From unconventional to extreme to functional materials.
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Transcript of From unconventional to extreme to functional materials.
From Unconventional to Extreme to Functional Materials
September 28, 2015
Nader Engheta
University of Pennsylvania Philadelphia, PA, USA
17 Equations that Changed the World
Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
17 Equations that Changed the World
Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
Pythagoras’s Theorem a2 +b2 = c2 Pythagoras 530 BC
Logarithms log(xy) = log(x)+ log(y) Neper, 1610
Calculus dfdt= lim f (t + h)− f (t)
h|h→0 Newton, 1668
Law of Gravity F =G m1m2r2
Newton, 1687
Wave Equation ∂2u∂t 2
= v2 ∂2u∂x2
D’Alambert, 1746
17 Equations that Changed the World
Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
Euler’s Formula for Polyhedra V − E + F = 2 Euler 1751
Normal Distributions Φ(x) = 12πσ
e−(x−µ )2
2σ 2 Gauss 1810
Fourier Transform F(ω) = f (x)e−2πixω dx−∞
+∞
∫ Fourier 1822
Navier-Stokes Eq Navier & Stokes, 1845 ρ∂v∂t+ v ⋅∇v
$
%&
'
()= −∇p+∇⋅T + f
Square Root of -1 Euler, 1750 i2 = −1
17 Equations that Changed the World
Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
Maxwell Equations ∇⋅D = ρ ∇⋅B = 0
∇× E = −∂B∂t
∇×H = J + ∂D∂t
Maxwell 1865
2nd law of thermodynamic dS ≥ 0 Boltzmann 1874
Relativity E =mc2 Einstein, 1905
Schrodinger’s Eq. i∂Ψ∂t
= HΨ Schrodinger 1927
Information Theory Shannon, 1949 H = −∑ p(x)log p(x)
17 Equations that Changed the World
Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
Chaos Theory xt+1 = kxt (1− xt ) R. May 1975
Black-Scholes Eq. 12σ 2S 2 ∂
2V∂S 2
+ rS ∂V∂S
+∂V∂t
− rV = 0 Black + Scholes 1990
James Clerk Maxwell’s Manuscript
Display in Royal Society, London, UK
James Clerk Maxwell’s Manuscript
Display in Royal Society, London, UK
James Clerk Maxwell’s Manuscript
Display in Royal Society, London, UK
Light-Matter Interaction
εµ
(2) ,....χ (3)χξ
σ
“Natural” Materials
“Artificially” Engineered Materials
● Particulate Composite Materials
, ,h h r h rn ε µ=
, ,c c r c rn ε µ=
● Composition
● Alignment
● Arrangement
● Density
● Host Medium
● Geometry/Shape
Metamaterials Samples (2000-2015)
Smith, Schultz group (2000)
Boeing group
Capasso group (2011)
Wegener group (2009)
Zhang group (2008)
Atwater group (2007)
Engheta group (2012) Giessen group (2008)
Metamaterial Applications (2000-2015)
Cloaking Superlens & Hyperlens
Ultrathin Cavities
ES Antennas Transformation Optics
ENZ & MNZ
Metasurfaces Metatronics
Going to the “Extreme” in Metamaterials
“Extreme” in Dimensionality
From 3D Metamaterials to 2D Metasurfaces
Shalaev & Boltasseva groups (2012) Capasso group (2011) Alu group (2012)
Brongersma & Hasman groups (2014) Maci group (2014) Brenner group (2014)
Ultimate Metasurface
Thinnest Metamaterials
http://math.ucr.edu/home/baez/graphene.jpg
A. Vakil and N. Engheta, Science, 2011
One-Atom-Thick Optical Devices
,Region 1: 0g iσ >
,Region 2: 0g iσ <
150c meVµ =
65c meVµ = mc =0.15eV
mc =0.065eV
A. Vakil and N. Engheta, Science, 2011
Experimental Verification of Mid IR Surface Wave on Graphene
Basov group, Nature (2012) Koppens, Hillenbrand and Garcia de Abajo, Nature (2012)
Graphene-coated dielectric waveguide: Hybrid Graphene-Dielectric Systems
A. Davoyan and N. Engheta, submitted under review
2D
3D
“Meta-Tube”
Squeezing THz energy into Nanoscale WG
Ez
2D taper 3D taper
A. Davoyan and N. Engheta, submitted under review
Information Processing at the Extreme
“Modular Blocks” in electronics
L
C
R
“Building Blocks” in Optics?
