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Engineering Space for Light w ith
Metamaterials
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Par t 1 : Elect r i ca l and Magn et ic
Me tama te r i a l s
Par t 2 : Nega t i ve- I nd ex Me tam a te r i a ls, NLO, and
su p er / h y p er - len s
Par t 3 : Cloak ing an d Tr ansfo r m a t ion Op t i cs
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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 and Transformation Optics
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Natural Optical Materials
Semiconduc to rs
Crys ta ls
W a t e r
m e t a l s
Ai rE,H ~exp[in(/c)z]
n = ()
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Materials & Metamaterials
, diagram: E,H ~exp[in(/c)z]n = ()
Cloak ing ( TO) a rea
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What is a metamaterial?
-
-
Metamaterial is an arrangement of artificial structural elements,
designed to achieve advantageous and unusual electromagnetic
properties.
= meta = beyond (Greek)
A natural material w ith itsatoms
A metamaterial with artificiastruc
llytured atoms
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Photonic crystals vs. Optical metamaterials:connections and differences
a>Properties described
using geometrical opticsand ray tracing
Example:
Optical crystals
Metamaterials
Example:
Photonics crystals
Phased array radar
X-ray diffraction optics
Example:
Lens system
Shadows
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Natural Crystals
... have lattice constants much smaller
than light wavelengths:a
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Photonic crystals
... have lattice constants comparable
to light wavelengths:a ~
can be artificial or natural
have properties governed by the
diffraction of the periodic structures
may exhibit a bandgap for
photons
typical ly are n o t well described
using effective parameters , , n, Z
often behave like but they are n o ttrue metamaterials
Bi k N t h l C t
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Metamaterials: Properties not found in nature?
( r e f r a c t i o n ! )
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Metamaterials: Artificial periodic structures?
Ho t -sp ot s in f r act a ls
Shalaev, Nonlinear Optics of Random Media,
Springer, 2000
Lycur gu s Cup ( 4 t h c e n t u r y
AD)
Ancient (first?) randommetamaterial (carved in Rome)w ith gold nano particles
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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
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Early (first?) Example of Meta-Atoms
Twisted jute elements
Artificial chiral molecules
Jagadis C. Bose, Proceeding of Royal Soc. London, 1898
On the Rotation of Plane of Polarization of Electric Waves by a Twisted Structure
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Early Electric Metamaterial: Artificial Dielectrics
W. E. Kock, Proc. IRE, Vol. 34, 1946
Per iod i c m e ta l -d ie lect r i c p la tes w i t h e f f ect i ve i ndex o f l ess t han 1
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gy
Noble metal: < 1 in nature
500 1000 1500 2000-250
-200
-150
-100
-50
0
50
Wavelength (nm)
Pe
rmittivityof
Silver
Re(), experiment
Im(), experimentRe(), Drude
Im(), Drude
2
0( )
( )
p
i
=
+
05.0
9.216
0.0212
p eV
eV
=
=
=
Drude model for permittivity: Si l ver pa ram e te rs :
Exp er im en ta l da t a f r om Johnson & Chr i s t y , PRB, 197 2
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gy
Array of Thin Wires and Tunable Plasma Frequency
J. Brow n, Proc. IEE 100 (1953)W. Rotman, Trans. IRE AP 10 (1962)J.B. Pendry, et al., Phys. Rev. Lett. (1996)
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Electrical metamaterials:metal wires arrays with tunable plasma frequency
A periodic array of thin metal w ires with
r
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Metal-Dielectric Composites and Mixing Rules
( )
1 1 2 2
1 2 1 2 2 1
c c
c c
= +
= +
( ) ( )( ) ( )
( ) ( )( ) ( )
hi
hi
hMG
hMG f22 +
=
+
Maxw e ll - Ga r n e t t ( MG) t h e or y :
Ef fec t i v e -Med ium Theor y ( EMT) :
(1 ) 0
( 1) ( 1)
m eff d eff
m eff d eff
f f
d d
+ =
+ +
f 1
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Composites with elongated inclusions
2 3/ 2 2 1/ 2 2 1/ 20 2( ) ( ) ( )
i j k
i
i j k
a a a dsq
s a s a s a
=
+ + +
(1 ) / q q =
(1 ) 0m eff d eff
m eff d eff
f f
+ =+ +
{ }21
4
2eff m d
= + [( 1) 1] [ ( 1) ]m df f = + + +
10-2
10-1
100
101
102
0
0.2
0.4
0.6
0.8
1
Aspect ratio, :1:1
Depolariza
tionfactor,p
Lorentz depolarization factor for a spheroid with aspect ratio :1:1
p(1:1:1)=1/3
Depo la r i za t i on fact o r :
Scr een ing f act o r :
Clausius -Mosso t t i y i e lds
shape- dep end ent EMT:
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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
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Absence (or very weak: 1)Optical Magnetism in Nature
the magnetic permeability () ceases to have any physical meaning atrelatively low frequencies there is certainly no meaning in using the magnetic
susceptibility from optical frequencies onwards, and in discussion of such
phenomena we must put =1.
