d ii ft ri ntn egative refractive index in...

$: d Ii ft Ri NtN egative Refractive Index in Opticsesperia.iesl.forth.gr/~kafesaki/Meta-School/pdfs/Shalaev2.pdf · Phys. Rev. Lett. (2005) 2 2.0 m 0.5 Nano-fishnet with round voids$
Birck Nanotechnology Center

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


Negative refractive index: A historical reviewg

… energy can be carried forward at the group velocity but in a direction that is group velocity but in a direction that is anti-parallel to the phase velocity…

Schuster, 1904

Sir Arthur Schuster Sir Horace Lamb

Negative refraction and backward propagation of waves

Mandel’stam, 1945

L. I. Mandel’stam

,

Left-handed materials: the electrodynamics of substances with simultaneously negative of substances with simultaneously negative values of and

Veselago, 1968

V. G. Veselago

Pendry, the one who whipped up the recent boom of NIM researches

Sir John Pendry

Perfect lens (2000)EM cloaking (2006)


Metamaterials with Negative Refraction g

εμn

2

Refraction:θ1

θ2

εμn

Figure of merit

θ1

n < 0, if ε′|μ| + μ′|ε| < 0

F = |n’|/n”

Single-negative:n<0 when ε′ < 0 whereas μ′ > 0 (F is low)

Double-negative:

θ1 θ2

n<0 with both ε′ < 0 and μ′ < 0 (F can be large)


Negative Refractive Index in Optics: State of the Art g p

Year and Research group

1st time posted and publication

Refractive index, n

Wavelength

Figure of MeritF=|n|/n Structure usedg oup publicatio index, n |n |/n

2005:

PurdueApril 13 (2005)arXiv:physics/0504091O L (2005)

0.3 1.5 m 0.1 Paired nanorodsOpt. Lett. (2005)

UNM & ColumbiaApril 28 (2005)arXiv:physics/0504208Phys. Rev. Lett. (2005)

2 2.0 m 0.5 Nano-fishnet with round voids

2006:2006:

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

Karlsruhe & ISU OL (2006) 1 1 4 m 3 0 Nano fishnetKarlsruhe & ISU OL. (2006) 1 1.4 m 3.0 Nano-fishnet

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

Purdue MRS Bulletin (2008) -0.8 725nm 1.1 Nano-fishnet Purdue MRS Bulletin (2008) -0.6 710nm 0.6

Purdue In preparation (2009) -0.25 580nm 0.3 Nano-fishnet

CalTech: negative refraction in the visible for MIM waveguide SPPs (2007)


Negative permeability and negative permittivityg p y g p y

Dielectric

E

HDielectric

Metal

k

Nanostrip pair (TM)

< 0 (resonant)

Nanostrip pair (TE)

< 0 (non-resonant)

Fishnet

and < 0 < 0 (resonant) < 0 (non-resonant) and < 0

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


Sample A: Double Negative NIM (n’=-0.8, FOM=1.1, at 725 nm) Sample B: Single Negative NIM (n’ 0 25 FOM 0 3 at 580 nm)Sample B: Single Negative NIM (n =-0.25, FOM=0.3, at 580 nm)

Sample A. period- E: 250 nm; H: 280 nm2

MRS Bulletin (2008)

1

2

vity

bili

ty2

42

-1

0

FOMRe(n)

Perm

ittiv

Perm

eab

-4

-2

0

0

1

500 nm

SampleB. period- E:220nm H:220nm

400 500 600 700 800 900-2

Wavelength (nm)

P P

400 500 600 700 800 900

-4

400 500 600 700 800 900Wavelength (nm)

500 nm

E

H

Stacking:E Stacking:

8 nm of Al2O343 nm of Ag45 nm of Al2O3

500 nm45 nm of Al2O343 nm of Ag8 nm of Al2O3


T iti M t t i l Transition Metamaterials

Litchinitser Gabitov Maimistov Sagdeev & Litchinitser, Gabitov, Maimistov, Sagdeev, & Shalaev (OL v. 33, 2350 (2008))


