Abstract
We investigate the plasmonic response of gold nanospheres calculated using discrete dipole approximation validated against the results from other discretization methods, namely the finite-difference time-domain method and the finite-element methods. Comparisons are also made with calculations from analytical methods such as the Mie solution and the null-field method with discrete sources. We consider the nanoparticle interacting with the incident field both in free space and sitting on a planar substrate. In the latter case, discrete dipole approximation with surface interaction is used; this includes the interaction with the ‘image dipoles’ using Sommerfeld integration.
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T. Nagao, G. Han, C. Hoang, J.S. Wi, A. Pucci, D. Weber, F. Neubrech, V.M. Silkin, D. Enders, O. Saito, M. Rana, Sci. Tech. Adv. Mater. 11, 054506 (2010)
B. Schaffer, U. Hohenester, A. Trugler, F. Hofer, Phys. Rev. B 79, 041401 (2009)
D.G. Georganopoulou, L. Chang, J.M. Nam, C.S. Thaxton, E.J. Mufson, W.L. Klein, C.A. Mirkin, Proc. Natl. Acad. Sci. USA. 102, 2273–2276 (2005)
J.C.Y. Kah, K.W. Kho, C.G.L. Lee, C.J.R. Sheppard, Z.X. Shen, K.C. Soo, M.C. Olivo, Int. J. Nanomed. 2, 785–798 (2007)
H.M. Hiep, T. Endo, K. Kerman, M. Chikae, D.K. Kim, S. Yamamura, Y. Takamura, E. Tamiya, Sci. Tech. Adv. Mater. 8, 331–338 (2007)
R. Esparza, G. Rosas, E. Valenzuela, S.A. Gamboa, U. Pal, R. Perez, Materia-Rio de Janeiro 13, 579–586 (2008)
M.P. Pileni, J. Phys. 23, 503102 (2011)
V.L.Y. Loke, M.P. Mengüç, T.A. Nieminen, JQSRT 112, 1711–1725 (2011)
E. Purcell, C. Pennypacker, Astrophys. J. 186, 705–714 (1973)
B. Draine, Astrophys. J. 333, 848–872 (1988)
S. Ahmed, Electron. Lett. 4, 387–389 (1968)
K.S. Yee, IEEE Trans. Antenn. Propag. 14, 302–307 (1966)
L. Lorenz, Videnskabernes Selskabs Skrifter 6, 2–62 (1890)
G. Mie, Ann. Phys. 25, 377–445 (1908)
T. Wriedt, JQSRT 106, 535–545 (2007)
P.C. Waterman, Proc. IEEE 53, 805–812 (1965)
T. Wriedt, JQSRT 110, 833–843 (2009)
J. Parsons, C.P. Burrows, J.R. Sambles, W.L. Barnes, J. Mod. Opt. 57, 356–365 (2010)
X.H. Huang, P.K. Jain, I.H. El-Sayed, M.A. El-Sayed, Lasers Med. Sci.23, 217–228 (2008)
K.M.M. Aung, Y.N. Tan, K.V. Desai, X.D. Su, Aust. J. Chem. 64, 1286–1292 (2011)
M. Quinten, Optical Properties of Nanoparticle Systems: Mie and Beyond. (Wiley, New York, 2011)
A. Vial, T. Laroche, Appl. Phys. B 93, 139–143 (2008)
W. Sellmeier, Ann. Phys. Chem. 219, 272–282 (1871)
R. Luebbers, F.P. Hunsberger, K.S. Kunz, R.B. Standler, M. Schneider, IEEE Trans. Electromagn. Compat. 32, 222–227 (1990)
B.T. Draine, P.J. Flatau, J. Opt. Soc. Am. A 11, 1491–1499 (1994)
V.L.Y. Loke, M.P. Mengüç, in Proceedings of ELS XII Helsinki 134–137 (2010)
Y. Saad, M.H. Schultz, SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)
B.T. Draine, J. Goodman, Astrophys. J. 405, 685–697 (1993)
V.L.Y. Loke, M.P. Mengüç, J. Opt. Soc. Am. A 27, 2293–2303 (2010)
A. Sommerfeld, Ann. Physik 28, 665–736 (1909)
W.C. Chew, Waves, Fields in Inhomogeneous Media. (Van Nostrand Reinhold, New York, 1990)
