metamaterials part2

8/8/2019 metamaterials part2

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BirckNanotechnology Center

Engineering Space for Light with

Metamaterials


Part 1: Electrical and Magnetic Metamaterials

Part 2: Negative-Index Metamaterials, NLO,and super/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


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Metamaterials with Negative Refraction

Single-negative:

n 0(F is low)

Double-negative:

n


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5


Negative Refractive Index in Optics: State of the Art

Year and Research

group

1st time posted and

publication

Refractive

index, nWavelength

Figure of Merit

F=|n|/n Structure used

2005:

PurdueApril 13 (2005)

arXiv:physics/0504091

Opt. Lett. (2005)0.3 1.5 m 0.1 Paired nanorods

UNM & ColumbiaApril 28 (2005)

arXiv:physics/0504208

Phys. Rev. Lett. (2005)2 2.0 m 0.5 Nano-fishnet with

round voids

2006:

UNM & Columbia J. of OSA B (2006) 4 1.8 m 2.0 Nano-fishnet withround voids

Karlsruhe & ISUOL. (2006)

OL (2007)

11 1.4 m1.4 m3.0

2.5

Nano-fishnet

3-layer nanofishnet

Karlsruhe & ISU OL (2006) 0.6 780 nm 0.5 Nano-fishnet

Purdue OL (2007)0.9-1.1

770 nm

810nm

0.7

1.3Nano-fishnet

see review: Nature Photonics v. 1, 41 (2007)


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Negative permeability and negative permittivity

E

H

k

Dielectric

Metal

Nanostrip pair (TM) < 0 (resonant)

Nanostrip pair (TE) < 0 (non-resonant)

Fishnet and < 0

S. Zhang, et al., PRL (2005)


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Sample Geometry (Fishnet Structure)

E-beam lithography

Period = 300 nm along both axis

Average width of strips along H = 130 nmAverage width of strips along E = 95 nm

H

E

Alumina

Silver

ITO300nm

30

0nm

Stacking:

10 nm of Al2O333 nm of Ag38 nm of Al2O333 nm of Ag10 nm of Al2O3

SEM image andprimary polarization

i k h l


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Solid line : Experimental

Spectra for Primary Polarization

Magnetic resonance around = 800 nm Electric resonance around = 600 nm

U. K. Chettiar, et al., Optics Letters 32, 1671 (2007)

Finite Elements

Dashed line: Simulated

Bi k N t h l C t


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Field Maps for Primary Polarization

Electrical Resonance, = 625 nm Magnetic Resonance, = 815 nm

E

H

k

Birck Nanotechnology Center


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Double Negative NIM (n=-1.0, FOM=1.3, at 810 nm)Single Negative NIM (n=-0.9, FOM=0.7, at 770 nm)

wavelength (nm)wavelength (nm)

permeability

permittivity

500 600 700 800 900-1

0

1

2

-4

-20

2

4

''

500 600 700 800 900

-1

0

1-n'/n"

-n'E

H

permeab

ility

permittiv

ity

'

'

wavelength (nm) wavelength (nm)

-n'/n"

-n'

E

H

700 800 900-1

0

1

700 800 900

0.5

1

1.5

-6

-4

-2

0

Chettiar et al

OL (2007)



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Summary on negative refractive index

A Double Negative NIM (Negative index material) isdemonstrated at a wavelength of ~810 nm

The sample exhibits a figure of merit (-n/n) of 1.3and a transmittance of 25% at 813 nm

The same sample shows Single Negative NIMbehavior for the orthogonal polarization at a

wavelength of ~770 nm with a figure of merit of 0.7and a transmittance of 10%



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Negative Refraction for Waveguide Modes

An mode index of ~ -5 is obtained at the

green light.

