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

Pythagoras’s Theorem a2
+b2
= c2
Pythagoras 530 BC
Logarithms log(xy) = log(x)+log(y) Neper, 1610
Calculus
df
dt
= lim
f (t + h)− f (t)
h
|h→0
Newton, 1668
Law of Gravity F = G
m1
m2
r2
Newton, 1687
Wave Equation
∂2
u
∂t2
= v2 ∂2
u
∂x2
D’Alambert, 1746

Euler’s Formula for
Polyhedra
V − E + F = 2 Euler 1751
Normal Distributions Φ(x) =
1
2πσ
e
−
(x−µ)2
2σ 2
Gauss 1810
Fourier Transform F(ω) = f (x)e−2πixω
dx
−∞
+∞
∫ Fourier 1822
Navier-Stokes Eq Navier & Stokes, 1845ρ
∂v
∂t
+ v⋅∇v
$
%
&
'
(
) = −∇p+ ∇⋅T + f
Square Root of -1 Euler, 1750i2
= −1

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, 1949H = −∑ p(x)log p(x)

Chaos Theory xt+1
= kxt
(1− xt
) R. May 1975
Black-Scholes Eq.
1
2
σ 2
S2 ∂2
V
∂S2
+ rS
∂V
∂S
+
∂V
∂t
− rV = 0 Black + Scholes 1990

James Clerk Maxwell’s Manuscript
Display in Royal Society, London, UK

Light-Matter Interaction
ε
µ
(2)
,....χ (3)
χ
ξ

σ

“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
AntennasTransformation 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
Input(y)
Output(y)
R
R
C
C CL
L
L
C
Input (t)
Output (t)

Equivalent C and L
60 nm
CSiO2 18
2 10C F−
≈ ×
633 nmλ =
( )Re 0ε <
L
Ag 15
7 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
Transmittance(%)
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 8
λ ( 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
Transmittance(%)
ParallelSeries
325nm250nm175nm

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 C
A. Vakil and N. Engheta

Metamaterial Processors
L
C
R
Tr
a λ<<
( )Re 0ε >
( )Re 0ε <
( )Im 0ε ≠
Metatronics
R
R
C
C CL
L
L
C
Electronic Processor

Metamaterials that Do Math
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014

Input OutputGRIN(+)
n1
metasurface Δ
GRIN(+)
w/2-w/2
n1
w/2-w/2
d
Metamaterials that Do Math
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)

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( )( )

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( )

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 / 2s2
( )( )"
#&
$
%'

Engineering Kernels Using MTM
g(y) = f (y')G(y − y')dy'∫

Metamaterial as “Edge Detector”
Photo: Tod Grubbs

Metamaterial “Eq. Solvers”?
Metamaterial
Eq. Solver
Metamaterial as a “solving” machine?
( )
( )
df x
af x
dx
=
( ) ( ) ( )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

Epsilon-and-Mu-Near-Zero (EMNZ)
Materials

How do we make such EMNZ structures?

ENZ Structures
( )Re 0ε ≅
ITO
kz
=ω µ0
ε0
εr
−
1
ω2
µo
εo
π
a
!
"
#
$
%
&
2
a
z
x
y
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
εi
>1
µeff
=
µo
Acell
Ah,cell
+ 2πR2
J1
ki
R( )
ki
RJ0
ki
R( )
!
"
#
#
$
%
&
&
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

3D EMNZ Cavity
εp
PEC
ENZ
H Field
E Field

3D EMNZ Cavity
(A) (B) (C)
ωres
/ωp

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
!

From unconventional to extreme to functional materials.

From unconventional to extreme to functional materials.

From unconventional to extreme to functional materials.

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From unconventional to extreme to functional materials.