Metasurface Hologram Invisibility - ppt

PhD candidate: Carlo Andrea Gonano
Supervisor: Prof. Riccardo Enrico Zich
PhD Thesis, 28th cycle, Electrical Engineering,
Politecnico di Milano, Italy
A PERSPECTIVE ON
METASURFACES, CIRCUITS,
HOLOGRAMS AND INVISIBILITY
26th January 2016

2PhD thesis - Gonano Carlo Andrea
This work was presented on 26 January 2016 for the final examination of a PhD course.
Some slides have been modified or cut and the videos are currently not available.
Further versions of this presentation could be published online in a next future.
https://www.researchgate.net/profile/Carlo_Gonano
https://polimi.academia.edu/CarloAndreaGonano
Full work:
Carlo Andrea Gonano, A perspective on metasurfaces, circuits, holograms and
invisibility, PhD Thesis, Politecnico di Milano, 2015.
The PhD thesis first-version will be soon available at the online institutional
archive “POLITesi”, Politecnico di Milano, Italy.
https://www.politesi.polimi.it/handle/10589/32801/advanced-search?locale=en
The author retains all the rights.
Milan, 6 february 2016.
Notes for the reader

1. Introduction on meta-materials and meta-surface
2. Boundary Conditions for Maxwell’s eq.s
8. Conclusions
9. Question time
3. Space Time BC
4. Radiated Plane Waves
5. Scattering and circuits
6. Holographic screen
7. Invisibility cloak
Summary

1- Introduction

Introduction on MTMs (I)
• Artificial bulk material
• Sub-wavelength unit cell : D x << l0
• Designed to exhibit specific properties
Metamaterial
definition:
THIS PHD THESIS IS ABOUT METAMATERIALS….
• Properties are due to MTM’s microscopic structure,
rather than to its chemical composition
That is quite a general definition!

Introduction on MTMs (II)
• At microscopic level, a MTM is composed by unit cells
• At macroscopic level, a MTM looks homogeneous
• Many kinds of metamaterials:
• Acoustic
• Elastic
• ElectroMagnetic
• Thermal
• etc…
Here we focus on ElectroMagnetic MTMs,
specially on metasurfaces
Example of DNG metamaterial’s
structure by David R. Smith [1]

ElectroMagnetic MTMs
• EM metamaterials can be
tailored to exhibit desired
permittivity e(w) and
permeability m(w)
e-m MTM classification
• Negative refraction
• Superluminal propagation
• Cloaking devices
DNG super-lens [1] ENZ-MNZ shell
cloaking device [2]
Paradoxical effects can
arise or be achieved!
• Etc…

Metasurfaces
Metasurface:
In this thesis we deal with a special class of MTM
2D metamaterial made by
a single layer of unit cells
Simulation of beam-redirection
by M. Selvanagayam et al. [4]
Many applications for antennas:
• More simply, an artificial thin screen
• Flat high-gain antennas
• Beam-steering
Spiral Leaky-wave antenna at
17 GHz by S. Maci et al. [3]
• Reflect and trasmit-
arrays
• One-way transparent
sheets
• Etc…

Metasurfaces
• The sources of the EM fields are electric charges and currents
OK, BUT WHAT IS OUR TASK?
• Control the EM fields using metasurfaces (screens)
• In general, a field is generated by some sources
How can we control fields?
1. Assign the desired behaviour (input- output fields)
2. Determine the required sources
3. Project the screen’s constitutive elements (e.g. circuits)
• Thus, try to control the sources!
BASIC DESIGN PROCEDURE:

2- Boundary Conditions for
Maxwell’s equations

Maxwell’s equations






-

t
B
E
BT



0









t
E
c
JB
E
e
e
T



2
0
0
0
1
/
m
e
( )




--



Ec
t
A
AB
A



2
0
0


A
t
TA








-


-


e
eA
A
JA
t
A
c
tc


0
2
2
2
2
0
0
2
2
2
2
0
1
1
m
m

“Classic” Maxwell’s eq.s in terms of E and B
Maxwell’s eq.s in terms of EM potentials A and A
For our purpose it’s better to rewrite them
Wave
eq.s
Lorentz
Gauge
Faraday
set

