Generalized Snell’s Laws - rqc.ru · Optical camouflage: Projecting background image onto masked...
Transcript of Generalized Snell’s Laws - rqc.ru · Optical camouflage: Projecting background image onto masked...
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And
The Exciting Science of Light with Metamaterials
Vladimir M. Shalaev
Birck Nanotechnology Center
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Outline
• Intro to metamaterials
• Nanophotonics enabled by Plasmonics and Metamaterials
• Toward Better Materials for MM and TO applications
• Negative-index metamaterials
• Transformation optics and cloaking
• Engineering PDOS & Sub-wavelength light confinement with Hyperbolic MMs
• Flat photonics with Metasurfaces: Generalized Snell’s Law, negative refraction, meta-lens, meta-hologram….
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Natural Optical Materials
S
S
k
E
H
k
E
H
Negative Index
Materials
Common
Transparent
Dielectrics
Electrical Plasma(Metals at optical
wavelengths)
Magnetic Plasma(Not naturally occurring at
optical wavelengths)
Evanescent waves
Evanescent waves
k
k
1
1
Semiconductors
Crystals
Water
metals
Air E,H ~exp[in(ω/c)z] n = ±√(εμ)
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What is a metamaterial?
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Metamaterial is an arrangement of artificial structural elements, designed to achieve
advantageous and unusual electromagnetic properties.
ta = meta = beyond (Greek)
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A natural material with its atoms A metamaterial with artificially structured
“atoms”
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Photonic crystals vs. Optical metamaterials: connections and differences
0 1 aa<<.
Effective medium
description using
Maxwell equations with
, , n, Z
a~
Structure dominates.
Properties determined
by diffraction and
interference
a>>
Properties described
using geometrical optics
and ray tracing
Example:
Optical crystals
Metamaterials
Example:
Photonics crystals
Phased array radar
X-ray diffraction optics
Example:
Lens system
Shadows
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Photonic crystals
... have lattice constants comparable to light
wavelengths: a ~
… can be artificial or natural
… have properties governed by the diffraction of
the periodic structures
… may exhibit a bandgap for photons
… typically are not well described using effective
parameters , , n, Z
… often behave like but they are not true
metamaterials
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Electrical Metamaterials (Plasmonics): Route to Nanophotonics
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Why Plasmonics/Electric MMs?
M. Brongersma, V. Shalaev, Science (2010)
Plasmonics will enable an improved synergy between electronic and photonic devices ̶ Plasmonics naturally interfaces with similar size electronic components ̶ Plasmonics naturally interfaces with similar operating speed photonic networks
Critical dimension active devices (nm)
Op
erat
ing
spee
d THz
GHz
MHz
kHz
10nm 100nm 1m 10m 1mm 100m
Semiconductor Electronics
Metallic Nanoplasmonics
Dielectric Photonics
The past
PHz
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Silicon Integrated Nanophotonics
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IBM Silicon Integrated NP Technology
IBM chip: BLUE optical waveguides and YELLOW copper wires
IBM 90nm Silicon Integrated Nanophotonics: Integrated photodetector (red feature) Modulator (blue feature) Silicon transistors (red sparks)
“After More Than a Decade of Research, Silicon Nanophotonics is Ready for Development of Commercial Applications.”
