IOP PUBLISHING NANOTECHNOLOGY Nanotechnology 20 (2009) 295203 (9pp) doi:10.1088/0957-4484/20/29/295203 Plasmon spectra in two-dimensional nanorod arrays Z H Nie 1 , D Fava 1 , E Kumacheva 1 , H E Ruda 2 and A Shik 2 1 Department of Chemistry, University of Toronto, Toronto, Ontario, M5S 3H6, Canada 2 Centre for Advanced Nanotechnology, University of Toronto, Toronto, Ontario, M5S 3E4, Canada Received 31 January 2009, in final form 22 May 2009 Published 1 July 2009 Online at stacks.iop.org/Nano/20/295203 Abstract For various types of ensembles of metal nanorods, the frequencies of longitudinal and transverse plasmons were calculated and correlations between the plasmon frequency shifts and the topology of nanorod arrays were found. The theoretical predictions were compared with the experimentally determined optical absorption in arrays of polymer-terminated Au nanorods obtained by self-assembly in selective solvents. 1. Introduction Optical properties of metal nanostructures are determined, to a great extent, by plasmon effects in a system of confined conduction electrons. For single nanoparticles these effects are well investigated, both theoretically and experimentally (see, e.g., [1]). Recently, there has been rapid progress in the area of the self-assembly of nanoparticles, in particular, in producing various types of arrays of metal nanorods (NRs), e.g. chains [2–4], bundles and bundled chains [3, 4], rings [3, 5], spheres [3, 6], lamellae [7] and raft-like structures [6]. In such systems of many interacting nanoparticles, plasmon phenomena are more complicated and less studied, although several general qualitative characteristics have been reported. It was demonstrated [1, 8, 9] that, by reducing the inter- nanoparticle separation in the direction of light polarization, a redshift in the plasmon resonance occurs, in contrast to a blueshift for the perpendicular direction of polarization. In this paper, we present analytical models that describe the polarization phenomena and the shifts in the plasmon resonance in arrays of metal NRs and use these models to explain the corresponding experimental results. We will consider the case of NRs with sufficiently large aspect ratio where the system differs dramatically from nanodot arrays and is characterized by strong dependence of optical characteristics on the light polarization related to the NR axes. We restrict ourselves to the quasi-static case when all dimensions of the NRs, as well as the distances between them, are smaller than the light wavelength λ, which is definitely fulfilled in our experiments. In this case, the high- frequency electric field distribution around NRs is found from the Laplace equation and the spectral dependence of the optical absorption is determined by the frequency dispersion of the metal dielectric constant ε m (ω) and not by absolute values of NR dimensions and their mutual separation, but only by the ratios of these geometric parameters. In the quasi-static case, the plasmon frequencies can be determined by preliminary calculation of the depolarization factors n (i ) for NRs forming the array (the superscript i = x , y , z describes the direction of light polarization). To do this, we assume that the NR array is placed in the external uniform electric field E 0 and calculate the distribution of electric potential and charge density in the system determined by the corresponding Laplace equation. Using this charge density distribution, we find the dipole moment P i of an individual NR and the depolarization factor determined as n (i ) = E 0 V /(4π P i ), where V is the NR volume. Once the depolarization factor is found, we can determine the electric field E inside the NR for an arbitrary dielectric constant ε of the latter. In the quasi-static case this field is uniform [10]: E i = ε e E 0i ε e + (ε m − ε e )n (i ) . (1) where ε e is the dielectric constant of the medium (solvent) surrounding metal NRs. Contrary to semiconducting NRs, whose electronic properties may be essentially influenced by the effects of size quantization, in metal particles these effects are usually of minor importance due to large values of the Fermi energy and electron effective mass. The typical confinement energies due to size quantization in Au NRs with the dimensions mentioned below do not exceed several meV, which is at least three orders of magnitude less than the Fermi energy in Au and hence will not contribute in a significant way to the plasmonic properties of the particles. This allows 0957-4484/09/295203+09$30.00 © 2009 IOP Publishing Ltd Printed in the UK 1