T f i Li ht ith M t t i l Transforming Light with...

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Birck Nanotechnology CenterBirck Nanotechnology Center

Vladimir M. Shalaev

T f i Li ht ith M t t i l

Purdue University

Transforming Light with Metamaterials

OUTLINE

• Intro to metamaterials• Electrical metamaterials for nanoplasmonics & nanophotonics• Electrical metamaterials for nanoplasmonics & nanophotonics• Magnetic metamaterials• Negative refractive index• Transition Metamaterials• Nonlinear Optics in Metamaterials• Transformation Optics & Optical Cloaking • Transformation Optics & Optical Cloaking

Birck Nanotechnology Center

What is a metamaterial?What is a metamaterial?

Metamaterial is an arrangement of artificial structural elements, d i d t hi d t d l l t ti designed to achieve advantageous and unusual electromagnetic properties.

= meta = beyond (Greek)

--

A metamaterial with artificially

2

A natural material with its atomsA metamaterial with artificially structured “atoms”


Photonic crystals vs. Optical metamaterials: connections d diffand differences

a<< . a~ a>>Effective mediumdescription using

Maxwell equations with

Structure dominates.Properties determined

by diffraction and

Properties describedusing geometrical optics

and ray tracing, , n, Z interference

Example:Optical crystals

Example:Photonics crystals

Example:Lens systemp y

Metamaterialsy

Phased array radarX-ray diffraction optics

Shadows

3


Metamaterials: Artificial periodic structures?Metamaterials: Artificial periodic structures?

“Hot-spots” in fractalsLycurgus Cup (4th century AD)

Ancient (first?) random

4

Shalaev, Nonlinear Optics of Random Media: Fractals and Composite Films, Springer, 2000

Ancient (first?) random metamaterial (carved in Rome!) with gold nano particles


Optical MaterialsOptical Materials

WaterAirE,H ~exp[in(ω/c)z]

n = ±√(εμ)Crystals

metals

n ±√(εμ)

Semiconductors

5

Cloaking (TO) area


Electrical Metamaterials:Electrical Metamaterials:a route to nanophotonicsp


Electrical Metamaterials ( t l t t )(metal nanostructures)

20 5.0

9 216 V Drude model for permittivity: Silver parameters:

50

0( )( )

p

i

9.2160.0212

p eVeV

0

Silv

er

-100

-50

ivity

of S

-200

-150

Per

mitt

i

Re(), experimentIm(), experimentRe() Drude

500 1000 1500 2000-250

200

Wavelength (nm)

Re(), DrudeIm(), Drude

7

Wavelength (nm)

Experimental data from Johnson & Christy, PRB, 1972


Electrical metamaterials:t l i ith t bl l fmetal wires arrays with tunable plasma frequency

2p

2 2 20

' " 1( / )

p

p

ii a r

2

2 2 c22

2ln( / )p

ca a r

A periodic array of thin metal wires with r<<a<<acts as a low frequency plasma

The effective is described with modified ωp

8

Plasma frequency depends on geometry rather than on material properties Pendry, PRL (1996)


Metal-Dielectric Composites and Mixing RulesMetal Dielectric Composites and Mixing Rules

1 1 2 2

1 2 1 2 2 1

c c

c c

1 2 1 2 2 1c c

hihMG f22

Maxwell-Garnett (MG) theory:

f « 1 hihMG

f22

Effective-Medium Theory (EMT):

(1 ) 0( 1) ( 1)m eff d efff fd d

9

( 1) ( 1)m eff d effd d


Nanophotonics enabled by plasminics

The operating speed of data transporting and processing systemsPhotonics

p y p

1TDWDMWDM

Plasmonics/nanophotonics

CMOS El t i

Photonics

1G130 nm

1 8 mCoaxial circuits

peed

(Hz) CMOS Electronics

1k

1M1.8 m

Telephone

Transcontinental cable

pera

ting

s

Communication networks

CMOS Electronics

1

1k Telephone

Telegraph

Op

Time

CMOS Electronics

Plasmonics

The ever-increasing need for faster information processing and transport is undeniable

Th d f t h t i i ti t k d bl 9 th

1825 1850 1875 1900 1925 1950 1975 2000 2025 2050Time

The speed of current photonic communication networks doubles every 9 months

Electronic components are running out of steam due to issues with RC-delay times


Optical Antennae as Electrical Metamaterials:Focusing Light to NanoscaleFocusing Light to Nanoscale

bow-tie antennasFabricated by AEBFabricated by AEB

H1

LC h t iLC-nanophotonics

Applications:Nano-laser, sensor, N h t i i it

11

Nanophotonic circuits


Optical Nanolaser(NSU C ll P d ) (NSU-Cornell-Purdue)

d)