The advantages of EM potentials
J.C. Maxwell
P.A.M. Dirac, “Is there an aether?”, Nature, vol. 168, pp. 906–907, 1951
• J.C. Maxwell originally (1865) wrote his equations in terms
of “Electromagnetic momentum”, that is vector potential A
“It is natural to regard it [A] as the velocity of some real
physical thing. Thus with the new theory of
electrodynamics we are rather forced to have an aether”
• Easy analogy with mechanics and fluid-dynamics
• Usefulness in Relativity and need in Quantum Mechanics
P.A.M. Dirac
• Aharonov-Bohm effect (1959): EM potentials are not a
mere math. construction
Why should we use the EM potentials instead of E and H?
• Numerical stability: no low-frequency catastrophe

Boundary Conditions for EM potentials (I)
BCs FOR SCALAR POTENTIAL
21
12
0 n
xx
AA
e

 







-


-

m ( ) 21120 nd AAe

- m
surface charges surface dipole
• In order to control the discontinuities for scalar potential and
its gradient across a surface you need charges and dipoles:

Boundary Conditions for EM potentials (II)
21
12
,0 n
x
A
x
A
J es














-


-m ( ) 21120 nAADe

-m
surface currents surface doublets
• In order to control the discontinuities for vector potential and
its gradient across a surface you need currents and doublets:
BCs FOR VECTOR POTENTIAL

Boundary Conditions for E and B
• The BCs for the Maxwell’s Eq.s in terms of E and B are:
NOT ALL THE DISCONTINUTIES ARE ALLOWED…
( )
( )



-
-
es
e
T
JBBn
EEn
,01221
01221 /


m
e ( )
( )


-
-
0
0
1221
1221


EEn
BBnT
discontinuity for En discontinuity for “Bt”

Limits for the classic BCs
• Need of magnetic currents
for Et discontinuities
The BCs written in terms of E and B have many limits:
• Need of magnetic monopoles
for Bn discontinuities
• Fail to describe static phenomena,
like the Volta Effect.
• E and B can get infinite
values on the boundary
( ) msJEEn ,1221

--
( ) m
T
BBn - 1221

Till now, neither magnetic currents nor
monopoles have ever been observed

3- Space -Time
Boundary Conditions

Space-Time Surf. Equivalence
• The Extended Huygens’ principle can be applied also to space-
time domains and fields
 
  dSd vnv m

m

 
 - dSyyd nxx )()()( ffff 



mm

)- mm
  yxN (1
Theorem for space-time Surface Equivalence
• Theorem for space-time gradient
and normals (vector case):
• Green’s function for Wave eq.:

Space-Time (N+1)-normals
0m
mdxn
1m
mnn
domain “at rest” “moving” domain
time-like (N+1)-normal
1-m
mnn space-like (N+1)-normal
ACTUALLY “UNITARY” AND PERPENDICULAR
TO SPACE-TIME BOUNDARY…

Relativistic notation for Maxwell’s eq.s
mm
 m JA 0



-

mmm
m
m
AAF
A 0







A
c
A A
 0m
(N+1)-potential







e
e
J
c
J  0m
(N+1)-current







 -

BcE
cE
F
T
0
0
/
/0


m
EM tensor

Charges and currents in Space-Time
mm
vQI e 0,

Dipoles and doublets in Space-Time
• Relativistic net doublet:
( ) mmm
21,1,2,
2
1
xIIDnet D-

Relativistic BC for EM fields
( ) mmm
m 21,1,2,0 nAAD --( ) 21,1,2,,0 
mmm
m nAAJ s -
What is it
useful for?
• Scattering for moving
bodies (e.g. RADARs)
• Echo-Doppler systems
(e.g. telemeters)
• Study of plasmas (e.g. MHD
numerical simulations )
• Relativistic Quantum
Mechanics
This form is analogous to the one found for space BCs!
(N+1)-current doublet tensor

4- Radiated plane waves

Planar radiating screen
• Once we know the sources, we calculate the radiated fields
Radiated electric and magnetic fields
xki
ss
T
t
eJJ
 D
 0
xki
es
n
T
enDJ
k
iA

