### Abstract

The effective relative permittivity dyadic of a composite material made by randomly embedding parallel, ellipsoidal, isotropic, metallic inclusions in an homogeneous, isotropic, dielectric host material is computed using the Bruggeman formalism with exact depolarization dyadics. Numerical calculations carried out for iron inclusions at 670 nm free-space wavelength indicate that the inclusion volume fraction at the percolation threshold is direction-dependent, being lower in those directions that the ellipsoids have longer extents. When the longest principal semi-axis of an ellipsoidal inclusion exceeds a certain relative size - about three to five times as large as the other two principal semi-axes - the Bruggeman estimate of the effective permittivity along this direction does not indicate a percolation threshold, becoming merely a simple weighting of the permittivities of the two materials in relation to their volume fractions.

Original language | English (US) |
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Pages (from-to) | 267-273 |

Number of pages | 7 |

Journal | Optics Communications |

Volume | 178 |

Issue number | 4 |

DOIs | |

State | Published - May 15 2000 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Physical and Theoretical Chemistry
- Electrical and Electronic Engineering

### Cite this

*Optics Communications*,

*178*(4), 267-273. https://doi.org/10.1016/S0030-4018(00)00657-X

}

*Optics Communications*, vol. 178, no. 4, pp. 267-273. https://doi.org/10.1016/S0030-4018(00)00657-X

**Homogenization of similarly oriented, metallic, ellipsoidal inclusions using the Bruggeman formalism.** / Sherwin, Joseph A.; Lakhtakia, Akhlesh; Michel, Bernhard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Homogenization of similarly oriented, metallic, ellipsoidal inclusions using the Bruggeman formalism

AU - Sherwin, Joseph A.

AU - Lakhtakia, Akhlesh

AU - Michel, Bernhard

PY - 2000/5/15

Y1 - 2000/5/15

N2 - The effective relative permittivity dyadic of a composite material made by randomly embedding parallel, ellipsoidal, isotropic, metallic inclusions in an homogeneous, isotropic, dielectric host material is computed using the Bruggeman formalism with exact depolarization dyadics. Numerical calculations carried out for iron inclusions at 670 nm free-space wavelength indicate that the inclusion volume fraction at the percolation threshold is direction-dependent, being lower in those directions that the ellipsoids have longer extents. When the longest principal semi-axis of an ellipsoidal inclusion exceeds a certain relative size - about three to five times as large as the other two principal semi-axes - the Bruggeman estimate of the effective permittivity along this direction does not indicate a percolation threshold, becoming merely a simple weighting of the permittivities of the two materials in relation to their volume fractions.

AB - The effective relative permittivity dyadic of a composite material made by randomly embedding parallel, ellipsoidal, isotropic, metallic inclusions in an homogeneous, isotropic, dielectric host material is computed using the Bruggeman formalism with exact depolarization dyadics. Numerical calculations carried out for iron inclusions at 670 nm free-space wavelength indicate that the inclusion volume fraction at the percolation threshold is direction-dependent, being lower in those directions that the ellipsoids have longer extents. When the longest principal semi-axis of an ellipsoidal inclusion exceeds a certain relative size - about three to five times as large as the other two principal semi-axes - the Bruggeman estimate of the effective permittivity along this direction does not indicate a percolation threshold, becoming merely a simple weighting of the permittivities of the two materials in relation to their volume fractions.

UR - http://www.scopus.com/inward/record.url?scp=0033734783&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033734783&partnerID=8YFLogxK

U2 - 10.1016/S0030-4018(00)00657-X

DO - 10.1016/S0030-4018(00)00657-X

M3 - Article

AN - SCOPUS:0033734783

VL - 178

SP - 267

EP - 273

JO - Optics Communications

JF - Optics Communications

SN - 0030-4018

IS - 4

ER -