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Springer Nature Singapore Pte Ltd. 2017

Balamati Choudhury (ed.) Metamaterial Inspired Electromagnetic Applications 10.1007/978-981-10-3836-5_1

1. Soft Computing for Metamaterial Structures

Balamati Choudhury 1

(1)

Centre for Electromagnetics, CSIR-National Aerospace Laboratories, Old Airport Road, Bengaluru, 560017, India

Balamati Choudhury

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1.1 Introduction

Metamaterials are one of the widely used artificially engineered materials in the area of electromagnetic (EM) applications as it exhibits certain properties that are not seen in naturally occurring materials. The most exciting property of metamaterials is the ability to show negative refractive index. The word metamaterial was proposed by Rodger M. Wasler of University of Texas. The root of this word, meta, is Greek, and it means beyond, i.e., metamaterial means beyond the material. Though the science of metamaterials is relatively new, Victor Veselago predicted the possibility of existence of doubly negative materials in 1968, in a Russian publication [].

Metamaterials are also known to be doubly negative materials or left-handed materials (LHM). Material with negative permeability and permittivity possess negative refractive index value, which not occurs in naturally occurring materials. Consequently, EM wave propagation through these materials follows left-handed coordinates as shown in Fig. ]. It is also important to note that LHM is necessarily dispersive in order to meet entropy conditions. This means that either the permittivity or permeability or both vary as a function of frequency. Other properties shown by LHM include inverted Doppler effect, inverted Cerenkov effect, artificial magnetism, reversal of Snells law.

Fig. 1.1

a Right-handed orientation of vectors E, H, K when r > 0, r > 0. b Left-handed orientation of vectors E, H, K when r < 0, r < 0

The reversal of Snells law can be explained through the Fig.. Consider the propagation of a ray through boundary between left-handed and right-handed media, ray 3 is the refracted ray when the second medium is right-handed, and ray 4 is the refracted ray when the second medium is left-handed.

Fig. 1.2

Reflection and refraction at the interface of two media when a n 2 > 0 (ray 3), b n 2 < 0 (ray 4)

By considering the field components at the dielectric interfaces, if the second medium is double-negative, then the refraction of light occurs in the same side of the incident beam, i.e., behave as medium which exhibits negative effective refractive index.

The most commonly used definition of metamaterials []. The dimensions of these metallic structures as well as the individual material properties and thickness of the substrate significantly affect the resonant frequency, hence resulting in a frequency-dependent material characteristics. The cellular size must be smaller than or equal to sub-wavelength. If the cell size is equal to a quarter of a wavelength, then is called effective-homogeneity limit. It ensures that refraction dominates scattering/diffraction when wave propagates through a metamaterial.

As mentioned earlier, metamaterials are periodic/aperiodic structures composed of metallic strips etched on dielectric substrates. The geometry of the metallic layer as well as the properties of the dielectric is responsible for the resonant characteristics of the metamaterial. Figure c resonates at three frequencies. These designs have been explored by many research groups around the world.

Fig. 1.3

Common metamaterial designs, a circular split-ring resonator, b electric ring resonator, c multi-band circular ring metamaterial structure, d square ring resonator

In order to respond to the magnetic component of the electromagnetic wave, the typically used element is split-ring resonator (SRR) and this magnetic atom was introduced by Pendry in 1999. According to Padilla et al. (2006), []. The structure consists of combination of a wire structure with negative permittivity and a split-ring resonator structure with negative permeability for the same frequency band, resulting in negative refraction.

Conventionally, metamaterials are simulated using software based on Finite Element Methods (FEM) or Finite Integration Techniques (FIT). This software enables the designer to study the scattering parameters (S-parameters) of the metamaterial structure and S-parameter retrieval method is used to obtain the effective material parameters. It is clear that the material characteristics are engineered through optimizing the various structural parameters such as thickness of dielectric, size, shape of the patterns in the metamaterial structure. One of the best choices for optimization in metamaterial design is the multidimensional artificial intelligent optimization algorithms.

Artificial intelligent optimization (soft computing or nature-based optimization) plays an important role in the design and optimization of various problems in engineering field. It is used to model and enable solutions to complex real-world problems for which the analytical solution methods do not exist. Soft computing is an optimization technique to find the solution of a problem which is very difficult to solve or with less mathematical formulations regarding the problem domain. The aim of these soft computing methods is to provide quick solutions which resemble human-like decisions.

The term soft computing was introduced by Zadeh (1992) [], Passino 2002).

Soft computing methods do not require extensive mathematical formulation of the problem. Thus, the necessity of exclusive domain-specific knowledge can be reduced. Also it can handle multiple variables and multiple objective functions simultaneously. These make the soft computing techniques quite useful in EM applications to provide cost-effective solution to the user in less computational time. From last decade onwards, various soft computing techniques are used in the field of electromagnetics. This book gives an introduction to the implementation of soft computing techniques in the design of metamaterial-based applications such as PIFA antennas, cloak, and radar absorbers.

1.2 Soft Computing Techniques

Soft computing is a computational technique based on behavior of biological systems and theory of natural selection. It is used in computer science to sort the problems whose solutions are unpredictable and uncertain. The main advantages of these techniques include robustness, low-cost solution, imprecision, and uncertainty. Soft computing technique is a best choice for problems without enough information about the problem domain. Classification of optimization techniques are given in Fig.. A brief description about different soft computing techniques is given in this section.

Fig. 1.4

Flowchart of optimization techniques

1.2.1 Neural Network (NN)

Neural network or artificial neural network is an information processing system or a computing system which consists of highly interconnected processing elements called as neurons working in parallel to solve particular problems. The artificial neural network was first developed by McCulloch in 1943 [ shows a typical structure of neural network.

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