 D






- 1
210001
1
2
1
m
xki
es
n
T
enDJ
k
iA

 D






 2
210002
1
2
1
m
Sources Radiated vector potential
111
0
1
1
Akk
k
IsE







--
xki
ee
T
t
eDD

D
 0
222
0
2
1
Akk
k
IsE







--
 11
0
1
1
AkiH


m
 22
0
2
1
AkiH


m

Radiated plane waves

Symmetric radiating screen
0;//;60.0 0  etst DkJkk

xki T
eA
 D1
10
xki T
eA
 D2
20
(video)

Anti-symmetric radiating screen
test knDJkk

//;0;60.0 210 
xki T
eA
 D1
10
xki T
eA
 D2
20
(video)

Leaky plane waves

Symmetric leaky wave
0;//;02.1 0  etst DkJkk

xki T
eA
 D1
10
xki T
eA
 D2
20
(video)

Anti-symmetric leaky wave
test knDJkk

//;0;02.1 210 
xki T
eA
 D1
10
xki T
eA
 D2
20
(video)

5- Scattering and circuits

Finite circuit screen
HOW IS THE SCREEN MADE?
• The BCs for EM potentials tell us the
screen should have 2 layers
• Small finite width: D x < l0 /(2p)
• Circuits are often used to model or
project MTMs
• We have to assign the desired
behaviour for the metasurfaces
• Need to define scattering properties
• Need to determine the constitutive
elements (e.g. impedances)

Scattering theory
VERY BRIEF SUMMARY…
EJ Y
tr,0intr EEE  S
J-Eirr irrZ
• Assign the desired scattering (input-output):
• Derive the radiation law from the BCs:
• Need to determine the control law:
Thus we have a
constitutive relation
• …after some calculi: 1
0 ))(( -
-- SISSYZirr
• Y can be interpreted as an
“admittance” matrix
material or circuit

Circuit model
Thin screen with assigned e and m



















D
D
H
E
i
H
E
r
r
0
0
210
21
0
0
e
m


• Constitutive relations for thin screen:
• Boundary Conditions:





















D
D






-






H
E
i
H
E
D
J
ec
s
0
0
210
21
0 01
101
0



100 D xk
• Circuit variables
EyV D
( ) zJII D 12
( ) eD
x
z
II
D
D
- 212
z
yx
L
D
DD
 00 m
y
zx
C
D
DD
 00 e
( ) ( )
( ) ( )


--

122
1
12
21122
1
IIZVV
IIZVV
M
E circuit
relation

Circuit screen (I)
• Solution for a symmetric 2-layer screen:
symmetric
component0
1
1
1
sC
Z
r
E
-

e
0
r
1
LsZ
r
M
m
m
-

MZ
2
1
MZ
2
1
EZ
anti-symmetric
component
Circuit unit cell
Important: active elements, like negative capacitors and
inductors, are required for some values of e and m
WHICH IMPEDANCES SHOULD BE
INSTALLED ON THE SCREEN?

Circuit screen (II)
( ) ( )21122
1
IIZVV E 
( ) ( )122
1
12 IIZVV M --
symmetric
anti-symmetric

Bulk screen
• Screens or bulk MTMs are composed by assembled unit cells
3D anisotropic
impedance star
3D anisotropic
impedance
octahedron

6- Holographic screen

Holographic metasurface
Ray model Wave model
• Huygens’ principle: equivalent surface source distribution
MAPPING A 3D FIELD ON A 2D SURFACE
• Basic surf. sources for EM fields: currents J and doublets De

Holographic pixel
• Subwavelength pixels :
• Visible spectrum: l0 = 380 - 750 nm
)2/(0 plDy nm40Dy
• Holographic image (30 cm x 40cm):
nanopixel
NEED TO COMPRESS THE INFORMATION!
!nanopixels105,7 13

TeraBytes!900• Excessive amount of data!
• Assign spatial, chromatic and angular resolutions
angular resolution N=9
• In fact, a pixel can look different
depending on the viewpoint
IDEA:
pixel phased array