Fi ) S h ti f th h b id ti l hit t b) TEM i f A ) SEM i fFig: a) Schematic of the hybrid nanoparticle architecture; b) TEM image of Au core; c) SEM image ofAu/silica/dye core-shell nanoparticles; d) SPASER mode (in false color), with = 525 nm and Q = 14.8; theinner and the outer circles represent 14 nm core and 44 nm shell Absorbed pumping per nanoparticle (10-13 J)

1 2 3 4 50700

400

500

600

700

. unit

s)

1 2 3 4 50

400

500

600

700

el. u

nits

) 1

Stimulated emission

100

200

300

400

Emiss

ion (r

el100

200

300

400

Em

issi

on (r

e

2

34 5

Stimulated emission spectra at differentpumps by OPO pulses at λ=488 nm

12

0

100

0 0.005 0.01 0.015 0.02 0.025Pumping (J)

0

100

490 510 530 550 570 590 610 630 650Wavelength (nm)

34,5


Magnetic Metamaterialsf th ti l for the optical range


Absence (or very weak: µ≈1) O ti l M ti i N t Optical Magnetism in Nature

Magnetic coupling to an atom: ~ 0/ 2B ee m c ea (Bohr magneton)

0eaElectric coupling to an atom: ~

Magnetic effect / electric effect 2 (1/137)2 < 10 -4

“ th ti bilit ( ) t h h i l i t l ti l l “… the magnetic permeability µ() ceases to have any physical meaning at relatively 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 µ=1.”

Landau and Lifshitz, ECM, Chapter 79.Landau and Lifshitz, ECM, Chapter 79.

14


Meta-Magnetics: from 10GHz to 200THzg

Terahertz magnetism

a) Yen, et al. ~ 1THz (2-SRR) – 2004 Katsarakis, 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

2004-2005 years: from 10 GHz to 200 THZ

2007: artificial magnetism across entire visible


Artificial Magnetic Metamaterials for Visibleg

Dielectric

E

HMetal

k

Nanorod pair Nanorod pair array Nanostrip pair

Nanostrip pair has a much stronger magnetic response

Podolskiy, Sarychev & Shalaev, JNOPM (2002) - µ < 0 & n < 0Lagar’kov, Sarychev PRB (1996) - µ > 0 Kildishev et al, JOSA B (2006); Shvets et al (2006) – strip pairsZheludev et al (2001) – pairs of rods for chirality


“Visible” artificial magnetismVisible artificial magnetism

ETM

HTE

kE

Hk

HE

wwb

p 2w

tdt

AgAl2O3Ag

w

35 40 2 bt nm d nm p w

glass substrate

p 2wb

bp

Purdue group

Width varies from 50 nm to 127 nm

Yuan, et al., Opt. Expr., 2007 – red lightCai, et al., Opt. Expr., 2007 – entire visible


Negative Magnetic Response in Visibleegat e ag et c espo se s b e

TM

EE

k


Metamagnetics with Rainbow ColorsMetamagnetics with Rainbow Colors

Tra

nsm

i

Refle

ctan

0 60.70.80.9 (a)

on 0 60 .70 .80 .9

A B CD

(c )

ittan

ce

nce

0.20.30.40.50.6

Tran

smis

sio

A B CD 0 .2

0 .30 .40 .50 .6

Ref

lect

ion D

E F

400 500 600 700 800 9000.00.1

Wavelength (nm)

E F

4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 00 .00 .1

W a ve le n g th (n m )

Sample # A B C D E F

Width w (nm) 95 118 127 143 164 173

Cai et al.Opt. Exp., 2007


Visible Meta-Magnetics: from Red to BlueVisible Meta Magnetics: from Red to Blue

800 1 0

700

750

800 Experimental Analytical Permeability 0.5

1.0

P

650

700(n

m)

-0.5

0.0

Perm

eab

550

600

m (

1 5

-1.0

bility ('

50 60 70 80 90 100 110 120 130450

500

-2.0

-1.5

')

m as a function of strip width “w”: experiment vs. theory

50 60 70 80 90 100 110 120 130Strip width, w (nm)

m pNegligible saturation effect on size-scaling


N ti R f ti I d Negative Refractive Index in Opticsin Optics

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