Plenary lecture of the XIV SBPMat Meeting, given by Prof. Nader Engheta (University of Pennsylvania) on September 28, 2015, in Rio de Janeiro (Brazil).
Botany krishna series 2nd semester Only Mcq type questions
From unconventional to extreme to functional materials.
1. From Unconventional to Extreme
to Functional Materials
September 28, 2015
Nader Engheta
University of Pennsylvania
Philadelphia, PA, USA
2. 17 Equations that Changed the World
Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
3. 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
4. 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) =
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
5. 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, 1949H = −∑ p(x)log p(x)
6. 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.
1
2
σ 2
S2 ∂2
V
∂S2
+ rS
∂V
∂S
+
∂V
∂t
− rV = 0 Black + Scholes 1990
12. “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
13. 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)
17. 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)
27. 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
33. “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
34. 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
35. Metatronic Filter Design
Y. Li, I. Liberal and N. Engheta, work in progress
F. Abbasi and N. Engheta, Optics Express, 2014
40. 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
41. 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
42. 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
43. 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
( )( )"
#&
$
%'
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
44. 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
45. Metamaterial as “Edge Detector”
A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
Photo: Tod Grubbs
46. 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
52. 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
53. 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)
54. 2D EMNZ Cavity
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
55. 2D EMNZ Cavity
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
56. 3D EMNZ Cavity
εp
PEC
ENZ
H Field
E Field
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
57. 3D EMNZ Cavity
(A) (B) (C)
ωres
/ωp
I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
58. EMNZ in Quantum Electrodynamics
Superradiance?
Subradiance?
Long-Range Collective States of Multi-emitters?
Long-Range Entanglement?
Cavity QED?
59. 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
!