IBM Press release, December 10, 2012
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ELECTRONIC-PHOTONIC INTEGRATION:
SUMMARY
Photonic circuit + High speed + High bandwidth - Component size is limited (>~ 100nm - 1 µm)
Modern communication systems Huge amount of data Ever increasing speed
Electronic circuit + Very compact (~ 10nm) - Operational speed is limited (RC-delay)
Electronic + Photonic circuit: NEED FOR NEW TECHNOLOGIES
Si NANOPHONICS (near-term)+ PLASMONICS/METAMATERIALS (~5 years)
Optical mode in waveguide > 0/2nCORE
Diffraction limit
www.mayang.com/textures/
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[ Bow-tie antennas ]
Other Applications: Sensors
from LC-contour to nanophotonic circuits (Engheta – ‘metatronics’)
OE (2009); NJP (2008); Metamaterials (2008); APL (2008)
OPTICAL NANOANTENNAE
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Optical Nanolaser Enabled by SPASER
Related prior theory: Stockman (SPASER)
Zhang group: Plasmon Laser (Nature,2009) Room-T Plasmon Laser (Nat. Mat, 2010) “Spasing Laser” – Zheludev, Stockman M. T. Hill, et al; C. Z. Ning, et al (electr. pump) Spotlight on Plasmon Lasers (Perspective, Science, 2011)- X. Zhang, et al
Optical MOSFET (Stockman)
Noginov, Shalaev, Wiesner groups, Nature (2009)
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Toward Better Materials for Plasmonic and MM Applications
(Boltasseva group, Purdue)
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METALS TO LESS-METALS:
Doped semiconductors + Intermetallics (nitrides, borides, silicides, …)
New Plasmonic Materials
A. Boltasseva and H.A. Atwater, Science 331 (2011)
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Alternative Plasmonic Materials
P. West, et al, Lasers & Photon. Rev. (2010) (Boltasseva group)
(see also work by the Noginov group)
Transparent Conductive Oxides
ε΄ becomes negative below 2μm
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Metallic: Golden luster
Titanium Nitride
G.V. Naik et al., Optical Materials Express 2 p. 478 (2012)
http://www.mini-lathe.com/Feat_Mach/Turbocam
OSA press release March 27, 2012
‘Researchers Discover a New Path for Light Through Metal: Novel Plasmonic Material May Merge Photonic and Electronic Technologies’
Hard & tough: high speed drill-bits
Well-established processing
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New Plasmonic Materials for HMMs
Performance of HMM devices: (A. Hoffman, Nature Materials 6(2007) 946–950)
FOM=Re{k}/Im{k}
Phys. Status Solidi RRL 4, 295 (2010) G..V. Naik and A. Boltasseva, Metamaterials 5(2011) 1-7
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Negative Refraction in all-Semiconductor based HMM
G. Naik, et al, PNAS (2012)
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Negative refraction in semiconductor-based metamaterials
• Semiconductors exhibit metallic
properties when heavily doped
• Aluminum doped zinc oxide (AZO)
exhibits metallic property in the
near-infrared
• Conventional metals replaced by
semiconductor-based ones such as
AZO can produce high
performance metamaterials
• The figure-of-merit of AZO/ZnO
metamaterial is 11: three orders
higher than metal-based designs
G. Naik, et al. PNAS (2012) (Boltasseva /Shalaev groups)
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Sir Arthur Schuster Sir Horace Lamb
L. I. Mandel’stam
V. G. Veselago
Sir John Pendry
… 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
Mandel’stam, 1945
Left-handed materials: the electrodynamics of substances
with simultaneously negative values of and
Veselago, 1968
Pendry, the one who whipped up the recent boom
of NIM researches
Perfect lens (2000)
EM cloaking (2006) Others: Sivukhin. Agranovich,…
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if ,0n
• Refraction:
• Figure of merit: θ1
θ2
θ1 θ2
"/|'| nnF
εμn
εμn
2
0 ||' ||'
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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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O. Hess, Nature 455, 299 (2008)
Negative Refraction Effects
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http://io9.com/5036183/secrets-of-the-metamaterials-that-will-make-you-invisible
Negative Refraction Effects
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V. M. Shalaev, Transforming Light, Science, Oct. 17, 2008
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Spatial profile of & tensors determines the distortion of coordinates
Seeking for profile of & to make light avoid particular region in space — optical cloaking
Fermat:
δ∫ndl = 0
n = √ε(r)μ(r)
“curving”
optical space
Distorted field line in distorted coordinate
Straight field line in Cartesian coordinate
Pendry et al., Science, 2006
Leonhard, Science, 2006
Greenleaf et al (2003)
L. S. Dolin, Izv. VUZ, 19614
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Form-invariance of Maxwell’s equations
