Negative-Index Metamaterials, NLO, and Super/Hyper-Lens

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 Birck Nanotechnology Center Outline

¾ What are metamaterials? ¾ Early electrical metamaterials ¾ Magnetic metamaterials ¾ Negative-index metamaterials ¾ Chiral metamaterials ¾ Nonlinear optics with metamaterials ¾ Super-resolution ¾ Optical cloaking

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Negative refractive index: A historical review

… energy can be carried forward at the group velocity but in a direction that is anti-parallel to the phase velocity… Schuster, 1904

Negative refraction and backward propagation of waves Sir Arthur Schuster Sir Horace Lamb Mandel’stam, 1945

L. I. Mandel’stam Left-handed materials: the electrodynamics of substances with simultaneously negative values of ε and μ Veselago, 1968

Pendry, the one who whipped up the V. G. Veselago recent boom of NIM researches

Perfect lens (2000) EM cloaking (2006) Sir John Pendry

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Metamaterials with Negative Refraction

E E H H k PIM k 2 i i n = εμ Refraction: n ±= εμ t E k t NIM H H k E

Warning! Negative refraction ≠ n < 0, if ε′|μ| + μ′|ε| < 0 negative refractive index Single-negative: (e.g. see Peccianti & Assanto: OE, 2007) n<0 when ε′ < 0 whereas μ′ > 0 (F is low) Figure of merit Double-negative: F = |n’|/n” n<0 with both ε′ < 0 and μ′ < 0 (F can be large)

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Negative Refractive Index in Optics: State of the Art

Year and Research 1st time posted and Refractive Wavelength Figure of Merit Structure used group publication index, n′ λ F=|n′|/n″

2005: April 13 (2005) Purdue arXiv:physics/0504091 −0.3 1.5 μm 0.1 Paired nanorods Opt. Lett. (2005)

April 28 (2005) Nano-fishnet with UNM & Columbia arXiv:physics/0504208 −2 2.0 μm 0.5 Phys. Rev. Lett. (2005) round voids 2006: Nano-fishnet with UNM & Columbia J. of OSA B (2006) −4 1.8 μm 2.0 round voids

OL. (2006) −1 1.4 μm 3.0 Nano-fishnet Karlsruhe & ISU OL (2007) −1 1.4 μm 2.5 3-layer nanofishnet

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

−0.9 770 nm 0.7 Purdue OL (2007) Nano-fishnet -1.1 810nm 1.3

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

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Negative permeability and negative permittivity

Dielectric Metal H E

Nanostrip pair (TM) Nanostrip pair (TE) Fishnet μ < 0 (resonant) ε < 0 (non-resonant) ε and μ < 0

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

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Sample Geometry (Fishnet Structure)

• E-beam lithography H • Period = 300 nm along both axis

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

SEM image and Stacking: primary polarization

10 nm of Al2O3 33 nm of Ag Alumina 38 nm of Al2O3 33 nm of Ag 3 Silver 10 nm of Al2O3 0 0 nm m ITO 0 n 30

7 Birck Nanotechnology Center Spectra for Primary Polarization

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

• Finite Elements

Solid line : Experimental Dashed line: Simulated

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

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Field Maps for Primary Polarization

H E

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

9 Birck Nanotechnology Center Double Negative NIM (n’=-1.0, FOM=1.3, at 810 nm) Single Negative NIM (n’=-0.9, FOM=0.7, at 770 nm)

4 2 -n'/n" ε' 1 μ' 2 1 0 0 H 0 -2

-n' permittivity -1 permeability E -4 -1 500 600 700 800 900 500 600 700 800 900 wavelength (nm) wavelength (nm)

1 0

-n'/n" μ' 1.5 -2 0 1 E ε' -4 -n' permittivity 0.5 permeability Chettiar et al H -1 -6 OL (2007) 700 800 900 700 800 900 wavelength (nm) wavelength (nm)

10 Birck Nanotechnology Center Summary on negative refractive index

• A Double Negative NIM (Negative index material) is demonstrated at a wavelength of ~810 nm

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

• The same sample shows Single Negative NIM behavior for the orthogonal polarization at a wavelength of ~770 nm with a figure of merit of 0.7 and a transmittance of 10%

11 Birck Nanotechnology Center Negative Refraction for Waveguide Modes

An mode index of ~ -5 is obtained at the green light. negative refraction for 2D SPPs in waveguides

Lezec, Dionne and Atwater, Science, 2007 12 Birck Nanotechnology Center Outline

13 Birck Nanotechnology Center Chiral Optical Elements

Bose’s Artificial chiral molecules: Twisted jute elements

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

Optical counterparts:

Decher, Klein, Wegener and Linden The Zheludev group, U. Southampton Opt. Exp., 2007 Appl. Phys. Lett., 2007

14 Birck Nanotechnology Center Chiral Effects in Optical Metamaterials

Circular dichroism:

Decher, Klein, Wegener and Linden Opt. Exp., 2007

Giant optical gyrotropy:

The Zheludev group, U. Southampton Appl. Phys. Lett., 2007

Chirality can ease obtaining n<0: Tretyakov, et al (2003), Pendry (Science 2004)

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16 Birck Nanotechnology Center SHG and THG from Magnetic Metamaterial

Excitation when magnetic resonance is excited (1st pol)

Excitation at 2nd pol. (no magnetic resonance)

SHG: Klein, Enkrich, Wegener, and Linden, Science, 2006 SHG & THG: Klein, Wegener, Feth and Linden, Opt. Express, 2007

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NLO in NIMs: SHG

Backward Waves in NIMs: Distributed feedback, cavity-like amplification, etc.

n1 < 0 and n2 > 0

2 2 1 dhk 1 2 dhk 2 2 2 =+ 0 1 2 )()( =− Czhzh 1 dz 2εε2 dz

Manley-Rowe Relations dS dS 21 =− ,0 dz dz

2 2 Phase-matching: ε = −ε = 2, kk 1221 1 2 )()( =− Czhzh

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SHG in NIMs: Nonlinear 100% Mirror

100% reflective SHG Mirror !

