Metamaterials

ABSTRACT

Metamaterials, artificial composite structures with exotic material properties, have

emerged as a new frontier of science involving physics, material science, engineering and

chemistry. Metamaterials are a new kind of artificial media, exhibiting electromagnetic

properties not found in nature. In fact, the word “meta” comes from the Greek word meaning

“beyond”. Among them, the class of “Left Handed” (LH), also known as “Double Negative”

(DNG) metamaterials shows unusual characteristics such as backward waves, negative

refraction or reverse Doppler effect. This seminar presents the fundamentals of metamaterials:

structure, electromagnetic properties and some applications.

CONTENTS

List of Figures vii

List of Abbreviations viii

1 Introduction 1

1.1 Definition of Metamaterials (MTMs) And Left-Handed (LH) MTMs 1

1.2 Theoretical Speculation by Viktor Veselago 2

2 Fundamentals of LH MTMs 4

2.1 Left-Handedness From Maxwell’s Equations 4

2.2 Reversal of Snell’s Law: Negative Refraction 5

3 Structure And EM Response 7

3.1 Renewed Interest And Experimental Evidence 7

3.2 Necessary Frequency Dispersion of The Constitutive Parameters 8

3.3 First Experimental LH MTM Prototype 8

4 Transmission Line Metamaterials 13

4.1 Composite Right/Left-Handed (CRLH) MTMs 15

5 Applications of Metamaterials 17

5.1 Filters Using SRR 17

5.2 Diplexers 18

5.3 Couplers 18

5.4 Perfect Lens 19

5.5 Invisibility Cloak 20

6 The Future of MTMs 23

6.1 Tunability 23

6.2 Active MTMs 23

6.3 Use of Different Materials 24

6.4 Rise In Frequency (Nanotechnology). 24

6.5 Full 3D Metamaterials 24

7 Conclusion 25

References 26

List of figures

Fig. 1.1: Permittivity-permeability ( ) and refractive index diagram (n) 2

Fig. 2.1: RHM-LHM tuple of vector k, E and H 5

Fig. 2.2: Refraction of an electromagnetic wave at the interface between two media 6

Fig. 3.1: First negative-ε/positive-μ and positive-ε/negative-μ MTM 9

Fig. 3.2: Equivalent circuit models of SRRs 11

Fig. 3.3: First experimental LH structures of TWs and SRRs 11

Fig. 3.4: Transmitted power versus frequency curve of SRR 12

Fig. 4.1: The equivalent circuit of the general transmission line 13

Fig. 4.2: Fundamentals of composite CRLH MTMs 16

Fig. 5.1: Resonance curve for a single SRR 17

Fig. 5.2: Forward and Backward couplers 18

Fig. 5.3: Refraction due to LH and RH medium 19

Fig. 5.4: A simple coordinate transformation 21

Fig. 5.5: A schematic of coordinate transformation & Ray trajectories 21

Fig. 5.6: Two dimensional microwave cloaking structure 22

List of abbreviations

CRLH Composite right/left-handed

LH Left-handed

LHM Left-Handed Materials

LW Leaky-wave

MTM Metamaterial

NRI Negative refractive index

PLH Purely left-handed

PRH Purely right-handed

RH Right-handed

SRR Split-ring resonator

TE Transverse electric

TEM Transverse electric-magnetic

TW Thin-wire

TL Transmission line

TLM Transmission line method

TM Transverse magnetic

ZOR Zeroth-order resonator

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DivisionofElectronicsEngg. 1

Chapter 1

Introduction

Chapter 1 introduces electromagnetic metamaterials (MTMs) and left-handed

(LH) MTMs from a general prospect. Section 1.1 defines them. Section 1.2 presents the

theoretical speculation by Viktor Veselago on the existence of “substances with

simultaneously negative ε and µ” in 1967, which is at the origin of all research on LH

MTMs.