Transition LayerTransition Layer

RHM LHMTransitionRHM LHMTransition0,, n 0,, n

0

Layer0,, n 0,, n

0

Layer

0

0 0

x or

0

0 0

x or

0

0 x

0

or

0

0 x

0

or

00

x

22

hx

1

hx

00

x

22

hx

1

hx


Simple explanationSimple explanation

PIM NIM(x)(x)


GeometryGeometry

zE H H

TE-wave

q0

Ey, Hz,Hx

PIM NIM

n = 0 x


Electromagnetic enhancementElectromagnetic enhancement

Litchinitser et al., OL (2008)


with Alex K. Popov p

Nonlinear Optics of NIMs: O ti l P t i A lifi ti (OPA) Optical Parametric Amplification (OPA)

• OPA: compensating losses with OPA • OPA: compensating losses with OPA (with χ(2) – Opt. Lett. 2006; with χ(3) – OL 2007)

A.K. Popov and V.M. Shalaev - OL 31, 2169 (2006) and OL (2007)

Laser Physics Letts 3, 293 (2006); APB 84, 131 (2006); JOSA B 23 535 (2006) ( ith G bit Lit hi t t l) JOSA B 23, 535 (2006) (with Gabitov, Litchintser, et al)

early work on SHG: Kivshar, et al; Zakhidov et al (2005)SHG Experiment in SRRs: Klein et al, Science 313, 502 (2006)


Three-dimensional Optical Metamaterials with a N ti R f ti I d Negative Refractive Index

Schematic and Sem image of 21-layer fishnet, p= 860nm, a= 565,b= 265nm

Stacking: alternating layersSem image of 3D fishnet NIM prism

Stacking: alternating layers50 nm of MgF2 and 30 nm of Ag

.Valentine, et al., Nature (2008)

also work by the Wegner & Giessen groups .

3D NIMs enable new means .to compensate for loss – OPA!


Optical Parametric Amplification (OPA) in NIMsp p ( )

213 3S - Control Field (pump)(n1 < 0, n2,n3 > 0)213

4x 107

2g

gL=4.805k=0

LHM

3

2η 1a,2

g Δk=0

0 0.5 10 z/L0 0.5 10 z/L

2122

22011

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

)2(4212121 /8/ hcg

Manley-Rowe Relations:

21

SSd 0

2

2

1

1

SS

dzd


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

B k d i NIM Backward waves in NIMs ->Distributed feedback & cavity-like amplification and gene ationamplification and generation

0k α1L = 1, α2L = 1/2

22011

2111 /)(,/)( azaaza gLa 3

)2(4212121 /8/ hcg

Resonances in output amplification and DFG

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


Optical Cloaking& &

Transformation OpticsTransformation Optics

VMS, Science, Oct. 17, 2008


Designing Space for Light with T f ti O tiTransformation Optics

Fermat:Fermat:δ∫ndl = 0√ ( ) ( )n = √ε(r)μ(r)

“curving” optical space

Straight field line in Cartesian coordinate

Distorted field line in distorted coordinate

Spatial profile of & tensors determines the distortion of

optical space

p p coordinate

Seeking for profile of & to make light avoid particular region in space — optical cloaking Pendry et al., Science, 2006Pendry et al., Science, 2006

Leonhard, Science, 2006Greenleaf et al (2003)L. S. Dolin, Izv. VUZ, 1961


Form-invariance of Maxwell’s equationsq

Coordinate transformation from x to coordinate x is described Coordinate transformation from x to coordinate x is described

using the Jacobian matrix G: ij i jg x x

( )E

Maxwell’s equation in xT TG G G G

Transformation of variables

( )( ) 0EH

1 1

;

( ) ; ( )T T

G G

E G E H G H

HE tE

( ) ; ( )

;

E G E H G HGJJG G

EH Jt G G

Ward and Pendry, J. Mod.Opt. 43, 777 (1996)Ward and Pendry, J. Mod.Opt. 43, 777 (1996)

Solutions to MEs -> works in near-zone (nanoscale) too)!