Macropixel: phased array
• Pixel radiated
fields
21
0
0- nD
c
s
E eIRR

 
JnH IRR

-21 
xki t
eJyxJ
 D
 0),(
xki
ee
t
eDyxD

D
 0,),(
Compressing the information…
• Spatial res: 1 mm?
• Phased array
sources
• Angular res. N : 28 kx, 28 ky
• Chromatic res.: 12 Byte/macropixel
• Holographic image
(30 cm x 40cm):
GigaBytes120

7- Invisibility cloak

Invisibility in popular culture
FROM MYTHS AND MAGIC TO SCIENCE FICTION

Transparency and light deflection
HOW CAN WE MAKE AN OBJECT INVISIBLE?
• Two main techniques (and their combinations):
optical transparency light deflection
• Conditions required for a cloaking device:
• No reflection and no refraction
• No shading (no absorption)
• No emission
unperturbed
outer light field

Invisibility by transparency
• The light interacts with the cloaked object, passing through it
• The object has the same impedance and
refractive index of the surrounding medium:
;0  0cc 
• Pirex bottle filled with and merged in glycerin





0
47.1
mmm GLYPIR
GLYPIR nn
Classic experiment:





GLYPIR
GLYPIR
cc


Scattering cancellation (I)
• Achieving bulk transparency by scattering cancellation
• The cloaking shell produces a destructive interference
• Opposite dipole oscillation:
• Problem: this technique works well just if you know in advance the
scattering properties of the cloaked object





0
0
21
21
mm
pp

• In some cases negative e2 and/or m2 could be
mandatory  ENG, MNG or DNG metamaterials!
• Need to cancel higher-order terms (e.g.: quadrupole moments)
0,0  me

Andrea Alù
Scattering cancellation (II)
• That technique has been deeply investigated by the groups of Nader
Engheta and Andrea Alù
Nader Engheta
Francesco Monticone[5] [5]
[6]

Invisibility by light bending
SUPERLUMINAL PROPAGATION
2
2
1
12
2 )(
r
Rr
RR
R
rr
-
-
 me
• Method based on Transformation Optics technique
• Exact calculus of the shell material properties
• Light is deflected around the cloaked object: no interaction
Cloaking device by J.B. Pendry
[2]
• Light should travel faster inside the shell...
0
1
c
k
v 
me
w

• Need for active ENZ,
MNZ metamaterials.
10  me
Very difficult to achieve for a broadband optical cloak!

Cloaking device (Pendry’s concept)
initial configuration transformed domain
(video)

The MTM cloak experiment - 2006
• Cilindrical MTM cloak at 8-12 GHz
(microwave region, l0 = 3 cm)
David Schurig
John B. Pendry
David R. Smith
[7]

Tachi’s technique
• Developed by S. Tachi’s group (2003)
• Retro-reflection projection technique
• Problem: it works just for few
viewpoints...
• Not a metasurface
• Easier to realize
[8]

Various camouflage techiques...
Well,they have some limits...

Invisibility metasurface
LET’S START FROM THE DESIRED FINAL RESULT
1. Zero scattering
2. Internal shielding
3. Broadband
4. Arbitrary geometry
5. Small thickness
• Now we desire to project an invisibility metasurface or screen
Required properties:
• Unperturbed external
incident fields
• Darkness inside the cloaked
region (hyp: the body does
not radiate)







inc
inc
BB
EE
22
22






0
0
1
1
B
E

Mathematical conditions on EM fields

BCs for invisibility
What material is the screen made of?
• Use the Boundary Conditions















-
-










2100
0
021 2
21
0 nH
E
i
i
nD
J t
ec
s
t







100 D xk
• Calculate the constitutive relations
• Thin screen hypothesis:



















t
t
t
t
H
E
iBc
D




000
1
01
1020

e
• Very strange relation: the E field
induces vortices De, while the H field
induces currents J
Tellegen material?
Usually in Nature the opposite happens!

