Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

Bravo-Castillero, J., Ramírez-Torres, A. , Sabina, F. J., García-Reimbert, C., Guinovart-Díaz, R. and Rodríguez-Ramos, R. (2020) Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites. Waves in Random and Complex Media, 30(4), pp. 593-613. (doi: 10.1080/17455030.2018.1546063)

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Abstract

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ramirez Torres, Dr Ariel
Authors: Bravo-Castillero, J., Ramírez-Torres, A., Sabina, F. J., García-Reimbert, C., Guinovart-Díaz, R., and Rodríguez-Ramos, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Waves in Random and Complex Media
Publisher:Taylor & Francis
ISSN:1745-5030
ISSN (Online):1745-5049
Published Online:18 November 2018

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