1. Metamaterials Aos Al-waidh Photonics in Engineering Research Group
General Engineering Research Institute
Liverpool John Moores University

2. Outlines Introduction to metamaterials Classification of materials
Photonic Crystal
Realisation of Metamaterials
Unit Cell Size
Metamaterial Application
Cloaking
Conclusions

3. 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.
He showed that an open ring (C shape) which axis is in the propagation direction could provide a negative permeability .
In the same paper, he showed that a periodic array of wires and ring could endow with negative index.
The analogy is as follows: Natural materials are made of atoms, which are dipoles.
These dipoles modify the light velocity by a factor n (the refractive index).
The ring and wire units play the role of atomic dipoles; wire acts as a ferroelectric atom,
while the ring acts as an inductor L and the open section as a capacitor C.
So the whole ring can be considered as a LC circuit. When the electromagnetic field passes
through the ring, an induced current is created and the generated field is perpendicular to
the magnetic field of the light. There is a magnetic resonance so the permeability is negative, and the index is negative too.
empty glass
regular water, n = 1.3
“negative” water, n = -1.3
Based on definition of J.Pendry 2000

4. 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”.
Negative refraction index
Positive refraction index

5. Is This Refraction Possible?
Yes as a backward wave
Is This Refraction Possible?
Expected refractions 1
ENERGY
Air
Material
like glass
PHASE
VELOCITY
Metamaterial
The concept of “Left Handedness” or “Double negative nature” of metamaterials was originally discussed by Veselago way back in He put forth the theory that the direction of phase of an EM wave would be opposite to that of the energy flow in a medium that exhibits negative permittivity and permeability simultaneously. He suggested that in such materials the electric filed E, the magnetic field H and the wave vector K form a left handed set of vectors which is why they are termed as “Left-Handed materials”. Because of the lack of any experimental evidence this theory remained as a mere prediction, until recently when Pendry et.al proposed an artificial material consisting of an array of split-ring resonators (SRRs) and thin wires. 2

6. Classification of materialsOR μ 1
(+, +)
(−, +)
Positive
Phase
Forward
Waves
Propagating
Standard optical materials
Evanescent
Metals (UV – Optical) 1
n<1 ε
Propagating
Metamaterials
Evanescent
Natural magnetic materials (up to GHz)
A medium with the permittivity greater than zero and permeability less than zero (ε > 0, μ < 0) will be designated a mu-negative (MNG) medium. In certain frequency regimes some gyrotropic materials exhibit this characteristic.
A medium with both permittivity and permeability less than zero (ε < 0, μ < 0) will be designated a DNG medium or left-handed media (LHM).
Negative
Phase
Backward Waves
(−, −)
(+, −)

7. Classification of materialsμ
POSITIVE REFRACTION
ABSORPTION
(ENG) ε < 0, μ > 0
Plasma
(DPS) Dielectrics ε
(DNG) ε < 0, μ < 0
Not found in nature
(MNG) ε > 0, μ < 0
Gyrotropic
A medium with both permittivity and permeability greater than zero (ε > 0, μ > 0) will be designated a double-positive (DPS) medium. Most naturally occurring media fall under this designation.
A medium with permittivity less than zero and permeability greater than zero (ε < 0,μ > 0) will be designated an epsilon-negative (ENG) medium
NEGATIVE REFRACTION!!
ABSORPTION

8. Classification of materials
ENG
DPS
Cloak
DNG
MNG

9. Realisation of Metamaterials
Negative ε
Thin metallic wires are arranged periodically
Effective permittivity takes negative values below plasma frequency
Negative μ
An array of split-ring resonators (SRRs) are arranged periodically

10. Realisation of Metamaterials
Embedding a metal split-ring and a metal rod creates left-handedness
Realisation of Metamaterials
ISRR Hx Ey
IROD
Magnetic resonance
(Negative μ)
Electric resonance
(Negative ε) y x z

11. Photonic Crystal
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, e and μ are not defined for photonic crystals as they are not homogeneous systems at their operational wavelength.

