Homogenization method for one-dimensional photonic crystals with magnetic and chiral inclusions
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Homogenization method for one-dimensional photonic crystals with magnetic and chiral inclusions Javier Flores M´endez 1,2 , Benito Zenteno Mateo 1 , Mario Moreno Moreno 3 , Alfredo Morales-S´anchez 3 , Gustavo M. Minquiz 1,2 , Hector V´ azquez Leal 4,5 , Israel Vivaldo-De la Cruz 1 , Silvia Cort´es-L´opez 1 , 1 Ana Cecilia Pi˜ n´on Reyes , and Roberto Ambrosio 1,a 1
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Benem´erita Universidad Aut´ onoma de Puebla-Ciudad Universitaria, Blvd. Valsequillo y Esquina, Av. San Claudio s/n, Col. San Manuel, C.P. 72570, Puebla, Pue, Mexico Tecnol´ ogico Nacional de Mexico/I.T. Puebla-Divisi´ on de Estudios de Posgrado e Investigaci´ on, Av. Tecnol´ ogico No. 420, Maravillas, C.P. 72220, Puebla, Pue, Mexico Instituto Nacional de Astrof´ısica, o ´ptica y Electr´ onica, Luis Enrique Erro No. 1, C.P.72840, Sta. Ma. Tonantzintla, Puebla, Pue, Mexico Facultad de Instrumentaci´ on Electr´ onica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltr´ an s/n, 91000, Xalapa, Veracruz, Mexico Consejo Veracruzano de Investigaci´ on Cient´ıfica y Desarrollo Tecnol´ ogico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Cuauht´emoc, 91069, Xalapa, Veracruz, Mexico Received 20 February 2020 / Received in final form 13 May 2020 Published online 1 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 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 electromagne
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