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Engineering Space for Light with
Metamaterials
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Part 1: Electrical and Magnetic Metamaterials
Part 2: Negative-Index Metamaterials, NLO, andsuper/hyper-lens
Part 3: Cloaking and Transformation Optics
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Outline
What are metamaterials?
Early electrical metamaterials Magnetic metamaterials
Negative-index metamaterials
Chiral metamaterials Nonlinear optics with metamaterials
Super-resolution
Optical cloaking andTransformation Optics
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Other versions of cloak/invisibility/transparency
Einc
Hinc P
( )0 DPS DPS incP E = ( )0 ENG ENG incP E =
0
1 0TM
c =
Alu and Engheta, PRE, 72, 016623,2005
Plasmonic scatteringancellation
Anomalous localizedresonance
Nicorovici, McPhedran and Milton,PRB, 1994Milton & Nicorovici, Proc. R. Soc.A, 2006
Other schemes include tunneling light transmissions (de Abajo) , activesources (Miller),invisible fish-scale structure (Zheludev et al)
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Invisibility: An Ancient Dream
Tarnhelm of invisibility
(Norse mythology)
Perseus helmet
(Greek mythology)
Ring of Gyges
(The Republic, Plato)
The 12 Dancing Princesses
(Brothers Grimm, Germany)
Cloaking devices
(Star Trek, USA)
Harry Potters cloak
(J. K. Rowling, UK)
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Invisibility in Nature: Chameleon Camouflage
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Invisibility by Transformation of Time-Space
Black hole
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Invisibility to Radar: Stealth Technology
Stealth technique:Radar cross-section reductions by absorbing paint / non-metallic frame / shape effect
i k h l
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Optical camouflage (Tachi lab, U. Tokyo)
From: http://www.star.t.u-tokyo.ac.jp
The camera + projector approach
Bi k N t h l C t
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Invisibility: from fiction to fact?
The Invisible Man by H. G.Wells (1897)
The invisible woman in TheFantastic 4 by Lee & Kirby (1961)
Examples with scientific elements:
"... it was an idea ... to lower the
refractive index of a substance,
solid or liquid, to that of air so
far as all practical purposes areconcerned. -- Chapter 19
"Certain First Principles"
"... she achieves these feats by
bending all wavelengths of light in
the vicinity around herself ...
without causing any visibledistortion. -- Introduction from
Wikipedia
Pendry et al.; Leonhard,Science, 2006(Earlier work: cloak ofthermal conductivity byGreenleaf et al., 2003)
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Designing Space for Light withTransformation Optics
Straight field line inCartesian coordinate
Distorted field line indistorted coordinate
Spatial profile of & tensors determines the distortion ofcoordinate
Seeking for profile of & to make light avoid particular region inspace optical cloaking
Pendry et al., Science, 2006
Fermat:
ndl = 0
n = (r)(r)
curvingoptical space
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Pendry et al., 2006
The bending of light due to the gradient in refractive index
in a desert mirage
A similarity in Mother Nature
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Cloaking based on coordinate transformation
General math. requirements and microwave demonstrations
2
r r
z z
r a
r
r
r a
b r a
b a r
= =
= =
= = Ideal case
Reduced parameter
Experimental data
Structure of the cloak
Schurig et al., Science, 2006
b ar r a
b
+
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How about optical frequencies?How about optical frequencies?
Scaling the microwave cloak design?
Intrinsic limits to the scaling of SRR size
High loss in resonant structures
TM incidence
To maintain
the dispersion
relation
z
z r
constant
constant
=
=
2
, ,r r z zr a r b r a
r r a b a r
= = = = = =
2
z
r
b r a
b a rr
r a
r a
r
=
=
=
2
2 2
1z
r
b
b a
b r a
b a r
=
= =
A constant permittivity
of a dielectric; 1
No magnetism required!
>
(for in-plane k)
Gradient inr direction
only; r changing from 0to 1.Cai, et al., Nature Photonics, 1, 224 (2007)
HE
k
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Nature Photonics (to be published)
Optical Cloaking with Metamaterials:
Can Objects be Invisible in the Visible?
Cover article of Nature Photonics (April, 2007)
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Structure of the cloak: Round brush
metal needles embedded in
dielectric host
Unit cell:
Flexible control ofr;Negligible perturbation in
Cai, et al., Nature Photonics, 1, 224 (2007)
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Cloaking performance: Field mapping movies
Example:Non-magnetic cloak @ 632.8nm with silver wires in silica
Cloak ONCloak OFF
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4.2m
A
10 m
r1
C
Plasmonic cloaking(Smolyaninov et al - collaboration)
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Scattering issue in a linear non-magnetic cloak
E
kH
E
kH
1zr b
r b
Z
= == =
Ideal cloak:
Perfectly matched impedance
results in zero scattering
1zr b
r b
aZb
=
=
= =
Linear non-magnetic cloak:
Detrimental scattering due to
impedance mismatch
Nonlinear transformation > no scattering
Linear transformation
b ar r a
b
= +
HE
k
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Designs of optical cloak withhigh-order transformations
Examples in cylindrical system
( ) ( )1
( ) ; 1 ; ( )r r r z z r r g r r r r g r r
= = = = = =
HE
kH
E
k
z r
r z
n
n
=
=
z r
r z
n
n
=
=
TE Simplification TM Simplification
( )2 2
2
( )
1
( )
r
z
r r g r r
g r r
=
=
=
( )2
2
( )
1
r
z
r r
g r r
=
=
=
Cai, et al APL (2008)
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Example: Optimized quadratic transformation
( ) 2( ) 1r g r a b p r b r a with p a b = = + + =
A second-order transformation for non-magnetic cloak with
minimized scattering
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Reduced scattering from nonlinear cloak
Normalized scattered field
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Suppression in both magnitude and directivity
Scattering radiation pattern
270
90
180 0
0.0 0.5 1.0
Ei
k
scatterer
linear
quadratic
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Towards experimental realization
We need a design that is
Less complicated in fabricationCompatibility with mature fabrication
techniques like direct deposition and direct
etching
Better loss featuresLoss might be ultimate limiting issue for cloaking
0.1r = 0.03r =
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Structures of realistic nonlinear TO cloaks
-1 0 1 2 30
0.005
0.01
0.015
0.02
0.025
0.03
real( )
imag()
r(a)
r(b)
(b)
(a)
||
found from Wieners bounds
cloak @ 532 nm with alternating silver- silicaslices based on nonlinear transformations
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Engineering Meta-Space for Light:
via Transformation Optics
Light concentrator
(b)
Fermat:
ndl = 0
n = (r)(r)
curvingoptical space
Flat hyperlens:- & -body lenses
Kildishev, VMS (OL, January 2008)
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Metamagnetics with rainbow colors
(single-negative) MM with n = -0.9 at770nm (double-negative) MM with n = -1at 810 nm
Chiral metamaterials
NLO with NIMs
Super-resolution
Optical cloak of invisibility
Engineered meta-space for light
Take Home Messages:
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Highlights of Purdue Meta-Research
Purdue Photonic Metamaterials
(a) 1-st optical negative-index MM (1.5 m; 2005)
(b) double-negative MM at shortest
(~800nm; 2007)(c) 1-st magnetic MM across entire visible (2007)
Transformation Optics with MMs:Flat hyperlens, concentrator, and cloak
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Cast of Characters
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Just published