshbach , Methods of Theoretical Physics , Part II, 1250 – 1251 ( McGraw-Hill, New York , 1953 )

Fichtner, W.

Garcia-Vidal, F. J.

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

J. A. Porto , F. J. Garcia-Vidal , and J. B. Pendry , “ Transmission resonances on metallic gratings with very narrow slits ,” Phys. Rev. Lett.   83 , 2845 – 2848 ( 1999 ).
[Crossref]

Ghaemi, H. F.

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

Gracia-Vidal, F. J.

F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
[Crossref]

Gray, S. K.

Gunnarsson, L.

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness , Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. ( Artech House, Boston , 2000 ).

Hamm, R. N.

E. T. Arakawa , M. W. Williams , R. N. Hamm , and R. H. Ritchie , “ Effect of damping on surface plasmon dispersion ,” Phys. Rev. Lett.   31 , 1127 – 1129 ( 1973 ).
[Crossref]

Han, Z.

Harel, E.

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

He, S.

Hicks, E. M.

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

Hietala, V.

S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
[Crossref] [PubMed]

Joannopoulos, J. D.

S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy , “ Optical constants of the noble metals ,” Phys. Rev. B   6 , 4370 – 4379 ( 1972 ).
[Crossref]

Jones, W. R.

J. J. Campbell and W. R. Jones , “ Symmetrically truncated right-angle corners in parallel plate and rectangular wavegudies ,” IEEE Trans. Microwave Theory and Tech. ,   MTT-16 , 517 ( 1968 ).
[Crossref]

Kall, M.

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

Kasemo, B.

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

Kik, P. G.

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

Koel, B. E.

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

Körner, T. O.

Kupka, T.

S. K. Gray and T. Kupka , “ Propagation of light in metallic nanowire arrays: Finite-difference time-domain results for silver cylinders ,” Phys. Rev. B   68 , 045415 ( 2003 ).
[Crossref]

Lezec, H. J.

F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
[Crossref]

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

Li, K.

K. Li , M. I. Stockman , and D. J. Bergman , “ Self-similar chain of metal nanospheres as an efficient nanolens ,” Phys. Rev. Lett.   91 , 227402 ( 2003 ).
[Crossref] [PubMed]

Lin, S.-Y.

S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
[Crossref] [PubMed]

Liu, L.

Maier, S. A.

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

Malloy, K. J.

W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
[Crossref] [PubMed]

Mansuripur, M.

Marcuvitz, N.

N. Marcuvitz , Waveguide Handbook ( Peter Peregrinus Ltd., London , 1986 ). First published in MIT Radiation Laboratory Series ( McGraw-Hill, New York , 1951 ).
[Crossref]

Martin-Moreno, L.

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

F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
[Crossref]

Meltzer, S.

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
[Crossref] [PubMed]

Minhas, B.

W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
[Crossref] [PubMed]

Moloney, J. V.

Morse, P. M.

P. M. Morse and H. Feshbach , Methods of Theoretical Physics , Part II, 1250 – 1251 ( McGraw-Hill, New York , 1953 )

Osgood, R. M.

Ozbay, E.

S. S. Akarca-Biyikli , I. Bulu , and E. Ozbay , “ Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture ,” Appl. Phys. Lett   85 , 1098 ( 2004 ).
[Crossref]

Pardo, F.

S. Collin , F. Pardo , R. Teissier , and J. L. Pellouard , “ Strong discontinuities in complex photonic band structure of transmission metallic gratings ,” Phys. Rev. B   63 , 033107 ( 2001 ).
[Crossref]

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J. A. Porto , F. J. Garcia-Vidal , and J. B. Pendry , “ Transmission resonances on metallic gratings with very narrow slits ,” Phys. Rev. Lett.   83 , 2845 – 2848 ( 1999 ).
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D.-K. Qing and G. Chen , “ Nanoscale optical waveguides with negative dielectric claddings ,” Phys. Rev. B   71 , 153107 ( 2005 ).
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S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Materials   2 , 229 – 232 ( 2003 ).
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E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
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E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
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A. V. Zayats and I. I. Smolyaninov , “ Near field photonics: surface plasmon polaritons and localized surface plasmons ,” J. Opt. A: Pure Appl. Opt.   5 , S16 – S50 ( 2003 ).
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E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

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A. Taflove and S. C. Hagness , Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. ( Artech House, Boston , 2000 ).

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S. Collin , F. Pardo , R. Teissier , and J. L. Pellouard , “ Strong discontinuities in complex photonic band structure of transmission metallic gratings ,” Phys. Rev. B   63 , 033107 ( 2001 ).
[Crossref]

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[Crossref] [PubMed]

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E. T. Arakawa , M. W. Williams , R. N. Hamm , and R. H. Ritchie , “ Effect of damping on surface plasmon dispersion ,” Phys. Rev. Lett.   31 , 1127 – 1129 ( 1973 ).
[Crossref]

Wolff, P.

