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8/8/2019 metamaterials part2
1/31
BirckNanotechnology Center
Engineering Space for Light with
Metamaterials
BirckNanotechnology Center
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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BirckNanotechnology Center
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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BirckNanotechnology Center
Metamaterials with Negative Refraction
Single-negative:
n 0(F is low)
Double-negative:
n
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BirckNanotechnology Center
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)
Birck Nanotechnology Center
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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
What are metamaterials?
Early electrical metamaterials Magnetic metamaterials
Negative-index metamaterials Chiral metamaterials
Nonlinear optics with metamaterials Super-resolution
Optical cloaking
BirckNanotechnology Center
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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
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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
What are metamaterials?
Early electrical metamaterials Magnetic metamaterials
Negative-index metamaterials Chiral metamaterials
Nonlinear optics with metamaterials
Super-resolution
Optical cloaking
BirckNanotechnology Center
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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
What are metamaterials?
Early electrical metamaterials Magnetic metamaterials
Negative-index metamaterials
Chiral metamaterials
Nonlinear optics with metamaterials
Super-resolution Optical cloaking
BirckNanotechnology Center
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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 = +