Plasmonics and Metamaterials | nanoHUB

Plasmonics and Metamaterials

Nick Fang

ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 1

Nick FangUniversity of [email protected]

Outline• Introduction to Metamaterials

• New Physics of Metmaterials– Artificial PlasmaArtificial Plasma– High Frequency Magnetism– Negative Refraction– Negative Refraction– Cloaking

• Outlook


New Frontiers of PhotonicsSubdiffraction imaging Sensing

Fang et al., Science, 2005

Telecom applications

Fang et al., Science, 2005

Invisibility cloaks

Van Duyne et al., MRS bulletin, 2005

MetamaterialsLogeeswaran et al., Appl. Phys. A, 2007

Chen et al., PRL, 2007


• Materials Today’s top 10 advances in material science over the past 50 years • Discover top 100 science stories of the year 2006

What are Meta-Materials ?Atomic Crystal Lattice Sub- Meta “Atoms”

1nm 10 nm -100 m


Metamaterials

• Definition by a think-tank futurist: “Metamaterials are new materials designated by manipulatingMetamaterials are new materials designated by manipulating extreme magnitudes of physical conditions during synthesis and manufacture.”

• Our Definition:A new class of ordered composites from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneities.


Metamaterial vs Natural Medium

Common Natural medium Metamat’l

Wave Propagation Quantum Waves Classical Waves

ThermalThermal excitation Significant Low?

Symmetry 230 crystal lattices Rotation, TranslationTopologyTopology …

Atomic Interaction

Hard or Soft sphere; nearest neighbor dominant

“Atoms” can be larger than lattice

Dopant and Defects Random Controllable


And More

Electromagnetic Metamaterials

• When and <0


(from Valerie Browning, DARPA)

Effective Medium Properties<B> In long wavelength limit(a<<), we take the

cell as an macroscopic point: all physical properties are smoothed in the cell volume

1 1( )exp( ) ( )exp( )

1 1

i iC C

E r iG r dV H r iG r dVV V

E H

1 1( )exp( ) ( )exp( )i iC C

D r iG r dV B r iG r dVV V

D B

D B

<H> <E>

D BE H

The effective and can be defined as ratios of the macroscopic fields:


Plasmonic “Atoms” and “Crystals”

Consider a sparse wire matrix:• “Diluted” electron density:

Natural metal exhibit negative at Optical Frequency:

2

How to lower the plasma frequency?

effn

• Diluted electron density:

21 ,p

i

0

22 eff

peff

n e

m

3 4

• Heavy Mass of Electrons (due to magnetic induction):

Natural bulk metal3 410 10 !eff em m

aApplications: Tunable optical high

Pendry, PRL,1996

2r pass filter (visible to THz)


How to Lower the Frequency?

• “Diluted” electron density– Lowered filling ratiog

• Heavy Mass of ElectronsM ti ff t– Magnetic effect

P mv eA

2 22

)/ln(2

2

20

0

22

raac

men

eff

effp


)(0 eff

Plasmonic Response

3

E 1

2

2

-1

0

erm

ittiv

ity (

)

2

21 p

-3

-2Pe

-5

-4

0 0.5 1 1.5 2

The wire medium exhibits <0 below the plasma frequency.


Frequency (/p)

frequency.

At <0


- Pendry, 1998

Physics of Surface Plasmon

dielectricE kzdielectricE kzdielectricE kz

(H. Raether, Surface Plasmons, Springer-

Verlag, 1988)

kx + + + + + +

z

+ + + + + +

z

z

kxxmetalHy metalHy metal

Hy

x

=ckx

• EM waves propagating along the interface between two media with their of opposite sign.

p

pp g

• Intensity maximum at interface; exponentially decays away from

1/ 21 2k


exponentially decays away from the interface. kx1 2

xkc

Propagation length of SPs

If consider the absorption in metal:''

1'11 i

Then, kx become a complex kx=kx’+ikx’’

21

'1'

k '1 1

c

kx

2'

''1

23

'

'1''

1

kx 2'

11 21

cx

The propagation length L

For silver: L=22 m at 514.5nmL=500 m at 1060 nmThe propagation length L

1''2 xkL

Potential for Chip Scale optical interconnects!


p

Field enhancement due to SPs

)2exp(1)exp(

)1/0(

)1/2(

110201

11120120122

0

2

dikrrdikttt

H

H

z

zy

2

yH

The ratio of the electromagnetic energy at two sides of the metal film:

)1/0( 1102010H zy

0 12

kziz kk 1

where2

k

kz

i

iz

kiik kk

r

ikik rt 1

z

20

2

21

3

21

212201

22

012)(

114radxxx

i

kkket

ctT

00'1 )1(

''

2'1

'max21

TThe maximum enhancement:


''1

'10

max 1 The maximum enhancement:For silver, at =350 nm, T~3X102

High f Magnetism?

e-B a

2r

Magnetism in natural materials f d b 100 GH !

Atome-

fades away above 100 GHz !

