Abstract

The reflection of the radially polarized surface wave on a metal wire at an abrupt end is derived. This theory allows for straightforward calculation of the reflection coefficient, including the phase and the amplitude, which will prove useful to the many applications in nanoplasmonics and terahertz spectroscopy. The theory shows excellent quantitative agreement with past comprehensive numerical simulations for small wires and for predicting the minima in reflection for larger wires. Using this theory, the wavelength dependent reflection is calculated for gold rods of diameter 10 nm, 26 nm and 85 nm, from which the Fabry-Perot resonance wavelengths are found. The Fabry-Perot resonances show good agreement with experimentally measured surface plasmon resonances in nanorods. This demonstrates the predictive ability of the theory for applications involving widely-used nanorods, optical antennas and plasmonic resonators.

© 2009 Optical Society of America

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References

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  1. A. Sommerfeld, "Ueber die Fortpflanzung elektrodynamischer Wellen lngs eines Drahtes," Annalen der Physik und Chemie 303, 233-290 (1899). URL http://dx.doi.org/10.1002/andp.18993030202.
    [CrossRef]
  2. G. Goubau, "SurfaceWaves and Their Application to Transmission Lines," J. Appl. Phys. 21, 1119-1128 (1950). URL http://link.aip.org/link/?JAP/21/1119/1.
    [CrossRef]
  3. K. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004). URL http://dx.doi.org/0.1038/nature03040.
    [CrossRef] [PubMed]
  4. M. Wächter, M. Nagel, and H. Kurz, "Frequency-dependent characterization of THz Sommerfeld wave propagation on single-wires," Opt. Express 13, 10815-10822 (2005). URL http://www.opticsexpress.org/ abstract.cfm?URI=oe-13-26-10815.
    [CrossRef] [PubMed]
  5. M. Walther, M. R. Freeman, and F. A. Hegmann, "Metal-wire terahertz time-domain spectroscopy," Appl. Phys. Lett. 87, 261107 (2005). URL http://link.aip.org/link/?APL/87/261107/1.
    [CrossRef]
  6. Q. Cao and J. Jahns, "Azimuthally polarized surface plasmons as effective terahertz waveguides," Opt. Express 13, 511-518 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI= oe-13-2-511.
    [CrossRef] [PubMed]
  7. K. Wang and D. M. Mittleman, "Dispersion of Surface Plasmon Polaritons on Metal Wires in the Terahertz Frequency Range," Phys. Rev. Lett. 96, 157401 (2006). URL http://link.aps.org/abstract/PRL/ v96/e157401.
    [CrossRef] [PubMed]
  8. J. A. Deibel, N. Berndsen, K. Wang, D. M. Mittleman, N. C. van der Valk, and P. C. M. Planken, "Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires," Opt. Express 14, 8772-8778 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI= oe-14-19-8772.
    [CrossRef] [PubMed]
  9. S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, "Terahertz Surface Plasmon-Polariton Propagation and Focusing on Periodically Corrugated Metal Wires," Phys. Rev. Lett. 97, 176805 (2006). URL http://link.aps.org/abstract/PRL/v97/e176805.
    [CrossRef] [PubMed]
  10. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver Nanowires as Surface Plasmon Resonators," Phys. Rev. Lett. 95, 257 - 403 (2005). URL http:// link.aps.org/doi/10.1103/PhysRevLett.95.257403.
    [CrossRef]
  11. P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005). http://www.sciencemag.org/cgi/reprint/308/5728/1607pdf, URL http://www.sciencemag.org/cgi/content/abstract/308/5728/1607.
    [CrossRef] [PubMed]
  12. L. Novotny, "Effective Wavelength Scaling for Optical Antennas," Phys. Rev. Lett. 98, 266802 (2007). URL http://link.aps.org/abstract/PRL/v98/e266802.
    [CrossRef] [PubMed]
  13. T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B 77, 115420 (2008). URL http://link.aps.org/abstract/ PRB/v77/e115420.
    [CrossRef]
  14. E. S. Barnard, J. S. White, A. Chandran, and M. L. Brongersma, "Spectral properties of plasmonic resonator antennas," Opt. Express 16,16529-16537 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-21-16529.
    [CrossRef] [PubMed]
  15. J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, "Fabry-Perot Resonances in One-Dimensional Plasmonic Nanostructures," Nano Lett. 9, 2372-2377 (2009). URL http://dx.doi.org/10.1021/nl900900r.
    [CrossRef] [PubMed]
  16. A. L. Oldenburg, M. N. Hansen, D. A. Zweifel, A. Wei, and S. A. Boppart, "Plasmon-resonant gold nanorods as low backscattering albedo contrast agents for optical coherence tomography," Opt. Express 14, 6724-6738 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-15-6724.
    [CrossRef] [PubMed]
  17. E. K. Payne, K. L. Shuford, S. Park, G. C. Schatz, and C. A. Mirkin, "Multipole Plasmon Resonances in Gold Nanorods," J. Phys. Chem. B 110, 2150-2154 (2006). URL http://dx.doi.org/10.1021/jp056606x.
    [CrossRef] [PubMed]
