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Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory

Departamento de Ingeniería, 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
Tecnológico Nacional de México/I.T. Puebla-División de Estudios de Posgrado e Investigación, Av. Tecnológico No. 420, Maravillas, C.P. 72220 Puebla, Pue, Mexico
Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro No. 1, 72840 Sta. Ma. Tonantzintla, Pue, Mexico
Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Veracruz, Mexico
Consejo Veracruzano de Investigación Científica y Desarrollo Tecnológico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Cuauhtémoc, 91069 Xalapa, Veracruz, Mexico
Author to whom correspondence should be addressed.
Materials 2020, 13(6), 1475; (registering DOI)
Received: 21 February 2020 / Revised: 15 March 2020 / Accepted: 20 March 2020 / Published: 24 March 2020
A homogenization theory that can go beyond the regime of long wavelengths is proposed, namely, a theory that is still valid for vectors of waves near the edge of the first zone of Brillouin. In this paper, we consider that the displacement vector and the magnetic induction fields have averages in the volume of the cell associated with the values of the electric and magnetic fields in the edges of the cell, so they satisfy Maxwell’s equations. Applying Fourier formalism, explicit expressions were obtained for the case of a photonic crystal with arbitrary periodicity. In the case of one-dimensional (1D) photonic crystals, the expressions for the tensor of the effective bianisotropic response (effective permittivity, permeability and crossed magneto-electric tensors) are remarkably simplified. Specifically, the effective permittivity and permeability tensors are calculated for the case of 1D photonic crystals with isotropic and anisotropic magnetic inclusions. Through a numerical calculation, the dependence of these effective tensors upon the filling fraction of the magnetic inclusion is shown and analyzed. Our results show good correspondence with the approach solution of Rytov’s effective medium. The derived formulas can be very useful for the design of anisotropic systems with specific optical properties that exhibit metamaterial behavior. View Full-Text
Keywords: photonic crystal; homogenization theory; effective parameters; metamaterial photonic crystal; homogenization theory; effective parameters; metamaterial
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Méndez, J.F.; Reyes, A.C.P.; Moreno, M.M.; Morales-Sánchez, A.; Minquiz, G.M.; Lázaro, R.C.A.; Leal, H.V.; García, F.C. Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory. Materials 2020, 13, 1475.

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