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Homogenization method for one-dimensional photonic crystals with magnetic and chiral inclusions

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An Erratum to this article was published on 03 August 2020

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Abstract

We have theoretically investigated the electromagnetic properties for one-dimensional (1D) photonic crystals with magnetic and artificial chiral inclusions in the quasi-static limit, that is when the size of the unit cell of the crystal is small with respect to the wavelength of the operating wave. We suggest a homogenization theory to determine the effective tensors of the optical response, to achieve this objective, we apply the Bloch’s plane waves method to describe the electromagnetic modes that can propagate in the periodic structure under consideration. Subsequently, the Maxwell’s “microscopic” equations are homogenized replacing the Bloch waves by plane waves that attenuate the fast oscillations of the electromagnetic fields within the unit cell (macroscopic level), i.e., the average-macroscopic electromagnetic fields are determined by the component corresponding to the null reciprocal lattice vector in the expansion in plane waves. The numerical implementation of our theory of homogenization allow us to study the effective bianisotropic electromagnetic response (effective dielectric permittivity, magnetic permeability and electric-magnetic coupling tensors, this last is described by an effective chiral parameter) for 1D photonic crystals whose constituents in its unit cell are a dielectric layer and another magnetic (both isotropic and anisotropic) or chiral inclusion layer. The results are illustrated and discussed by the effective parameters as a function of the filling fraction of the inclusion and show for each case of homogeneous effective medium different components of anisotropy in the electromagnetic response of permittivity, permeability and chirality with the increase of the filling fraction. Besides, the behaviors of the obtained graphs agree well with Rytov’s formulas of effective medium. The relevant results of this theory will be very useful for the study and better understanding of the nature and design of metamaterials with predetermined anisotropic optical properties.

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Change history

  • 03 August 2020

    Reference 42 is corrected to: 42. T.G. Mackay, A. Lakhtakia, SPIE Rev. 1, 018003 (2010)

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Authors and Affiliations

  1. Benemérita Universidad Autónoma de Puebla-Ciudad Universitaria, Blvd. Valsequillo y Esquina, Av. San Claudio s/n, Col. San Manuel, C.P. 72570, Puebla, Pue, Mexico

    Javier Flores Méndez, Benito Zenteno Mateo, Gustavo M. Minquiz, Israel Vivaldo-De la Cruz, Silvia Cortés-López, Ana Cecilia Piñón Reyes & Roberto Ambrosio

  2. Tecnológico Nacional de Mexico/I.T. Puebla-División de Estudios de Posgrado e Investigación, Av. Tecnológico No. 420, Maravillas, C.P. 72220, Puebla, Pue, Mexico

    Javier Flores Méndez & Gustavo M. Minquiz

  3. Instituto Nacional de Astrofísica, óptica y Electrónica, Luis Enrique Erro No. 1, C.P.72840, Sta. Ma. Tonantzintla, Puebla, Pue, Mexico

    Mario Moreno Moreno & Alfredo Morales-Sánchez

  4. Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán s/n, 91000, Xalapa, Veracruz, Mexico

    Hector Vázquez Leal

  5. Consejo Veracruzano de Investigación Científica y Desarrollo Tecnológico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Cuauhtémoc, 91069, Xalapa, Veracruz, Mexico

    Hector Vázquez Leal

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  1. Javier Flores Méndez
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  2. Benito Zenteno Mateo
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Méndez, J.F., Mateo, B.Z., Moreno, M.M. et al. Homogenization method for one-dimensional photonic crystals with magnetic and chiral inclusions. Eur. Phys. J. B 93, 124 (2020). https://doi.org/10.1140/epjb/e2020-10095-4

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