Optics
Waveguide
Lens
Mirror
from: D. Prather's group
“Lumped” Circuit Elements in Nanophotonics?
L C R
Nano-Optics
? ? ? ? ?
Radio Frequency (RF) electronics
Optical Metatronics: Materials Become Circuits
Engheta, Physics Worlds, 23(9), 31 (2010)
Engheta, Science, 317, 1698 (2007)
Engheta, Salandrino, Alu, Phys. Rev. Lett, (2005)
Sun, Edwards, Alu, Engheta, Nature Materials (2012)
Electronics a λ<<
( )Re 0ε >
C
( )Re 0ε <
E
H L
( )Im 0ε ≠
E
H
E
H
Metatronics
R
Optical Metatronics for Information Processing?
f x, y, z;t( )
Metastructures
g x, y, z;t( )
Analogy between Electronics and Photonics
Inpu
t (y)
Out
put (
y)
R
R
C
C CL
LL
CInput (t) Output (t)
Equivalent C and L
60 nm
CSiO2 182 10C F−≈ ×
633 nmλ =
( )Re 0ε <
LAg 157 10L H−≈ ×
First Metatronic Circuit in mid IR
Y. Sun, B. Edwards, A. Alu, and N. Engheta, Nature Materials, March 2012
“empty circle”: Experimental data “Thick line”: Circuit theory “Thin line” : Full wave simulation
Magenta: w ~ 75 nm, g ~ 75 nm Royal blue: w ~ 125 nm, g ~ 75 nm Red: w ~ 225 nm, g ~ 75 nm
800 1000 1200
30
40
50
60
70
80
90
14 13 12 11 10 9 8
Tran
smitta
nce
( % )
800 1000 1200
30
40
50
60
70
80
90
14 13 12 11 10 9 8
800 1000 1200
14 13 12 11 10 9 8
λ ( µm )
ν ( cm-1 )
800 1000 1200
14 13 12 11 10 9 8λ ( µm )
ν ( cm-1 )
800 1000 1200
30
40
50
60
70
80
90
14 13 12 11 10 9 8
800 1000 1200
30
40
50
60
70
80
90
14 13 12 11 10 9 8
Tran
smitta
nce
( % )
Para
llel
Seri
es
325nm 250nm 175nm
TCO NIR Metatronic Circuits Experimental Results
Caglayan, Hong, Edwards, Kagan, Engheta, Phys. Rev. Lett. 111, 073904 (2013)
“Stereo-Circuits” Different “Circuits” for Different “Views”
Alu and Engheta, New Journal of Physics, 2009
EH
L
C
E
H
L
C
Salandrino, Alu, Engheta, JOSA B, Part 1, 2007 Alu, Salandrino, Engheta, JOSA B, Part 2, 2007
Integrated Metatronic Circuits (IMC)
Inspired by the work of Jack Kilby (1959)
Integrated Metatronic Circuits
F. Abbasi and N. Engheta, Optics Express, 2014
http://www.cedmagic.com/history/integrated-circuit-1958.html
Metatronic Filter Design
Y. Li, I. Liberal and N. Engheta, work in progress F. Abbasi and N. Engheta, Optics Express, 2014
Thinnest Possible Circuits?