2 2 1 2 )()( =− Czhzh

Finite Slab:

κLC = hC 10 )/arccos(

2 = κ − zLCCzh )](tan[)(

1 = κ − zLCCzh )](cos[/)(

Semi-Infinite Slab:

2 == 1 zhzhC )()(,0 += zzhzh )]/(1/[)( 2 10 0 Other work on SHG: )2( 2 2 = [κ hz ]− 1 = ωεπχκ22 /4 2ck 0 10 Kivshar et al; Zakhidov et al

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Optical Parametric Amplification (OPA) in NIMs

(n < 0, n ,n > 0) - Control Field (pump) ω ω += ω213 1 2 3 S3

x 10 7 LHM 4 gL=4.805 Δ k=0 1a,2g

η 2

0 0 0.5 z/L 1

2 2 2 4 )2( η a = 111 η gL = 11 azaaza 20 η g = /)(,/)(,/)( aza 122 L g = ( 212121 )( /8/ )χπμμεεωωhc 3

Manley-Rowe Relations: Popov, VMS, Opt. Lett. (2006) d ⎛ SS ⎞ ⎜ 1 − 2 ⎟ = 0 Appl. Phys. B (2006) ⎜ ⎟ For SHG see also Agranovich et al dz ⎝ 1 == ωω2 ⎠ and Kivshar et al

20 Birck Nanotechnology Center OPA in NIMs: Loss-Compensator and Cavity-Free Oscillator

Backward waves in NIMs -> Distributed feedback & cavity-like amplification and generation

Popov, VMS, OL (2006)

k =Δ 0 2 2 4 )2( η = η = /)(,/)( azaaza g = ( 212121 )( /8/ )χπμμεεωωhc 3 a 111 gL 2011

Resonances in output amplification and DFG α1L = 1, α2L = 1/2

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

21 Birck Nanotechnology Center OPA with 4WM

Four-level χ(3) centers embedded in NIM χ(3) -OPA assisted by the Raman Gain:

ω4 – signal; ω1, ω3 – control fields ω2= ω1+ω3- ω4 − idler (Raman-enhanced; contributes back to OPA at ω4)

• χ(3) -OPA: compensation of losses:

transparency and amplification at ω4 • Cavity-free generation of counter- propagating entangled right- and left-handed photons .• Control of local optical parameters through quantum interference

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

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23 Birck Nanotechnology Center Super-resolution: Amplification of Evanescent Waves Enables sub-λ Image!

Waves scattered by an object have all the Fourier components 222 kzxy= kkk0 −− 22 The propagating waves are limited to: kkkktxy= +<0 To resolve features , we must have 22 2 Δ λπtt= 2/ λkk<Δ , Δ< ⇒txyz =k +k >k0 ,k < 0 The evanescent waves are “re-grown” in a NIM slab and fully recovered at the image plane

Conventional lens NIM slab lens

Pendry, PRL, 2000

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Perfect Lens

z n = −1 (ε = -1; μ = -1) Object 1 Focus2 Focus β n =−== βββα)sin()'sin()'sin()sin( α β' ⎛ 2 2 ⎞ ),( = ∑ q exp⎜ ()−+ zqnkiiqyAzyE ⎟ q ⎝ ⎠ aa bb shiftPhase =

( 22 ) ⎜⎛ ()2 −−−−+−+ 2 zqkiiqyzqkiiqy ⎟⎞ = 0 ⎝ ⎠

h = a+b

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The Poor Man’s (Near-Field) Superlens (ε < 0, µ =1)

Original implementation by Pendry: use a plasmonic material (silver film) to image 10 nm features with hw = 3.48 eV;

2 2 ε = 5.7 – 9 /ω + 0.4i (= - εh) a

Ag PMMA

Quartz Cr

365 nm Illuminatio n

Near-field super-lens (NFSL) super-resolution with superlens: Zhang et al. (2005); Blaikie, et al (2005) Mid-IR: Shvets et al. (2006)

26 Birck Nanotechnology Center SuperlensSuperlens HighHigh andand LowLow Ordinary Lens: evanescent field lost

Super Lens: evanescent field enhanced but decays away from the lens * LIMITED TO NEAR FIELD * EXPONENTIALLY SENSITIVE TO DISORDER, LOSSES,... Hyper Lens: evanescent field converted to propagating waves (that do not mix with the others) 27 Birck Nanotechnology Center

Hyperlens: Converting evanescent components to propagating waves (Narimanov eta al; Engheta et al)

Far-field sub-λ imaging Birck Nanotechnology Center Optical Hyperlens

Theory: Jacob, Narimanov, OL, 2006 Salandrino, Engehta, PRB, 2006 Experiments: Z. Liu et al., Science, 2007 Smolyaninov et al., Science, 2007

29 Birck Nanotechnology Center Advanced Optical Hyperlens

(a) (b)

Impedance-matched hyperlens Flat hyperlenses: ½- & ‘¼-body lenses Kildishev, Narimanov (Opt. Lett., 2007) Kildishev, Shalaev (Opt. Lett., 2008)

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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