## Comprehensive three-dimensional split-field finite-difference time-domain method for analysis of periodic plasmonic nanostructures: near- and far-field formulation |

JOSA B, Vol. 28, Issue 11, pp. 2690-2700 (2011)

http://dx.doi.org/10.1364/JOSAB.28.002690

Enhanced HTML Acrobat PDF (1241 KB)

### Abstract

The three-dimensional split-field finite-difference time-domain (SF-FDTD) method is combined with the total-field–scattered-field method for injecting a plane wave. A formulation is derived for calculating the incidence transformed fields of SF-FDTD on a one-dimensional auxiliary grid. The resulting fields obtained in the scattered zone are used to calculate the far fields, based on a proposed fully time-domain near-to-far-field transformation. The far-field information is used to calculate the extinction cross section of the periodic structure under oblique incidence. To analyze metallic periodic structures, a formulation with a reduced number of variables is proposed based on the auxiliary differential equation method for dispersive media.

© 2011 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.0050) Diffraction and gratings : Diffraction and gratings

(240.6680) Optics at surfaces : Surface plasmons

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Numerical Approximation and Analysis

**History**

Original Manuscript: July 11, 2011

Revised Manuscript: September 12, 2011

Manuscript Accepted: September 12, 2011

Published: October 19, 2011

**Virtual Issues**

Vol. 7, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Afsaneh Shahmansouri and Bizhan Rashidian, "Comprehensive three-dimensional split-field finite-difference time-domain method for analysis of periodic plasmonic nanostructures: near- and far-field formulation," J. Opt. Soc. Am. B **28**, 2690-2700 (2011)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-11-2690

Sort: Year | Journal | Reset

### References

- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).
- E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimmers,” J. Chem. Phys. 120, 357–366(2004). [CrossRef] [PubMed]
- S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403, 62–67 (2005). [CrossRef]
- B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000). [CrossRef] [PubMed]
- S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125, 2896–2898 (2003). [CrossRef] [PubMed]
- C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. 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, 7337–7342 (2003). [CrossRef]
- S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004). [CrossRef] [PubMed]
- S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612(2004). [CrossRef] [PubMed]
- E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, 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, 1065–1070 (2005). [CrossRef] [PubMed]
- B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008). [CrossRef]
- B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902(2008). [CrossRef] [PubMed]
- Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008). [CrossRef]
- W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008). [CrossRef]
- C. P. Burrows and W. L. Barnes, “Large spectral extinction due to overlap of dipolar and quadrupolar plasmonic modes of metallic nanoparticles in arrays,” Opt. Express 18, 3187–3198(2010). [CrossRef] [PubMed]
- K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference-Time-Domain Method (Artech House, 2005).
- M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic structures: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993). [CrossRef]
- Y. C. Kao and R. G. Atkins, “A finite-difference time-domain approach for frequency selective surfaces at oblique incidence,” in Proceedings of Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.
- J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998). [CrossRef]
- P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propag. 42, 1317–1324 (1994). [CrossRef]
- J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994). [CrossRef]
- A. Aminian and Y. Rahmat-Samii, “Spectral FDTD: a novel technique for the analysis of oblique incident plane wave on periodic structures,” IEEE Trans. Antennas Propag. 54, 1818–1825(2006). [CrossRef]
- I. Valuev, A. Deinega, and S. Belousov, “Iterative technique for analysis of periodic structures at oblique incidence in the finite-difference time-domain method,” Opt. Lett. 33, 1491–1493(2008). [CrossRef] [PubMed]
- F. I. Baida and A. Belkhir, “Split-field FDTD method for oblique incidence study of periodic dispersive metallic structures,” Opt. Lett. 34, 2453–2455 (2009). [CrossRef] [PubMed]
- A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010). [CrossRef]
- http://www.nvidia.com.
- S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996). [CrossRef]
- J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339(2000). [CrossRef]
- J. A. Roden, J. P. Skinner, and S. L. Johns, “Shielding effectiveness of three dimensional gratings using the periodic FDTD technique and CPML absorbing boundary condition,” in IEEE/ACES International Conference on Wireless Communications and Applied Computational Electromagnetics (IEEE, 2005), pp. 128–131.
- C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14, 11870–11884 (2006). [CrossRef] [PubMed]
- R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991). [CrossRef]
- Y. A. Kao and R. G. Atkins, “A finite difference-time domain approach for frequency selective surfaces at oblique incidence,” in Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.
- J. G. Maloney and M. P. Kesler, “Analysis of antenna arrays using the split-field update FDTD method,” in Antennas and Propagation Society International Symposium (IEEE, 1998), pp. 2036–2039.
- B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000). [CrossRef]
- H. Mosallaei and Y. Rahmat-Samii, “Grand challenges in analyzing EM band-gap structures: an FDTD/Prony technique based on the split-field approach,” in Antennas and Propagation Society International Symposium (IEEE, 2001), pp. 47–50.
- N. Farahat and Raj Mittra, “Analysis of frequency selective surfaces using the finite difference time domain (FDTD) method,” in Antennas and Propagation Society International Symposium (IEEE, 2002), pp. 568–571.
- S. M. Amjadi and M. Soleimani, “Design of band-pass waveguide filter using frequency selective surfaces loaded with surface mount capacitors based on split-field update FDTD method,” Prog. Electromagn. Res. B 3, 271–281 (2008). [CrossRef]
- A. Belkhir and F. I. Baida, “Three-dimensional finite-difference time-domain algorithm for oblique incidence with adaptation of perfectly matched layers and nonuniform meshing: application to the study of a radar dome,” Phys. Rev. E 77, 056701(2008). [CrossRef]
- A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]
- M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1980). [PubMed]
- M. Meier and A. Wokaun, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” J. Opt. Soc. Am. B 2, 931–949 (1985). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.