University of Zagreb, Croatia
Who are we and what are we doing?
University of Zagreb (1669), nowadays 50 000 students •Faculty of Electrical Engineering and Computing (1956) •13 departments
with 4000
students
•Department of Wireless Communications •
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15 members of staff 4 post‐doc researchers 15 Ph.D. students 80 undegraduate students International collaboration
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Air Force Research Laboratory, Hanscom AFB, USA University of Bologna, Italy
University of Siena, Italy
Brunel University, Department of Systems Engineering, UK Chalmers University of Technology, Department of Electromagnetics, Goeteborg, Sweden Motorola, Electromagnetics Research Laboratory, Florida, USA Swiss Federal Institute of Technology, Zuerich, Switzerland Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland Universidad Carlos III de Madrid, Spain Universidad Autonoma Barcelona, Spain Technical University of Budapest, Department of Microwave Telecommunications, Hungary Technical University of Graz, Institut fur Elektro‐ and Biomedizinische Technik, Austria Third University of Rome, Department of Electrical Engineering, Italy University of Essex, Department of Electronics Systems Engineering, UK University of Gent, Department of Information Technology, Belgium University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia University of Massachusetts Amherst, Department of Electrical and Computer Engineering, USA University of Utah, Electrical Engineering Department, Salt Lake City, Utah, USA Teaching and research
Stream I - Communications
Courses • Communication Systems • Mobile Communications • Radio‐Frequency Systems • Digital Broadcasting • Optical Communication Systems • Satellite Communication Technology • Optical Networks • Mobile Systems Planning • Wireless Access Networks • Multimedia Technologies • Video Communication Technologies Teaching and research
Stream II – Electromagnetics and Antennas
Courses • Applied Electromagnetics • Antennas and Propagation • Microwave Engineering • Radio‐Frequency and Microwave Measurements • EMC and EMI Protection of Communication Systems • Remote Sensing and Radiometry • Innovative Electromagnetic Systems • Radar Systems • ECM and Electronic Warfare Applied electromagnetics
Silvio Hrabar
Faculty of Electrical Engineering and
Computing, University of Zagreb, Croatia
The Course Structure
Part I
Artificial electromagnetic materials
Part I
Metamaterial-based guiding structures
Part III
Metamaterial-based antennas and scatterrers
Part IV
Active Metamaterials
Part V
New directions
Part I
Basic physics of metamaterials
•Mathematics versus Physics and Engineering
•Electromagnetics of Classical (“Positive”) Materials
•Are “Negative” Materials Possible?
•New Physical Phenomena - Fundamental research
•Conclusions
Mathematics versus Physics and Engineering
Mathematics
Physics
Service ?
Engineering
What is the difference among engineers ,
physicists and mathematicians ?
Model gives non-physical
results – Why ?
Observation
Reality
Prediction
Model
Project
Is the basic theory correct?
Scientist
Engineer
Mathematics
Physics
Engineering
Electromagnetics of Classical (“Positive”) Materials
The Story of Electricity
•Ancient Greece – Why does amber attract papyrus ?
•Charles Augustin de Coulomb (1736-1806)
and concept of Electric field
Q4
Q5
Q3
Q0
Qn

F02
Q2

Q0 Q2 
F  K 2 a12
R02

QQ 
QQ 
QQ 
F  K 0 2 2 a12  K 0 2 3 a13  ...K 0 2 n a1n
R02
R03
R0 n
 Q 


Q3 
Qn  
2

F  Q0  K 2 a12  2 a13 ... 2 a1n   Q0 E

R0 n
R03
  R02



F
E  lim
Q0 0 Q0
The Story of Magnetism
•Ancient Greece – a strange rock from island of Magnesia
Hendrik Antoon Lorentz

F02
Q2
Q0



F  Q0 E  f (v , Q0 , R02 )
    
 Q0 E  v  B E  B.



F  QE

v
Concept of B field
Andre Marie Ampere (1775-1836)

Wedding of Electricity and Magnetism –
Electromagnetism (Electromagnetics)
•Michael Farady (1791-1867)

B
V 
t
Are the E and B Vectors
Enough?
Yes in principle, but what
about the influence of
matter?
…atomic dimensions are on
order of 10-11 m!


D    E Electric flux density


H   1  B Magnetic field
How to describe the vector field?
– A concept of divergence
•Example – the flow of water in a pipe
 
 
  S  v  S v cos(  ),
3
m
m
 m2 .
s
s

div v  lim
V 0


all fluxes of v
V

  
 
  
  a x  a y  a z   v .
y
z 
 x
How to describe the vector field?
– A concept of curl
•Example – the flow of water in river
•Distribution of velocities of rotation (curl)
razdioba brzine okretanja
(rotor)
•Distribution of water velocities (field)
razdioba brzine vode
u rijeci (polje)
•River rijeka
obala
•River bank
•The curl ‘detector’ detektor
rotora
(a propeller)







curl v  (variation of v in x direction) a x  (variation of v in y direction) a y  (variation v in z direction) az



a x a y az

 


curl v    v 
x y y
v x v y vz
James Clerk Maxwell (1831-1879)

