Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles
Optics Express, Vol. 16, Issue 8, pp. 5544-5555 (2008)
http://dx.doi.org/10.1364/OE.16.005544
Acrobat PDF (2555 KB)
Abstract
In this paper we investigate for the first time the near-field optical behavior of two-dimensional Fibonacci plasmonic lattices fabricated by electron-beam lithography on transparent quartz substrates. In particular, by performing near-field optical microscopy measurements and three dimensional Finite Difference Time Domain simulations we demonstrate that near-field coupling of nanoparticle dimers in Fibonacci arrays results in a quasi-periodic lattice of localized nanoparticle plasmons. The possibility to accurately predict the spatial distribution of enhanced localized plasmon modes in quasi-periodic Fibonacci arrays can have a significant impact for the design and fabrication of novel nano-plasmonics devices.
© 2008 Optical Society of America
1. Introduction
1. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Maters. 2, 229–232 (2003). [CrossRef]
7. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000). [CrossRef]
4. E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. VanDuyne, L. Gunnarson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography,” Nano Lett. 51065 (2005). [CrossRef] [PubMed]
1. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Maters. 2, 229–232 (2003). [CrossRef]
7. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000). [CrossRef]
13. H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1762 (2002). [CrossRef]
14. G. Veronis and S. Fan, “Bands and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). [CrossRef]
16. L. Dal Negro and Ning-Ning Feng, “Spectral Gaps and mode localization in Fibonacci chains of metal nanoparticles,” Opt. Express 15, 14396 (2007). [CrossRef] [PubMed]
22. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in Optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987). [CrossRef] [PubMed]
22. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in Optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987). [CrossRef] [PubMed]
23. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994). [CrossRef] [PubMed]
24. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994). [CrossRef]
25. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, L. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003). [CrossRef] [PubMed]
26. M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005). [CrossRef]
2. Design and fabrication of two-dimensional Fibonacci lattices
27. R. Lifshitz, “The square fibonacci tiling,” J. Alloys and Compounds 342, 186 (2002). [CrossRef]
27. R. Lifshitz, “The square fibonacci tiling,” J. Alloys and Compounds 342, 186 (2002). [CrossRef]
29. N. Ferralis, A. W. Szmodis, and R. D. Diehl, “Diffraction from one and twoo dimensional quasicrystalline gratings,” Am. J. Phys. 72, 1241 (2004). [CrossRef]
31. A. Apostolico and V. E. Brimkov, “Fibonacci arrays and their two-dimensional properties,” Theret. Comp. Sci. 237, 263 (200). [CrossRef]
32. C. L. Hynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, N. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle Optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B. 107, 7337 (2003). [CrossRef]
3. Near-field optical characterization of Fibonacci arrays
33. M. Mrejen, A. Isreael, H. Taha, M. Palchan, and A. Lewis, “Near-field characterization of extraordinary optical transmission in sub-wavelength aperture arrays,” Opt. Express , 15, 9129 (2007). [CrossRef] [PubMed]
34. J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B. 64, 045411 (2001). [CrossRef]
33. M. Mrejen, A. Isreael, H. Taha, M. Palchan, and A. Lewis, “Near-field characterization of extraordinary optical transmission in sub-wavelength aperture arrays,” Opt. Express , 15, 9129 (2007). [CrossRef] [PubMed]
35. B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, and L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492 (1997). [CrossRef]
4. Discussion
38. A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antennas Propag. 39, 1518 (1991). [CrossRef]
39. W. H. Pernice, F. P. Payne, and D. F. Gallagher, “Numerical investigation of field enhancement by metal nano-particles using a hybrid FDTD-PSTD algorithm,” Opt. Express 15, 11433 (2007). [CrossRef] [PubMed]
40. S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 20540 (2003). [CrossRef]
4. Summary
Acknowledgments
References and links
1. | S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Maters. 2, 229–232 (2003). [CrossRef] |
2. | R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The Next Chip-Scale Technology,” Materials Today 9, 20–27 (2006). [CrossRef] |
3. | S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics - A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501 (2001). [CrossRef] |
4. | E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. VanDuyne, L. Gunnarson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography,” Nano Lett. 51065 (2005). [CrossRef] [PubMed] |
5. | L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonant wavelength and width,” J. Phys. Chem. B , 1077343 (2003). [CrossRef] |
6. | K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape and dielectric environment,” J. Phys. Chem. B , 107668 (2003). [CrossRef] |
7. | M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B. 62, 356–359 (2000). [CrossRef] |
8. | C. Girard and R. Quidant, “Near-field optical transmittance of metal particle chain waveguides,” Opt. Express 12, 6141 (2004). [CrossRef] [PubMed] |
9. | S. Y. Park and D. Stroud, “Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B. 69, 125418 (2004). [CrossRef] |
10. | U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995). |
11. | P. Clippe, R. Evrard, and A. A. Lucas, “Aggregation effect on the infrared absorption spectrum of small ionic crystals,” Phys. Rev. B 14, 1715 (1976). [CrossRef] |
