Dr. Felipe Pérez-Rodríguez Profile

Dr. Felipe Pérez-Rodríguez

at Benemérita Univ Autónoma de Puebla

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Proceedings Article | 23 March 2015 Paper

Anisotropic mass density by three-dimensional elastic metamaterials

E. Gutiérrez-Reyes, J. Flores-Méndez, Ana González, F. Pérez-Rodríguez

Proceedings Volume 9438, 94381H (2015) https://doi.org/10.1117/12.2084270

KEYWORDS: Metamaterials, Crystals, Anisotropy, Virtual colonoscopy, Protactinium, Liquids, Aluminum, Liquid crystals, Solids, Homogenization

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We have applied a homogenization theory¹, which is based on the Fourier formalism, to calculate the effective parameters of phononic crystals having liquid inclusions embedded in a solid host matrix. The theory provides explicit formulas for determining all the components of the effective mass density and stiffness tensors, which are valid in the long wavelength limit for arbitrary Bravais lattice and any form of the inclusions inside the unit cell. In the previous work¹, it was shown that rectangular two-dimensional lattices of water-filled holes in an elastic host matrix exhibit solid-like behavior with strongly anisotropic mass density in the low-frequency limit. Such metamaterials were called metasolids. In the present work, we analyze the metasolid behavior of liquid-solid three-dimensional phononic crystals. In particular we have analyzed the effect of the type of Bravais lattice and form of the liquid inclusions on the anisotropy of the effective mass density. In the analysis we have considered different solid host materials (Al, Si, and ribbon) with isolated inclusions of water. We have established that the anisotropy of the effective mass density is considerably strong when the homogenized phononic crystals do not possess inversion symmetry because of the inclusion shape. Our results could be useful for designing metamaterials with predetermined elastic properties.

Proceedings Article | 14 September 2006 Paper

From photonic crystals (via homogenization) to metamaterials

Peter Halevi, Felipe Pérez-Rodríguez

Proceedings Volume 6320, 63200T (2006) https://doi.org/10.1117/12.681021

KEYWORDS: Photonic crystals, Dielectrics, Magnetism, Electromagnetism, Homogenization, Metamaterials, Photonic metamaterials, Crystal optics, Maxwell's equations, Dispersion

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A very general mean-field theory is presented for a photonic crystal (either dielectric or metallo-dielectric) with arbitrary 3D Bravais lattice and arbitrary shape of the inclusions within the unit cell. The material properties are described by using a generalized conductivity at every point in the unit cell. After averaging over many unit cells for small Bloch wave vectors in comparison with the inverse of the lattice constant, we have derived the macroscopic response for the artificially structured material. In the most general case, such a response turns out to be bi-anisotropic, having terms associated with the permittivity, and permeability, and magnetoelectric tensors. We have derived explicit expressions for the four tensors in terms of the geometry and material parameters of the inclusions. Nevertheless, for a photonic crystal with inversion symmetry the magnetoelectric tensors in the bi-anisotropic constitutive relation vanish. In addition, we have verified that for cubic symmetry the system becomes bi-isotropic, being characterized by two frequency-dependent scalars, namely the permittivity and permeability. It is very important that, in general, the permittivity and permeability tensors are diagonal in different reference systems. The principal axes of the permeability tensor (unlike those of the permittivity tensor) depend on the direction of the wave vector. This necessitates the development of a new Crystal Optics for anisotropic photonic metamaterials.

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