1 Department of Applied Electronics University of Roma Tre Rome, Italy Potential Applications of Antennas with Metamaterial Loading Filiberto Bilotti 2 Road Map The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions
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Department of Applied ElectronicsUniversity of Roma TreRome, Italy
Potential Applications of Antennas with Metamaterial Loading
Filiberto Bilotti
2
Road Map
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
2
3
The history of metamaterials
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
4
What are metamaterials?Why to use metamaterials?
Metamaterials are artificially engineeredmaterials exhibiting unusual properties that cannot be found in nature.
Metamaterials allows going beyond the classical physical restrictions and limitationsof electrodynamics.
3
5
From natural materialsto complex materials 1/2
First Stage: observation and investigation of the physical phenomena in nature
, ,c c r c rn ε µ= , ,c c r c rn ε µ=
Natural materials
The arrangement of atomes and
molecules determinesthe physical behavior
Optical frequencies
6
From natural materialsto complex materials 2/2
Second Stage: design of artificial materials to imitate the nature at lower frequencies
, ,h h r h rn ε µ=
CompositionAlignment
ArrangementDensity
GeometryHost medium
4
7
From complex materialsto metamaterials
Third Stage: design of artificial materials that exhibit unusual (anomalous, surprising, …) features that cannot be found in nature
8
Microwave applicationsof metamaterials
Fourth Stage: investigate the exciting features of metamaterials to propose novel concepts for microwave components
electronic circuitsradiating components
DPS DNG
5
9
Come back to the nature…Fifth Stage: design of nanostructures to bring back to the nature the unusual properties discovered at microwave frequencies
Naturaloptical
materials
Complexmaterials
Meta materials
Artificialdielectrics
Exoticshapes
Nanotructures
µwaveapplications
of metamaterials
10
Metamaterial terminology
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
6
11
εRe[ ]
µRe[ ]
DPSk ∈ ℜ
DNG∈ ℜk
ENG
k ∈ ℑMNG
∈ ℑkMNZMNZ
ENZ
ENZ
RegularDielectrics
Metamaterialterminology 1/2
12
Metamaterialterminology 2/2
= ω µε
DPS ENG MNG DNG
k propagation evanescent evanescent propagation
waveβ −jα −jα β
7
13
Complementarymetamaterial pairs
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
Field distribution in metallic cavities filled by DPS/DPS and DPS/DNG slabs (sizereduction).
Complementary metamaterial pairs 5/6
10
19
DPSENG
d1
k1
MNG
d2
k2
1 21 1 2 2
1 2
| |tanh( d )- tanh( d ) 0µ µα α =
α α
1 1 2 2d | |d 0µ − µ =
1 2
2 1
d | |d
µ=
µ
i id 1α
A metallic cavity filled by a DPS(or ENG)/MNG pair works as a cavity filled by a DPS/DNG pair.
Complementary metamaterial pairs 6/6
20
Compact scatterersand compact antennas 1/2
DPS
incE
incHDPS
incE
incH
incE
incHDPS
SNG
incE
incHDPS
SNG
incE
incH
incE
incH
DPSDPS
DPSSNG
DPSSNG
Resonantcompact bi-
layer scatterers
Resonantcompact bi-
layer antennas
RECIPROCITY
11
21
DPS
ENG
Ziolkowski’s groupresonant sub-λ
dipole antennas
Roma Tre – UPenn resonant sub-λ
patch and leakywave antennas
Compact scatterersand compact antennas 2/2
DPS DNG
22
Patch Antennas with Metamaterial Loading
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
Standard rectangular patchSurface – wave contribution (degraded radiation pattern and poor efficiency)
Substrate thickness:λ/20 – λ/100
L
28
Radiation mechanism and design 2/3
The electric field may be assumed vertically directedThe magnetic field does not have the vertical component (TMz modes)
15
29
Radiation mechanism and design 3/3
Fringing effect is responsible for the radiationThe electric field must be out of phase at the two radiating edges of the patch.