Coordinate transformation from x to coordinate x is described using the
Jacobian matrix G: ij i jg x x
( )
( ) 0
E
H
HEt
EH Jt
Maxwell’s equation in x
1 1
;
( ) ; ( )
;
T T
T T
G G G G
G G
E G E H G H
GJJ
G G
Transformation of variables
Ward and Pendry, J. Mod.Opt. 43, 777 (1996)
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Pendry et al., 2006
The bending of light due to the gradient in refractive index in a desert mirage
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Kildishev, VMS (OL, 2008); Shalaev, Science 322, 384 (2008)
Optical Black Hole (Zhang group; Narimanov,Kildishev)
(b)
Fermat: δ∫ndl = 0 n = √ε(r)μ(r)
curving optical space
Planar hyperlens (Kildishev and VMS) (Schurig et al; Zhang group)
Light concentrator (also, Schurig et al)
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Narimanov, Kildishev
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Invisibility in Nature, Physics and Technology
• Natural camouflage
• Black hole
• …
Current technologies to achieve invisibility:
Stealth technique: Radar cross-section reductions by absorbing paint / non-metallic frame / shape effect…
F-117 “Nighthawk” Stealth Fighter
Optical camouflage: Projecting background image onto masked object.
Optical Camouflage, Tachi Lab, U. of Tokyo, Japan
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The Invisible Man by H. G. Wells (1897)
“The invisible woman” in The Fantastic 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 are concerned.” -- Chapter 19
"Certain First Principles"
"... she achieves these feats by bending all
wavelengths of light in the vicinity around
herself ... without causing any visible
distortion.” -- Introduction from Wikipedia
Pendry et al.; Leonhard, Science, 2006 (Earlier work: cloak of thermal conductivity by Greenleaf et al., 2003)
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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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metal needles embedded in dielectric host
Unit cell:
Flexible control of r ;
Negligible perturbation in
Cai, et al., Nature Photonics, 1, 224 (2007)
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Cloaking performance: Field mapping movies
Example: cloak @ 632.8nm with silver wires in silica
Cloak ON Cloak OFF
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J. Li and J. B. Pendry , Phys. Rev. Lett., 2008
picture from discovery.com
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Progress Towards True Invisibility on May.17, 2009, under Science www.codingfuture.com
Theory: J. Li, J. Pendry
GHz: Smith et al (Duke)
Optical: Zhang et al (Berkeley)
Lipson et al (Cornel)
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Signal
Signal
Signal
Signal
Control C
Wave guide
Wave guide
Wave guide
Wave guide
(a)
(b)
(c)
(d)
Control C
Control C
Control C
Control A
Control A
Control A
Control A
Turn on Control A
Turn of fControl C
A B C
A B C
A B C
A B C
M. W. McCall and et al., Journal of Optics, 2011 Gaeta eta al, experiment
Star Trek transporter
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Modern cosmology describes Universe as collection of spaces connected by black holes and wormholes. These spaces may have different topology and different number of dimensions.
Using transformation optics we can create “optical spaces” having non-trivial topology, which cannot normally fit into Euclidean 3D space:
Even metric signature of the “optical space” may differ from the (+ - - - ) signature of the Minkowski space. In hyperbolic materials (Smolyaninov, Narimanov – PRL, 2010):
2
2
2
2
2
2
1
2
22
2 1
yxztc
01 02
02
4
2
2
3
2
2
2
2
2
1
2
xxxx Flashes of light are observed during metric signature transitions : toy Big Bang physics
2T K-G
41
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Hyperbolic Metamaterials: Engineering Photonic Density of States
& Subwavelength Light Confinement
S. Ishii, et al, Laser Photonics Rev., 1–7 (2013)
DOI 10.1002/lpor.201200095
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Cover article
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Hyperbolic Metamaterials (HMMs)
A metamaterial has hyperbolic dispersion relation
22 2 2x y z
k k k
c
hyperbolic dispersion
Jacob, et al., Opt. Express, 2006
22 2 2x y z
k k k
c
x
y
z
22 2 2
x y zk k k
c
normal dispersion
Transverse Negative (TN) Transverse Positive (TP)
x
y z
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PHOTONIC DENSITY OF STATES (PDOS)
Iso-frequency surface at ω
Iso-frequency surface at ω+δω
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QED IN THE ’HYPERSPACE’
• Rate of SE, can be understood as property of atom-environment system
• Environment (cavity, PhC, nanowire) enhances density of states
(Dipole matrix element)2
Environment strongly alters the rate of SE through the available PDOS!
