Transcript Presentation

Negative refraction &
metamaterials
Femius Koenderink
Center for Nanophotonics
FOM Institute AMOLF
Amsterdam
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Optical materials
Maxwell’s equations
Material properties
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Light: plane wave
Refractive index
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Natural materials
Damped solutions
Propagating waves
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General materials
Damped solutions
Propagating waves
Propagating waves
Damped solutions
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What is special about e<0, m<0
Veselago (1968, Russian only)
Conventional choice:
If e<0, m<0, one should choose:
propagating waves with
`Negative index of refraction’
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Snell’s law with negative index
S1
S2
Negative refraction
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Snell’s law
Exactly what does negative
refraction mean ??
kin
k||
k
Negative refraction
(1) k|| conservation is required
two possible solutions !
How does nature choose
which solution is physical ?
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Snell’s law
Energy flux
kin
k||
k
Exactly what does negative
refraction mean ??
(1) k|| is conserved
(2) Causality:
carry energy away from
the interface
Negative refraction
Phase fronts (k) travel
opposite to energy if n<0 !
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Refraction movies
Positive refraction
n=1
n=2
Negative refraction
n=1
n=-1
W.J. Schaich, Indiania
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Snell’s law
Plane wave:
(1) k, E, B
Energy flux
kin
k||
k
(2) Energy flow S
Energy flow
to the left
Negative refraction
E
S
B
H
k
Phase fronts
To the right
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Negative index slab
NIM slab
A flat negative
index slab
focuses light
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Conventional lenses
Ray optics:
Image is flipped & sharp
Sharp features (large
Exact wave optics:
Image sharpness limited to l/2
) don’t reach the lens
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Perfect lens
The negative index slab creates a perfect image
by amplifying the evanescent field via surface modes
Does amplification violate
energy conservation ?
No.
n=-1 is a resonant effect
that needs time to build up
Surface modes
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More bizarre optics
Superlens: we have taken e=m=-1
Question: what if we take e(r), m(r) arbitrary ?
`Transformation optics’
Bend light in space continuously by transforming e & m
Sir John Pendry
Maxwell equations
map onto Maxwell
with modified e,m
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Negative lens as example
Stretch a thin sheet in space
into a slab of thickness d
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Negative lens as example
d
Insert proper
e and m
to expand space
Stretch a thin sheet in space
into a slab of thickness d
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Negative lens as example
d
n=-1
n=+1
The perfect lens
(n=-1, d/2 thickness)
‘annihilates’
a slab of n=1, d/2 thick
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Perfect cloaking
Price to pay:
(1) e and m smoothly vary with r
(2) e and m depend on polarization
Conceal an object in the sphere r<R1 by bending all rays around it
Transformation optics: blow up the origin to a sphere of radius R1
push the fields in r<R2 into R1<r<R2
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Perfect cloaking
A perfect cloak
- keeps external radiation out, and internal radiation inside the cloak
- works for any incident wave field
- cloaks the object in near and far field
- leaves no imprint on the phase of scattered light
Min Qiu, KTH Stockholm
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Snags in perfect cloaking ?
A
B
Note that ray B is much longer
than ray A
Phase front comes through flat
Isn’t ray B `superluminal’ ?
Superluminality is forbidden for
energy or information transport
i.e. wavepackets
Cloaking does not violate causality (relativity)
Cloaking only works at a single frequency, not for pulses
Cloaking corresponds to a resonance with a build up time
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Conclusions
1. Negative e and m: transparent, left-handed plane waves
2. Negative refraction
3. Perfect lens
Microscopy, lithography
4. Transformation optics Perfect cloaking
5. Perfect lenses & cloaks: near-field, resonant phenomena
Questions
• How can we realize negative e and m ?
• How can we prove negative e and m ?
• Demonstrations of the perfect lens ?
• Was anything cloaked yet ?
• What limits cloaking and lensing
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Metamaterials
Questions
• How can we realize negative e and m ?
