We calculate, in the quasistatic coupled dipole approximation, the analytical expressions of the effective dielectric tensor of a single layer of polydisperse ellipsoidal nanoparticles with two of their principal axes in the layer's plane and embedded in a homogeneous dielectric medium. The organization (isotropic or anisotropic) and orientation (without or with a preferential in-plane orientation) of the nanoparticles is taken into account, together with their (possibly correlated) in-plane size, in-plane projected shape, and height distributions. In particular, we propose to describe the response of a layer of nanoparticles presenting a height distribution by using a vertically graded effective medium model. The expressions are tested in the case of finely characterized dielectric/silver/dielectric granular trilayers grown by means of vapor deposition in which the silver coalesced nanoparticles present correlated in-plane size and in-plane projected shape/height distributions and a moderate surface coverage of about 25$\%$. A satisfactory quantitative agreement is obtained between the simulated and measured surface plasmon extinction bands of the metal nanoparticles. This agreement is permitted by the capability of the effective medium model of taking into account the ellipsoidal shape of the nanoparticles. The significant role of the size and shape distributions is also demonstrated.

• Received 16 December 2011

DOI:https://doi.org/10.1103/PhysRevB.86.045415