Dispersive contour-path algorithm for the two-dimensional finite-difference time-domain method
Optics Express, Vol. 16, Issue 10, pp. 7397-7406 (2008)
http://dx.doi.org/10.1364/OE.16.007397
Acrobat PDF (150 KB)
Abstract
We have extended the contour-path effective-permittivity (CP-EP) finite-difference time-domain (FDTD) algorithm by A. Mohammadi et al., Opt. Express 13, 10367 (2005), to linear dispersive materials using the Z-transform formalism. We test our method against staircasing and the exact solution for plasmon spectra of metal nanoparticles. We show that the dispersive contour-path (DCP) approach yields better results than staircasing, especially for the cancellation of spurious resonances.
© 2008 Optical Society of America
1. Introduction
2. J.-Y. Lee and N.-H. Myung, “Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces,” Microwave Opt. Technol. Lett. 23, 245–249 (1999). [CrossRef]
3. A. Ditkowski, K. Dridi, and J. S. Hesthaven, “Convergent Cartesian grid methods for Maxwell’s equations in complex geometries,” J. Comput. Phys. 170, 39–80 (2001). [CrossRef]
5. K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, “Staircase-free finite-difference time-domain formulation for general materials in complex geometries,” IEEE Trans. Antennas Propag. 49, 749–756 (2001). [CrossRef]
6. T. I. Kosmanis and T. D. Tsiboukis, “A systematic and topologically stable conformal finite-difference time-domain algorithm for modeling curved dielectric interfaces in three dimensions,” IEEE Trans. Microwave Theory Tech. 51, 839–847 (2003). [CrossRef]
7. J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, “A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media,” IEEE Trans. Antennas Propag. 51, 1760–1770 (2003). [CrossRef]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
9. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-20-2972. [CrossRef] [PubMed]
2. J.-Y. Lee and N.-H. Myung, “Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces,” Microwave Opt. Technol. Lett. 23, 245–249 (1999). [CrossRef]
7. J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, “A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media,” IEEE Trans. Antennas Propag. 51, 1760–1770 (2003). [CrossRef]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
9. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-20-2972. [CrossRef] [PubMed]
10. W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mat. Today 9, 28–35 (2006). [CrossRef]
11. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007). [CrossRef]
12. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]
13. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005). [CrossRef]
14. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed]
15. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mat. Today 9, 20–27 (2006). [CrossRef]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
17. Y. Zhao and Y. Hao, “Finite-difference time-domain study of guided modes in nano-plasmonic waveguides,” IEEE Trans. Antennas Propag. 55, 3070–3077 (2007). [CrossRef]
18. A. Deinega and I. Valuev, “Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method,” Opt. Lett. 32, 3429–3431 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3429. [CrossRef] [PubMed]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
17. Y. Zhao and Y. Hao, “Finite-difference time-domain study of guided modes in nano-plasmonic waveguides,” IEEE Trans. Antennas Propag. 55, 3070–3077 (2007). [CrossRef]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
18. A. Deinega and I. Valuev, “Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method,” Opt. Lett. 32, 3429–3431 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3429. [CrossRef] [PubMed]
2. J.-Y. Lee and N.-H. Myung, “Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces,” Microwave Opt. Technol. Lett. 23, 245–249 (1999). [CrossRef]
7. J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, “A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media,” IEEE Trans. Antennas Propag. 51, 1760–1770 (2003). [CrossRef]
9. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-20-2972. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
19. D. M. Sullivan, “Z-transform theory and the FDTD method,” IEEE Trans. Antennas Propag. 44, 28–34 (1996). [CrossRef]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
2. Dispersive contour-path method
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
3. Numerical tests and discussion
22. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]
23. C. Oubre and P. Nordlander, “Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method,” J. Phys. Chem. B 108, 17740–17747 (2004). [CrossRef]
24. C. Oubre and P. Nordlander, “Finite-difference time-domain studies of the optical properties of nanoshell dimers,” J. Phys. Chem. B 109, 10042–10051 (2005). [CrossRef]
26. 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, 1518–1524 (1991). [CrossRef]