Invisibility in nature, physics and technologyy , p y gy

• Natural camouflage Natural camouflage • Black hole• …

h l i hi i i ibiliCurrent technologies to achieve invisibility: Stealth technique:Radar cross-section reductions by absorbing

Optical camouflage:Projecting background image onto masked objecty g

paint / non-metallic frame / shape effect…Projecting background image onto masked object.

F-117 “Nighthawk” Stealth Fighter Optical Camouflage, Tachi Lab, U. of Tokyo, Japan


Invisibility: from fiction to fact?Invisibility: from fiction to fact?

Examples with scientific elements:

The Invisible Man by H. G. Wells (1897)

“The invisible woman” in The Fantastic 4 by Lee & Kirby (1961)

"... it was an idea ... to lower the "... she achieves these feats by t as a dea to o e t erefractive index of a substance, solid or liquid, to that of air — so f ll ti l

s e ac e es t ese eats bybending all wavelengths of light in the vicinity around herself ...

ith t i i ibl far as all practical purposes are concerned.” -- Chapter 19 "Certain First Principles"

without causing any visible distortion.” -- Introduction from Wikipedia

Pendry et al.; Leonhard, Science, 2006

40

(Earlier work: cloak of thermal conductivity by Greenleaf et al., 2003)


Transformation Optics and CloakingTransformation Optics and Cloaking


Camouflaging bumps on a metal surfaceCamouflaging bumps on a metal surface

P f t C d tPerfect ConductorJ. Li, J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking”

D. Smith, et al – MW experiment (Science -2009)Zhang et al – optical experiment(Nature Materials -2009)


Optical Cloaking with Metamaterials:C Obj t b I i ibl i th Vi ibl ?Can Objects be Invisible in the Visible?

λ = 632 nm

Nature Photonics (April, 2007)[GHz-cloak: Duke team]


Structure of optical cloak: “Round brush” Structure of optical cloak: Round brush

Cai, et al., Nature Photonics, 1, 224 (2007)

Unit cell:

Fle ible cont ol of Flexible control of r ;

Negligible perturbation in

metal needles embedded in dielectric host


Cloaking performance: Field mapping moviesg p pp g

Example:Example:Non-magnetic cloak @ 632.8nm with silver wires in silica

Cloak ONCloak OFF Cloak ONCloak OFF


Scattering issue in a linear non-magnetic cloakScattering issue in a linear non magnetic cloak

Linear transformation HE

b ar r ab

E

k

E

Ideal cloak:

kH1z

r br b

Z

Perfectly matched impedance results

E

in zero scattering

Linear non-magnetic cloak:

kH1z

r br b

aZ b

Detrimental scattering due to impedance mismatch

46

impedance mismatch

Nonlinear transformation –> no scattering


High-order transformation for cloakingg g

( ) 2( ) 1 b b ith bé ù¢ ¢ ¢+ +

2-nd order transformation for non-magnetic cloak:

( ) 2( ) 1r g r a b p r b r a with p a bé ù¢ ¢ ¢= = - + - + =ê úë û

47

W. Cai et al (APL 91, 111105, 2007); with G. Milton


Towards experimental realizationTowards experimental realization

We need a design that is …g

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

4848


Structures of realistic high-order TO cloaks g

0.03

0 02

0.025 ||

0.015

0.02

mag

( )

0 005

0.01

i

(a) (b)

(b) (a)

-1 0 1 2 30

0.005

real( )

r(a) r(b)

real()