Landau and L i f sh i t z , ECM, Chap t er 79 .
Magne t i c coup l i ng t o an a tom : ~ 0/ 2B ee m c ea = =
0eaElect r i c coup l i ng t o an a t om : ~
( Bo h r m a gn e t o n )
Magne t i c e f f ect / e l ect r i c e f f ect 2 (1 / 1 3 7 )2 < 1 0 - 4
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SRRs: first magnetic metamaterials
Th e or y : Pe n d r y e t a l ., 1 9 9 9 .
A bu l k m e ta l has no
m a g n et i s m i n o p t i cs
Makeitaring:loop
currentinducedbyH
A m e ta l r in g : w e ak
m agne t i c response
Cu tth erin gto
in trodu ceresonan ce
A sp li t r i n g :
m agne t i c resonance
Dou
bleth
ering
to
stre
ngthe
n th
e
reso
nanc
e
Dou ble SRR:
enhanced m agne t i c
resonance
Sp l i t - r i ng r esona t o r ( SRR)
Exp e r im e n t : Sm i t h e t a l ., 2 0 0 0 .
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Artificial magnetic resonators:Earlier form and Todays design
SRR fo r GHz m agne t i c r esonan ce ( Hardy e t a l ., 198 1) :
Nanostrip (or nanorod) Pair
EHk
SRR C-shaped Rod
M od e r n m a g n et i c u n i t s f o r o p t i ca l m et a m a g n et i sm :
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Limits of size scaling in SRRs
Di rect sca l i ng -d ow n t he SRR d im ens ions doesn t
h e lp m u ch
total coil kinetic L L L= +
Zhou e t a l , PRL (2 00 5) ; K lein , et a l ., OL (2 00 6)
coil
L size1
kinetic
Lsize
totalC size
2
1 1 1
( / ) ( ) .res
total total L C A size B size C size size const
=
+ +
Sa t u ra t i on
Loss i n m e ta l g i ves k i n e t i c
i nduc tance
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Progress in Optical Magnetism Metamaterials
Terahertz magnetism
a) Yen, et al. ~ 1THz (2-SRR) 2004Katsarakis, et al (SRR 5 layers) - 2005
b) Zhang et al ~50THz (SRR+mirror) - 2005c) Linden, et al. 100THz (1-SRR) -2004d) Enkrich, et al. 200THz (u-shaped)-2005
2004-2007 years:
from 10 GHz to 500 THZ
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Magnetic Metamaterial: Nanorod to Nanostrip
E
H
k
Dielectric
Metal
Nanorod pair Nanorod pair array Nanostrip pair
Nanostrip pair has a much stronger magnetic response
Lagarkov, Sarychev PRB (1996) - > 0
Podolsk iy, Sarychev & Shalaev, JNOPM(2002) - < 0 & n < 0
Kildishev et al, JOSA B(2006); Shvets et al JOSA (2006) strip pairs
(Svirko, et al, APL (2001) - crossed rods for chirality)
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Visible magnetism: structure and geometries
35 40 2b
t nm d nm p w= =
Pur due g roup
Yuan , et a l ., Op t . Ex p r ., 2007 red l i gh t
Ca i , e t a l ., Op t . Exp r . , 20 07 a l l t he v i s ib le
glass substrate
p 2wb
tdt
AgAl
2O3
Ag
ww
b
k
EH
TM
k
H
E
TE
W i d t h v a r ie s f r o m 5 0 n m t o 1 2 7 n m
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E
k
TM
Negative Magnetic Response
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E
k
TM
Negative Magnetic Response
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Magnetic Colors: visualizing magnetism
Resonant TM
Transmiss ion
N on - res onan t TE
T ransmiss ion
Resonan t TM
Ref lec t ion
N on - r esonan t TE
Ref lec t ion
Sample # A B C D E F
Width w (nm) 50 69 83 98 118 127Cai , e t a l . , Opt . Ex pr . , 1 5,3 3 3 3 ( 2 0 0 7 )
400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Transmission
Wavelength (nm)
A
B
C
D
E
F
400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wavelength (nm)
A
B
C
D
E
F
400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Reflection
Wavelength (nm)
A
B
C
D
E
F
400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wavelength (nm)
A
B
C
DE
F
160 m
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Magnetism across the whole visible
m as a f u n ct i o n of st r i p w i dt h w : ex pe r im en t v s . t h eo ry Neg l i g i b l e sa tu ra t i on e f fect on si ze -sca l i ng ( as opposed t o SRRs)
50 60 70 80 90 100 110 120 130450
500
550
600
650
700
750
800 Experimental
Analytical
Permeability
Strip width, w (nm)
m
(nm)
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Permeab
ility(')
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Engineering Space for Light w ith
Metamaterials
Par t 1 : Elect r i ca l an d Magn e t i c Me t am at e r i a l s
Par t 2 : Nega t i ve - I nd ex Met am at er i a l s, NLO,an d su p er / h y p er - l en s
Pa r t 3 : Cloak ing and Tr ansfo r m a t ion Op t i cs