Homogenization of 3-D Periodic Bianisotropic Metamaterials

A novel homogenization technique, combining an asymptotic multiscale method with wave-field conception, is proposed for computing the quasi-static effective parameters of three-dimensional lattices of general bianisotropic composite materials. This technique is based on the decomposition of the fields into an averaged nonoscillating part and a corrected term with microoscillation. This paper provides an original and accurate way to model the electromagnetic fields in fine microstructures of bianisotropic particles with complex inclusion shapes when the wavelength is larger than the periodicity of the microstructure. The effects of the interaction between edges and corners of adjacent inclusions on the macroscopic effective parameters have been studied, and numerical results and verifications have been presented.

I. Introduction

Composite structured materials have attracted growing interest in recent years due to their potential applications such as optical waveguides, high-dielectric thin-film capacitors, captive video disk units, and novel antennas [1]–[3]. Recently, a new class of these structured materials metamaterials with simultaneously negative permittivity and permeability has inspired great interests in their unique physical properties [3]–[6]. They have shown great potential in many applications such as super lenses, filters, subwavelength resonant cavities, waveguides, and antennas. It is of particular interest to consider the bianisotropy [7], [8] of the metamaterials, such as the design of complementary split-ring resonators (SRRs) [9] and extraction of bianisotropic constitutive parameters for SRR-based metamaterials from -parameters [10]. It was recently shown that negative refraction can be achieved by materials with positive parameters provided one of the materials is chiral or gyrotropic [11], [12].