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Metamaterials

Aos Al-waidh

Photonics in Engineering Research Group

General Engineering Research Institute

Liverpool John Moores University

E-mail: A.M.Al-Waidh@2009.ljmu.ac.uk

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Outlines• Introduction to metamaterials

• Classification of materials

• Photonic Crystal

• Realisation of Metamaterials

• Unit Cell Size

• Metamaterial Application

• Cloaking

• Conclusions

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Introduction To Metamaterials

Metamaterials are periodic or quasi-periodic, sub-wavelength metal structures. The electro-magnetic material properties are derived from its structure rather than inheriting them directly from its material composition.

Based on definition of J.Pendry 2000

empty glass

regular water, n = 1.3

“negative” water, n = -1.3

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GROUP Positive refraction index Negative refraction index

Introduction To Metamaterials

This term is particularly used when the resulting material has properties that are not found in naturally formed substances as indicated by the prefix “meta”.

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1

2

ENERGY

PHASEVELOCITY

Air

Materiallike glass

Metamaterial

Yes as a backward wave

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μ

ε

PropagatingStandard optical

materialsEvanescent

Metals (UV – Optical)

EvanescentNatural magnetic

materials (up to GHz)

PropagatingMetamaterials

(−, +) (+, +)

(−, −) (+, −)

OR

Negative Phase

PositivePhase

Backward Waves

ForwardWaves

n n

1

1

n<1

Classification of materials

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μ

ε

Classification of materials

(DNG) ε < 0, μ < 0Not found in nature

(MNG) ε > 0, μ < 0Gyrotropic

(DPS) Dielectrics

(ENG) ε < 0, μ > 0Plasma

ABSORPTION

ABSORPTION

POSITIVE REFRACTION

NEGATIVE REFRACTION!!

( )( )n

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DPSENGMNG

Classification of materials

DNG

Cloak

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Realisation of Metamaterials

Negative ε• Thin metallic wires are arranged periodically• Effective permittivity takes negative values below plasma

frequencyNegative μ• An array of split-ring resonators (SRRs) are arranged

periodically

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EyHx

ISRR

IROD

y x

z

Magnetic resonance

(Negative μ)

Electric resonance

(Negative ε)

Realisation of MetamaterialsEmbedding a metal split-ring and a metal rod creates left-handedness

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• Another example of composite material with negative refraction index is the photonic crystal:

• Photonic crystals may behave as if they possess a negative refractive effect without actually having a negative refractive index. Additionally, and μ are not defined for photonic crystals as they are not homogeneous systems at their operational wavelength.

Photonic Crystal

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/a0 1

a <<< a a >>

vs. a

Effective mediumdescription using Maxwell equations with µ and Example:Metamaterials

Properties determinedby diffraction andInterference Example:Photonics crystals

Properties describedusing geometrical optic and ray tracing Example:Lens systemShadows

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Not this one0,0 kHE

,,

The right hand rule

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Not this oneIf then is a left set of vectors:

0,0 kHE

,,

The left hand rule !

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a

a

w

w

schematics of the elementary cell.

d•A simple calculation can be carried out to verify the UV laser capability to create the required size.

•Mostly the open ring resonator can be considered as an LC circuit where the capacitance can described by the usual textbook formula.

Unit Cell Size

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•For a large capacitor with the separation between the plates is small compared to the dimensions of the plates, to ensure a uniform distribution of the field over plate’s area:•C ∝ plate area/distance •And the inductance by the formula for a coil with N windings: •L ∝ coil area/length (for N = 1)

a

a

w

w

schematics of the elementary cell.

d

Unit Cell Size

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For simplicity, we can consider the width of the metal is equal to the distance between the capacitor plates (a)C = oc ad/a where:c = the effective permittivity of the material in between the plates andd= the metal thicknessL = o w2/d where:W= width = length of the coil

a

a

w

w

schematics of the elementary cell.

d

Unit Cell Size

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LC-resonance frequency:

LC = 1/ =

Where c =

And the LC-resonance wavelength

LC =

Lcc

cw 1

00

1

cLC

wc 22

a

a

w

w

schematics of the elementary cell.

d

Unit Cell Size

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•For relevant parameters c ≈ 3.5 this yield LC ≈ 10 ×w. •Thus, for microwave wavelength of ≈ 10 mm, the linear dimension of the coil would need to be on the order of w = 1 mm, implying minimum feature sizes around 200.

a

a

w

w

schematics of the elementary cell.

d

Unit Cell Size

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Negative phase velocity, reversal of Doppler Effect and Backward Cerenkov radiation are interesting novel physical properties emerging from left-handed metamaterials phenomena.

The Perfect Lens

Metamaterial Application

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Cloaking deviceIs it real, how?Can I borrow your cloak to get my PhD ?

Metamaterial Application

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Its not that simple

No tricks No

Cloaking device

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Another approachvirtual invisibilityRetro-reflective Projection Technology, Optical Camouflage

Cloaking device

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What we are locking for ?

Cloaking device

True invisibility

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The idea is to create a region that is inaccessible

To be realised by creating a new material

We need to manipulate space

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-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6y’

x’

y

x

Constant x:

Constant y:

Forbidden:

Purely geometrical distortion of space: No material yet

Hole in space

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Transformation of a region

Preserve form of Maxwell’s equations

Predict form of permittivity and permeability to use in the original frame

for cloaking

Realisation

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Fill the original empty space with this material

Now we have a cloaking device

The cloak

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LIGHTSOURCE

OBJECT

METAMATERIAL

LIGHTRAYS

A 3D Possibility

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• Meta-materials have been shown to have remarkable applications

• LHM s and negative materials can be used to overcome diffraction limit and construct a super-lens

• A super-lens enables ultra-deep sub-surface imaging

• Very new field, lots of work to do (theory and experiments)

Conclusions

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Thanks for your attention.