L=λ/2
30
Cavity model for analyzingpatch antennas 1/2
Cavity model (since the substrate is very thin, only TMz modes are present)
PEC
PMC
The modes of the patch may becalculated as the modes of the
PEC-PMC cavity
2 2[m,n ,0] 0TM
r r
c1 m nf2 L W
π π⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟π µ ε ⎝ ⎠ ⎝ ⎠
LW
Imposing the boundary conditionsthe calculation of the resonantfrequencies is straightforward
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31
The dominant mode along x is the TM100
The magnetic currents at theradiating edges are responsible
for the radiation
Electric current densitydistribution of the dominant mode
on the patch surface
Cavity model for analyzingpatch antennas 2/2
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DPS DPS
DPS DNG
z
xy
W
Ld
Rectangular patch antennas with metamaterial loading
DPS DNG
DNG DPS
Is it possible to apply the same concept to microstrip antennas?
xy
xy
z z
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33
z
xW
L
d1 1,ε µ 2 2,ε µ
TMm00
( )1-η LηL
[ ] ( )[ ]1 21 2
1 2
k tan L k tan 1 L kk
ωεη = − − η
ωµ
η ε−
− η ε2
11L 0→
≤ η ≤0 1
Filling Factor
Dispersion Equation for TMm00 modes
Cavity model for patch antennas with MTMs 1/6
The dispersion equation may be written with the explicit presenceof the filling factor η.
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Cavity model for patch antennas with MTMs 2/6
When L is very small compared to λ, if the two materials have Re[ε]>0, the dispersion equation cannot be satisfied for any value of η.
As in the 1D-cavity, when L is small compared to λ, the total length L is not relevant for the dispersion equation to be satisfied: the only relevant quantities are the filling factor η and the permittivities of the two materials.
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35
-2.5 -2.4 -2.3 -2.2 -2.1 -2.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Res
onan
t Fre
quen
cy [
GH
z ]
εENG / ε0
W
0 02 ,ε µL/2
d0,ENGε µL/2
L = 50 mm
Cavity model for patch antennas with MTMs 3/6
Also in this case there is no need for a DNG material: an ENG medium is enough.
η ε−
− η ε2
11f0 = 2.44 GHzεr = 2.2
36
0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.200.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
µENG
= µ0
µENG = 3µ0
µDNG
= -µ0
µDNG
= -3µ0
Res
onan
t Fre
quen
cy [
GH
z ]
Plasma Frequency [GHz]
⎛ ω ⎞ε = − ε⎜ ⎟⎜ ⎟ω⎝ ⎠
2p
021
W
0 02 ,ε µL/2
d0,ENGε µL/2
L = 50 mm
Cavity model for patch antennas with MTMs 4/6
Permeability variations do not affect the resonant frequency.
Drudedispersion
model
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37
Cavity model for patch antennas with MTMs 5/6
Ez component Hx component
0.00 0.01 0.02 0.03 0.04 0.05-300
-150
0
150
300
450
600
750
Ele
ctric
Fie
ld E
z [ V
/ m
]
y [ m ]
ε2 = 2.2, f = 2.44 GHz ε2 = -2.2, f = 0.50 GHz
0.00 0.01 0.02 0.03 0.04 0.050.0
0.2
0.4
0.6
0.8
1.0
Mag
netic
Fie
ld H
x [ A
/ m
]
y [ m ]
ε2 = 2.2, f = 2.44 GHz ε2 = -2.2, f = 0.50 GHz
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Cavity model for patch antennas with MTMs 6/6
DPS ENG DPS DPS
Radiation from this kind of antenna is very poor.
f = 0.50 GHz f = 2.44 GHz
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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0-15
-10
-5
0
5
10
15
20
25
30
Rel
ativ
e P
erm
ittiv
ity
Frequency [GHz]
Re[ε2]
Im[ε2]
Full wave simulations for the rectangular patch 1/7
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
60
Natural Modes of a Grounded Slab 1/2
( ) ( )( ) ( )
0 0
0 0
TE: cos sin 0
TM: cos sin 0
y y y y
y y y y
k k d j k k d
k k d j k k d
µ µ
ε ε
+ =
+ =
y
xd ε, µ
( )0I: max ,k kβ > 0, ∈ ℑy yk k
0II: k kβ< < 0,∈ℜ ∈ ℑy yk k
Suraface waves (only with negativeconstitutive parameters)
Regular surface waves
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61
Natural Modes of a Grounded Slab 2/2
( ) ( )( ) ( )
0 0
0 0
TE: cos sin 0
TM: cos sin 0
y y y y
y y y y
k k d j k k d
k k d j k k d
µ µ
ε ε
+ =
+ =
y
xd ε, µ
Leaky waves (only with anomalousconstitutive parameters) with high leakagefactor. Low directivity.