1.1 Definition of metamaterials (MTMs) and left-handed (LH) MTMs

Electromagnetic metamaterials (MTMs) are broadly defined as artificial effectively

homogeneous electromagnetic structures with unusual properties not readily available in

nature. An effectively homogeneous structure is a structure whose structural average cell size

p is much smaller than the guided wavelength λg . Therefore, this average cell size should

be at least smaller than a quarter of wavelength, p < λg /4. The condition p = λg /4 is

referred as the effective-homogeneity limit or effective-homogeneity condition, to ensure that

refractive phenomena will dominate over scattering/diffraction phenomena when a wave

propagates inside the MTM medium. If the condition of effective-homogeneity is satisfied,

the structure behaves as a real material in the sense that electromagnetic waves are essentially

myopic to the lattice and only probe the average, or effective, macroscopic and well-defined

constitutive parameters, which depend on the nature of the unit cell; the structure is thus

electromagnetically uniform along the direction of propagation. The constitutive parameters

are the permittivity ε and the permeability µ, which are related to the refractive index n by

where and are the relative permittivity and permeability related to the free space

permittivity and permeability by ε0 = ε/εr = 8.854 x 10−12 and µ0 = µ/µr = 4π x 10−7,

respectively. The sign ± for the double-valued square root function has been a priori

admitted for generality.

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The four possible sign combinations in the pair (ε, µ) are (+, +), (+, −), (−, +), and (−, −),

as illustrated in the ε − µ diagram of Fig 1.1. Whereas the first three combinations are well

known in conventional materials, the last one [(−, −)], with simultaneously negative

permittivity and permeability, corresponds to the new class of left-handed (LH) materials. LH

materials, as a consequence of their double negative parameters, are characterized by

antiparallel phase and group velocities, or negative refractive index (NRI)

LH structures are clearly MTMs, according to the definition given above, since they

are artificial (fabricated by human hands), effectively homogeneous (p < λg /4), and

exhibit highly unusual properties (εr , µr < 0). It should be noted that, although the term

MTM has been used most often in reference to LH structures in the literature, MTMs

may encompass a much broader range of structures. However, LH structures have been by far

the most popular of the MTMs, due to their exceptional property of negative refractive index.

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1.2 Theoretical speculation by Viktor Veselago

The history of MTMs started in 1967 with the visionary speculation on the existence of

“substances with simultaneously negative values of ε and µ” (fourth quadrant in Fig 1.1) by

the Russian physicist Viktor Veselago. In his paper, Veselago called these “substances” LH to

express the fact that they would allow the propagation of electromagnetic waves with the

electric field, the magnetic field, and the phase constant vectors building a left-handed triad,

compared with conventional materials where this triad is known to be right-handed.

Several fundamental phenomena occurring in or in association with LH media were predicted

by Veselago:

1. Necessary frequency dispersion of the constitutive parameters.

2. Reversal of Doppler Effect.

3. Reversal of Vavilov-Cerenkov radiation.

4. Reversal of the boundary conditions relating the normal components of the electric

and magnetic fields at the interface between a conventional/right- handed (RH)

medium and a LH medium.

5. Reversal of Snell’s law.

6. Subsequent negative refraction at the interface between a RH medium and a LH

medium.

7. Transformation of a point source into a point image by a LH slab .

8. Interchange of convergence and divergence effects in convex and concave lenses,

respectively, when the lens is made.

9. Plasmonic expressions of the constitutive parameters in resonant-type LH media.

Veselago concluded his paper by discussing potential real (natural) “substances” that could

exhibit left-handedness. He suggested that “gyrotropic substances possessing plasma and

magnetic properties” (“pure ferromagnetic metals or semiconductors”), “in which both ε and

µ are tensors” (anisotropic structures), could possibly be LH. However, he recognized,

“Unfortunately, we do not know of even a single substance which could be isotropic and have

µ < 0,” thereby pointing out how difficult it seemed to realize a practical LH structure. No LH

material was indeed discovered at that time.

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Chapter 2

Fundamentals of LH MTMs

2.1 Left-handedness from Maxwell’s equations

Four Maxwell’s equations can explain all electromagnetic phenomena. In order to study

the propagation of waves through various media, four possible solutions to the wave equation

have been considered. The first one is satisfied with ε and μ positive, which is the normal

solution. Under this solution, waves propagate. Two other solutions can be those with

different sign of ε and μ, i.e., ε < 0 and μ > 0 or vice versa. In these cases, waves cannot be

propagated and they are attenuated. Veselago predicted other possible solution with negative

values of ε and μ. Under this solution, waves can be propagated, obtaining a considerable

difference in wave propagation.

