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A Fsica dos metamateriais: darefrao negativa aos mantos dainvisibilidade
UFRJ, October 2009
Felipe A. Pinheiro
Instituto de Fsica
Universidade Federal do Rio de [email protected]
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What is Negative Refraction (NR) ?
What are the main consequences of NR? Electromagnetic properties of NR media.
What are the applications of NR and
metameterials ? Perfect lens
Cloaking
How to achieve NR ? Alternative routes to NR ?
The chiral route to NR.
Outline
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What is negative refraction ?Left-Handed materials
02
2
2
2 =
tc
EE
Wave equation
)exp(),( 0 tt = rkErE
Plane wave
02
22 =
E
ck
Propagation occurs if
0,0 >>
0,0
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What is negative refraction ?
Left-Handed materials
x
y
zk
E
H
S
0,0 >> 0,0
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What is negative refraction ?
S
vp
Phase velocity
Energy flow and
group velocity
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What is negative refraction ?
Left-Handed materials: Dispersion
Electromagnetic energy 0)()(
8
1 22 >
+
= HEU
In LH media, e and m mustdepend on the frequency !
Otherwise { } 08
1 22
0
)(>
Kramers-Kronigrelations )( )(
Complex
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What is negative refraction ?Left-Handed materials:Index of refractionVeselago (1968)
)()()( =n)exp()()( i= )exp()()( i=
Passive materials 0)( >in
)exp()()( ninn =
n,,0
Im
Re
emn
m=0
m=1
)()()( =n
( )mn 221 ++= 1,0=m
Only m=0 is physical 0)( >in
0)(
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What is negative refraction ?
Opaque
Opaque
0>0>
0>n
0
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What is negative refraction ?
Normal refraction
Snell-Descartes Law (1621)
2211 sennsenn =
=n
Willebrord Snell van Roijen(or Snellius) (1580- 1626)
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What is negative refraction ?
02
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What are the main consequences of NR?
J. Pendry,D. Smith,
Sci. Am. 7/2006
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What are the applications of NR ?
Perfect lens: Snell's law
J. Pendry, PRL 85, 3966 (2000)
Focusing
O I
No dephasing between pointsource and image (n=-1)
No reflection (n=-1)
zz kk 12 =
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Applications: Perfect lens
The Fermat's principleLight takes the shortest optical
path between two points.
For a lens, the shortest opticalpath between object and image is:
Both paths converge at the same pointbecause both correspond to a minimum.
Applications: Perfect lens
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Applications: Perfect lens
The Fermat's principle for negative refraction
02
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Normal lens
x
z
D D
lTo resolve two points at distance D > /2xk
2
222
ckk zx
=+
2max == Decay
exponentially
Resolution:
== max2
xk
Difractionlimit !
Applications: Perfect lens
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n possible
No resolutionlimit !
Sub-wavelengthimaging possible
Applications: Perfect lens
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How to achieve NR ?
What is a Metamaterial?Conventional materials:properties derive from their
constituent atoms.
Metamaterials:properties derive from their constituent
units. These units can be engineered.
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How to achieve NR ?
MetamaterialsElectric response: negative e Arrays of thin metallic wires
l
2r
2
2
1)(
p
eff =
)/ln(2
2
rll
cp
=
Effective parameters rl,>>
mml 5= lr 003.0=
GHzp
6.66
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How to achieve NR ?
MetamaterialsMagnetic response: negative m Split Ring Resonators
inner radius = 2.0mm
width of each ring = 1.0mm
spacing between ring edges = 0.1mm
lattice constant = 10.0mm
22
2
1)(
+=
LC
eff
F
GHzLC
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How to achieve NR ?
Metamaterials
David Smith and Shelly Schultz, UCSD
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How to achieve NR ?
Transmission measurements
4.5 5.0 5.5 6.0 6.5 7.0
Trans
mittedPow
er(dBm)
Frequency (GHz)
>0 >0
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Further experimental
evidence of NRAfter many criticisms,
intense debateP.M. Valanju, et al., PRL. 88,187401 (2002).
