Evaluation of efficiency of optical effective medium theories by comparison with the generalized Mie theory for metal nanoparticles

Abstract

The study of fundamental properties of particles with dimensions of a few nanometers embedded in dielectric matrices is characterized by a remarkable interest during more than one century. In general, macroscopic electrodynamic response of a such heterogeneous composite material depends, beside the optical material constants, on a large number of microscopic parameters like: particle size distribution; particle surfacelinterface structure; shape; surrounding material and topologies of the many-particles system. There is a variety of different theoretical models to trace hack the macroscopic behavior of the composite to the properties of its constituents. Among the electrodynamic ones we can distinguish between appreciative models of the kind of Effective Medium Theories (EffMT) and theories which are in the frame of electrodynamics. The latter are based upon Mie's solution for one single spherical particle. The Generalize Mie Theory (GMT) [1,2] takes into account the exact geometric amangement coordinates of all spherical particles in a many-particle sample and calculates the complete electrodynamic interaction near-fields among all particles with all particles including multimode and retardation effects. Alternatively, optical properties of composite materials may be described in ternis of effective dielectric functions developed from the atomic polarizability and the material density. Maxwell Garnet Theory (MGT) based on the LorentzLorenz relation is one example of this kind of approach. The general idea of EffMTs is to replace the heterogeneous composite material by a fictitious homogeneous material with the same linear response. The simple transfer of LorentzLorenz theory derived for point dipoles to nanoparticles in composite materials disregards the enormous differences in size between atoms and particles. Hence, the optical response of the particles is basically restricted to the dipole excitation without retardation effects. The next constraint compared to the theories is that the detailed distribution of particles in the sample is replaced by one averaging parameter of the volume concentrationf'of particles in the whole macroscopic sample. These restrictions have oRen been disregarded when numerically comparison between optical experiments on special composite samples and their description by MGT was performed. So, there is a problem which we, in this contribution, try to clarify by numerical comparison of MGT with GMT. The aim is to derive applicability conditions for MGT in practical work, which, in fact, prove to be very strict, in particular for nanoparticles of good metals like silver.