Q
D 
V

B  0

  D
H  J 
t


B
E  
t


D  E


B  H
Solution of these
equations is a wave!
What is a Plane EM Harmonic Wave ?
The simplest solution of source-free vector wave equation


2
2
 Ek E 0

 ReB e


a





a
 ReB e e


j t  jk z 
j t j ( z ) 
e( x, t )  A cos( t  k  z )a x  Re Ae e
a x  Re Ae e
ax

h( y , t )  B cos( t  k  z )a y

j t  jk z
e
j t
y
j ( z)
y
Wave vector
 2  
k
a0 , k   ( x, y , z )

Poynting vector
  
P  EH
From Theory towards Applications…
•Heinrich Rudolf Hertz (1857-1894)
•Nikola Tesla (1856-1943)
•Guglielmo Marconi (1874-1937)
…. and here we are !
 
E, H ,  , .
Are “Negative” Materials Possible?
(Are some solutions of Maxwell equations meaningless?)
What would happen if  and  were
negative numbers? (Veselago, 1968)
• A plane wave solution
of Maxwell equations:
E
P
k
Forward wave

E  Ae
 
k  u0  
  
P  EH

 jk r
H
Right-handed
material
E
Backward wave
P
H
Sign ambiguity
k
Left-handed
material
What is a velocity of EM wave (or any wave )?
A concept of phase velocity and group velocity
vp 

k

vg 
k
v p  0, v g  0
•Copyright Dr. Dan Russel
27
The wave on a rope
v p  0, v g  0
•Copyright Dr. Dan Russel2828
One-dimensional Wave Propagation in Material with
 >0 and  >0 (forward wave propagation )
E
Vp>0
Vg>0
source
+
0
X
One-dimensional Wave Propagation in Material with
 <0 and  <0 (backward wave propagation )
Vp<0
Vg>0
E
source
+
0
X
• Thus, in LHM the direction of the energy flow (P)
is opposite to the direction of the phase velocity
(k)
• This peculiar behavior causes ‘reversion’ of many
basic electromagnetic properties such as Snell law
and Doppler effect, Cherenkov radiation e.t.c.
‘Reversion’ of Snell Law
air (r=1,  r=1)
Left-handed
material
Material
with
r<0,  r<0
Right-handed
material
Material with
 
r>0,  r>0
Concave and Convex Lenses using material
with
 <0 and  <0
What it really matters is actually not  <0 and
 <0 , it is the existence of the backward wave
propagation !
Had anybody studied this issue before Veselago?
Malyuzhinets ‘A note on the radiation principles’ (1951)
Pocklington ‘Growth of a wave-group when the
group velocity is negative’ (1905)
Lamb, ‘On group velocity’ (1904)
The Concept of Metamaterial
Inclusion-based Approach
a
host material
scatterer (implant)
E
P
H
incoming plane wave
•a~,
Photonic Bandgap Structure
Photonic Crystals
• a, the structure behaves
as a homogenous material
with some new  and  
metamaterial
Thin-wire Plasma-like Structure with  <0
( Rotman 1962, Pendry 1998)

reffz
E
P
H
1
 p 

 1  

r



a  
a
 1
r
real part
0
fp
f
imaginary part
2
The ‘Split-ring Resonator’ Structure with 0
(Pendry 1999)
r
real part
0
Imaginary part
1
0
f0
r  
a  
f mp
f
The first reported Backward-wave Material
(Smith et al. 2000)
Split-ring resonator
SRRs only
Wires only
Thin-wire media
SRRs + Wires
k   
SRR’sSRR’s
and
Wires
wires
only
only: : <0>0 <0,
>0,
<0k, becomes
kisbecomes
again positive
 backward-wave

nono
propagation
propagation
propagation
real number
imaginary
imaginary
number
number
Capacitivelly loaded loops and thin-wire
structure (Hrabar, Barbaric; 2000 –1/3)
Capacitivelly loaded loops and thin-wire
structure (Hrabar, Barbaric 2000; –2/3)
Capacitivelly loaded loops and thin-wire
structure (Hrabar, Barbaric 2000; –3/3)
0
transmission [dB ]
-20
-40
-60
-80
-100
LHM
wire medium
capacitively loaded loops
-120
-140
8
9
10
11
12
13
frequency [Ghz]
14
15
16
The SRR behaves as capacitivelly loaded loop
(Hrabar, Bartolic, Eres; 2002)
H  Hi  H s
Calculated
effective
permeability




