Surface Science 425 (1999) 313–325 Optical absorption spectra of arrays of metal particles from cluster calculations: cluster size and shape eﬀects V. Russier*, M.P. Pileni Structure et Re ´activite ´ des Syste `mes Interfaciaux, URA 1662 du CNRS, Universite ´ P. et M. Curie, BP 52, 4, Place Jussieu, F-75252 Paris Cedex 05, France Received 22 October 1998; accepted for publication 21 January 1999 Abstract The cluster-like calculations of optical extinction cross-sections, considered as a way to determine the inﬂuence of the interparticle interactions in inﬁnite arrays of metal particles, is investigated. The importance of the cluster size on the calculated results is determined through the location of the plasmon resonance frequencies. The convergence, with the number N of particles of the cluster, of the shift between plasmon frequencies is found to depend on the dimensionality of the cluster. For two-dimensional clusters only a weak convergence, proportional to 1/N1/2, is obtained. The inﬂuence of the shape of the cluster is also investigated for two-dimensional systems. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Clusters; Optical absorption; Plasmons 1. Introduction intrinsic properties of the particles and on the environment. Indeed, diﬀerent physical elements Optical properties are widely used to character- can be invoked to interpret the optical spectra of ize thin granular metallic ﬁlms, composed of metal these systems, such as the shape and size of the islands deposited on a substrate and more generally particles [3,4,8,16–21], the mutual interactions of two-phase composite systems including metal [14–27] between neighboring particles, the image particles of nanometric size, deposited on a sub- dipoles induced by the dielectric discontinuity due strate. Numerous experimental measurements of to the substrate [3,4,16–19,28,29,38]. When the absorption spectra of such systems are available, interparticle distance is suﬃciently small, and concerning for instance the granular ﬁlms depos- especially when the embedded particles are nearly ited under vacuum conditions [1–4], two-dimen- spherical, the mutual interactions between particles sional arrays of metal particles [5,6 ], or nanosized are expected to play a signiﬁcant role in the optical metal particles embedded in a dielectric medium response. A convenient way to calculate the eﬀect and deposited on a substrate [7–15]. In general, of these interactions is to use a cluster type of one characterizes the optical response by the plas- approach, where the extinction cross-section is mon resonance peaks, which depends both on the calculated for a cluster including a ﬁnite number of metal spheres [14–27]. In this approach, the extinction cross-section is calculated from the solu- * Corresponding author. E-mail address: vr@sri.jussieu.fr ( V. Russier) tion of the Maxwell equations without approxima- 0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0039-6028(99)00217-4