Research Article Deficiency of Standard Effective-Medium Approximation for Ellipsometry of Layers of Nanoparticles E. G. Bortchagovsky, 1,2 A. Dejneka, 3 L. Jastrabik, 3 V. Z. Lozovski, 2 and T. O. Mishakova 2 1 Institute of Semiconductor Physics, NASU, pr. Nauki 41, 03028 Kiev, Ukraine 2 Institute of High Technologies, Taras Shevchenko National University of Kiev, pr. Glushkova 4g, 03033 Kiev, Ukraine 3 Institute of Physics of the AV ˇ CR, Na Slovance 2, 182 21 Praha 8, Czech Republic Correspondence should be addressed to E. G. Bortchagovsky; bortch@yahoo.com Received 16 September 2015; Accepted 18 November 2015 Academic Editor: Mohamed Bououdina Copyright © 2015 E. G. Bortchagovsky et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Correct description of optical properties of layers of disordered interacting nanoparticles is the problem. Contrary to volumes of nanocomposites, when standard models of efective-medium approximations (EMA) work well, two-dimensional case of layers has intrinsic anisotropy, which infuences interparticle interactions. Te defciency of standard Maxwell-Garnett model in the application to the ellipsometry of layers of gold nanoparticles is demonstrated. It demands the modifcation of EMA models and one way of this is considered in this paper. Contrary to existing 2D models with phenomenological parameters, the proposed Green function approach uses the same number of parameters as standard 3D EMA models for explicit calculations of efective parameters of layers of disordered nanoparticles. 1. Introduction Peculiar properties of composites comprising metallic nanoparticles attracted attention for millenniums and have been exploited in the production of fascinating art pieces like the Lycurgus cup, stainless glasses, Deruta ceramics, and so forth. Properties of composites found the explanation in the efective-medium approximation (EMA) models, which in the optical case defne efective dielectric function from averaged felds according to the expression ⟨⟩ = ⟨⟩ =  ef ⟨⟩. First of those models was developed already in the end of the 19th century [1]. Up to now, those models, namely, Maxwell-Garnett (MG) and self-consistent Bruggeman ones, are the most popular in the description of optical properties of nanocomposites. Although very little information about the composite is included into those models, their robustness is defned by restrictive bounds for the possible resulting dielectric function [2]. Tese models are also widely used for layers of nanopar- ticles schematically shown in Figure 1. However, as these models are based on the Lorentz sphere formalism, their application to such layers creates some problems as already reported in literature [3–5]. Te reason is that the planar geometry of the layer gives obvious geometrical anisotropy along and across the layer. As a result, electromagnetic interparticle interactions along and across the layer are diferent [6] as shown in Figure 2. In a three-dimensional case, we should expect two more neighbor dipoles with repulsive interactions resulting in zero sum feld from all neighbors at the position of the central particle. Tis is the meaning of the Lorentz sphere formalism of averaged feld for regular lattices as well as for random uniform distribution of particles. However, for the layer the average feld from neighbor dipoles is not zero. In the case of the longitudinal polarization, the total interaction is attractive in average resulting in a redshif of the nanoparticle resonance, but for the transverse polarization the interaction is always repulsive which results in the blueshif of the resonance [6]. Such a diference splits the resonance of 3D composite into two resonances for 2D layer of nanoparticles. In fact, more detailed account of even only dipolar interparticle interactions in the case of randomly distributed inclusions in 3D composite indicates some deviation of the local feld from zero [7, 8]. It is so called fuctuations of Hindawi Publishing Corporation Journal of Nanomaterials Volume 2015, Article ID 602848, 8 pages http://dx.doi.org/10.1155/2015/602848