  18. S. B. Chaney, S. Shanmukh, R. A. Dluhy, and Y.-P. Zhao, "Aligned silver nanorod arrays produce high sensitivity surface-enhanced Raman spectroscopy substrates," Appl. Phys. Lett. 87, 031908 (2005). URL http://link.aip.org/link/?APL/87/031908/1.
    [CrossRef]
  19. H. V. Chu, Y. Liu, Y. Huang, and Y. Zhao, "A high sensitive fiber SERS probe based on silver nanorod arrays," Opt. Express 15, 12230-12239 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-19-12230.
    [CrossRef] [PubMed]
  20. K. C. Toussaint, M. Liu, M. Pelton, J. Pesic, M. J. Guffey, P. Guyot-Sionnest, and N. F. Scherer, "Plasmonresonance-based optical trapping of single and multiple Au nanoparticles," Opt. Express 15, 12017-12029 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-19-12017.
    [CrossRef] [PubMed]
  21. F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, "Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial," Phys. Rev. B 79, 075103 (2009). URL http://link.aps.org/abstract/PRB/v79/e075103.
    [CrossRef]
  22. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "Lambda/4 Resonance of an Optical Monopole Antenna Probed by Single Molecule Fluorescence," Nano Lett. 7, 28-33 (2006). URL http://dx.doi.org/10.1021/nl061726h.
    [CrossRef]
  23. X.-W. Chen, V. Sandoghdar, and M. Agio, "Highly efficient interfacing of guided plasmons and photons in nanowires," Nano Lett. ASAP (2009). URL http://pubs.acs.org/doi/full/10.1021/nl9019424.
    [CrossRef] [PubMed]
  24. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, "Generation of single optical plasmons in metallic nanowires coupled to quantum dots," Nature 450, 402-406 (2007). URL http://dx.doi.org/10.1038/nature06230.
    [CrossRef] [PubMed]
  25. A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. de Leon Snapp, A. V. Akimov, M.-H. Jo, M. D. Lukin, and H. Park, "Near-field electrical detection of optical plasmons and single-plasmon sources," Nat. Phys. 5, 475-479 (2009). URL http://dx.doi.org/10.1038/nphys1284.
    [CrossRef]
  26. R. Gordon, "Vectorial method for calculating the Fresnel reflection of surface plasmon polaritons," Phys. Rev. B 74, 153417 (2006). URL http://link.aps.org/abstract/PRB/v74/e153417.
    [CrossRef]
  27. R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Phys. Rev. B 73, 153405 (2006). URL http://link.aps.org/abstract/PRB/v73/e153405.
    [CrossRef]
  28. R. Gordon, "Near-field interference in a subwavelength double slit in a perfect conductor," J. Opt. A 8, L1-L3 (2006). URL http://stacks.iop.org/1464-4258/8/L1.
    [CrossRef]
  29. R. Gordon, "Angle-dependent optical transmission through a narrow slit in a thick metal film," Phys. Rev. B 75, 193401 (2007). URL http://link.aps.org/abstract/PRB/v75/e193401.
    [CrossRef]
  30. P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972). URL http://link.aps.org/doi/10.1103/PhysRevB.6.4370.
    [CrossRef]
  31. S. J. Al-Bader and H. A. Jamid, "Diffraction of surface plasmon modes on abruptly terminated metallic nanowires," Phys. Rev. B 76, 235410 (2007). URL http://link.aps.org/abstract/PRB/v76/e235410.
    [CrossRef]
  32. R. Pregla, Analysis of Electromagnetic Fields and Waves: The Method of Lines (John Wiley and Sons Ltd., West Sussex (England), 2008).
    [CrossRef]
  33. A.-S. A.-M. Al-Sherbini, "Thermal instability of gold nanorods in micellar solution of water/glycerol mixtures," Colloids and Surfaces A 246, 61-69 (2004). URL 10.1016/j.colsurfa.2004.06.038.
    [CrossRef]
  34. J. Pérez-Juste, L. Liz-Marzán, S. Carnie, D. Chan, and P. Mulvaney, "Electric-Field-Directed Growth of Gold Nanorods in Aqueous Surfactant Solutions," Advanced Functional Materials 14, 571-579 (2004). URL http://dx.doi.org/10.1002/adfm.200305068.
    [CrossRef]
  35. K.-S. Lee and M. A. El-Sayed, "Dependence of the Enhanced Optical Scattering Efficiency Relative to That of Absorption for Gold Metal Nanorods on Aspect Ratio, Size, End-Cap Shape, and Medium Refractive Index," J. Phys. Chem. B 109, 20,331-20,338 (2005). URL http://dx.doi.org/10.1021/jp054385p.
  36. S. W. Prescott and P. Mulvaney, "Gold nanorod extinction spectra," J. Appl. Phys. 99, 123504 (2006). URL http://link.aip.org/link/?JAP/99/123504/1.
    [CrossRef]
  37. C. Ungureanu, R. G. Rayavarapu, S. Manohar, and T. G. van Leeuwen, "Discrete dipole approximation simulations of gold nanorod optical properties: Choice of input parameters and comparison with experiment," J. Appl. Phys. 105, 102032 (2009). URL http://link.aip.org/link/?JAP/105/102032/1.
    [CrossRef]
  38. Q. Min and R. Gordon, "Squeezing light into subwavelength metallic tapers: single mode matching method," J. Nanophotonics 3, 033505 (2009). URL http://link.aip.org/link/?JNP/3/033505/1.
    [CrossRef]
  39. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, "Nanowire Plasmon Excitation by Adiabatic Mode Transformation," Phys. Rev. Lett. 102, 203904 (2009). URL http://link.aps.org/abstract/PRL/v102/e203904.r
    [CrossRef] [PubMed]