12. | M. Quinten and U. Kreibig, “Absorption and Elastic-Scattering of Light by Particle Aggregates,” Appl. Opt. 32, 6173 (1993). [CrossRef] [PubMed] |
13. | H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1762 (2002). [CrossRef] |
14. | G. Veronis and S. Fan, “Bands and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). [CrossRef] |
15. | A. Boltasseva and S. I. Bozhevolnyi, “Directional couplers using long-range surface plasmon polariton waveguides,” IEEE JSTQE. 12, 1233 (2006). |
16. | L. Dal Negro and Ning-Ning Feng, “Spectral Gaps and mode localization in Fibonacci chains of metal nanoparticles,” Opt. Express 15, 14396 (2007). [CrossRef] [PubMed] |
17. | C. Janot, Quasicrystals: A Primer (Oxford University Press, NY, 1997) |
18. | A. Rudinger and F. Piechon, “On the multifractal spectrum of the Fibonacci chain,” J. Phys. A.: Math. Gen. 31, 155–164 (1998). [CrossRef] |
19. | E. Macia, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397 (2006). [CrossRef] |
20. | D. Levine and P. J. Steinhardt, “Quasicrystals: definition and structure,” Phys. Rev. B 34, 596–616 (1986). [CrossRef] |
21. | M. Kohmoto, B. Sutherland, and C. Tang, “Critical wave functions and a Cantor-set spectrum of a onedimensional quasicrystal model,” Phys. Rev. B 35, 1020–1033 (1987). [CrossRef] |
22. | M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization in Optics: Quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987). [CrossRef] [PubMed] |
23. | W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994). [CrossRef] [PubMed] |
24. | T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B 50, 4220–4223 (1994). [CrossRef] |
25. | L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, L. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 055501 (2003). [CrossRef] [PubMed] |
26. | M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005). [CrossRef] |
27. | R. Lifshitz, “The square fibonacci tiling,” J. Alloys and Compounds 342, 186 (2002). [CrossRef] |
28. | X. Fu, Y. Liu, B. Cheng, and D. Zheng, “Spectral structure of two-dimensional Fibonacci quasilattices,” Phys. Rev. B 43, 10808 (1991). [CrossRef] |
29. | N. Ferralis, A. W. Szmodis, and R. D. Diehl, “Diffraction from one and twoo dimensional quasicrystalline gratings,” Am. J. Phys. 72, 1241 (2004). [CrossRef] |
30. | L. DalNegro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, in print. |
31. | A. Apostolico and V. E. Brimkov, “Fibonacci arrays and their two-dimensional properties,” Theret. Comp. Sci. 237, 263 (200). [CrossRef] |
32. | C. L. Hynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, N. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle Optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B. 107, 7337 (2003). [CrossRef] |
33. | M. Mrejen, A. Isreael, H. Taha, M. Palchan, and A. Lewis, “Near-field characterization of extraordinary optical transmission in sub-wavelength aperture arrays,” Opt. Express , 15, 9129 (2007). [CrossRef] [PubMed] |
34. | J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B. 64, 045411 (2001). [CrossRef] |
35. | B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, and L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492 (1997). [CrossRef] |
36. | A. Taflove, Computational Electrodynamics:The Finite-Difference Time-Domain Method (Artech House, 1995). |
37. | OmniSim software by Photon Design, Oxford, UK. |
38. | A. C. Cangellaris and D. B. Wright, “Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena,” IEEE Trans. Antennas Propag. 39, 1518 (1991). [CrossRef] |
39. | W. H. Pernice, F. P. Payne, and D. F. Gallagher, “Numerical investigation of field enhancement by metal nano-particles using a hybrid FDTD-PSTD algorithm,” Opt. Express 15, 11433 (2007). [CrossRef] [PubMed] |
40. | S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 20540 (2003). [CrossRef] |
OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
ToC Category:
Optics at Surfaces
History
Original Manuscript: February 11, 2008
Revised Manuscript: March 22, 2008
Manuscript Accepted: March 25, 2008
Published: April 4, 2008
Virtual Issues
Vol. 3, Iss. 5 Virtual Journal for Biomedical Optics
Citation
Ramona Dallapiccola, Ashwin Gopinath, Francesco Stellacci, and Luca Dal Negro, "Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles," Opt. Express 16, 5544-5555 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5544
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References
- . S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Maters. 2, 229-232 (2003). [CrossRef]
- . R. Zia, J. A. Schuller, and M. L. Brongersma, "Plasmonics: The Next Chip-Scale Technology," Maters. Today 9, 20-27 (2006). [CrossRef]
- . S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A Route to Nanoscale Optical Devices," Adv. Mater. 13, 1501 (2001). [CrossRef]
- . E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. VanDuyne, L. Gunnarson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065 (2005). [CrossRef] [PubMed]
- . L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonant wavelength and width," J. Phys. Chem. B 107, 7343 (2003) [CrossRef]
- . K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The optical properties of metal nanoparticles: the influence of size, shape and dielectric environment," J. Phys. Chem. B 107, 668 (2003). [CrossRef]
- . M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, 356-359 (2000). [CrossRef]
- . C. Girard and R. Quidant, "Near-field optical transmittance of metal particle chain waveguides," Opt. Express 12, 6141 (2004). [CrossRef] [PubMed]
- . S. Y. Park and D. Stroud, "Surface-plasmon relations in chains of metallic nanoparticles: an exact quasistatic calculation," Phys. Rev. B. 69, 125418 (2004). [CrossRef]
- . U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).