27. CRC Handbook of Chemistry and Physics, 87th ed., D. R. Lide, ed. (CRC-Press, 2006) http://www.hbcpnetbase.com.
28. A. Vial, A.-S. Grimault, D. Macías, D. Biarchesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005). [CrossRef]
29. O. Ramadan and A. Y. Oztoprak, “Z-transform implementation of the perfectly matched layer for truncating FDTD domains,” IEEE Microwave Wirel. Compon. Lett. 13, 402–404 (2003). [CrossRef]
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
22. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]
30. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005). [CrossRef] [PubMed]
31. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]
16. A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
4. Conclusions
8. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
19. D. M. Sullivan, “Z-transform theory and the FDTD method,” IEEE Trans. Antennas Propag. 44, 28–34 (1996). [CrossRef]
Acknowledgments
References and links
1. | A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005). |
2. | J.-Y. Lee and N.-H. Myung, “Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces,” Microwave Opt. Technol. Lett. 23, 245–249 (1999). [CrossRef] |
3. | A. Ditkowski, K. Dridi, and J. S. Hesthaven, “Convergent Cartesian grid methods for Maxwell’s equations in complex geometries,” J. Comput. Phys. 170, 39–80 (2001). [CrossRef] |
4. | W. Yu and R. Mittra, “A conformal finite difference time domain technique for modeling curved dielectric surfaces,” Microwave Opt. Technol. Lett. 11, 25–27 (2001). |
5. | K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, “Staircase-free finite-difference time-domain formulation for general materials in complex geometries,” IEEE Trans. Antennas Propag. 49, 749–756 (2001). [CrossRef] |
6. | T. I. Kosmanis and T. D. Tsiboukis, “A systematic and topologically stable conformal finite-difference time-domain algorithm for modeling curved dielectric interfaces in three dimensions,” IEEE Trans. Microwave Theory Tech. 51, 839–847 (2003). [CrossRef] |
7. | J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, “A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media,” IEEE Trans. Antennas Propag. 51, 1760–1770 (2003). [CrossRef] |
8. | A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367–10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed] |
9. | A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-20-2972. [CrossRef] [PubMed] |
10. | W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mat. Today 9, 28–35 (2006). [CrossRef] |
11. | V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007). [CrossRef] |
12. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed] |
13. | S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005). [CrossRef] |
14. | E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed] |
15. | R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mat. Today 9, 20–27 (2006). [CrossRef] |
16. | A. Mohammadi and M. Agio, “Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces,” Opt. Express 14, 11330–11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed] |
17. | Y. Zhao and Y. Hao, “Finite-difference time-domain study of guided modes in nano-plasmonic waveguides,” IEEE Trans. Antennas Propag. 55, 3070–3077 (2007). [CrossRef] |
18. | A. Deinega and I. Valuev, “Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method,” Opt. Lett. 32, 3429–3431 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3429. [CrossRef] [PubMed] |
19. | D. M. Sullivan, “Z-transform theory and the FDTD method,” IEEE Trans. Antennas Propag. 44, 28–34 (1996). [CrossRef] |
20. | M. Born and E. Wold, Principles of Optics, 7th ed. (Cambridge U. Press, 1999). |
21. | C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983). |
22. | H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef] |
23. | C. Oubre and P. Nordlander, “Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method,” J. Phys. Chem. B 108, 17740–17747 (2004). [CrossRef] |
24. | C. Oubre and P. Nordlander, “Finite-difference time-domain studies of the optical properties of nanoshell dimers,” J. Phys. Chem. B 109, 10042–10051 (2005). [CrossRef] |
25. | F. Kaminski, V. Sandoghdar, and M. Agio, “Finite-difference time-domain modeling of decay rates in the near field of metal nanostructures,” J. Comput. Theor. Nanosci. 4, 635–643 (2007). |
26. | 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, 1518–1524 (1991). [CrossRef] |
27. | CRC Handbook of Chemistry and Physics, 87th ed., D. R. Lide, ed. (CRC-Press, 2006) http://www.hbcpnetbase.com. |
28. | A. Vial, A.-S. Grimault, D. Macías, D. Biarchesi, and M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005). [CrossRef] |
29. | O. Ramadan and A. Y. Oztoprak, “Z-transform implementation of the perfectly matched layer for truncating FDTD domains,” IEEE Microwave Wirel. Compon. Lett. 13, 402–404 (2003). [CrossRef] |
30. | P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005). [CrossRef] [PubMed] |
31. | P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed] |
32. | Ch. Hafner, Post-Modern Electromagnetics: Using Intelligent MaXwell Solvers, (John Wiley & Sons, 1999). |
OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.0130) Integrated optics : Integrated optics
(290.0290) Scattering : Scattering
ToC Category:
Numerical Methods
History
Original Manuscript: March 20, 2008
Revised Manuscript: April 23, 2008
Manuscript Accepted: April 27, 2008
Published: May 6, 2008
Citation
Ahmad Mohammadi, Tahmineh Jalali, and Mario Agio, "Dispersive contour-path algorithm for
the two-dimensional finite-difference
time-domain method," Opt. Express 16, 7397-7406 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7397
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References
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
- J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces," Microwave Opt. Technol. Lett. 23, 245-249 (1999). [CrossRef]
- A. Ditkowski, K. Dridi, and J. S. Hesthaven, "Convergent Cartesian grid methods for Maxwell�??s equations in complex geometries," J. Comput. Phys. 170, 39-80 (2001). [CrossRef]
- W. Yu and R. Mittra, "A conformal finite difference time domain technique for modeling curved dielectric surfaces," Microwave Opt. Technol. Lett. 11, 25-27 (2001).
- K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, "Staircase-free finite-difference time-domain formulation for general materials in complex geometries," IEEE Trans. Antennas Propag. 49, 749-756 (2001). [CrossRef]
- T. I. Kosmanis and T. D. Tsiboukis, "A systematic and topologically stable conformal finite-difference timedomain algorithm for modeling curved dielectric interfaces in three dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003). [CrossRef]
- J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003). [CrossRef]
- A. Mohammadi, H. Nadgaran, and M. Agio, "Contour-path effective permittivities for the twodimensional finite-difference time-domain method," Opt. Express 13, 10367-10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367. [CrossRef] [PubMed]
- A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-20-2972. [CrossRef] [PubMed]
- W. J. Padilla, D. N. Basov, and D. R. Smith, "Negative refractive index metamaterials," Mat. Today 9, 28-35 (2006). [CrossRef]
- V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007). [CrossRef]
- W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003). [CrossRef] [PubMed]
- S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005). [CrossRef]
- E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006). [CrossRef] [PubMed]
- R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9,20-27 (2006). [CrossRef]
- A. Mohammadi and M. Agio, "Dispersive contour-path finite-difference time-domain algorithm for modeling surface plasmon polaritons at flat interfaces," Opt. Express 14, 11330-11338 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-23-11330. [CrossRef] [PubMed]
- Y. Zhao and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007). [CrossRef]
- A. Deinega and I. Valuev, "Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method," Opt. Lett. 32, 3429-3431 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3429. [CrossRef] [PubMed]
- D. M. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996). [CrossRef]
- M. Born and E. Wold, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).
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