1 or - FER

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Applied Electromagnetics

Silvio Hrabar

Faculty of Electrical Engineering and

Computing, University of Zagreb, Croatia

Part I

Part I

The Course Structure

Artificial electromagnetic materials

Metamaterial-based guiding structures

Part III

Part IV

Part V

Metamaterial-based antennas and scatterrers

Active Metamaterials

New directions

Part IV

Active Metamaterials

• Why

all

passive metamaterials are

inherently

narrowband ? Example – ‘invisibility cloak’

• Is it possible to go around basic dispersion constraints ?

• Novel concept of ultra-broadband active ENZ or

MNZ metamaterials based on non-Foster elements –

Analytical and experimental results

Conclusions

How to make an object ‘invisible’?

• One should reduce (or ideally completely suppress) scattering …

Transmitting antenna

S inc

Transmitting and receiving antenna

So, suppressing should be done in all possible directions

(cloaking!)

Method I – Cancellation of scattered field by

‘reversed’ scattering (Engheta 2005)

Experimental verification will be reported soon

In order to obtain ‘negative polarizability’ one needs

plasmonic coating (

 r

<1)

v p

c



In other words, a coating must support propagation of fast waves (v p

>c)

Method II – ‘Transformation Electromagnetics’

(Dollin 1961, Pendry 2006)

Experimental verification already reported

r

z

'

'

'

R

1

z

r

(

R

2

R

2

R

1 )

'

r

'

'

z

'

'

r

'

z

(

r r

'

r r

'

R

2

'

'

R

1

R

1

R

2

R

1

)

2

r

'

r

'

R

1

Again, a shell (cloak) must support propagation of fast waves (v p

>c)

Method III – Guiding the waves through the object

(Tretyakov et al , 2007)

Experimental verification already reported

A material that supports propagation of fast waves (v p

>c) is not needed but cloaking space is extremely small (<

/10)

Thus, it seems that existence of fast waves is necessary for cloaking of moderate or big objects

(all dimensions >

/10) that are not narrow and elongated!

Usual (simplified) explanation of cloaking effect v p

free space

= c

a hidden object an object

v p

= c

a cloak





v p

>c (either ε



r

<1 or

r

<1)



For perfect cloaking EM waves traveling along all different ‘paths’ must experience exactly the same delays (the same phase shifts)!

Influence of the frequency of operation on cloaking v p

free space

= c

a hidden object an object

v p

= c

a cloak path i



i

 

d i

 

d i k i

c

r



v p

>c (either ε



r

<1 or

r

<1)



Inserted phase shift depends both on the frequency and

(

,

i

)

r

(

,

i

)

dispersion properties of used

(meta)material!

 r

A or

 r

Dispersion models of passive materials

(metamaterials) with ε r

<1 or

r

<1

Hypothetical dispersionless

1

ENZ (MNZ) material

0

ENG (MNG)

 r

B or

 r

1

0

 p

 s

Realistic dispersive material

Since the realistic model is highly dispersive one may expect (significant) influence of frequency on MTM operation

E

Resonance is always present in passive metamaterials – WHY? )

dielectric

+

+

-

-

+

+

-

+

-

-

URL: http://www.walterfendt.de/ph14e/resonance.htm

© Walter Fendt, September 9, 1998

Majority of proposed cloak designs are inherently narrowband

Schurig, Pendry at al,

Scienceexpress 2006

BW

0.24%

Ivsic, Sipus, Hrabar, IEEE

Tran. on AP, May 2009.

BW

10%

Silveirinha, Alù, Engheta, Physical

Review E 2007

1.2

1

0.8

0.6

0.4

0.2

What would happen in one had a dispersionless

‘plasmonic’ ( ε r

Example of a cloak with

<1) metamaterial ?

isotropic plasmonic shell

1.4

i

 

d i

c

r

(

,

i

)

r

(

,

i

)

Silveirinha, Alù, Physical Review E

2007

Drude model

No dispersion

0

1 1.1

optimal design frequency

1.2

1.3

Normalized frequency

1.4

1.5

Use of dispersionless plasmonic metamaterial would enable broadband cloaking!

Is it possible to construct passive dispersionless ‘ ( ε r

ENZ metamaterial ?