In the propagation of electromagnetic waves, the direction of energy flow is given by a

right-hand rule, involving , and .

The Maxwell’s equations for a monochromatic plane wave propagating in an

isotropic, homogenous medium are given by:

From these equations, it can be readily seen that , and form a right-handed

triplet of vectors, as a plane wave propagates in a normal dielectric materials with ε>0 and

μ>0. In contrast, these vectors form a left-handed triplet in materials with ϵ>0 and μ >0.

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Moreover, the Poynting vector, defines as = × ,is antiparallel to the wave vector in

such materials. It is further proved that the phase refractive index given by

must take a negative sign, so that the causality is still conserved.

Due to the aforementioned exotic properties, materials with simultaneous negative

permittivity and permeability are called left-handed materials(LHMs), or negative-Index

materials(NIMs).

Negative-index materials give rise to a host of counterintuitive phenomena as

Veselago discussed in his seminal paper such as reversal of Snell’s law, reversal of Doppler

Effect and reversal of Vavilov-Cerenkov radiation.

2.2 Reversal of Snell’s law: negative refraction

It was undoubtedly the concept of negative refraction that brought metamaterials to

prominence. Seriously studied for the first time by Veselago, negative refraction is achieved

when at the same frequency,

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Using Maxwell’s equations to calculate the refractive index gives,

and conventional materials take the positive sign. Veselago showed that, if condition (1) is

met, the negative sign for n is the one that satisfies causality.

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Chapter 3

Structure and EM response

3.1 Renewed interest and experimental evidence

It was in 1968 Victor Veselago, a Russian physicist, examined the characteristics of

electromagnetic wave propagation in a theoretical medium with simultaneous negative

electric Permittivity ε and magnetic permeability μ. Although he was aware of the

inexistence, by the time, of such media, he discussed its feasibility, having into account the

frequency dispersive behavior of both permittivity and permeability, allowing then frequency

bands where negative values of ε and μ could be reached. The work derives a negative phase

velocity (backward waves) while the group velocity is still positive, according to the causality

principle; and a negative refractive index, giving rise to negative refraction, as follows from

Snell’s law.

After the work of Veselago was published, the problem of LH media was almost

forgotten for nearly 30 years. The main reason was aforementioned unachievability of such

media. The return of artificial media theory came in 1992, when Mamdouh et al. proposed an

omega particle as a unit cell of artificial chiral medium. Unfortunately the authors did not

realize that such medium can also embody negative permittivity and permeability. In those

years also the interest in the Veselago's work was risen, mainly in the publications written by

J. B. Pendry et al. The first publication showed how to make negative permittivity medium at

microwave frequencies. For this purpose the 2D matrix of thin wires "wire medium", which

simulates Plasmon behaviour of metals on optical frequencies, was proposed. In the following

paper the Pendry's working group extended this idea to the 3D wire net, by which the

isotropic behaviour was achieved. The negative permeability was however still unknown.

That was published in the year 1999. In this, probably the most important publication in

metamaterials, the proposal of a small resonant particle; the split ring resonator (SRR), the

basic constituent of artificial negative permeability media, was described.

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3.2 Necessary frequency dispersion of the constitutive parameters

A frequency-dispersive or simply dispersive medium is a medium in which the

propagation constant (β) is a nonlinear function of frequency, which results in frequency-

dependent group velocity and leads to distortion of modulated signals. This implies that either

εr or μr (or both) have to be functions of frequency.

In his seminal paper, Veselago concluded that simultaneous values of ε and μ can be

realized only when there is frequency dispersion. In fact, it can be seen from the relation

that when there is no frequency dispersion nor absorption we cannot have ε<0 and μ<0, since

in that case the total energy would be negative. When there is a frequency dispersion,

however, the relation must be replaced by

Eqs. (3,1) are the general entropy conditions for the constitutive parameters. These entropy

conditions show that simultaneously negative ε and μ are physically impossible in a non-

dispersive medium since they would violate the law of entropy. They also show that, in

contrast in a dispersive medium, simultaneously negative ε and μ are allowed, as long as the

frequency dependent ε and μ satisfy the conditions of Eqs. (3.1). For this to be achieved, ε and

μ must be positive in some parts of their spectrum, to compensate for the negative parts,

which shows that a LH medium is necessarily dispersive.

