Analysis and Synthesis of Magnetically Negative (MNG) Material using Softcomputing Techniques

Abstract

Unique properties of Metamaterial are widely used in Electromagnetic Engineering, and the metamaterial has gained significant attention to be a major research area. Some of its recent research areas are carpet cloaking and metasurface design. The unique properties of these materials include simultaneous negative electromagnetic property, i.e., both permeability and permittivity are negative, because of which a negative refractive index is generated.Thus there are three primary classes of metamaterials. When only the permittivity is negative, the material is called ENG (Electrical Negative). Similarly material with only negative permeability is known as MNG (Magnetic Negative). Further when both are negative the material is regarded as DNG (Double Negative). Out of these three, the analysis and synthesis of MNG is very complicated and difficult. Therefore, the focus in this work is only on MNG, and the word "metamaterial" refers to MNG unless otherwise mentioned specifically. These type of materials don’t occur in nature and hence manufactured by making array of small unit cells of specific structure(s) made up of conductors. Although the concept of the existence of negative refractive index was proposed in the 1960s by Veselago, it took around 40 years to be verified practically when smith et al. did the experiment in 2001. They used an array of unit cell structures as Split-Ring-Resonators (SRR) and thin wires to verify the concept. Thereafter researchers are working to develop different forms of metamaterial unit cells and for which metamaterial is still an open area of research. However, while designing a metamaterial unit cell, absence of an empirical formula makes the model analysis and synthesis difficult. Although with the help of EM simulation tools this is possible, it usually is too difficult, time consuming and costly. Due to this researchers are motivated to look for alternative methods. In this work, some techniques to develop CAD models are presented based on soft computing techniques for metamaterial analysis and synthesis. Use of different soft computing techniques in the field of microwave engineering is documented in the literature. However, unconventional unit cell structures are difficult to analysis because of unavailability of predefined mathematical formulas and equivalent analysis. This can be done by the complex Modified Nicolson-Ross-Weir (NRW) method with the support of EM simulation tools which are expensive. Frequency dependency of metamaterial characteristics for any kind of unit cell structure follows a similar pattern which is obtained from Lorentz model. The basic idea in this work, which develops CAD Models for metamaterial unit cell of unconventional structures is based on the assumption that each type of unit cell can be mapped to an equivalent SRR structure, for which empirical formula is available. This is done by implementing the concept of Space Mapping technique or surrogate based modeling. Most important contribution of the work is the development of Space Mapped CAD model for analysis of an Ω atom. The developed model is validated with a Deformed-Ω atom, which is developed by integrating the concept of Space Mapping (SM) and Artificial Neural Network. Thereafter, the work progresses with proposing CAD models for synthesis of SRR. The objective is to find the design parameters of SRR for a desired material characteristic and frequency. With the availability of only a complex non-linear analysis formula, the synthesis becomes a reverse engineering problem, which is difficult to process. Three different models are proposed to solve the problem. The first approach is use of Inverse Artificial Neural Network concept, which uses a trained neural network (IANN) to perform output-to-input mapping. The developed CAD model using this approach includes integration of three concepts: IANN, Prior Knowledge Input-Difference (PKI-D) and SM. Although the model is capable of synthesizing a metamaterial unit cell, still it has some disadvantages. To overcome the disadvantages (such as lower convergence rate, lower accuracy and complex programming), use of Evolutionary Algorithms (Genetic Algorithm and Differential Evolution) is proposed. While developing CAD model based on EA, the methodology is first tested by synthesizing Rectangular Microstrip Antenna (RMPA) and then using the same concept, an SRR is synthesized. A comparison shows DE based model to be more efficient than IANN and GA based models in terms of convergence speed, accuracy and robustness.