<1)

The energy within a differential volume of vacuum

W

0

W e

W m

1

2

0

E

2

1

2

0

H

2

The energy within a differential volume of dispersionless material

W

W e

W m

1

2

0

r

E

2

1

2

0

r

H

2

Thus, having dispersionless material with ε r

<1would mean amount of energy that is lower than energy in vacuum!

The energy within a differential volume of dispersive material

W

W e

W m

1

2

0

(



r

)

E

2

1

2

0

(



r

)

H

2

Since W>0, it follows that

(



r

)

0 ,

(



r

)

0 .

The only way to have ε r

<1 in passive material is to redistribute excess of the energy from the electric field into the magnetic field!

This process is frequency depended, so the existence of dispersionless passive ENZ metamaterial is impossible!

Energy-dispersion constraints lead to Foster theoem!

What is the minimal capacitance of a capacitor that occupies some cubic volume of space ?

 l

 l

C

min

Q

V

0

S

l

0

l

2

l

0

l

S

S

PEC plate

What is the minimal inductance of an inductor that occupies some cubic volume of space ?

 l

 l

L

min

I

0





HdS

JdS

l

0

l

PEC cube

What happens in one redistributes part of the energy from the electric field into the magnetic field (or vice versa) ?

L

 l

C

Y

C eff j

C

C

j

1

L

1

2

L

j

1

2

L

0

l

1

2

L

j

C eff

L

 l

C

Z

L eff

j

L

L

j

1

C

1

2

C

j

1

0

l

1

2

C

2

C

j

L eff

There are many reports in MTM community that do not take care of these basic constraints!

•IEEE Antennas and Wireless Propagation Letters,

•Vol. 8, pp. 1154 – 1157, November 2009 unit   cell  

???

The Concept of Artificial Material

( Metamaterial)

a host material scatterer (implant)

E

P

• If

a



,

the structure can be analysed as a homogenous material with some new

 and

 metamaterial

All kinds of passive metamaterials redistribute energy from the electric field into magnetic field (or vice versa)!

MTM with



MTM with



 a volume of space occupied with an

MTM inclusion a volume of space occupied with an

MTM inclusion

E excitation

W e

W m

H excitation

W m

W e

Due to this redistribution all passive metamaterials are inherently dispersive!

Example 1 - Wire Medium (Rotman 1962, Pendry 1998)

Z

 l

E

Y

P

a r

1





p



2

H

2

E

 

 2 

E

j

 

x

2

V

 

ZY V

2

Free-space

j

X series



j

 



j

Y shunt

E

V

Wires

0

0

 r

<0

0 f<f p

 r

<0

0

1 f>f p

0>

 r

>1

0

a



r

 reffz f p

1 real part imaginary part f

 l

 l

 l

Example 2: Metamaterial Transmission Line

Concept

H

L



E

(Caloz et al. 2002, Iyer et al. 2002, Oliner 2002)

H

 forward-wave

propagation

C backward-wave

propagation

C









E

L







C

 l

 l

Extension of the C-L

Backward-wave

Transmission Line to 2D

Case

(Iyer et al. 2002)

Example 3: Wire-loop and capacitivelly loaded loop

(SRR), (Smith 1999, Schelkunoff 1955, Hrabar et al

2003)

Hi r

Hs

R

C

L

E i nc

E s ca t

Z

V=L E ef in

Z

I

Z

I

V=-

 

in

V

0

 

j



0

AH i

Z

I

R

L

C

Lorentz model

µ or

0

1

0 f

0 f mp f

Can one go around the dispersion-energy limitations?

W

W e

W m

1

2

0

(



r

)

E

2

1

2

0

(



r

)

H

2

(



r

)

0 ,

(



r

)

0 .

???

The only way is to use active medium (i.e. to introduce active elements that do not obey Foster theorem!)

Active medium should introduce ‘assisting negative restoring force’ !

F as

One would need a ‘negative spring’ or a‘negative weight’

•URL: http://www.walterfendt.de/ph14e/resonance.htm

© Walter Fendt, September 9, 1998

jX  

Basic principle of Non-Foster reactive elements (negative C and negative L)

I

X

C

X

L

I I f

V

Z

V

Z

V

0

V

‐ jX  

X

C

X

L

Z

A=+2

V

0

=2

Z in

V in

I in

V l

I l

 

Z l

Classical NIC Designs

How to access the Stability Issue

Use of ordinary stability factors (Rolett, Stern …) can give completely wrong predictions!

