1 negative refraction & metamaterials femius koenderink center for nanophotonics fom institute...
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Negative refraction &metamaterials
Femius Koenderink
Center for NanophotonicsFOM Institute AMOLFAmsterdam
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What is special about <0, <0
Veselago (1968, Russian only)
Conventional choice:
If <0, <0, one should choose:
propagating waves with`Negative index of refraction’
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Snell’s law
Negative refraction
Exactly what does negativerefraction mean ??
(1) k|| conservation is required
kin
k|| k
two possible solutions !How does nature choosewhich solution is physical ?
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Snell’s law
Negative refraction
Exactly what does negativerefraction mean ??
(1) k|| is conserved (2) Causality: carry energy away from the interface
kin
k|| k
Energy flux
Phase fronts (k) travel opposite to energy if n<0 !
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Snell’s law
Negative refraction
kin
k|| k
Energy flux
Plane wave:
(1) k, E, B
E
B
kPhase frontsTo the right
(2) Energy flow S
HS
Energy flowto the left
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Conventional lenses
Ray optics:Image is flipped & sharp
Exact wave optics:Image sharpness limited to /2
Sharp features (large ) 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
Surface modes
Does amplification violateenergy conservation ?
No. n=-1 is a resonant effectthat needs time to build up
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More bizarre opticsSuperlens: we have taken ==-1Question: what if we take (r), (r) arbitrary ?
`Transformation optics’Bend light in space continuously by transforming
Sir John Pendry
Maxwell equationsmap onto Maxwell
with modified
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Negative lens as example
Insert proper and
to expand space
Stretch a thin sheet in spaceinto a slab of thickness d
d
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Negative lens as example
n=-1 n=+1
d
The perfect lens(n=-1, d/2 thickness)
‘annihilates’
a slab of n=1, d/2 thick
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Perfect cloaking
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
Price to pay:(1) and smoothly vary with r
(2) and depend on polarization
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Perfect cloakingA 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 ?
B
Note that ray B is much longerthan ray A
Phase front comes through flatIsn’t ray B `superluminal’ ?
Superluminality is forbidden forenergy or information transport i.e. wavepackets
A
Cloaking does not violate causality (relativity)Cloaking only works at a single frequency, not for pulsesCloaking corresponds to a resonance with a build up time
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Conclusions
1. Negative and transparent, left-handed plane waves2. Negative refraction3. Perfect lensMicroscopy, lithography4. Transformation optics Perfect cloaking5. Perfect lenses & cloaks: near-field, resonant phenomena
Questions• How can we realize negative and ?• How can we prove negative and ?• 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 and ?• How can we prove negative and ?• Demonstrations of the perfect lens ?• Was anything cloaked yet ?• What limits cloaking and lensing
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How to create arbitrary Conventional material
Polarizableatoms
`Meta material’
Artificial ‘atoms’Magnetic polarizabilityForm effective medium
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Length scales
/a1
Ph
oto
nic
cry
stals
(B
rag
g)
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Meta
mate
rials
Eff
ect
ive m
ed
ium
Con
ven
tion
al m
ate
rials
1000
Geom
etr
ical op
tics
Ray o
pti
cs
0.1
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Metamaterial challenges
Creating negative is easy (any metal)For negative we need
(1) /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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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 metamaterialCopper SRR, 0.7 cm size1 cm pitch lattice, =2.5 cm
Science 2001 Shelby, Smith Schultz
cm-sized printed circuit boardmicrowave negative
Calculation Pendry et al, ‘99
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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
200 nm sized SRR’s, Gold on glass=1500 nm
Karlsruhe (2005) AMOLF (2008)
Can we make smaller split rings for ~ 500 nm wavelength ?
No: at visible metals have a plasmon response
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Fishnet structures
Fishnet of Ag (30 nm) and dielectric (MgF2) (50 nm)
Wedge experimentat 1500 nm
Valentine et al. (Berkeley)Nature 2008
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From microwave to visible
Soukoulis, Linden, WegenerScience (review) 2007
2000-2006Scaling split ringsfrom:1 cm to 100 nm
2007-2008NIR / visible:
-wire pairs-fishnets
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Questions
• What about the superlens ?• What about cloaking ?
• Practical challenges for negative and
• Conceptual challenges
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Superlens
Poor mans superlens: plasmon slab (<0 only)
Surface modesAmplify evanscent field
Berkeley: image `Nano’ through 35 nm silver slab in photoresist
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Superlens
Object (mask)2 um scale
AFM of resistwith superlens
AFM of resistAg replaced byPMMA
Atomic Force Microscope to detect sub-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 (=3cm)Cloaked object: metal cylinder
No cloak
Cloak
Schurig et al., Science 2006
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Practical challenges
1. Absorption & dispersion 2. Anisotropy
Negative implies absorptionCurrent 1/e decay length ~ 4
A. Planar arraysB. Out-of-plane response
Spatial inhomogeneityVector anisotropy
Question: Can we make 3D isotropic NIM’s ?
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Possible 3D materials
Wegener group: split ring barsExtremely difficult to make
Giessen group: split ring stacks3D but anisotropic
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Conceptual challenges
‘Resonant amplification’‘Superluminal rays’
In time: how does-the perfect image form-cloaking set in
Time domainSpatial
Magnifying super lensCorner cubesCavitiesDifferent cloaks
Transformation optics
n=-1
n=-1
Sources
Emitters in cloaksEmitters coupled byperfect lenses
Emission rate ?