Reflection From Metafilms on Interfaces

The reflection tensor of a metafilm with bianisotropic elements on a dielectric interface is analytically derived. First, using the dipole approximation, the nanoparticles are replaced with electric and magnetic dipoles. Next, the local fields are obtained as the superposition of the background field and the interaction fields (sum of fields by all dipoles and their images). The latter is written in a form that directly results in either fast-converging series or series with closed-form solutions. Utilizing the local fields, the collective polarizability tensor and the dipole intensities are determined. Then, assuming the array to be dense, the dipole array is replaced with current sheets, for which the radiated fields in the presence of a substrate are well-known. Next, the reflection tensor is derived, validated, and discussed. Moreover, using a numerical scheme, the polarizability tensor of a bianisotropic nanoparticle in free space is calculated. Using the computed polarizability tensor and the derived analytical expressions, reflection from a metafilm with bianisotropic nanoparticles on an interface is obtained. Finally, the more complex problems of embedded particles and oblique illumination are briefly addressed.