metamaterials part1

8/8/2019 metamaterials part1

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Bi rck Nanotechnology Center

Engineering Space for Light w ith

Metamaterials


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


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


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

metamaterials part1

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