Absorber, waveguide and emitter
The screen is made by a non-reciprocal material
• The inner side is different from the outer one
• It can behave as a perfect absorber,
waveguide or emitter (!)
• Amazing, but that’s consistent with
the calculated scattering matrix S:
absorbing wave-guiding emitting



















-


-
2
1
2221
1211
2
1
E
E
SS
SS
E
E







-
 0
0
lim
1
G
G
S
G
intr EE S

Invisibility circuit screen
Deriving a circuit model...
• From scattering to circuit constitutive relation:



















2
1
2
1
0
00
I
I
ZV
V
( )04
1
0
00
2
4
1
0
//
1
CsL
CLs
sL
Z -
-

• Need for active non-Foster elements
• Non-symmetric unit cell (as expected)
• Intrinsically unstable!
• Other configurations are possible

Technical difficulties
OK, BUT CAN IT ACTUALLY BE CONSTRUCTED?
Unfortunately, there are many serious difficulties
• In my personal opinion, the answer is “no”... at least for now.
• Need for nanoscale unit cells: )2/(0 plDy nm40Dy
• Need for active nano-elements for broadband cloaking
• Extremely high “switching” frequency:
• Probable high costs for the production
of a single metasurface
2
m1 cells!1025.6 14

THz7904000 f
However, those are just technological and
economical limits, not physical ones
We cannot exclude that someday they will be overcome

WHAT HAS BEEN DONE:
• Study of the metamaterial topic
Conclusions
• Boundary Conditions with EM potentials
• Theorems for Space-time Boundary Conditions
• Scattering and circuit model for a metasurface
• Test for a plane infinite radiating screen
INVESTIGATED APPLICATIONS:
• Holographic television (3D dynamical images)
• Invisibility cloak
• Screen with assigned permittivity e and permeability m

THANKS FOR THE
ATTENTION.
ANY QUESTION?
That’s all, in brief…

• The cross fertilization of sciences
• Ancient metamaterials
• Multi-screen system
• Bulk MTM simulation
• Extended Huygens’ principle
• Magnetic monopoles and currents
• About invisibility
• References
Extra details

The whole thesis is 224 pages long, it
contains over 80 figures and 1000 equations.
DISCLAIMER:
THIS PRESENTATION IS JUST A
SUMMARY

Cross fertilization of the sciences
James Clerk Maxwell
“In a University we are especially bound to recognize not only
the unity of science itself, but the communion of the workers in
science. We are too apt to suppose that we are congregated
here merely to be within reach of certain appliances of study,
such as museums and laboratories, libraries and lecturers, so
that each of us may study what he prefers. […]. We cannot,
therefore, do better than improve the shining hour in helping
forward the cross-fertilization of the sciences”
J.C. Maxwell, “The Telephone”, Nature, 15, 1878

Ancient optical metamaterials
• Stained glasses of
the XIIIth century
cathedrals
Stained glasses in the Saint-Chapelle, Paris
Lycurgus cup, VI Century Ag-Au alloy nanoparticle
within glass
• Roman “Lycurgus cup”
(VIth Century)
• Different colours are due to
metallic nano-inclusions
• Controlled massive
production
Plasmonic
resonance!

Multi-screen system

Active screen – 1 radiating layer
• Electric field radiated by 1 current sheet
0,00,
2
1
- SIRR JE


00
0,)(
xxki
IRRIRR eExE
-


Symmetric field
Wave amplitude
0
0
c
k
w

Wavenumber
(video)

Active screen – 2 radiating layers
• Electric field radiated by 2
current sheets
Coherent radiation
Symmetric
Anti -
symmetric
2 layers are always sufficient
(video)

• Electric field radiated by
10 current sheets
Coherent radiation
phased array
Other config. are possible
Active screen – 10 radiating layers
(video)

Bulk MTM simulations

Bulk MTM - dielectric
vacuum
lossy dielectric
vacuum
)05.01(2.25 ir e
• Slab made of a lossy dielectric. E.g.: glass panel.
1rm
Incident wave
Relative permittivity
Relative permeability
Reflected wave
Transmitted wave
(video)

Bulk MTM - metal
vacuum metal vacuum
ir 05.00e
1rm
• Metallic slab, e.g. silver mirror
(non-magnetic)
High reflectivity
Unmatched,
lossy
(video)

Bulk MTM – ideal DNG
1-re
1-rm
• Ideal Double Negative material
BACKWARD PROPAGATION!
,0,0  rr me
Perfectly matched,
no losses
(video)

Bulk MTM - superluminal
• Epsilon Near Zero (ENZ) material 1)Re(0  re
SUPERLUMINAL PHASE VELOCITY
)05.01(0.25 ir e
1rm
0 rr em
(video)

