Effective dielectric tensor for electromagnetic wave propagation in random media

Mikael C. Rechtsman, S. Torquato

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We derive exact strong-contrast expansions for the effective dielectric tensor εe of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the n -point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for εe to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids, and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing n -point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the coarseness of the composite, i.e., local-volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.

Original languageEnglish (US)
Article number084901
JournalJournal of Applied Physics
Volume103
Issue number8
DOIs
StatePublished - May 9 2008

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wave propagation
electromagnetic radiation
tensors
attenuation
approximation
coarseness
microstructure
expansion
composite materials
spheroids
phase contrast
three dimensional models
wavelengths
inhomogeneity
disorders
permittivity
thresholds
scattering

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "Effective dielectric tensor for electromagnetic wave propagation in random media",
abstract = "We derive exact strong-contrast expansions for the effective dielectric tensor εe of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the n -point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for εe to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids, and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing n -point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the coarseness of the composite, i.e., local-volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.",
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Effective dielectric tensor for electromagnetic wave propagation in random media. / Rechtsman, Mikael C.; Torquato, S.

In: Journal of Applied Physics, Vol. 103, No. 8, 084901, 09.05.2008.

Research output: Contribution to journalArticle

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AB - We derive exact strong-contrast expansions for the effective dielectric tensor εe of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the n -point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for εe to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids, and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing n -point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the coarseness of the composite, i.e., local-volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.

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