0iIf σ > Inductor L
0iIf σ < Capacitor CA. Vakil and N. Engheta
Metamaterial Processors
L
C
R
Tr
a λ<<
( )Re 0ε >
( )Re 0ε <
( )Im 0ε ≠
Metatronics
R
R
C
C CL
LL
C
Electronic Processor
Metamaterials that Do Math
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Input Output GRIN(+)
n 1
metasurface Δ
GRIN(+)
w/2
-w/2
n 1
w/2
-w/2
d
Metamaterials that Do Math
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
F. Monticone, N. Mohammadi Estakhri, A. Alù, PRL (2013)
Metamaterial as Differentiator
0
1
-‐5λ Width 5λ
Re(Sim.)(x1.4) Im(Sim.)(x1.4)
1
0
-1-5λ
5λ
Derivative (MS)
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Metamaterial as 2nd Differentiator
-‐0.5
0.0
0.5
-‐5λ Width 5λ
Re(Sim.)(x3.8) Im(Sim.)(x3.8)
1
0
-1-5λ
5λ
Derivative (MS)
εms y( ) / εo = µms y( ) / µo = i2 λo / 2πΔ( )"#
$%ln −iW / 2y( )( )
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Metamaterial as Integrator
-‐4
-‐2
0
-‐5λ Width 5λ
Re(Sim.)(x8.5) Im(Sim.)(x8.5)
1
0
-1-5λ
5λ
Derivative (MS)
εms y( ) / εo = µms y( ) / µo = i λo / 2πΔ( )"#
$%ln iy / d( )
εms y( ) / εo = µms y( ) / µo = − λo / 4Δ( )#$
%&sign y / d( )
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Metamaterial as Convolver
-‐3
0
3
-‐5λ Width 5λ
Re(Sim.)(x14) Im(Sim.)(x14)
1
0
-1-5λ
5λ
Derivative (MS)
εms y( ) / εo = µms y( ) / µo = i λo / 2πΔ( )"#
$%ln i / sinc Wk y / 2s
2( )( )"#&
$%'
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Engineering Kernels Using MTM
!
g(y) = f (y ')G(y − y ')dy '∫
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Metamaterial as “Edge Detector”
!
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Photo: Tod Grubbs
Metamaterial “Eq. Solvers”?
Metamaterial Eq. Solver
Metamaterial as a “solving” machine?
( ) ( )df x af xdx
=
( ) ( ) ( )k u x f u du af x− =∫
Informatic Metamaterials ( )f x ( )df x
dx
“Extreme” Parameters and “Extreme” in Cavity Resonators
ωn ω 'n ≠ωn
Conventional High-Q Cavity
Which Material?
?
Epsilon-and-Mu-Near-Zero (EMNZ) Materials
How do we make such EMNZ structures?
ENZ Structures
( )Re 0ε ≅
ITO
kz =ω µ0ε0 εr −1
ω 2µoεo
πa!
"#
$
%&
2
a
z
xy
Bi1.5Sb0.5Te1.8Se1.2
Zheludev Group
How do we make an EMNZ structure?
M. Silveirinha and N. Engheta Physical Review B, 75, 075119 (2007)
ENZ
ε i >1
µeff =µoAcell
Ah,cell + 2πR2J1 kiR( )kiRJ0 kiR( )
!
"
##
$
%
&&
A. Mahmoud and N. Engheta, Nature Communications, Dec 2014
CT Chan’s group Nature Materials, 10, 582-585 (2011)
2D EMNZ Cavity
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
2D EMNZ Cavity
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
3D EMNZ Cavity
ε pPEC
ENZ
H Field
E Field
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
3D EMNZ Cavity
(A) (B) (C)
ωres /ω p
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
EMNZ in Quantum Electrodynamics
Superradiance?
Subradiance?
Long-Range Collective States of Multi-emitters?
Long-Range Entanglement?
Cavity QED?
Summary
Metamaterials can perform processing, functionality at the compact scale
Metamaterials can play important roles in quantum electrodynamics
Sculpting waves using extreme scenarios can play interesting roles
Metatronic Processing Quantum MTM One-Atom-Thick
Optical Devices !
Thank you very much