(Pendry et al, IEEE MTT, 1999)j Array of Split Ring Resonators

---

+

++

H0C

Bg

The strong capacitive coupling bet een ind cti e c rrent loops


between inductive current loops leads the magnetic resonance

Artificial Magnetism

H0H inside the cylinder:

k

eff =

0

eff


0 0<<1, No Resonance

Artificial Magnetism (2)

1' ( )i L i

Resonance by Impedance Coupling

' ( )i L izC

1 1F F

0 0 0

1 12 ( ( )) 2 2(1 ) 1

F Fi iz z ir r r

Resonance, Re()<0 when 21 zF Resonance, Re() 0 when0

1Fr


Split-Ring Resonators

2 20

32

dzr

0=0

0

1MP F 1 F

R=11, a=25, d=2


The Swiss Roll Structure


Enhanced Coupling by adding more turns, Lower resonant Freq

Application Example: Open MRI


M. C. K. Wiltshire et al., Science 291, 849 (2001).

Dispersion with Magnetic Resonance

0: resonant frequency(->inf)

MP: “Magnetic Plasma” Frequency( 0)


(=0)

To Higher Frequency: Resistance Issue

Hampered Performance at Hi h F (S l


Higher Frequency (Scale Effect)

Metamaterial for telecomChallenges: Fiber-optic communication systems require devices operating in

near-IR [λ = 1312nm/229THz (min. dispersion), 1550nm/193THz (min. attenuation)][λ 1312nm/229THz (min. dispersion), 1550nm/193THz (min. attenuation)]

50nm!!!

Breakdown of linear scaling and saturation of resonant response of SRRs at optical freqZhou et al PRL 2005


of resonant response of SRRs at optical freqZhou et al., PRL, 2005

Combining the building blocks

20

1

2

3

ty (

)

2

21 p

-5

-4

-3

-2

-1

Per

mitt

ivit

5

10

()

50 0.5 1 1.5 2

Frequency (/p)

2

2 20

1 F

-5

0

Per

mea

bilit

y

-100 0.5 1 1.5 2

Frequency (/p)

F th b ildi bl k i h i t f t t i l


From these building blocks, a rich variety of metamaterial structures can be developed.

LHM with both – and -

Merger of SRR and Plasmon Wires: -> LHM

Smith et al PRL 2000;Science 2001


Smith et al, PRL, 2000;Science, 2001

Implications of <0, <0

Direction of Energy Flow: S E H

Di ti f Ph k E BDirection of Phase Velocity:

Phase and Energy propagation directions are thus antiparallel:

|| k E B E H S

“L f h d d i l ”


“Left-handed materials”

Negative Refractionr

i

For TE WavesH

E

,

• Boundary Conditions:

tt

y

1tE 1tH 1nE 1nH 1tk 1nkn̂1:RH

2tE 2tH 2nE 2nH 2tk 2nk2:LH

E E ( )


1 1 2 2 n nE E

1 1 2 2 n nH H2

1

sgn( )sgn( )

nn

Frequency Dispersion

The permittivity and permeability must be causal analytic functions; Kramers-Kronig applies:

"1' 1x

PV dx

' 11"x

PV dx

functions; Kramers Kronig applies:

1 PV dxx

x

1

1

2 21 1 04 4mediumU E H


Measurement of Refractive Index


Measurement of Refractive Index


Shelby, Smith et al, Science, 2001

Rerouting EM Waves

Controlling Electromagnetic Fields , J. B.Pendry et al,Science 321,2006

Distorted fieldFree space field

tHE

0

EH

tHEq 0

E


tH

0

tEHq

0

Metamaterial Cloak

RrR

212 )(

rRRrr

12

21 RrR 21

2R

12 RR

12

2

RRR


12

Invisibility cloak

• “The cloak would act like you've opened up a hole inspace," "All light or other electromagnetic waves areswept around the area, guided by the metamaterialto emerge on the other side as if they had passedthrough an empty volume of space.“through an empty volume of space.

-David Smith ,Duke University


Smith et al, Science 2006

Towards optical metamaterialsNanoimprintIon/E-beam lithography Microfabrication Bulk machining

1000Nanoimprint Microfabrication

AnisotropicMetallic rods(2005)

MDM (2006-07)

Hyperlens (2007)

Superlens(2005-07)

Plasmonic

Bulk machining

uenc

ies

10

100Plasmonic+NIMNIMMagnetic

p

SiC superlens (2006)

(2005)

LSR (2007)

Semiconductormetamaterial

Fishnet(2005-07)

Hz)

ptic

al fr

eq

1

10 p ( )metamaterial (2007) Terahertz

resonators (2004)

Terahertz confinedncy

(THO

0.1Terahertz confined surface plasmon(2008)

requ

en

• SRR: Split-ring resonator• LSR: L-shaped resonator

1E-3

0.01 SRR(2000-03)

Fr • MDM: Metal-dielectric-metal• NIM: Negative index materials


0.01 0.1 1 10 100 1000 100001E 3

Feature size (m)

Other interesting Topics

• The Maxwell Stress Tensor: how the artificial atoms interactatoms interact

• Moving media: Negative Doppler effectMoving media: Negative Doppler effect

• High f magnetism: how to demonstrate magnetic• High f magnetism: how to demonstrate magnetic effect?– The Meissner effect and phase transitionp– Magnonic lattice?


References• Extremely-Low-Frequency Plasmons in Metallic Mesostructures,J.B. Pendry,

A.T. Holden, W.J. Stewart and I. Youngs, Phys. Rev. Lett., 25, 4773 (1996).

• Low Frequency Plasmons in Thin Wire Structures, J.B. Pendry, AJ Holden, DJ Robbins, and WJ Stewart, J. Phys. Cond. Matt., 10, 4785 (1998).

• Magnetism from Conductors, and Enhanced Non-Linear Phenomena, JB Pendry, AJ Holden, DJ Robbins, and WJ Stewart, IEEE transactions on microwave theory and techniques 47,2075 (1999).

• Metamaterials and Negative Refractive Index, DR Smith, JB Pendry, MCK Wiltshire, Science 305 788-92 (2004)

• Metamaterials and the Control of Electromagnetic Fields, JB Pendry, Proceedings of the Ninth Rochester Conference on Coherence and Quantum Optics (2007)


Optics (2007)

Plasmonics and Metamaterials | nanoHUB

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