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