Other

A. Sommerfeld, "Ueber die Fortpflanzung elektrodynamischer Wellen lngs eines Drahtes," Annalen der Physik und Chemie 303, 233-290 (1899). URL http://dx.doi.org/10.1002/andp.18993030202.
[CrossRef]

G. Goubau, "SurfaceWaves and Their Application to Transmission Lines," J. Appl. Phys. 21, 1119-1128 (1950). URL http://link.aip.org/link/?JAP/21/1119/1.
[CrossRef]

K. Wang and D. M. Mittleman, "Metal wires for terahertz wave guiding," Nature 432, 376-379 (2004). URL http://dx.doi.org/0.1038/nature03040.
[CrossRef] [PubMed]

M. Wächter, M. Nagel, and H. Kurz, "Frequency-dependent characterization of THz Sommerfeld wave propagation on single-wires," Opt. Express 13, 10815-10822 (2005). URL http://www.opticsexpress.org/ abstract.cfm?URI=oe-13-26-10815.
[CrossRef] [PubMed]

M. Walther, M. R. Freeman, and F. A. Hegmann, "Metal-wire terahertz time-domain spectroscopy," Appl. Phys. Lett. 87, 261107 (2005). URL http://link.aip.org/link/?APL/87/261107/1.
[CrossRef]

Q. Cao and J. Jahns, "Azimuthally polarized surface plasmons as effective terahertz waveguides," Opt. Express 13, 511-518 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI= oe-13-2-511.
[CrossRef] [PubMed]

K. Wang and D. M. Mittleman, "Dispersion of Surface Plasmon Polaritons on Metal Wires in the Terahertz Frequency Range," Phys. Rev. Lett. 96, 157401 (2006). URL http://link.aps.org/abstract/PRL/ v96/e157401.
[CrossRef] [PubMed]

J. A. Deibel, N. Berndsen, K. Wang, D. M. Mittleman, N. C. van der Valk, and P. C. M. Planken, "Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires," Opt. Express 14, 8772-8778 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI= oe-14-19-8772.
[CrossRef] [PubMed]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, "Terahertz Surface Plasmon-Polariton Propagation and Focusing on Periodically Corrugated Metal Wires," Phys. Rev. Lett. 97, 176805 (2006). URL http://link.aps.org/abstract/PRL/v97/e176805.
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver Nanowires as Surface Plasmon Resonators," Phys. Rev. Lett. 95, 257 - 403 (2005). URL http:// link.aps.org/doi/10.1103/PhysRevLett.95.257403.
[CrossRef]

P. Muhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant Optical Antennas," Science 308, 1607-1609 (2005). http://www.sciencemag.org/cgi/reprint/308/5728/1607pdf, URL http://www.sciencemag.org/cgi/content/abstract/308/5728/1607.
[CrossRef] [PubMed]

