Dielectric tensor of a rectangular arrangement of Ag nanoparticles in anisotropic [formula omitted]: Analysis of the negative epsilon conditions

Abstract

In the present paper we report the optical response of an ordered array of silver (Ag) nanoparticles (NPs) using the uniaxial LiNbO3 as a model case. We investigate the anisotropic effects on the effective dielectric tensor taking into account the charges interaction of particles. The Ag NPs dielectric function is described through a modified Drude model whereas the LiNbO3 dielectric functions are deduced from their experimentally established Sellmeier equations. The effective dielectric tensor components of the ensemble aggregates of Ag NPs and uniaxial LiNbO3 crystal are treated through the extended Maxwell–Garnett approximation. Following the asymmetric behaviour of uniaxial crystals, Ag NPs are sited in the ordinary plane of the crystal, giving rise to different responses in the x, y and z directions of applied electric field. Real and imaginary parts of the effective dielectric tensor components of the aggregate ensemble are investigated in terms of different structural parameters, such as the interparticle spacings, the NPs filling factor and sizes of spherically embedded nanoparticles. We demonstrate that an adequate choice of structural parameters such as NPs sizes, interparticle separation gaps or the filling factor can determine the optical properties of layered Ag–embedded uniaxial crystals such as LiNbO3. We show that the negative epsilon (NE) condition is satisfied from a critical size of Ag NPs when the filling factor and the interparticles distances (a and b) have particular values. This condition defines an interval of energies, called NE range, which clearly depend on values of structural parameters defined in the model. This NE range shows some type of bandwidth anisotropy when it is compared among the x-, y-, z- and xy-components of the effective dielectric tensor. We analyze some anisotropic features such as the bandwidth and shift resonance energies in the real and imaginary parts of the dielectric tensor when structural parameters change.