Superluminal Transmission Line
• In 2012 the group of S. Hrabar experimented a
broadband superluminal propagation
• ENZ Trasmission Line with shunted negative capacitors
0c
k
v 
w
 0c
k
vg 



w• Superluminal phase
and group velocities:
Apparently, there is no contradiction with
Relativity theory
• The signal velocity is not superluminal (really?)
[9, 10]

Extended Huygens’ principle

Fields and sources
• Need to calculate the sources associated to field’s
discontinuities across the surface or boundary
• General relation among
field f and its sources J: Jf )(S
• We start considering
a closed boundary
dividing two domains
Here the Huygens’
principle could be
helpful…

Mapping a 3D field on a 2D surface
The original configuration of sources J1 inside
domain 1 can be replaced by an equivalent
boundary distribution J1,d such that field f is
unchanged outside and null inside.
Extended Huygens’ Principle:
THAT IS VALID ALSO FOR STATIC FIELDS!
Original source configuration Equivalent boundary sources

Huygens’ principle for gravity (I)
• The Extended Huygens’ principle can be applied also to static gravity
• The mass is the source of the gravity field g
homogeneous lumped hollow
• Let’s consider three different planets having all the same mass
• Spherical symmetry, but different internal “source” distribution
Are these distributions equivalent outside?

Huygens’ principle for gravity (II)
• Outside, the three planets generates the same gravity field g(r)
homogeneous lumped hollow
• The “hollow” planet can be regarded as the equivalent
surface source distribution for the other two planets

Love and Schelkunoff Surf. Equivalence
( )1221, EEnJ ms

--
( )1221, HHnJ es

-
• In 1901 A.E.H. Love formulated his
surface equivalence principle for
EM fields
• In 1936 S. Schelkunoff extended it,
deriving the Boundary Conditions
surf. magnetic current
surf. electric current
Problem: do magnetic currents exists?

Magnetic monopoles
and currents

The magnetic field is not a vector
• The magnetic field B is not a “true” vector, but a pseudovector
• In fact, it does not respect usual
vector reflection rules
- C. A. Gonano, and R. E. Zich, “Cross product in N Dimensions - the doublewedge product”,
Arxiv, August 2014
• In a wider, ND view, B is
a matrix or tensor
- C. A. Gonano, Estensione in N-D di prodotto vettore e rotore e loro applicazioni,
Master’s thesis, Politecnico di Milano (2011).
ijjiij AAB // -
For further details, see also:

Magnetic monopoles
BUT WHAT IS A MAGNETIC MONOPOLE?
• Let consider field E: its “monopòles” are the
electric charges, isolable and observable
• A magnet generates a field B and its poles are
called North and South: can they be isolated?
• Problem: breaking a magnet you will not obtain
two magnetic monopòles, but two magnets!
• This difference between fields E and B has be
known for a long time…
HOWEVER, WHY THE
DIVERGENCE OF B
SHOULD BE ALWAYS ZERO ?






m
T
e
T
B
E

e


0/











--
t
E
c
JB
t
B
JE
e
m




2
0
0
1
m
Dirac’s symmetrisation
Symmetrized Maxwell’s Equations
In absence of magnetic monopòles and currents we get back the “classic”
Maxwell’s eq.s and EM force
• In 1931 Paul A. M. Dirac, starting from a quantistic approach, symmetrizes
Maxwell’s eq.s adding magnetic monopòles and currents
The generalized EM force per unit of volume is:






- EJ
c
BBJEf mmee

2
00
11

m


WHY THE DIVERGENCE OF B SHOULD BE
ALWAYS ZERO ?
• In “A Treatise on Electricity and Magnetism” (1873) J. C. Maxwell reports
that experimentally magnetic flux F(B) is always zero across a closed
surface
• In 1894 Pierre Curie defends the possible existence of “magnetic charge”
• In early XIX cent., Gauss and Weber already considered the question
• In his “Wirbelbewegung”(1858) H. von Helmholtz calculates the force
exterted on a “magnetic particle” by an electric current
• In 1931 Paul A. Dirac, starting from a quantistic approach, symmetrizes
Maxwell eq.s adding magnetic monopòles and currents
Hystory of “magnetic particles”