N. Garcia and M. Nieto-Verperinas, PRL 88, 207403 (2002).
Observation of Snell'slaw for LHM
1) A. Houck et al.,PRL 90 137401 (2003)
2) C.G. Parazzoli et al.,PRL 90, 107401 (2003)
from Ref.1
Microwave regime
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Applications of NRPerfect lens
Fang, N., Lee, H., Sun, C., Zhang, X., Sub-diffraction-limited opticalimaging with a silver superlens, Science 308, 534 (2005)
Recovery evanescent waves in an imagevia the excitation of surface plasmons in
a silver slab
60-nm resolution: 1/6 of
illuminating l !
~ 40 nm
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Applications of metamaterials:
Electromagnetic cloakingHow to bend light ?
A simple example: refraction at a surface
2211 sennsenn =Snell's law
Mirage the refractive indexvaries continuously near the surface
Atmospheric seeing
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How to bend light ?
Einstein's general theory of relativity
Gravity changes geometry
Thus gravity should bend light
Sobral eclipse (1919)
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How to bend light ?
Transformation opticsGeneral relativity
No gravitational fields Massive objects distorts space and
thus light rays Metric g
Einsteins metric has exactly the same effect on lightas a refractive index
Maxwell's equations are invariant uponchanging the coordinate system
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How to bend light ?
Electromagnetic cloak
Maxwell's equations are invariant uponchanging the coordinate system but with scaledeandm
Hide the object by bending lightaround the object (mirage effect).
Grading the index of refraction inthe cloak using metamaterials.
J.B. Pendry, D. Schurig, D.R. Smith,Science 312, 1780 (2006)
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Electromagnetic cloak
Metamaterial cloakfor microwaves
D. Schurig et al. Science 314, 977 (2006)
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Electromagnetic cloak
Sim.
Exp.
A cloaking experiment at 8.5GHz.
D. Schurig et al. Science 314, 977 (2006)
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Electromagnetic cloak
Towards the visiblethe carpet cloak!
Idea: J. Li and J. B. Pendry, PRL 101, 203901 (2008).
Experiment: J. Valentine et al., Nature Materials (2009)
L. Gabrielli et al., cond-mat 0904.3508 (2009)
U.C. Berkeley (2009) Felipe Pinheiro, Cincia Hoje junho (2009)
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Electromagnetic cloak
Towards the visiblethe carpet cloak!
U.C. Berkeley (2009)
Near Infrared
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Electromagnetic cloakU.C. Berkeley (2009)
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Electromagnetic cloak
Perspectives for the future
Herbert G. Wells (1897)
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Alternative routes to NR ?
Shalaev group (Purdue)
Parallel "nanorods" of goldthat conduct
plasmons in the near-infrared.
Soukoulis group (Iowa)
NR at the interfaceair-photonic crystals
(square array of aluminarods in the air)
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Alternative routes to NR ?
The chiral route to NRJ. B. Pendry, Science 306, 1353 (2004)
Isotropic chiral media0
)(
c
nk =
n>If the chirality parameter vp opposite to energy flow (NR)for one polarization state
Homogeneouschiral medium
Homogeneousachiral medium with
resonant dipoles
Homogeneouschiralmedium withresonant dipoles
NRB
Ingredients Resonance + Chirality
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What is
I call any geometrical figure, or group of
points, chiral, and say that it has chirality,if its image in a plane mirror, ideally realized,
cannot be brought to coincide with itself .
Lord Kelvin, Baltimore Lectures, 1884
??
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Some Manifestationsof Chirality in Nature
The DNA (1953)
Discovery of the optical rotatory power oflight by Arago (1811).
Parity violating "vector-axial vector" theory of the weak
interaction by Feynman, Gell-Mann, Marshak andSudarshan (1958).
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The chiral route to NR
Chiral planar metamaterialsHuge optical activity and NR
N. Zheludev group, Southampton, UK
15mm
Nature Photonics 3, 133 (2009)PRB 79, 035407 (2009)
Viewpoint in Physics 2, 3 (2009)
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Conclusions
Metamaterials offer an enormous potential for
new physics and applications.Super lens Overcomes the diffraction limitEmerging field Transformation optics
Cloaking at visible frequencies.New chapters should be added to textbookson Electrodynamics.Nice example of a contemporary researchtopic that can be presented to high-schoolstudents.Old and well-established concepts of physics
can be the subject of a lively debate.
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