L. Novotny, "Effective Wavelength Scaling for Optical Antennas," Phys. Rev. Lett. 98, 266802 (2007). URL http://link.aps.org/abstract/PRL/v98/e266802.
[CrossRef] [PubMed]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, "Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration," Phys. Rev. B 77, 115420 (2008). URL http://link.aps.org/abstract/ PRB/v77/e115420.
[CrossRef]

E. S. Barnard, J. S. White, A. Chandran, and M. L. Brongersma, "Spectral properties of plasmonic resonator antennas," Opt. Express 16,16529-16537 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-21-16529.
[CrossRef] [PubMed]

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, "Fabry-Perot Resonances in One-Dimensional Plasmonic Nanostructures," Nano Lett. 9, 2372-2377 (2009). URL http://dx.doi.org/10.1021/nl900900r.
[CrossRef] [PubMed]

A. L. Oldenburg, M. N. Hansen, D. A. Zweifel, A. Wei, and S. A. Boppart, "Plasmon-resonant gold nanorods as low backscattering albedo contrast agents for optical coherence tomography," Opt. Express 14, 6724-6738 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-15-6724.
[CrossRef] [PubMed]

E. K. Payne, K. L. Shuford, S. Park, G. C. Schatz, and C. A. Mirkin, "Multipole Plasmon Resonances in Gold Nanorods," J. Phys. Chem. B 110, 2150-2154 (2006). URL http://dx.doi.org/10.1021/jp056606x.
[CrossRef] [PubMed]

S. B. Chaney, S. Shanmukh, R. A. Dluhy, and Y.-P. Zhao, "Aligned silver nanorod arrays produce high sensitivity surface-enhanced Raman spectroscopy substrates," Appl. Phys. Lett. 87, 031908 (2005). URL http://link.aip.org/link/?APL/87/031908/1.
[CrossRef]

H. V. Chu, Y. Liu, Y. Huang, and Y. Zhao, "A high sensitive fiber SERS probe based on silver nanorod arrays," Opt. Express 15, 12230-12239 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-19-12230.
[CrossRef] [PubMed]

K. C. Toussaint, M. Liu, M. Pelton, J. Pesic, M. J. Guffey, P. Guyot-Sionnest, and N. F. Scherer, "Plasmonresonance-based optical trapping of single and multiple Au nanoparticles," Opt. Express 15, 12017-12029 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-19-12017.
[CrossRef] [PubMed]

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, "Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial," Phys. Rev. B 79, 075103 (2009). URL http://link.aps.org/abstract/PRB/v79/e075103.
[CrossRef]

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, "Lambda/4 Resonance of an Optical Monopole Antenna Probed by Single Molecule Fluorescence," Nano Lett. 7, 28-33 (2006). URL http://dx.doi.org/10.1021/nl061726h.
[CrossRef]

X.-W. Chen, V. Sandoghdar, and M. Agio, "Highly efficient interfacing of guided plasmons and photons in nanowires," Nano Lett. ASAP (2009). URL http://pubs.acs.org/doi/full/10.1021/nl9019424.
[CrossRef] [PubMed]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, "Generation of single optical plasmons in metallic nanowires coupled to quantum dots," Nature 450, 402-406 (2007). URL http://dx.doi.org/10.1038/nature06230.
[CrossRef] [PubMed]

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. de Leon Snapp, A. V. Akimov, M.-H. Jo, M. D. Lukin, and H. Park, "Near-field electrical detection of optical plasmons and single-plasmon sources," Nat. Phys. 5, 475-479 (2009). URL http://dx.doi.org/10.1038/nphys1284.
[CrossRef]

R. Gordon, "Vectorial method for calculating the Fresnel reflection of surface plasmon polaritons," Phys. Rev. B 74, 153417 (2006). URL http://link.aps.org/abstract/PRB/v74/e153417.
[CrossRef]

R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Phys. Rev. B 73, 153405 (2006). URL http://link.aps.org/abstract/PRB/v73/e153405.
[CrossRef]

R. Gordon, "Near-field interference in a subwavelength double slit in a perfect conductor," J. Opt. A 8, L1-L3 (2006). URL http://stacks.iop.org/1464-4258/8/L1.
[CrossRef]

R. Gordon, "Angle-dependent optical transmission through a narrow slit in a thick metal film," Phys. Rev. B 75, 193401 (2007). URL http://link.aps.org/abstract/PRB/v75/e193401.
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972). URL http://link.aps.org/doi/10.1103/PhysRevB.6.4370.
[CrossRef]

S. J. Al-Bader and H. A. Jamid, "Diffraction of surface plasmon modes on abruptly terminated metallic nanowires," Phys. Rev. B 76, 235410 (2007). URL http://link.aps.org/abstract/PRB/v76/e235410.
[CrossRef]