- .P. Clippe, R. Evrard, and A. A. Lucas, "Aggregation effect on the infrared absorption spectrum of small ionic crystals," Phys. Rev. B 14, 1715 (1976). [CrossRef]
- .M. Quinten, and U. Kreibig, "Absorption and Elastic-Scattering of Light by Particle Aggregates," Appl. Opt. 32, 6173 (1993). [CrossRef] [PubMed]
- . H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762 (2002). [CrossRef]
- . G. Veronis and S. Fan, "Bands and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005). [CrossRef]
- . A. Boltasseva and S. I. Bozhevolnyi, "Directional couplers using long-range surface plasmon polariton waveguides," IEEE JSTQE. 12, 1233 (2006).
- . L. Dal Negro and Ning-Ning Feng, "Spectral Gaps and mode localization in Fibonacci chains of metal nanoparticles," Opt. Express 15, 14396 (2007). [CrossRef] [PubMed]
- . C. Janot, Quasicrystals: A Primer (Oxford University Press, NY, 1997)
- . A. Rudinger and F. Piechon, "On the multifractal spectrum of the Fibonacci chain," J. Phys. A.: Math. Gen. 31, 155-164 (1998). [CrossRef]
- . E. Macia, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397 (2006). [CrossRef]
- . D. Levine and P. J. Steinhardt, "Quasicrystals: definition and structure," Phys. Rev. B 34, 596-616 (1986). [CrossRef]
- . M. Kohmoto, B. Sutherland, and C. Tang, "Critical wave functions and a Cantor-set spectrum of a one-dimensional quasicrystal model," Phys. Rev. B 35, 1020-1033 (1987). [CrossRef]
- . M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization in Optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987). [CrossRef] [PubMed]
- . W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633-636 (1994). [CrossRef] [PubMed]
- . T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, "Photonic dispersion relation in a one-dimensional quasicrystal," Phys. Rev. B 50, 4220-4223 (1994). [CrossRef]
- . L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, L. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003). [CrossRef] [PubMed]
- . M. Ghulinyan, C. J. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, "Light pulse propagation in Fibonacci quasicrystals," Phys. Rev. B 71, 094204 (2005). [CrossRef]
- . R. Lifshitz, "The square fibonacci tiling," J. Alloys and Compounds 342, 186 (2002). [CrossRef]
- . X. Fu,Y. Liu, B. Cheng, and D. Zheng, "Spectral structure of two-dimensional Fibonacci quasilattices," Phys. Rev. B 43, 10808 (1991). [CrossRef]
- . N. Ferralis, A. W. Szmodis, and R. D. Diehl, "Diffraction from one and twoo dimensional quasicrystalline gratings," Am. J. Phys. 72, 1241 (2004). [CrossRef]
- . L. Dal Negro, N. N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A, in print.
- . A. Apostolico and V. E. Brimkov, "Fibonacci arrays and their two-dimensional properties," Theret. Comp. Sci. 237, 263 (200). [CrossRef]
- . C. L. Hynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, N. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, "Nanoparticle Optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays," J. Phys. Chem. B. 107, 7337 (2003). [CrossRef]
- . M. Mrejen, A. Isreael, H. Taha, M. Palchan, and A. Lewis, "Near-field characterization of extraordinary optical transmission in sub-wavelength aperture arrays," Opt. Express 15, 9129 (2007). [CrossRef] [PubMed]
- . J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B. 64, 045411 (2001). [CrossRef]
- . B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, and L. Novotny, "Facts and artifacts in near-field optical microscopy," J. Appl. Phys. 81, 2492 (1997). [CrossRef]
- . A. Taflove, Computational Electrodynamics:The Finite-Difference Time-Domain Method (Artech House, 1995).
- . OmniSim software by Photon Design, Oxford, UK.
- . A. C. Cangellaris and D. B. Wright, "Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena," IEEE Trans. Antennas Propag. 39, 1518 (1991). [CrossRef]
- . W. H. Pernice, F. P. Payne, and D. F. Gallagher, "Numerical investigation of field enhancement by metal nano-particles using a hybrid FDTD-PSTD algorithm," Opt. Express 15, 11433 (2007). [CrossRef] [PubMed]
- .S. A. Maier, P. G. Kik, and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 20540 (2003). [CrossRef]
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