Fermi’s Golden Rule:
Available density of states for emitted light
Coupling of emitter to field (depends on the mode volume)
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: Ford and Weber (1984)
QED: Hughes group (2009)
Calculation Methods:
EMISSION POWER SPECTRUM
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Diffraction from double slits
– FWHM = 45 nm at = 465 nm
Diffraction inside Hyperbolic Media
• Hyperbolic metamaterial (HMM) – Ag/SiO2 lamellar HMM
– High-k waves are supported
– Propagation of high-k waves is confined
eff
x
eff
z
2.78 0.22
6.31 0.15
i
i
S
=465 nm
=465 nm
(15 nm Ag/15 nm SiO2)3
S. Thongrattanasiri and V. A. Podolskiy, Opt. Lett. (2009) Satoshi Ishii et al, in preparation
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Subwavelength Interference (Experiment)
Ag/SiO2 HMM sample SiO2 sample
• For Ag/SiO2 HMM sample: FWHM = 83 nm (< ) • For SiO2 sample: FWHM = 542 nm (~ )
1. Sample fabrication
Deposition and FIB
2. Photolithography
Photoresist exposure, develop
3. AFM scan
=465 nm
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Flat Photonics with Metasurfaces: Generalized Snell’s Law,
Negative Refraction, and much more....
Birck Nanotechnology Center
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Principle of Least Action
Maupertuis felt that “Nature is thrifty in all its actions”, and applied the principle broadly
Pierre Louis Maupertuis (1698-1759)
Leonhard Euler (1707-1783)
Louis de Broglie (1892-1987)
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Principle of least action → The momenta difference between blue and red path is zero
Generalized Snell’s Law (Capasso Group)
For refraction
For reflection
see also S. Larouche and D.R. Smith, OL v. 37, 2391 (2012)
A
B
ni
Ф Ф+dФdr
θt
θr
nt
In essence, momentum conservation!
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Generalized Snell’s Law
N. Yu, et al. Science, 2011 (Capasso Group)
Demonstrated at 8 µm wavelength
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Broadband light bending with plasmonic nanoantennas
ΛΛ/8
xyz
200
1920
240
1760
220
1600
200
1440
180
unit: nm
X. Ni, et al. Science-Express, Dec. 22, 2011 (Shalaev & Boltasseva groups) Science v. 335, 427 (2012)
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Incident Angle Sweep – Refraction
λ = 1500 nm
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λ = 1500 nm
Incident Angle Sweep – Reflection
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θi = 30⁰
Broadband!
Broadband Negative Refraction
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Ultra-thin planar meta-lenses: design
• Au film (30 nm) by electron beam evaporation
• Babinet antennas fabrication by focused ion beam (FIB)
r
X. Ni etal (2012)
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Ultra-thin planar meta-lenses: experiment
sample
x-polarizer
y-polarizer
Ar/Kr laser (676 nm / 530 nm / 476 nm)
Z = 0 μm
Z = 7 μm
Z = 10 μm
Focal length: 2.5 μm Focal length: 4 μm Focal length: 7 μm
wavelength 676 nm
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Take home messages
• Nanophotonics enabled by Plasmonics and Metamaterials
• Toward Better Materials for MM and TO applications
• Negative-index metamaterials
• Transformation optics and cloaking
• Engineering PDOS & Sub-wavelength light confinement with Hyperbolic MMs
• Flat photonics with Metasurfaces: Generalized Snell’s Law, negative refraction, meta-lens, meta-hologram….