PowerPoint-Pr

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A journey through a strange classical optical
world
Bernd Hüttner CPhys FInstP Institute of Technical
Physics DLR Stuttgart
Left-handed media
Metamaterials
Negative refractive index
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plasmon waves and other waves
7. Faster than light
8. Summary
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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A short historical background
V G Veselago, "The electrodynamics of substances
with simultaneously negative values of eps and
mu", Usp. Fiz. Nauk 92, 517-526 (1967)
A Schuster in his book An Introduction to the
Theory of Optics (Edward Arnold, London, 1904).
H Lamb (1904), H C Pocklington (1905), G D
Malyuzhinets, (1951), D V Sivukhin, (1957)
R Zengerle (1980)
J B Pendry Negative Refraction Makes a Perfect
Lens PHYSICAL REVIEW LETTERS 85 (2000) 3966-3969
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Objections raised against the topic

• Valanju et al. PRL 88 (2002) 187401-Wave
  Refraction in Negative-
• Index Media Always Positive and Very
  Inhomogeneous

2. G W 't Hooft PRL 87 (2001) 249701 - Comment
on Negative Refraction Makes a Perfect
Lens
3. C M Williams - arXivphysics 0105034 (2001) -
Some Problems with Negative Refraction
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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Photonic crystals
1995
2003
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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Definition
Left-handed metamaterials (LHMs) are composite
materials with effective electrical permittivity,
e, and magnetic permeability, µ, both negative
over a common frequency band.
What is changed in electrodynamics due to these
properties?
Taking plane monochromatic fields Maxwells
equations read
Note, the changed signs
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• By the standard procedure we get for the wave
  equation

no change between LHS and RHS
Poynting vector
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• RHS

LHS
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Two (strange) consequences for LHM
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Why is n lt 0?
1. Simple explanation
2. A physical consideration
2nd order Maxwell equation
1st order Maxwell equation
RHS e gt 0, m gt 0, n gt 0
LHS e lt 0, m lt 0, n lt 0
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whole parameter space
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3. An other physical consideration
The averaged density of the electromagnetic
energy is defined by
Note the derivatives has to be positive since the
energy must be positive and therefore LHS possess
in any case dispersion and via KKR absorption
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Kramers-Kronig relation
causality
Titchmarshtheorem KKR
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• Because the energy is transported with the group
  velocity we find

This may be rewritten as
Since the denominator is positive the group
velocity is parallel to the Poynting vector and
antiparallel to the wave vector.
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• The group velocity, however, is also given by

We see n lt 0 for vanishing dispersion of n
This should be not confused with the
superluminal, subluminal or negative velocity of
light in RHS. These effects result exclusively
from the dispersion of n.
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Dispersion of ?, ? and n
Lorentz-model
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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Reflection and refraction
Optically speaking a slab of space with
thickness 2W is removed. Optical way is zero !
µ 1
but what is with
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Snellius law for LHS
Due to homogeneity in space we have k0x k1x
k2x
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First example
water n 1.3
negative water n -1.3
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Second example real part of electric field of a
wedge

• 2.6
• left-measured
• right-calculated

• -1.4
• left-measured
• right-calculated

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General expression for the reflection and
transmission
The geometry of the problem is plotted in the
figure where r1 -r1.
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1. s-polarized
e1 m11, e2 m2 -1 and u0 0 we get R 0
T 1
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2. p-polarized
R 0 why and what does this mean?
Impedance of free space
Impedance for e m -1
invisible!
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Reflectivity of s-polarized beam of one film
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Absorption or reflection of a normal system
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Reflection of a normal system
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Reflection of a LHS
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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Invisibility
Al plate, d17µm
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An other miracle Cloaking of a field
For the cylindrical lens, cloaking occurs for
distances r0 less than r if ecem
The animation shows a coated cylinder with ein1,
es-1i10-7, rout4, rin2 placed in a uniform
electric field. A polarizable molecule moves
from the right. The dashed line marks the circle
rr. The polarizable molecule has a strong
induced dipole moment and perturbs the field
around the coated cylinder strongly. It then
enters the cloaking region, and it and the
coated cylinder do not perturb the external field.
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There is more behind the curtain 1. outside the
film
perfect lens beating the diffraction limit
How can this happen?
Let the wave propagate in the z-direction
the larger kx and ky the better the resolution
but kz becomes imaginary if
How does negative slab avoid this limit?
Due to amplification of the evanescent waves
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Amplification of evanescent waves
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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How can we understand this?
Analogy enhanced transmission through
perforated metallic films
Ag d280nm hole diameter d / l 0.35 L750nm
hole distant area of holes 11 h 320nm
thickness dopt11nm optical depth Tfilm10-13
solid film
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Detailed analysis shows it is a resonance
phenomenon with the surface plasmon mode.
Surface-plasmon condition
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Interplay of plasma surface modes and cavity modes
The animation shows how the primarily CM mode at
0.302eV (excited by a normal incident TM
polarized plane wave) in the lamellar grating
structure with h1.25µm, evolves into a
primarily SP mode at 0.354eV when the contact
thickness is reduced to h0.6µm along with the
resulting affect on the enhanced transmission.
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Beyond the diffraction limit Plane with two
slits of width l/20
e2.2
e1
e-1 µ-1
e-1i10-3 µ-1i10-3
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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There is more behind the curtain 2. inside the
film
The peak starts at the exit before it arrives the
entry
Example. Pulse propagation for n -0.5
Oje, is this mad?!
No, it isnt!
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An explanation
Let us define the rephasing length l of the medium
where vg is the group velocity
If the rephasing length is zero then the waves
are in phase at ww0
Remember, Fourier components in same phase
interfere constructively
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RHS LHS RHS
Peak is at z0 at t0
the rephasing length lII inside the medium
becomes zero at a position z0 ct / ng.
t lt 0
At z0 the relative phase difference between
different Fourier components vanishes and a peak
of the pulse is reproduced due to constructive
interference and localized near the exit point of
the medium such that 0 gt t gt ngL/c.
The exit pulse is formed long before the peak of
the pulse enters the medium
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At a later time t such that 0 gt t gt t, the
position of the rephasing point inside the medium
z0 ct/ng decreases i.e., z0 lt z0 and hence
the peak moves with negative velocity -vg inside
the medium.
t0 peaks meet at z0 and interfere
destructively.
since 0 gttgtngL/c is z0 gt L
Region 3
0gttgtt z0 gt z0 the peak moves forward
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Gold plates (300nm) and stripes (100nm) on glass
and MgF2 as spacer layer
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Overview
1. Short historical background
2. What are metamaterials?
3. Electrodynamics of metamaterials
4. Optical properties of metamaterials
5. Invisibility, cloaking, perfect lens
6. Surface plamon waves and other waves
7. Faster than light
8. Summary
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Summary
Metamaterials have new properties
1. S and vg are antiparallel to k and vp
2. Angle of refraction is opposite to the angle
of incidence
3. A slab acts like a lens. The optical way is
zero
4. Make perfect lenses, R 0, T 1
5. Make bodies invisible
6. Can be tuned in many ways
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nW 1.35 nG 1.5
nW -1.35 nG 1.5
nW 1.35 nG -1.5
nW -1.35 nG -1.5