3.3 First experimental LH MTM prototype

After Veselago’s paper, more than 30 years elapsed until the first LH material was

conceived and demonstrated experimentally. This LH material was not a natural

substance, as expected by Veselago, but an artificial effectively homogeneous structure

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(i.e., a MTM), which was proposed by Smith and colleagues at University of California,

San Diego (UCSD). This structure was inspired by the pioneering works of Pendry at

Imperial College, London. Pendry introduced the plasmonic-type negative-ε/positive-μ and

positive-ε/negative-μ structures shown in Fig 3.1, which can be designed to have their

plasmonic frequency in the microwave range. Both of these structures have an average cell

size p much smaller than the guided wavelength λg (p≪λg) and are therefore effectively

homogeneous structures, or MTMs.

The negative-ε/positive-µ MTM is the metal thin-wire (TW) structure shown in Fig

3.1(a). If the excitation electric field E is parallel to the axis of the wires (E z), so as to induce

a current along them and generate equivalent electric dipole moments, this MTM exhibits a

plasmonic-type permittivity frequency function of the form.

where ω is the plasma frequency is the electric plasma frequency, tunable in the GHz range, and ζ is the damping factor related to material losses.

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It clearly appears in this formula that

which reduces if ζ = 0 to ,

On the other hand, permeability is simply µ = µ0, since no magnetic material is present

and no magnetic dipole moment is generated. It should be noted that the wires are

assumed to be much longer than wavelength (theoretically infinite), which means that the

wires are excited at frequencies situated far below their first resonance.

The positive-ε/negative-µ MTM is the metal split-ring resonator (SRR) structure

shown in Fig 3.1(b). SRR consists of two concentric rings in general placed on a dielectric

substrate. Both rings have the same width and are separated by the gap. Each ring is also cut

by a gap, width of which is not very important (this gap is usually of size similar to width). If

the excitation magnetic field H is perpendicular to the plane of the rings (H y), so as

to induce resonating currents in the loop and generate equivalent magnetic dipole

moments, this MTM exhibits a plasmonic-type permeability frequency function of the

form

Where F is the geometrical factor, ω is the magnetic resonance frequency, tunable in the

GHz range, and ζ is the damping factor related to material losses. It should be noted that

the SRR structure has a magnetic response despite the fact that it does not include

magnetic conducting materials due to the presence of artificial magnetic dipole moments

provided by the ring resonators. The above equation reveals that a frequency range can exist

in which Re(µr ) < 0 in general (ζ ≠ 0). In the loss-less case (ζ ≠0), it appears that

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The equivalent circuit of a SRR is shown in Fig 3.2. In the double ring configuration

[Fig3.2 (a)], capacitive coupling and inductive coupling between the larger and smaller rings

are modeled by a coupling capacitance (Cm) and by a transformer (transforming ratio n),

respectively. In the single ring configuration [Fig 3.2(b)], the circuit model is that of the

simplest RLC resonator with resonant frequency ω0 = 1/√ . The double SRR is essentially

equivalent to the single SRR if mutual coupling is weak, because the dimensions of the two

rings are very close to each other, so that L1 ≈ L2 ≈ L and C1 ≈ C2 ≈ C, resulting in a

combined resonance frequency close to that of the single SRR with same dimensions but with

a larger magnetic moment due to higher current density.

In 2000, Smith et al. combined the TW and SRR structures of Pendry into the

composite structure shown in Fig 3.3(a), which represented the first experimental LH MTM

prototype.

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The arguments consisted of the following: 1) designing a TW structure and a SRR structure

with overlapping frequency ranges of negative permittivity and permeability; 2) combining

the two structures into a composite TW-SRR structure, which is shown in Fig 3.3(a); and 3)

launching an electromagnetic wave e−jβr through the structure and concluding from a fact that

a passband (or maximum transmission coefficient, experimentally) appears in the frequency

range of interest proves that the constitutive parameters are simultaneously negative in this

range on the basis of the fact that β = nk0 = ± √ has to be real in a passband. That this

passband [the dashed line in Fig. 3.4] occurs within the previously forbidden region of the

split ring dispersion curves indicates that the negative εeff for this region has combined with

the negative μeff to allow propagation.

