On the surface effect in thin molecular or composite layers

Homogenization of an Array of S-Shaped Particles Located on a Dielectric Interface

“…This relation, as the usual ClausiusMossotti relation, allows to find the constitutive parameters of the bulk structure which is equivalent to the original 2D grid (in the meaning explained above). This equivalence has been confirmed and has been used to calculate the reflection and transmission coefficients for various frequencies [14] and angles of incidence [17,15] for the case of nonresonant particles.…”

“…In this section we briefly explain the theory of homogenization using the model of [17] which has been developed also in [14,15,18]. This model replaces the square grid of parallel identical dipoles with polarizability a and period d by an effective layer of thickness d p and bulk dielectric susceptibility κ p .…”

“…Let us assume that we know the polarizability a xx of the electric dipoles that compose the square grid with period d. Following [17] and [18], we must calculate the averaged field at any position. To do this, we must average the true electric field (which is the addition of the field of incident wave with the field generated by the grid of dipoles and the dielectric substrate).…”

“…The theory originates in very old classical works by Ewald and Oseen. The frequency bounds of validity for this quasi-static approximation have been studied analytically [13] and numerically [14]. However, the case of resonant dipoles is still weakly studied.…”

“…Following [17] and [14], a planar grid of dipoles embedded in a dielectric host medium is presented as a layer of effective bulk medium. This can be done under two conditions.…”