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Chapter 1

Introduction

1.1 Metamaterials: Overview

Metamateials(MTMs) are defined as artificial effectively homogeneous electromagnetic

structures with properties which are not found in naturally occurring materials. Instead

of constructing materials at the chemical level, these are constructed with materials at

the macroscopic level. Natural occurring materials are made up of individual atoms which

are separated from each other by distances on the order of angstroms. At an elementary

level phenomena like reflection, diffraction and refraction are determined by length of unit

cell of atom. For a homogeneous structure it is essential that the average unit cell size

p should be smaller than a quarter of wavelength g: p < g/4 . This condition ensure

that refractive phenomena will dominate over scattering and diffraction effects, when wave

travels through the media. Thus waves are essentially unaware to lattice structure and

structure remains electromagnetically uniform along the direction of propagation [1].

In 1968, Victor Veselago, a Russian physicist theoretically investigated plane wave

propagation in a media with simultaneously negative permittivity () and negative perme-

ability () [2]. After 30 years Pendry et al successfully demonstrated negative permittivity

[3-4] and negative permeability [5], while Smith et al developed composite negative index

medium [6]. Veselagos theoretical prediction of existence of negative refractive index

material was demonstrated by smith et al in laboratory.

As Metamaterials are artificial structure, they enable us to control over waves and pro-

vide new functionalities. MTMs are expected to make impact over the technologies where

electromagnetic radiation are used. The concept of invisibility, perfect lens, microwave

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absorber and near field imaging have opened new areas of research, while incorporation of

MTMs has improved the performances of devices such as antennas, filters, couplers and

many more.

1.2 Left Handed MTMs

Under the condition of effective homogeneity, material properties are defined by macro-

scopic constitutive parameter permittivity and permeability which depend on nature

of unit cell. Pair of these two parameter make four different sign combinations as shown

in - diagram of Fig. 1.1. The abbreviations DPS, ENG, MNG and DNG are assigned

to double-positive materials ( 0, 0, quadrant- I), epsilon-negative materials ( 0, 0,

quadrant-II), mu-negative materials ( 0, 0, quadrant-IV) and double-negative materials

( 0, 0, quadrant-III) respectively. DPS materials include the list of commonly occurring

materials like most of the dielectrics. ENG materials have natural examples like plasma

or metals at optical frequencies. Similarly some ferrimagnetic materials show MNG char-

acteristics. But DNG materials have no natural analogue, hence are called metamaterials

in stricter sense.

1.3 Zero Index Metamaterial

1.4 Motivation

1.5 Outline of Thesis

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Figure 1.1: Representation of various materials in permittivity-permeability ( ) di-agram; Courtesy: C. Caloz and T. Itoh, Electromagnetic Metamaterials: TransmissionLine Theory and Microwave Applications: The Engineering Approach, John Wiley, 2006.

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Chapter 2

Theory of Left Handed Materials

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