Effective permittivity for resonant plasmonic nanoparticle systems via dressed polarizability

We present an effective medium theory for resonant plasmonic nanoparticle systems. By utilizing the notion of dressed polarizability to describe dipolar particle interactions, we show that even highly concentrated, resonant plasmonic particles can be correctly described by the effective medium theory. The effective permittivity tensor of a nanoparticle monolayer is found explicitly and the resulting absorbance spectrum is shown to agree with rigorous numerical results from the FDTD model. The effective theory based on dressed polarizability provides a powerful tool to tailor resonant optical behaviors and design diverse plasmonic devices. ©2012 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (160.3918) Metamaterials. References and links 1. C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005). 2. W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007). 3. N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005). 4. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008). 5. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23(17), 1331–1333 (1998). 6. J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010). 7. T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008). 8. M. Quinten and U. Kreibig, “Absorption and elastic scattering of light by particle aggregates,” Appl. Opt. 32(30), 6173–6182 (1993). 9. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). 10. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004). 11. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley-VCH Verlag GmbH & Co. KGaA., 1998). 12. T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University Press, 1999). 13. R. Ruppin, “Validity range of the Maxwell-Garnett theory,” Phys. Status Solidi B 87(2), 619–624 (1978). 14. R. G. Barrera, G. Monsivais, and W. L. Mochán, “Renormalized polarizability in the Maxwell Garnett theory,” Phys. Rev. B Condens. Matter 38(8), 5371–5379 (1988). 15. R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of twodimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991). 16. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8(11), 581–583 (1983). 17. A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B 26(3), 517–527 (2009). 18. A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A, Pure Appl. Opt. 9(7), 745–748 (2007). 19. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006). 20. P. B. Johnson and R. W. Christy, “Optical constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). #168798 $15.00 USD Received 17 May 2012; revised 29 Jun 2012; accepted 29 Jun 2012; published 5 Jul 2012 (C) 2012 OSA 16 July 2012 / Vol. 20, No. 15 / OPTICS EXPRESS 16480 21. R. Rojas and F. Claro, “Electromagnetic response of an array of particles: normal-mode theory,” Phys. Rev. B Condens. Matter 34(6), 3730–3736 (1986).