K 0 S
H  H i 1  j

j


R  jL 
C 

5

real part
imaginary part
4
3
2
1
r
Z
Hi
Hs
I
Za
Vo
0
+
Z
I
-1
-2
-3
-4
7
7.5
8
8.5
9
Frequency [GHz]
9.5
10
Demonstration of negative permeability by
measurement of transmission coefficient
Transmitting
loop
Receiving
loop
Capacitivelly Loaded loops (the inclusions)
Demonstration of negative permeability by
measurement of transmission coefficient
Bare loops
Capacitivelly Loaded loops
(the inclusions)
Schelkunoff, Friis –’Antennas, Theory and Practice’, 1952
Interpretation using Transmisison Line
Theory
i(x,t)
Rx
Gx
v(x,t)
i(x+x,t)
Lx
Cx
I(x)
v(x+x,t)
V(x)
x (x<<
x
Z  R  j L
Y  G  j C
d 2V
dx
2
d 2V
dx 2
 ZYV
 ZY I
I(x+x)
Z x
Yx
V(x+x)
x (x <<
x+x
x
Vinc Vref
Z
R  j L
Z0 



I inc I ref
Y
G  j C
  jk    j 
R  jL G  jC 
x+x
Wire Medium as Transmission Line (Hrabar 2003,2006)
E
p
 r  1  
 
a  
a
 1
r
P
H

 2 E    2  E  j 
 2V
x
I(H)
Z
  ZY V   j  X series
2
Y
l
 j  E
 j  Y shunt V
Freespace Wires
0
V(E)

0
0
r <0
l
l
reffz
1
f<fp
r <0
0
f>fp
0>r>1
l



2
0
real part
imaginary par
fp
f
How to obtain the negative electric polarizabilty (and
therefore negative permitivity) using a simple
inclusion in RF and microwave regime ?
real part
εr
R
C
Einc
Z
Es ca t
V=L
o ef E in
Za
+
Z
Imaginary
0
L
part
1
0
f0
I
f •p
mp
f
Demonstration of negative permittivity by
measurement of transmission coefficient
Transmitting
monopole
Receiving
monopole
Inductivelly loaded monopoles
(the inclusions)
Demonstration of negative permittivity by
measurement of transmission coefficient
Bare monopoles
Inductivelly loaded monopoles
(the inclusions)
Achieving Backward-wave Propagation using
Transmission Line Concept
(Caloz et al. 2002, Iyer et al. 2002, Oliner 2002)
L

forward-wave
propagation
C
l

C

backward-wave
propagation
L
l

•What is unique (measurable) signature of BW
propagation in 1D ? –That is a phase distribution.
 = arg(S21)
2<0
2<0
 2BW
 1BW
0
l1
 1FW
 2FW
l1
 2BW >  1BW
P2
backward-wave TL
k2
l2
length
forward-wave TL
 2FW <  1FW
1>0
1>0
P1
k1
l2
Demonstration of FW and BW propagation by
Measurement of Phase distribution
L
C
l
C
L
l
Microstrip Backward-wave Transmission Line
(Caloz et al. 2002)
Extension of the C-L Backward-wave
Transmission Line to 2D Case
(Iyer et al. 2002)
Classification of Metamaterials •Single‐
negative materials (SNG) •Double‐
negative materials (DNG) •Double‐
positive materials (DPS) •Single‐
negative materials (SNG) Resonance is always
present in passive
metamaterials – WHY? )
•URL: http://www.walterfendt.de/ph14e/resonance.htm
© Walter Fendt, September 9, 1998
Dispersion models of passive materials
(metamaterials) with εr<1 or r<1
•Lorentz model
• r
real part
•Drude model
reffz
real part
1
imaginary part
0
fp
f
0
•Imaginary
part
1
0
f0
f mp
f
Both of these models are highly dispersive for
0< εr<1 (or 0< r<1)
New Physical Phenomena Fundamental research
Experimental Verification of Negative
Refraction (Shelby et al. 2001)
Experimental Verification of Negative
Refraction (Shelby et al. 2001)
Experimental Verification of Negative
Refraction (Houck et al. 2003)
Experimental Verification of Negative
Refraction (Hrabar, Bartolic; 2003-1/2)
1
2
3
Experimental Verification of Negative
Refraction (Hrabar, Bartolic; 2003-2/2)
1
2
3
Simulation of Negative Refraction at Planparallel Slab with n=-1
(Ziolkowski; 2003)
Verification of BW propagation by measurement of
Negative Refraction (Hrabar,
Bartolic, Sipus, 2004)
double rings
1
a)
d
b)
22
1
1
 x x
a) A case of ‘forward-wave’ slab (>0,>0)
b) A case of ‘backward-wave’ slab (<0,<0)
metallic plate
absorber
E
H
P
Super Lens’ with no Resolution Limit
(Pendry, 2000)
r=1
r=1
source
Propagating part of
Fourier spectrum
r =-1
r=-1
r =1
r=1
focus
Evanescent part of
Fourier spectrum
Experimental verification (Grbic et al. 2004 –1/2)
Figure taken from G. Eleftheriades (University of Toronto)
presentation slides
Experimental verification (Grbic et al. 2004 – 2/2)
Figure taken from G. Eleftheriades (University of Toronto)
presentation slides
Conclusions
• Metamaterials offer new exciting physical
phenomena, which are very often counterintuitive !
• In author’s opinion, this area is not in its
infant phase any more and applications, that
make use of new intriguing phenomena are
expected to come in coming years!
• It is an interdisciplinary field which needs
extensive collaboration of different worlds
(math, physics, engineering, at least!)