No experimental evidence
• In september 2009, Science reported that J. Morris, A. Tennant et al. from
the Helmholtz-Zentrum Berlin had detected a quasi-magnetic monopole
in spin ice dysprosium titanate (Dy2Ti2O7)
• On december 2009 at CERN started the Monopole and Exotics Detector At
the LHC (MoEDAL)
Nowaday, isolated “magnetic charges” have never been observed, though
many experiments have been brought on to detect them
A moving magnetic monopole would
cause an E field, so it could be
detected by measuring the current
induced in a conducting ring
HOW TO FIND MONOPOLES?
However, this would be not sufficient to prove their
existence! Magnetic current could be solenoidal!

“The invisible man”

Invisibility by transparency
• The light interacts with the cloaked object, passing through it
• The object has the same impedance and
refractive index of the surrounding medium:
;0  0cc 
• Pirex bottle filled with and merged in glycerin





0
47.1
mmm GLYPIR
GLYPIR nn
Classic experiment:





GLYPIR
GLYPIR
cc


“The Invisible Man” by H.G. Wells
“You make the glass invisible by putting it
into a liquid of nearly the same refractive
index; a transparent thing becomes
invisible if it is put in any medium of almost
the same refractive index. And if you will
consider only a second, you will see also
that the powder of glass might be made to
vanish in air, if its refractive index could be
made the same as that of air; for then
there would be no refraction or reflection
as the light passed from glass to air.”
• The same principle was well explained by H.G. Wells in his
novel “The Invisible Man” (1897):
• Problem: the human body is made by many different tissues
and it is not optically homogeneous...
;0  0cc 

Invisibility metasurface
LET’S START FROM THE DESIRED FINAL RESULT
1. Zero scattering
2. Internal shielding
3. Broadband
4. Arbitrary geometry
5. Small thickness
• Now we desire to project an invisibility metasurface or screen
Required properties:
• Unperturbed external
incident fields
• Darkness inside the cloaked
region (hypothesis: the
body does not radiate)







inc
inc
BB
EE
22
22






0
0
1
1
B
E

Mathematical conditions on EM fields

Internal shielding
• The cloaked object could emit some radiation
• Need for an internal
screen in order to confine
radiation inside
• Common metallic mirror
• A perfect internal shielding is
probably impossible because of the
black-body radiation
• The external and the
internal screen must not
interact through EM field
• …however, at T = 20°C the emitted visible
light is very low and thus it can be neglected

[1] - J. B. Pendry, “Negative refraction,” Contemporary Physics, vol. 45, no. 3, pp. 191–202, 2004.
[2] - J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science, vol.
312, no. 5781, pp. 1780–1782, 2006.
[3] – S. Maci et al. "Metasurfing: Addressing waves on impenetrable metasurfaces." Antennas
and Wireless Propagation Letters, IEEE ,10 pp. 1499-1502, 2011.
[4] - M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using
orthogonal electric and magnetic currents for wavefront manipulation,” Optics express, vol. 21,
no. 12, pp. 14 409–14 429, 2013.
[5] - A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic
shells,” Physical review letters, vol. 100, no. 11, p. 113901, 2008.
[6]- P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster
metasurfaces,” Physical review letters, vol. 111, no. 23, p. 233001, 2013.
[7] - D. Schurig et al., “Metamaterial electromagnetic cloak at microwave frequencies,” Science,
vol. 314, no. 5801, pp. 977–980, 2006.
[8] - S. Tachi, “Telexistence and retro-reflective projection technology (RPT),” in Proceedings of
the 5th Virtual Reality International Conference (VRIC2003) pp, vol. 69, 2003, pp. 1–69
[9] - S. Hrabar et al., “Negative capacitor paves the way to ultra-broadband metamaterials,”
Applied physics letters, vol. 99, no. 25, p. 254103, 2011.
[10] - S. Hrabar at al., “Ultra-broadband simultaneous superluminal phase and group velocities in
non-Foster epsilon-near-zero metamaterial,” Applied physics letters, vol. 102, no. 5, p. 054108,
2013.
References

Metasurface Hologram Invisibility - ppt

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