metamaterials part3

8/8/2019 metamaterials part3

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BirckNanotechnology Center

Engineering Space for Light with

Metamaterials


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)

Birck Nanotechnology Center


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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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