Lezec, Dionne and Atwater, Science, 2007

negative refraction for 2DSPPs in waveguides



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Outline




Nonlinear optics with metamaterials Super-resolution

Optical cloaking



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gy

Chiral Optical Elements

Boses Artificial chiral molecules: Twisted jute elements

J. C. Bose, Proceeding of Royal Soc. London, 1898

Optical counterparts:

Decher, Klein, Wegener and Linden

Opt. Exp., 2007

The Zheludev group, U. Southampton

Appl. Phys. Lett., 2007



15/3115

gy

Chiral Effects in Optical Metamaterials

Circular dichroism:

Giant optical gyrotropy:

Decher, Klein, Wegener and Linden

Opt. Exp., 2007

The Zheludev group, U. Southampton

Appl. Phys. Lett., 2007

Chirality can ease obtaining n


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Outline





Super-resolution

Optical cloaking



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SHG and THG from Magnetic Metamaterial

Excitation when magneticresonance is excited (1st pol)

SHG: Klein, Enkrich, Wegener, and Linden, Science, 2006

SHG & THG: Klein, Wegener, Feth and Linden, Opt. Express, 2007

Excitation at 2nd pol.(no magnetic resonance)



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NLO in NIMs: SHG

Backward Waves in NIMs:

Distributed feedback, cavity-like amplification, etc.

02

2

2

2

2

2

1

1

1 =+dz

dhk

dz

dhk

Czhzh = )()( 22

2

1

Manley-Rowe Relations

,021 =dz

dS

dz

dS

Czhzh = )()( 222

112212, kk == Phase-matching:

n1 < 0 and n2 > 0



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SHG in NIMs: Nonlinear 100% Mirror

[ ] 1100 = hz 222

22

)2( /4 ck =

)](cos[/)(1 zLCCzh = )](tan[)(2 zLCCzh =

)/arccos( 10hCLC =

Finite Slab:

Semi-Infinite Slab:

)()(,0 12 zhzhC ==

)]/(1/[)( 0102 zzhzh +=

100% reflective SHG Mirror !

Czhzh = )()( 222

1

Other work on SHG:

Kivshar et al; Zakhidov et al



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Optical Parametric Amplification (OPA) in NIMs

213 +=

Manley-Rowe Relations:

02

2

1

1

=

SS

dz

d

0 0.5 10

2

4x 10

7

z/L

1a,

2g gL=4.805

k=0

LHM

3S - Control Field (pump)(n1 < 0, n2,n3 > 0)

2122

22011

2111 /)(,/)(,/)( LggLa azaazaaza === ( )( ) 3

)2(4212121 /8/ hcg =

Popov, VMS, Opt. Lett. (2006)

Appl. Phys. B (2006)

For SHG see also Agranovich et al

and Kivshar et al



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OPA in NIMs:Loss-Compensator and Cavity-Free Oscillator

2

2011

2

111

/)(,/)( azaazagLa

== ( ) 3

)2(4

212121 /8/ hcg =

0=k

Backward waves in NIMs ->

Distributed feedback & cavity-like

amplification and generation

Popov, VMS, OL (2006)

Resonances in output amplification and DFG

OPA-Compensated Losses

Cavity-free (no mirrors) Parametric Oscillations Generation of Entangled Counter-propagating LH and RH photons

1L = 1, 2L = 1/2



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(3) -OPA assisted by the Raman Gain:

4 signal; 1, 3 control fields2= 1+3-4 idler

(Raman-enhanced; contributes back to OPA at 4)

Four-level (3) centers embedded in NIM

.

(3) -OPA: compensation of losses:transparency and amplification at 4

Cavity-free generation of counter-

propagating entangled right- and left-handed

photons Control of local optical parameters through

quantum interference

OPA with 4WM

Popov, et al OL (2007)See talk tomorrow by Popov et al on NLO in MMs



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Outline



Negative-index metamaterials

Chiral metamaterials


Super-resolution Optical cloaking



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Super-resolution:Amplification of Evanescent Waves Enables sub- Image!

Waves scattered by an object have all the Fourier components

The propagating waves are limited to:

To resolve features , we must have

The evanescent waves are re-grown in a NIM slab and fully recovered at the image plane

2 2 2

0 z x yk k k k = 2 2

0t x yk k k k = +

metamaterials part2

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