In the few years after the first experimental demonstration of a LH structure by

Smith et al., a large number of both theoretical and experimental reports confirmed the

existence and main properties of LH materials predicted by Veselago.

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Chapter 4

Transmission line metamaterials

Although very exciting from a physics point of view, the initial TW-SRR MTMs seem of

little practical interest for engineering applications because these structures are resonant, and

consequently exhibit high loss and narrow bandwidth.17 A structure made of resonating

elements generally does not constitute a good transmission medium for a modulated signal

because of the quality factor intrinsically associated with each resonator. Due to the

weaknesses of resonant-type LH structures, there was a need for alternative architectures.

Therefore, recognizing the analogy between LH waves and conventional backward waves ,

three groups introduced, almost simultaneously in June 2002, a transmission line (TL)

approach of metamaterials: Eleftheriades et. al , Oliner and Caloz et al. .

The planar version of a metamaterial can be treated as a transmission line. Here we

effectively apply the circuit approach based on the equivalent circuit of the transmission line

consisting of lumped elements. This circuit, shown in Fig. 4.1a, consists of series impedance

Z and parallel admittance Y and represents the element of the line with length d, which must

be much shorter than the wavelength λ in order to form a unit cell.

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The standard lossless line has Z =jωL, Y=jωC as shown in Fig. 4.1b, then

Where Z0 is the characteristics impedance, γ is the propagation constant, vp is the phase

velocity and vg is the group velocity. This corresponds to the propagation of the standard TEM

forward wave along the line. Both velocities vp and vg are positive.

Now let us consider the dual case with the corresponding equivalent circuit shown in

Fig. 4 . 1 c where the positions of the capacitance and inductance have been exchanged. In

this way we have changed the original L-C low-pass structure into the C-L high-pass

structure. The latter lines are denoted as left handed and represent the planar version of a

metamaterial. Now for the lossless line we have α=0, Z =1/(jωCL) and Y=jωLL .

Consequently,

This indicates that the group velocity has an opposite direction comparing to the phase

velocity. This features the backward wave.

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4.1 Composite right/left-handed (CRLH) MTMs

The concept of composite right/left-handed (CRLH) MTM, introduced by Caloz et al. in

2003. The TL structures shown in Fig 4.1c are constituted of series (interdigital) capacitors CL

and shunt (stub) inductors LL, intended to provide left-handedness from the explanations of

the previous section. However, as a wave propagates along the structures, the associated

currents and voltages induce other natural effects. As currents flow along CL, magnetic fluxes

are induced and therefore a series inductance LR is also present; in addition, voltage gradients

exist between the upper conductors and the ground plane, which corresponds to a shunt

capacitance CR . As a consequence, a purely LH (PLH) structure does not exist, even in a

restricted frequency range, since a real LH structure necessarily includes (LR , CR )

contributions in addition to the (LL, CL) reactances. This was the motivation for the

introduction of the term “composite right/left-handed” (CRLH), allowing to account for the

exact natural of practical LH media.

The essential characteristics of a CRLH TL MTM can be inferred from analysis of the

equivalent circuit of Fig 4.2(a). At low frequencies, LR and CR tend to be short and open,

respectively, so that the equivalent circuit is essentially reduced to the series-CL/shunt-LL

circuit, which is LH since it has antiparallel phase and group velocities; this LH circuit is of

highpass nature; therefore, below a certain cutoff, a LH stopband is present. At high

frequencies, CL and LL tend to be short and open, respectively, so that the equivalent circuit is

essentially reduced to the series-LR /shunt-CR circuit, which is RH since it has parallel phase

and group velocities; this LH circuit is of lowpass nature; therefore, above a certain cutoff, a

RH stopband is present. In general, the series resonance ωse and shunt resonance ωsh are

different, so that a gap exists between the LH and the RH ranges. However, if these

resonances are made equal, or are “balanced,” this gap disappears, and an infinite-wavelength

(λg = 2π/|β|) propagation is achieved at the transition frequency ω0.

