Design Optimizaton Of Micro-Structural Configuration Of Left-Handed Materials

The materials are often required to exhibit prescribed/specific and excellent properties in advanced engineering. In some cases, these requirements may not be fulfilled by existed materials found in nature and developed in engineering. As a new material, the Left-handed material (LHM) with its unique electromagnetic properties has aroused widespread attention in the academic and engineering fields.In this dissertation, the electromagnetic propagation characteristics of left-handed materials and the design optimization program of micro-structural configuration are investigated, and a systematic approach for designing micro-structural configuration of left-handed materials is established. Furthermore, the retrieval method for macro effective electromagnetic parameters of LHMs is studied, and a theoretical system of characterizing the relationship between effective electromagnetic parameter and micro-structure is presented. Based on the idea of topology optimization, the mathematical formulations and the corresponding solving methods for design optimization of the micro-structural configuration of LHMs with specific electromagnetic properties are established. Finally, several left-handed materials with new configuration have been discovered and identified based on the numerical simulation techniques and experimental test verification technologies. The main content and results are given in the following paragraphs:1. Analysis of the dispersion characteristics and transmission properties of meta-materials with split-ring resonators (SRRs). SRRs-type LHMs have been the focus of current research. It benefits the designs of multi-functional material to analyze the propagation, dispersion characteristics, and the transmission properties of electromagnetic wave in periodic SRRs structures.In this dissertation, we study the transmission properties of LHMs and SRRs, and analyze the dependence of the transmission on parameters of the system such as the size and shape of the SRRs, size of the wires, and the constants of the dielectric board. The results show that:there is no qualitative difference during the different shapes of the SRRs. The magnetic resonance frequency of the SRRs is mainly dependent on compassed area of the outer SRRs. The resonant response of the LHMs caused mainly by SRRs, and the increase of the dielectric constant of the background will bring about the decrease of the magnetic resonance frequencies. However, the dependence of the thickness of the background is quite small. The influence of the width of the metal wires relative to the LHMs is small, and the optimum position of the wires is that of median position, with a lowest magnetic resonance frequency. Of all the size of the SRRs, the outer ring radius has most effect on the transmission properties. Compared with the typical SRRs, a single SRR can also produce negative permeability, and there is no essential difference with the SRRs. Furthermore, the resonant characteristics of SRR in THz frequencies are studied, and the possibility of achieving terahertz LHMs is discussed. The formulation and the solving algorithm of size optimization for LHMs are achieved, and three micro-structural configurations with different objects are presented.2. Systematic approach and general method for designing new micro-structural configuration of LHMs. The novel property of the LHMs induces many design requirements for new LHMs. However, most of existing configurations of LHMs were obtained by the typical SRRs-Wire structure, i.e., changing the shape and (or) the size of the billet topology (configuration) proposed by Pendry. This design approach is mainly based on the accumulation of experience and intuition inspiration, with a great disadvantage. Thus, an effective and systematic method for designing the micro-structural configurations of LHMs is quite desirable. In the dissertation, systematic approach and conventional method for designing new micro-structural configuration of LHMs with required properties base on topology optimization technique are established. By choosing the arrangements of the metal film pieces as design variables and the maximum width of negative refraction as objective, several typical micro-structural configurations of LHMs are designed, which include integrative LHM with simultaneous negative permittivity and permeability. Experimental results show good agreement with the transmission properties of the designed configuration using numerical method.3. Design of multilayer Left-handed materials based on ferrite. Magnetic response of ferrite at GHz is useful to design ferrite-based LHMs. Based on the theory of equivalent layer, the propagation of electromagnetic wave in periodic multi-layer film system is analyzed. By using metal-ferrite film LHMs, the relationship between effective electromagnetic parameter and the symmetrical unit cell is presented, and the design method for several objectives, such as minimum refractive indices under specified frequency, material with prescribed negative refractive index, as well as the unit cell with a fixed length, is established. Our study have shown that the topology optimization design of one-dimensional film LHMs can be performed by controlling the layout and the ratio of the contrasting materials in the unit cell, and the nature of the negative refraction can be changed significantly.4. Analysis of electromagnetic properties of granular LHMs. Based on the Wiener bounds and the Hashin-shtrikman bounds, we theoretically investigate the possible existence of granular LHMs using Bruggeman formalism. While the two component mediums have negative permittivity (permeability), the application scope of the Bruggeman theory is extended, and the theoretical model of designing granular LHMs is established. The results show that if the component material is single-negative (negative permittivity or permeability) material, there can be two types of composites:one is double-negative medium (but not LHMs), the other is a typical LHMs. Due to the advantage of the homogenization effect, this granular LHMs can be a more broad application prospects.The work of this dissertation is supported by the National Natural Science Foundation of China through the Grant No.s (90605002,90816025,10721026), the National Key Basic Research Program of China (Grant No.2006CB601205), and the Special found for state key laboratory from ministry of science and technology of China (Grant No.S08102). The financial contributions are gratefully acknowledged.