R. Pregla, Analysis of Electromagnetic Fields and Waves: The Method of Lines (John Wiley and Sons Ltd., West Sussex (England), 2008).
[CrossRef]

A.-S. A.-M. Al-Sherbini, "Thermal instability of gold nanorods in micellar solution of water/glycerol mixtures," Colloids and Surfaces A 246, 61-69 (2004). URL 10.1016/j.colsurfa.2004.06.038.
[CrossRef]

J. Pérez-Juste, L. Liz-Marzán, S. Carnie, D. Chan, and P. Mulvaney, "Electric-Field-Directed Growth of Gold Nanorods in Aqueous Surfactant Solutions," Advanced Functional Materials 14, 571-579 (2004). URL http://dx.doi.org/10.1002/adfm.200305068.
[CrossRef]

K.-S. Lee and M. A. El-Sayed, "Dependence of the Enhanced Optical Scattering Efficiency Relative to That of Absorption for Gold Metal Nanorods on Aspect Ratio, Size, End-Cap Shape, and Medium Refractive Index," J. Phys. Chem. B 109, 20,331-20,338 (2005). URL http://dx.doi.org/10.1021/jp054385p.

S. W. Prescott and P. Mulvaney, "Gold nanorod extinction spectra," J. Appl. Phys. 99, 123504 (2006). URL http://link.aip.org/link/?JAP/99/123504/1.
[CrossRef]

C. Ungureanu, R. G. Rayavarapu, S. Manohar, and T. G. van Leeuwen, "Discrete dipole approximation simulations of gold nanorod optical properties: Choice of input parameters and comparison with experiment," J. Appl. Phys. 105, 102032 (2009). URL http://link.aip.org/link/?JAP/105/102032/1.
[CrossRef]

Q. Min and R. Gordon, "Squeezing light into subwavelength metallic tapers: single mode matching method," J. Nanophotonics 3, 033505 (2009). URL http://link.aip.org/link/?JNP/3/033505/1.
[CrossRef]

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, "Nanowire Plasmon Excitation by Adiabatic Mode Transformation," Phys. Rev. Lett. 102, 203904 (2009). URL http://link.aps.org/abstract/PRL/v102/e203904.r
[CrossRef] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Reflection amplitude, R=|r|2, for the surface wave reflecting at a terminated wire (εm =-16) in free-space for free-space wavelength of 632.8 nm, as calculated from Eq. (10). Dashed line extracted from Fig. 4 of Ref [31], where a comprehensive numerical simulation of Maxwell’s equations was used for similar parameters (except εm =-16+0.53i). (b) Reflection phase for the same conditions as (a).

Fig. 2.
Fig. 2.

Reflection (a) amplitude and (b) phase of abruptly terminated gold nanowires in water for diameters of 10 nm (blue), 26 nm (red) and 85 nm (black).

Fig. 3.
Fig. 3.

Comparison between calculated Fabry-Perot resonances and experimentally measured plasmon resonances. (a) 85 nm diameter nanorods of varying length. Solid lines show resonances calculated using Eq. (12) for m=1 (blue), 2 (red), 3 (green) and 4 (black). Data points are experimentally measured values attributed to those resonances [17]. (b) 10 nm (blue) and 26 nm (red) diameter nanorods of various lengths. Data points are experimentally measured values for diameters of 10 nm (blue) [33] and 26 nm (red) [34].

Equations (12)

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

Eρ (ρ,ϕ,z=0)(1+r)βωε0εr(ρ)F(ρ)
Hϕ (ρ,ϕ,z=0)(1r)F(ρ)
F(ρ)={I1(pmρ)I1(pma)ifρ<aK1(pdρ)K1(pda)ifρ>a
K0(pda)I1(pma)K1(pda)I0(pma)=εdpmεmpd.
Eρ(ρ,ϕ,z=0+)=0t(k)k02εdk2ωε0εdJ1(kr)dk
Hϕ(ρ,ϕ,z=0+)=0t(k)J1(kr)dk
t(k)=(1+r)kaβεdωε0k02εdk2[A1(k)+A2(k)]
A1(k)=pmI2(pma)J1(ka)+kI1(pma)J2(ka)I1(pma)εm(k2+pm2)
A2(k)=pdK2(pda)J1(ka)kK1(pda)J2(ka)K1(pda)εd(k2+pd2).
r=1G1+G
G=02βεdkk02εdk2[A1(k)+A2(k)]2dkI1(pma)2I0(pma)I2(pma)εmI1(pma)2K1(pda)2K0(pda)K2(pda)εdK1(pda)2.
l=mπϕβ

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