Effective parameters retrieval for complex metamaterials with low symmetries

¹ Department of Physics and Materials Science, City University of Hong Kong - Tat Chee Avenue, Kowloon Tong, Hong Kong
² Department of Physics, Hong Kong University of Science and Technology - Clear Water Bay, Kowloon, Hong Kong
³ School of Physics and Astronomy, University of Birmingham - Birmingham B15 2TT, UK, EU
⁴ Shenzhen Research Institute, City University of Hong Kong - Shenzhen, PRC

^(a) j.li@bham.ac.uk

Received: 6 December 2012
Accepted: 20 March 2013

Abstract

We have derived a closed-form expression relating the S-parameters and the general constitutive matrix as a radiatively corrected local effective medium formula, which can work for thin metamaterials with low symmetries at normal incidence. We apply our approach to typical metamaterials possessing negative permeability or negative refractive index, and then to metamaterials with generally low symmetries. Our results show that anti-resonance for the extracted constitutive parameters from our formula is avoided while the effective medium is found to well represent a metamaterial with low symmetry except very near to resonance. Our approach will be useful for modelling metamaterials with low symmetries using an effective medium, as well as for serving as a starting point for designing future complex metamaterials with desired optical properties.