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Zhijie Gong [1; 2] and Chao Wu [1; 2; 3] and Quan Li [1; 2] and Zeyong Wei [1; 2; 3] and Hongqiang Li [1; 2; 3]

Academic Editor: Pavel Lejcek

1, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China, tongji.edu.cn

2, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, Tongji University, Shanghai 200092, China, tongji.edu.cn

3, The Institute of Dongguan-Tongji University, Dongguan, Guangdong 523808, China, idtu.cn

Received Apr 28, 2017; Revised Aug 13, 2017; Accepted Aug 20, 2017

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Metamaterial (MM) refers to a kind of artificial materials with subwavelength-sized embedded metal resonators which gives nearly any value of constitutive parameters (ε,μ). Such engineered media can offer novel electromagnetic properties beyond natural materials, such as negative refraction [1–3], perfect lens [4], invisible cloaking [5], and perfect absorption [6]. To realize these exotic properties in practical applications, design and fabrication of MMs are marching towards being three-dimensional [7]. It is an appropriate and simple way to construct 3D MM structures by stacking single layer structures [8–15], as planar metal structure could be easily fabricated by mature technologies such as electron beam lithography [9, 13, 14, 16–20], membrane projection lithography [21], direct laser writing [22–24], and electroplating [25]. For a MM slab with finite thickness, effective permittivity and permeability can be retrieved from reflection and transmission coefficients, known as effective parameter retrieval technique [26, 27]. Later improvements generalized this technique to oblique incidence [28] and chirality [11, 29–35] case, allowing a complete characterization of MMs.

Since single layer structures can be described with their effective constitutive parameters, the design and characterization of multilayer MMs should be easily accomplished based on the effective parameter retrieval technique. However, the retrieved parameters are directly related to a particular field, and the interaction between building blocks from different layers is inevitable in a multilayer MM. Thus, effective parameters obtained for single layer structure in vacuum cannot characterize its contribution when this layer is stacked in multilayer system. In other words, the effective parameters are not robust. For example, previous...

  

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