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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3150">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3150</a>
    [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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6106">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6106</a>
    [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, 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, Jr., "A study of high-index-contrast 90 degree waveguide bend structures," Opt. Express 8, 517-528 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-9-517</a>
    [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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6645">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6645</a>
    [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 onedimensional metallic gratings with subwavelength aperture," Appl. Phys. Lett 85, 1098 (2004).
    [CrossRef]

Appl. Phys. Lett (1)

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

Appl. Phys. Lett. (1)

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

IEEE Trans. Microwave Theory and Tech. (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]

J. Opt. A: Pure Appl. Opt. (1)

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 (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]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824-830 (2003).
[CrossRef]

Nature Materials (1)

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]

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]

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

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, J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Other (4)

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

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

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

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.

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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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