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This gives the possibility of designing resonators of zeroth order oscillating on this

resonant frequency ω0 which does not depend on the resonator length and even with

resonances of negative orders. The planar LHTL’s were applied in a number of microwave

elements mostly utilizing the CRLH TLs. The new properties of these circuits include: dual-

band operation, bandwidth enhancement, arbitrary coupling level and negative and zeroth-

order resonance.

The dual-band property follows from the possibility of the CRLH TL to satisfy the

condition of having desired characteristic impedance and a phase constant at two

independent frequencies, one in the LH band and the second one in the RH band. This was

used in dual-band quarter wavelength stubs that have simultaneously the electrical length λ/4

and 3λ/4 at any arbitrary pair of frequencies. These stubs were applied in dual-band

quadrature hybrids and Wilkinson power dividers, and dual band quadrature mixers.

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Chapter 5

Applications of metamaterials

5.1 Filters using SRR

SRR characteristics are strongly dependent on frequency, being resonant structures.

This means that they can switch from quadrant I to IV as frequency varies. So transmission

and stop bands are achieved. To do that, a combination of different size SRRs can make a

stop-band or bandpass filters.

Figure 5.1 shows a measured absorption curve of a SRR similar to that shown in the inset.

The Q-factor, as measured from the absorption curve, was found to be greater than 600 at the

resonance frequency of ~4.85 GHz.

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5.2 Diplexers

Diplexer is a passive device that combines two different frequency signals to share the

same propagation channel. The dual-band property follows from the possibility of the

CRLH TL to satisfy the condition of having desired characteristic impedance and a phase

constant at two independent frequencies, one in the LH band and the second one in the RH

band.

5.3 Couplers

A coupler transfers part of an electromagnetic wave, propagating through a transmission

line, to another. For ordinary RH media, the transmission is forward. If the transmission line

is LH, then backward coupling can send power back.

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5.4 Perfect lens

Perhaps one of the most striking predictions for MTMs came in 2000, when Pendry

showed that a flat slab of NI material could produce a focus with resolution exceeding the

diffraction limit. This was an extraordinary prediction, since it required that the normally

exponentially decaying evanescent terms produced by a source would actually be recovered in

the image formed by the slab. All sources of EM radiation possess both propagating

components and components that stay fixed, decaying rapidly away with distance from the

source. Mathematically, all EM sources can be expressed as a superposition of propagating

plane waves and exponentially decaying near-fields. These exponentially decaying terms

cannot be recovered by any known positive index lens. Since the near field is responsible for

conveying the finest details of an object, their absence limits the resolution of positive index

optics to roughly λ/2 – the diffraction limit. However, Pendry predicted that an NI lens would

actually be able to recover the exponentially decaying near-field components at the image,

thereby exhibiting resolution beyond the diffraction limit.

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5.5 Invisibility cloak

Invisibility cloaking can be accomplished by manipulating the paths traversed by light

through a novel optical material. Metamaterials direct and control the propagation and

transmission of specified parts of the light spectrum and demonstrate the potential to render

an object seemingly invisible. Metamaterial cloaking, based on transformation optics,

describes the process of shielding something from view by controlling electromagnetic

radiation. Objects in the defined location are still present, but incident waves are guided

around them without being affected by the object itself.

Transformation optics

Metamaterials give enormous choice of material parameters for electromagnetic

applications. So much so that we might ask if there is a new way to design electromagnetic

systems exploiting this new flexibility. In an ideal world magnetic and electrical field lines

can be placed anywhere that the laws of physics allow and a suitable metamaterial found to

accommodate the desired configuration of fields. It was to answer the question of what

parameters to choose for the metamaterial that we developed transformation optics. The idea

is quite straightforward: start with a field pattern that obeys Maxwell’s equations for a system

that is topologically similar to the desired configuration but confined either to free space or a

simple configuration of permittivity and permeability, then distort the system until the fields

are in the desired configuration. If we imagine that the original system was embedded in an

elastic matrix in which Cartesian coordinate lines were drawn, then after distortion the

deformed coordinates could be described by a coordinate transformation. Next rewrite

Maxwell’s equations using the new coordinate system. Some time ago it was shown that

Maxwell’s equation is of the same form in any coordinate system but the precise values of

permittivity and permeability will change. These new values of permittivity and permeability

are the ones we must give to our metamaterial if we want the fields to take up the distorted

configuration.