• How can we prove negative e and m ?
• Demonstrations of the perfect lens ?
• Was anything cloaked yet ?
• What limits cloaking and lensing
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How to create arbitrary e,m
Conventional material
`Meta material’
Polarizable
atoms
Artificial ‘atoms’
Magnetic polarizability
Form effective medium
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0.1
1
l/a
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Conventional materials
Effective medium
Metamaterials
Photonic crystals (Bragg)
Ray optics
Geometrical optics
Length scales
1000
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Metamaterial challenges
Creating negative e is easy (any metal)
For negative m we need
(1) l/10 sized artificial atoms with a magnetic response
(2) That do not consist of any magnetic material
We use
(3) Localized currents induced by incident radiation to
circulate in loops
(4) Resonances to get the strongest magnetic response
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Artificial atom - SRR
Split ring resonator has a resonance at
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How does the SRR work ?
Faraday: flux change sets up a voltage over a loop
Ohm’s law: current depending on impedance
Resonance when |Z| is minimum (or 0)
Circulating current I has a magnetic dipole moment
(pointing out of the loop)
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Pioneering metamaterial
Copper SRR, 0.7 cm size
1 cm pitch lattice, l=2.5 cm
Science 2001
Shelby, Smith Schultz
Calculation Pendry et al, ‘99
cm-sized printed circuit board
microwave negative m
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First demonstration of negative
refraction
Idea: beam deflection by a negative index wedge
Measurement for microwaves
(10.2 GHz, or 3 cm wavelength)
Shelby, Smith, Schultz, Science 2001
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Smallest split rings
Karlsruhe (2005)
AMOLF (2008)
200 nm sized SRR’s,
Gold on glass
l=1500 nm
Can we make smaller split rings for l~ 500 nm wavelength ?
No: at visible w metals have a plasmon response
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Magnetic response from wire pairs
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Fishnet structures
Fishnet of Ag (30 nm) and dielectric (MgF2) (50 nm)
Wedge experiment
at 1500 nm
Valentine et al. (Berkeley)
Nature 2008
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Fishnet dispersion
Negative index
for l > 1450 nm
Changes with l
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From microwave to visible
2000-2006
Scaling split rings
from:
1 cm to 100 nm
2007-2008
NIR / visible:
-wire pairs
-fishnets
Soukoulis, Linden, Wegener
Science (review) 2007
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Questions
• What about the superlens ?
• What about cloaking ?
• Practical challenges for negative e and m
• Conceptual challenges
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Superlens
Poor mans superlens: plasmon slab (e<0 only)
Surface modes
Amplify evanscent field
Berkeley: image `Nano’ through 35 nm silver slab in photoresist
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Superlens
Object (mask)
2 um scale
AFM of resist
with superlens
AFM of resist
Ag replaced by
PMMA
Atomic Force Microscope to detect sub-l features in the image
Result: the opaque 35 nm Ag slab makes the image sharper !
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Cloaking
2-dimensional experiment at microwave frequencies (l=3cm)
Cloaked object: metal cylinder
No cloak
Cloak
Schurig et al., Science 2006
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Practical challenges
1. Absorption & dispersion
2. Anisotropy
A. Planar arrays
B. Out-of-plane
response
Spatial inhomogeneity
Vector anisotropy
Question:
Can we make 3D isotropic NIM’s ?
Negative m implies absorption
Current 1/e decay length ~ 4 l
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Possible 3D materials
Wegener group: split ring bars
Extremely difficult to make
Giessen group: split ring stacks
3D but anisotropic
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Conceptual challenges
Time domain
Spatial
Sources
n=-1
n=-1
Magnifying super lens
Corner cubes
Cavities
Different cloaks
Transformation optics
‘Resonant amplification’ Emitters in cloaks
‘Superluminal rays’
Emitters coupled by
perfect lenses
In time: how does
-the perfect image form Emission rate ?
-cloaking set in
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