On the homogenization of thin isotropic layers

Abstract

Homogenization of extremely thin dielectric or composite layers is considered. Special attention is focused on the fact that the permittivity near the surface of the slab is affected by the presence of the boundary. This makes the effective permittivity inhomogeneous, and the slab becomes effectively anisotropic. The anisotropy effect cannot be neglected for slabs whose thickness is on the order of the depth of one molecular or inclusion layer. The analysis results in approximate second-order boundary conditions, which describe electromagnetic properties of the layer. Numerical examples show that the effect in reflection coefficient cannot be neglected if the depth of the boundary layer is a quarter of the slab thickness. Also, the magnitude of the boundary effect increases for higher slab permittivities.Index Terms-Material modeling, surface effect, thin layers.

Dielectric mixtures: electrical properties and modeling

“…Although these equations for regular structures with round shapes (spheres or cylinders) are valid for low concentrations, at high frequencies the sizes of the particles are playing an important role [251,252,253,202,254,255,256]. Finally, other periodic structures have also been presented in the literature such as spherical particles [257,258,247,246,11], cylindrical inclusions [259,250] tilings (checkerboard) structures [21,260,261,262,263,264] and layered structures [265,266,267].…”

Applications of capacitance tomography in gas–solid fluidized bed systems

“…If ε 1 and ε 2 are comparable and q is small (i.e., low-contrast and tenuous mixtures), this approximation provides good results (Tretyakov & Sihvola, 2000).…”

Complex-media electromagnetics and metamaterials

“…My first early works in this field were in homogenizing multi-layered structures [51][52][53][54] and in mixture rules for composites formed by general bianistropic particles [45]. In studies of thin layers, we focused on the surface effects, which were seen to modify the bulk properties of the layer material [55,56]. Furthermore, we worked on analytical methods to find effective-medium model parameters for dense arrays of dipoles [57,58], including particles with nonreciprocal responses [59].…”