T. W. Ebbesen , H. J. Lezec , H. F. Ghaemi , T. Thio , and P. Wolff , “ Extraordinary optical transmission through sub-wavelength hole arrays ,” Nature (London)   391 , 667 – 669 ( 1998 ).
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G. Veronis and S. Fan , “ Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides ,” Appl. Phys. Lett.   87 , 131102 ( 2005 ).
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A. V. Zayats and I. I. Smolyaninov , “ Near field photonics: surface plasmon polaritons and localized surface plasmons ,” J. Opt. A: Pure Appl. Opt.   5 , S16 – S50 ( 2003 ).
[Crossref]

Nano Letters (1)

E. M. Hicks , S. Zou , G. C. Schatz , K. G. Spears , R. P. Van Duyne , L. Gunnarsson , T. Rindzevlclus , B. Kasemo , and M. Kall , “ Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography ,” Nano Letters   5 , 1065 – 1070 ( 2005 ).
[Crossref] [PubMed]

Nature (London) (2)

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

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[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (4)

S. Collin , F. Pardo , R. Teissier , and J. L. Pellouard , “ Strong discontinuities in complex photonic band structure of transmission metallic gratings ,” Phys. Rev. B   63 , 033107 ( 2001 ).
[Crossref]

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[Crossref]

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[Crossref]

D.-K. Qing and G. Chen , “ Nanoscale optical waveguides with negative dielectric claddings ,” Phys. Rev. B   71 , 153107 ( 2005 ).
[Crossref]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (5)

K. Li , M. I. Stockman , and D. J. Bergman , “ Self-similar chain of metal nanospheres as an efficient nanolens ,” Phys. Rev. Lett.   91 , 227402 ( 2003 ).
[Crossref] [PubMed]

J. A. Porto , F. J. Garcia-Vidal , and J. B. Pendry , “ Transmission resonances on metallic gratings with very narrow slits ,” Phys. Rev. Lett.   83 , 2845 – 2848 ( 1999 ).
[Crossref]

W. J. Fan , S. Zhang , B. Minhas , K. J. Malloy , and S. R. J. Brueck , “ Enhanced infrared transmission through subwavelength coaxial metallic arrays ,” Phys. Rev. Lett.   94 , 033902 ( 2005 ).
[Crossref] [PubMed]

F. J. Gracia-Vidal , H. J. Lezec , T. W. Ebbesen , and L. Martin-Moreno , “ Multiple paths to enhance optical transmission through a single subwavelength silit ,” Phys. Rev. Lett.   90 , 213901 ( 2003 ).
[Crossref]

E. T. Arakawa , M. W. Williams , R. N. Hamm , and R. H. Ritchie , “ Effect of damping on surface plasmon dispersion ,” Phys. Rev. Lett.   31 , 1127 – 1129 ( 1973 ).
[Crossref]

Science (1)

S.-Y. Lin , E. Chow , V. Hietala , P. R. Villeneuve , and J. D. Joannopoulos , “ Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal ,” Science   282 , 274 – 276 ( 1998 ).
[Crossref] [PubMed]

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A. Taflove and S. C. Hagness , Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. ( Artech House, Boston , 2000 ).

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C. A. Balanis , Advanced Engineering Electromagnetics ( John Wiley & Sons, New York , 1989 ).

Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagrams of the systems studied: straight, right-angle bend, and U-turn slit structures.

Fig. 2.
Fig. 2.

(a) The Ag dielectric constant, with the solid curves being our Drude-Lorentz model and the symbols being empirical data [19]. (b) Bending transmittance, Tb , for a PEC right-angle bend with two different slit widths, d. (c) The same as (b) except now with the Drude-Lorentz Ag model.

Fig. 3.
Fig. 3.

Transmittance results for a rounded outer bend wall (red solid curve) are compared with the corresponding transmittance through a straight slit (blue long-dashed curve) and rectangle outer wall (green short-dashed curve.

Fig. 4.
Fig. 4.

(a) Dispersion relation of the lowest, even mode for a d = 100 nm straight slit in silver, with being the real part of the propagation constant. (b) The extinctions coefficient of as a function of wavelength, the imaginary part of propagation constant.

Fig. 5.
Fig. 5.

The square of the magnitude of the (real) electric field for times (a) t, (b) t + 0.4 × 10-15 s, and (c) t + 0.8 × 10-15 s, where t is a time such that the steady state limit has been achieved (see text).

Fig. 6.
Fig. 6.

Transmittance results for U-turn. The outer wall is rounded as in the right-side figure of Fig. 1.

Fig. 7.
Fig. 7.

(1.5MB, video for wave propagation) The square of the magnitude of the (real) electric field propagating in a U-turn waveguide.

Equations (2)

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ε M ( ω ) = ε ω D 2 ω 2 + i γ D ω m = 1 2 g L m ω L m 2 Δ ε ω 2 ω L m 2 + i 2 γ L m ω .
E ( t ) = D ( t ) P D ( t ) m = 1 2 P L m ( t ) ε 0 ε

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