12.  vs. a /a 0 1  a <<<    a a >>  Effective medium
a <<<    a a >> 
Effective medium
description using
Maxwell equations with µ and 
Example:
Metamaterials
Properties determined
by diffraction and
Interference
Example:
Photonics crystals
Properties described
using geometrical optic and ray tracing Example:
Lens system
Shadows

13. The right hand rule
Not this one
If then is a right set of vectors:

14. The left hand rule !
Not this one
If then is a left set of vectors:

15. Unit Cell Size a 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.

16. Unit Cell Size a w
schematics of the elementary cell. d
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)

17. Unit Cell Size a w
schematics of the elementary cell. d
For simplicity, we can consider the width of the metal is equal to the distance between the capacitor plates (a)
C = oc ad/a where:
c = the effective permittivity of the material in between the plates and
d= the metal thickness
L = o w2/d where:
W= width = length of the coil

18. Unit Cell Size d LC-resonance frequency: LC = 1/ = Where c = w
schematics of the elementary cell. d
LC-resonance frequency:
LC = 1/ =
Where c =
And the LC-resonance wavelength
LC =

19. Unit Cell Size For relevant parameters c ≈ 3.5w
schematics of the elementary cell. d
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.

20. Metamaterial Application
Negative phase velocity, reversal of Doppler Effect and Backward Cerenkov radiation are interesting novel physical properties emerging from left-handed metamaterials phenomena.
The Doppler effect, named after Christian Andreas Doppler, is the apparent change in frequency or wavelength of a wave
that is perceived by an observer moving relative to the source of the waves.
Cherenkov radiation (also spelled Cerenkov or sometimes Čerenkov) is electromagnetic radiation
emitted when a charged particle passes through an insulator at a speed greater than that of light in the medium.
The Perfect Lens

21. Metamaterial Application
Cloaking device
Is it real, how?
Can I borrow your cloak to get my PhD ?

22. Cloaking device
Its not that simple
No tricks No

23. Cloaking device
Retro-reflective Projection Technology, Optical Camouflage
Another approach
virtual invisibility
The cloak is made of rrt materials
First a digital camera captured the seen behind the person wearing the cloak then
Hi tech approaches that use cameras and projectors

24. Cloaking device What we are locking for ? True invisibility
If we can control light to bend backward or around the object and not reflect back to our eye, they will appear invisible

25. creating a new material The idea is to create a region
We need to manipulate space
To be realised by
creating a new material
The idea is to create a region
that is inaccessible 25

26. Hole in space y’ y x x’ Purely geometrical distortion of space:
Constant x:
Constant y:
Forbidden:
Purely geometrical distortion of space:
No material yet
Use transformation optics. In this method we consider space, represented here by a Cartesian coordinate system, and mathematically create a hole in the fabric of space, and distort the coordinate system. The pink circle now represents our cloaked region which is invisible because the space that the light travels in has been deformed, and therefore no light can be scattered from it. The simple mathematical calculation that has been performed is then applied to Maxwell's equations. In order to retain the invariance of Maxwell’s equations, the properties of the transform are subsumed into a new form of spatially dependent permittivity and permeability, which now give the same cloaking effect as creating the hole in space. x x’

27. Transformation of a region Preserve form of Maxwell’s equations
Realisation
Transformation of a region
Preserve form of Maxwell’s equations
Predict form of permittivity and permeability to use in the original frame for cloaking

28. Fill the original empty space with this material
The cloak
Fill the original empty space with this material
Now we have a
cloaking device

29. A 3D Possibility
LIGHT
SOURCE
OBJECT
LIGHT
RAYS
METAMATERIAL

30. Conclusions
Meta-materials have been shown to have remarkable applications
LHM s and negative e 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)

31. Thanks for your attention.