Transition from Planar to Bulk Properties in Multi-Layer System

Vinogradov, P. V.; Dmitriev, Yu. N.; Romanenko, V. E.

doi:10.1080/02726349708908562

Cited by 8 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The surface effect is more pronounced for media with high permittivity values. These theoretical results are in qualitative agreement with the numerical simulations for the effective conductivity of thin films that are reported in [3]. Unfortunately, the quantitative comparison is not possible because polarizabilities of single inclusions are not specified in [3].…”

Section: Numerical Examplessupporting

confidence: 84%

“…These theoretical results are in qualitative agreement with the numerical simulations for the effective conductivity of thin films that are reported in [3]. Unfortunately, the quantitative comparison is not possible because polarizabilities of single inclusions are not specified in [3]. It is interesting to note that when the slab gets extremely thin (zero value of 1 2 ), both the transverse and normal components take equal values and the slab is effectively isotropic.…”

Section: Numerical Examplessupporting

confidence: 82%

“…Two-dimensional mixtures, i.e., thin layers as result from the homogenization in the plane, have been analyzed [2]; however, there the surface-to-bulk transition is not considered. Numerical simulations of this transition based on summation of quasi-static dipole fields [1] and on the planar percolation model [3] are available in the literature.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the homogenization of thin isotropic layers

Tretyakov

Sihvola

2000

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Examplessupporting

confidence: 84%

Section: Numerical Examplessupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the homogenization of thin isotropic layers

Tretyakov

Sihvola

2000

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

show abstract

“…The model applied in these studies is a regular array of point dipole scatterers, of which the effective permittivity is calculated. It has been shown that the effective permittivity of a single-layer array differs greatly from that of a bulk material (Simovski, Popov, & He, 2000), though this difference is completely eliminated when the sample comprises four to five layers (Vinogradov, Dmitriev, & Romanenko, 1997). The thickness of the boundary layer in dipole arrays is found to be about the distance between dipoles (Simovski, Popov, & He, 2000), i.e., the inhomogeneity scale of the problem.…”

Section: Introductionmentioning

confidence: 99%

The Thickness Dependence of Resonance Frequency in Anisotropic Composites with Long Conductive Fibers

et al. 2005

View full text Add to dashboard Cite

The resonant frequency of long conductive fibers embedded in an anisotropic composite as a function of layer thickness is studied both numerically and experimentally and is discussed in terms of the equivalent permittivity of the layer. A simple empirical exponential law is suggested to fit the thickness dependence of the equivalent permittivity. The law involves a critical thickness value, below which the layer can no longer be treated as a bulk material for a fiber of given length and thickness. The critical thickness is retrieved from numerical data for different permittivity values of isotropic and anisotropic layers and for different fiber length.

show abstract