•30

How to access the Stability Issue

1 GHz

Unstable!

1 GHz

Unstable!

4 GHz

4 GHz

Use of ordinary stability factors (Rolett, Stern …) can give completely wrong predictions!

•31

C

0

How to access the Stability Issue

u

(

t

)

CR du

(

t

)

dt

0

u

(

t

)

u

( 0 )

e

t

 

V = 1V

0_

C

0

u

(

t

)

CR du

(

t

)

dt u

(

t

)

u

( 0 )

e

t

RC

0

u

( 0 )

e

R t

C

•32

New idea : Introduction of negative capacitance into

TL (Hrabar et al , APS 2008)

Negative capacitance

Positive capacitance

C

C

1

C

2

C e

C

C

C

C

e

0

0

Negative capacitor is inherently unstable, but overall capacitance

>0 and this circuit is stable !

0

1

2D ENZ Unit Cell for Cloak Design - Experiments

(Hrabar et al, Metamaterial Conference 09)



Microstrip line real imaginary circuitry is located on the ground plane side

air

A circuit simulator (ADS) model of 2D active plasmonic cloak

Air

Dispersionless ENZ

PEC

Total of 89 x 89 (7921 c ells) cloak

C<0

19 c ells

45 c ells

49 c ells

89 c ells

Measurement data are used target

Results of circuit simulation (ADS) of 2D active plasmonic cloak

An ADS model of 2D active plasmonic cloak

(Hrabar et al. , Metamaterials Journal, 2010)

1D Unit Cells in RF Regime

Fast OPAMP-based (10 MHz -40 MHz)

MOSFET-based (80 MHz -300MHz)

BF999

Experimental Active ENZ TL with Three Unit Cells

(l = 1 m)

Z

0

Realistic

C

Realistic

C

Realistic

C

 x=



 x=



 x=



Measurement of effective permittivity of ENZ

Active TL with Three Unit Cells

ENZ switched OFF

ENZ switched ON

Measurement of Phase and Group Velocity of

ENZ Active TL with Three Unit Cells

vp vg

Transient Behavior - Measurement in Time Domain

Input

Z

0

 x=



Realistic

C

 x=



Realistic

C

 x=



Realistic

C

Output

Input

Measurement in Time Domain

Output ( ENZoff )

Output ( ENZ on )

ENZ behavior achieved within one quarter of a period (2.5 nS)

Further research – Track 1 –

Towards anisotropic MTM

Further research – Track 2 –

Towards “Matched Nihility (MENZ)”

L+L neg

Z

Y

C+C neg

 l

0

r

1 ,

Z

0

Z

,

Y

0

r

1 ,

ZY

.

It might be possible to obtain broadband “superluminal” behavior with matching to free space.

Further research – Track 2 –

How to mach MTM to free space?

a) Basic idea of TEM line with flared ends, b) Simulated E field distribution inside empty line, c) Simulated E field distribution inside line filled with fictitious continuous ENZ material, d) Simulated E field distribution inside line periodically loaded with negat capacitors

V

I

Development of negative inductance

Z

A=+2

V

0

=2

Further research – Track 3 - Towards Volumetric dispersionless ENZ and MNZ MTM

dipole

CN

PP   capacitor Input   port loop

L

N

Input   loop Output   loop

Negative   inductor

Negative   capacitors

Further research – Track 4 - Towards

“Frequency independent TL”

• Is it possible to completely exclude the influence of the frequency on the TL behaviour ?

Z

L

1

C

1

Y

-L

2

-C

2

 l

j

ZY

j

ZY

 l

 l

j

L

1

l

1

j

L

2

l

j

1

j

C

1

l

j

C

2

l

j

L

1

L

2

C

2

C

1

Further research – Track 5 - Towards

“Frequency independent TL”

How to increase the frequency of operation?

Use microelectronic technology !

Would it be possible to build microelectronic version of active non-Foster TL unit cell?

Conclusions

• All passive metamaterials suffer from narrowband operation caused by their dispersive nature

• This drawback can be overcome by use of non-

Foster elements

• It is feasible to obtain a multi-octave bandwidth with stable operation

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