Bulk effective dielectric constant of a composite with a periodic microgeometry

Bergman, David J.; Dunn, Keh‐Jim

doi:10.1103/physrevb.45.13262

Cited by 132 publications

(72 citation statements)

References 9 publications

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“…Among the latter, one finds extensions of the Maxwell-Garnett theory that go beyond dipolar interactions, 29,17 spectral representations, 31,33 or direct derivation of the light dispersion relation. 32 Here, we have used a different method that consists in finding the dielectric function ǫ eff of the equivalent homogeneous medium that has the same reflectance as the crystal surface;…”

Section: 31-34mentioning

confidence: 99%

Electron energy loss and induced photon emission in photonic crystals

Abajo

Blanco

2003

Phys. Rev. B

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The interaction of a fast electron with a photonic crystal is investigated by solving the Maxwell equations exactly for the external field provided by the electron in the presence of the crystal. The energy loss is obtained from the retarding force exerted on the electron by the induced electric field. The features of the energy loss spectra are shown to be related to the photonic band structure of the crystal. Two different regimes are discussed: for small lattice constants a relative to the wavelength of the associated electron excitations λ, an effective medium theory can be used to describe the material; however, for a ∼ λ the photonic band structure plays an important role. Special attention is paid to the frequency gap regions in the latter case.

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Section: 31-34mentioning

confidence: 99%

Electron energy loss and induced photon emission in photonic crystals

Abajo

Blanco

2003

Phys. Rev. B

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“…[15][16][17] For the core-shell type of microstructure that we are considering, it can be shown from the double-inclusion method that [18][19][20] …”

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confidence: 99%

Electric energy density of dielectric nanocomposites

Zhang

Ducharme

2007

Applied Physics Letters

279

211

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Dielectric materials with large electric energy density are actively pursued for many applications. The authors analyze the effective permittivity, breakdown strength, and electric energy density of dielectric nanocomposites using an effective medium approximation, modeling the nanocomposite as a three-phase material by the double-inclusion method. The addition of nanoparticles enhances the permittivity but reduces the breakdown strength, making the potential gain in electric energy density small. In addition, the interfacial interaction shifts the “percolation” threshold toward lower volume fraction of nanoparticles. The analysis suggests that the microstructure of nanocomposites must be carefully controlled to maintain high dielectric strength and therefore realize enhanced electric energy density.

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“…Numerous practical applications of photonic crystals made strong impact to the theory of homogenization. During a short period of time the new powerful methods have been developed and many new results have been obtained [8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Index of refraction of a photonic crystal of carbon nanotubes and homogenization of optically anisotropic periodic composites

Gumen

Krokhin

2008

Low Temperature Physics

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We consider the long-wavelength limit for a periodic arrangement of carbon nanotubes. Using the Fourier expansion method we develop an effective-medium theory for photonic crystal of aligned optically anisotropic cylinders. Exact analytical formulas for the effective dielectric constants for the E and H eigenmodes are obtained for arbitrary 2D Bravais lattice and arbitrary cross-section of anisotropic cylinders. It is shown that depending on the symmetry of the unit cell photonic crystal of anisotropic cylinders behaves in the low-frequency limit like uniaxial or biaxial optical crystal. The developed theory of homogenization is in a good agreement with existing experimental results for the dielectric tensor of photonic crystals of carbon nanotubes.

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Bulk effective dielectric constant of a composite with a periodic microgeometry

Cited by 132 publications

References 9 publications

Electron energy loss and induced photon emission in photonic crystals

Electron energy loss and induced photon emission in photonic crystals

Electric energy density of dielectric nanocomposites

Index of refraction of a photonic crystal of carbon nanotubes and homogenization of optically anisotropic periodic composites

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