R. Schmehl, B.M. Nebeker, E.D. Hirleman, J. Opt. Soc. Am. A 14, 3026–3036 (1997)
A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edn. (Artech House, Boston, 2005)
J.P. Berenger, J. Comput. Phys. 114, 185–200 (1994)
Z.S. Sacks, D.M. Kingsland, R. Lee, J.F. Lee, IEEE Trans. Antenn. Propag. 43, 1460–1463 (1995)
S. Gedney, IEEE Trans. Antennas Propagat AP-44, 1630–1639 (1996)
J.A. Roden, S.D. Gedney, Microw. Opt. Tech. Lett. 27, 334–339 (2000)
Lumerical FDTD Solutions Package Reference Guide for FDTD Solutions v7.0.1 ed (2010)
M.A. Morgan, K.K. Mei, IEEE Trans. Antenn. Propag. 27, 202–214 (1979)
R. Mittra, O. Ramahi, Finite element and finite difference methods in Electromagnetic Scattering, vol. II, ed. by M. Morgan (Elsevier, New York, 1990)
J.L. Volakis, A. Chatterjee, L.C. Kempel, Finite Element Method for Electromagnetics. (IEEE Press, New York, 1998)
X.Q. Sheng, J.M. Jin, J.M. Song, C.C. Lu, W.C. Chew, IEEE T. Antenn. Propag. 46, 303–311 (1998)
COMSOL Multiphysics RF Module Reference Guide v3.5a ed (2008)
G.M. Huda, E.U. Donev, M.P. Mengüç, J.T. Hastings, Opt. Express 19, 12679–12687 (2011)
COMSOL Mie scattering off plasmonic nanoparticle and radar cross-section computations (2008) http://www.comsol.com/showroom/gallery/3459/
P. Debye, Ann. Phys. 30, 57–136 (1909)
C. Mätzler, MATLAB functions for Mie scattering and absorption v2 Tech. Rep. Research Report No. 2002-11 University of Bern (2002)
A. Doicu, Y.A. Eremin, T. Wriedt, Opt. Commun. 159, 266–277 (1999)
A. Doicu, Y. Eremin, T. Wriedt, Comput. Phys. Commun. 134, 1–10 (2001)
M.I. Mishchenko, L.D. Travis, A.A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering. (Cambridge University Press, Cambridge, 2006)
D.W. Mackowski, JQSRT 109 770–788 ISSN 0022-4073 (2008) http://www.sciencedirect.com/science/article/pii/S0022407307002282
M. Quinten, A. Pack, R. Wannemacher, Appl. Phys. B 68, 87–92 (1999)
M. Born, E. Wolf, Principles of Optics, 7th edn. (Cambridge University Press, Cambridge, 1999)
M.A. Yurkin, A.G. Hoekstra, JQSRT 112, 2234–2247 (2011)
M.A. Yurkin, de D. Kanter, A.G. Hoekstra, J. Nanophoton. 4, 041585 (2010)
M.A. Yurkin, M. Min, A.G. Hoekstra, Phys. Rev. E 82, 036703–12 (2010)
N. Geuquet, L. Henrard, Ultramicroscopy 110, 1075–1080 (2010)
R.J. Lytle, D.L. Lager, Numerical evaluation of Sommerfeld integrals. Technical report (1974). UCRL-51688 Lawrence Livermore Laboratory Livermore, California
Acknowledgments
This work was supported by the US National Science Foundation (NSF Grant no. CMMI-0800658), the TUBITAK-1001 (Grant no. 109M170) and the FP-7-PEOPLE-IRG-2008 (Grant no. 239382 NF-RAD).
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Loke, V.L.Y., Huda, G.M., Donev, E.U. et al. Comparison between discrete dipole approximation and other modelling methods for the plasmonic response of gold nanospheres. Appl. Phys. B 115, 237–246 (2014). https://doi.org/10.1007/s00340-013-5594-z
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DOI: https://doi.org/10.1007/s00340-013-5594-z