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As a challenge for transformation optics there are two main problems for constructing

a cloak of invisibility: first scattered radiation must be eliminated and hence no radiation must

reach the hidden object; second the hidden object must cast no shadow. The latter is the more

difficult of the two to achieve. Pendry suggested to construct a cloak that guides radiation

around the hidden space but allowing to resume its original course on the far side. An

observer would see the same radiation as if neither the cloak nor the hidden object were

present. One advantage of this scheme is that any object can be placed inside the cloak and

still remain hidden.

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In 2006, D. Schurig et al presented the first practical realization of such a cloak: in

their demonstration, a copper cylinder is ‘hidden’ inside a cloak constructed according to the

previous theoretical prescription. The cloak is constructed using artificially structured

metamaterials, designed for operation over a band of microwave frequencies. The cloak

decreases scattering from the hidden object whilst at the same time reducing its shadow, so

that the cloak and object combined begin to resemble free space. Operating frequency is

8.5GHz. The cloak is shown in Fig. 5.6.

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Chapter 6

The future of MTMs

The special properties of CRLH structures, provide guesses about many new

applications. Also, the present limitations of such structures mean exciting challenges for the

future.

6.1 Tunability

It would be desirable to control the frequency behaviour of MTMs. This can be done by

adding electronically controllable extra capacitance or inductance (i.e. including varactors

into the base transmission line or ferroelectric/ ferrimagnetic media ). Modification of the

geometry of the structure has also been suggested

6.2 Active MTMs

Active MTMs represent entirely unexplored fields to date. It may be predicted that

novel active applications will soon emerge from the new paradigm of MTMs and MTM TL

structures and extend the range of available active microwave and optoelectronic devices

An immediate direction for integration of active components into MTMs is

compensation of losses, which has been a critical issue in many MTMs and in particular in

SRR/TW structures. In the same manner as (passive) varactors were distributed along MTM

TL structures, transistors may be implemented, for instance to equalize and modulate the

profile of the fields along a leaky wave structure to control its radiation characteristics, or to

develop enhanced gain-bandwidth distributed power amplifiers. In the future, MTMs may

become part of complex radio-frequency integrated circuits (RFICs) and monolithic

microwave integrated circuits (MMICs) technology implementations.

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6.3 Use of different materials

MTMs are made mostly of metallic conductors and dielectric substrates. Moreover,

the rise in frequencies, up to Terahertz, and the applications to active devices, requires

materials other than metallic to reduce losses

6.4 Rise in frequency (Nanotechnology).

The size of the constituent “metaparticles” is related to the wavelengths of the signals

interacting with the medium. So, as the frequency increases, nanotechnology becomes more

and more important.

6.5 Full 3D metamaterials

Most of the to-day applications are based on planar structures. Nevertheless, an ideal

MM would be a 3D isotropic and homogeneous structure. Some works for the terahertz bands

have started recently.

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Chapter 7

Conclusion

Metamaterials are a brand new kind of artificial media whose properties emerge from the

structure itself, instead of their single constituents. Their electromagnetic properties have not

been found in natural media, giving rise to a broad range of applications. Without any doubt,

metamaterials have become an extremely exciting research area. The unique electromagnetic

properties provided by metamaterials attract considerable attention of researchers from

multiple disciplines. In turn, this will spark the merging of knowledge and expertise across

different areas, further driving the astounding advance of metamaterials research. Within only

ten years, we have witnessed many remarkable breakthroughs, such as negative refraction,

superlens and invisible cloak. Many other fascinating discoveries and applications are waiting

for us to explore. With the complete degree of freedom to control over material properties,

what we could do next is only limited by our imagination. The challenge calls for an

interdisciplinary research including physics, engineering, chemistry, mathematics and even

biology.

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References

1. Cabeceira, A.C.L.; Barba, I.; Grande, A., "Metamaterials, a chance for high frequency

electronics?," Electron Devices (CDE), 2013 Spanish Conference on , vol., no.,

pp.159,162, 12-14 Feb. 2013

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