ε found from Wiener’s bounds

l k @ 530 ith lt ti il ili Cai, et al, (OE, 2008)

cloak @ 530 nm with alternating silver- silica slices based on nonlinear transformations-ε >>1 - problem


Bandwidth problem in electromagnetic cloakBandwidth problem in electromagnetic cloak

F t’ Fermat’s principle

vp = c/n vs ≤ c

Curved wave Refractive Phase velocityvp vs

Di i trajectory index n<1

yvp>c

Dispersive material

s

- operating frequency - operating bandwidth

s s – geometrical cross-section

s - scattering cross-section

50

Chen, et al., PRB, 76, 241104 (2007)


Wavelength Multiplexing CloakWavelength Multiplexing Cloak

1 32

Combination of techniques: Virtual inner boundary

Di i t lPhysical boundaries the cloaking device

Dispersion control Active medium or EIT?

Virtual inner boundary for 0z r

51

different wavelengths Kildishev, et al (NJP, 2008)


Broadband Optical Cloakingp gin Tapered Waveguides

I I Smolayninov V N Smolyaninova A V KildishevI.I. Smolayninov, V.N. Smolyaninova, A.V. Kildishevand V.M. Shalaev

(PRL , May 29, 2009)


Emulating Anisotropic Metamaterials i h T d W id

ss

~~ 2~

,

with Tapered Waveguides ,

A space between a spherical and a planar surface (a) mapped onto a planar anisotropic MM (b)onto a planar anisotropic MM (b)

(c) Distribution of radial (top),(c) st but o o ad a (top),azimuthal (middle), and axial components of ε = μ in equivalent planar MM. Dashed lines show same components in the ideal cloak. same components in the ideal cloak.

(d) Normalized profile of optimal and “plane-sphere” waveguides for a cloak with radius of b0 = 172 µm. cloak with radius of b0 172 µm.


Broadband Optical Cloaki T d W idin Tapered Waveguide


Fermat Principle and Waveguide Cloak

Cloaking Hamiltonian: (Narimanov, OE, 2008 )

p g

neff L = const

Dispersion law of a guided mode:

(Fermat)

guided mode

cphase = / k cgroup = d/ dk

=ck

neff = c / cphase = ck / ff

light line

near cutoff

k

neff = 0cgroup = 0


Fermat principle:

cgroup = d/ dk 0 light tries to avoid the “slow regionnear cutoffgroup /

near cutoffnear cutoff

light propagation in a waveguideg p p g gnear cutoff:


Broadband Cloaking in Tapered Waveguide g p g

Cloaked area

( ) ( )2 2 2

2 2 2 2( ) ( )c k m l d k k br r fw r p r r -é ù= + + = + -ê úë û( ) ( )r r fê úë û


Broadband Optical Cloakp

λ=515nm λ=488nm

( ) ( )2 2 2

2 ( )c k m l dw r p ré ù+ +( ) ( )2 2 2

( )

( )

c k m l d

k k b

r

r f

w r p r

r -

é ù= + + ê úë û= + -( )r f r


Engineering Meta-Space for Light:g g a pa o gvia Transformation Optics

ildi h ( ) i

Fermat: δ∫ndl = 0

Kildishev, VMS (OL, 2008); VMS, Science 322, 384 (2008)

(b)

n = √ε(r)μ(r)curving &

nano”crafting”Light concentrator

nano”crafting”optical space

Light concentrator Optical Black Hole (also, Schurig et al) (Narimanov, Kildishev)

Planar hyperlensMagnifies; no loss problem


Highlights of Purdue “Meta-Research”Highlights of Purdue Meta Research

Purdue Photonic MetamaterialsPurdue Photonic Metamaterials(a) 1-st optical negative-index MM (1.5 µm; 2005) (b) Negative index MM at shortest λ (~580nm; 2009)(c) 1-st magnetic MM across entire visible (2007)

H

Transformation Optics with MMs:Flat hyperlens, concentrator, and cloak

E

500 nm


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