Leaky waves (only with anomalousconstitutive parameters) with low leakagefactor. High directivity.
0III: Re[ ]< <k kβ 0 0Re[ ] , Re[ ]> <y yk k k k
( )0IV: Re[ ] min ,< k kβ 0 0Re[ ] , Re[ ]< <y yk k k k1
0sin (Re[ ]/ )− kθ β
62
ENZ-MNZ metamaterials for high directivity LW radiators
( )0IV: Re[ ] min ,< k kβ 0 0Re[ ] , Re[ ]< <y yk k k k
( ) ( )( ) ( )
0 0
0 0
TE: cos sin 0
TM: cos sin 0
y y y y
y y y y
k k d j k k d
k k d j k k d
µ µ
ε ε
+ =
+ =
( )0 2 2
0 2 2
2 1,
2
,
Nd
kNd
k
πµ µ
βπε ε
β
−≅
−
≅−
An almost real solution may be found if the two terms of each equation become sufficiently small. By inspection, it is easy to derive the conditions for both the constitutive parameters and d.
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63
( )( ) ( )
2 2 22 0 1 2 0 2 2 0 1 2
2 2 20 2 1 2 0 2 1 2 2
TE:
TM:
− = − +
+ = − −
TE TE TE TEy y
TM TM TM TMy y y
f f k j k f f
k f f j k f f k
µ µ µ µ
µ ε
( )( )
cot /
tan /
=
=
TEi yi yi i i
TMi yi yi i i
f k k d
f k k d
µ
ε
Groundedmetamaterial
bi-layer
Groundedmetamaterial bi-layerdispersion equations
Grounded bi-layers planar uniform LW antennas 1/7
64
[ ]( )( )
1 2 0
1 2 0
Im 0
TE: max ,
TM: max ,
β
µ µ µ
ε ε ε
( )( )
21 2 2 2 1
21 2 1 1 2
TE: /
TM: /
y
y
d d k
d d k
µ µ
ε ε
1 1 2 2max , 1y yk d k d⎡ ⎤⎣ ⎦Sub-λ thickness
condition
High directivityconditions
Retardation effects are not significant: depending on the polarization, onlyone constitutive parameter is involved.
The near field is dominated by the TM LW whose E field is almost
radially directed. This is a good hintfor both feed and inclusion design.
L = 75 cmDrude dispersion for ε
Compact cylindricalleaky wave antennas 11/15
41
81
The amplitude of the Poynting vectordecays along the antenna axis
The electric field is radially directed
f = 1.975 GHzf = 1.975 GHz
Compact cylindricalleaky wave antennas 12/15
82
1.960 1.965 1.970 1.975 1.980 1.985105°
110°
115°
120°
125°
130°
135°
140°
145°
150°
155°
160°
Bea
m D
irect
ion
[deg
rees
]
Frequency [GHz]
Scanning features of the cylindrical leaky wave antenna
as a function of frequency
f = 1.975 GHz
Compact cylindricalleaky wave antennas 13/15
42
83
The 3D radiation patterns show that the structure is long enough not to have back-radiation.
f = 1.975 GHz f = 1.985 GHzf = 1.960 GHz
Compact cylindricalleaky wave antennas 14/15
84
A smaller structure gives reduceddirectivity while the back-radiation is
increased, due to the reflections at the no-feeding end.
f = 1.975 GHz f = 1.985 GHzf = 1.960 GHz
L = 25 cm
Compact cylindricalleaky wave antennas 15/15
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85
Conclusions
The history of metamaterialsMetamaterial terminologyComplementary metamaterial pairsPatch antennas with metamaterial loadingLeaky wave antennas with metamaterialloadingConclusions
86
Metamaterial complementary pairs are able to overcome the diffraction limit in the design of microwave components.Sub-wavelength cavities, waveguides, scatterers, and antennas may be obtained.Patch antennas and leaky wave antennaswith sub-wavelength resonant dimensions have been presented in details.
Conclusions
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87
Acknowledgements
Prof. Lucio Vegni (University of Roma Tre)
Dr. Andrea Alù (University of Roma Tre)
Prof. Nader Engheta (University of Pennsylvania)
88
ReferencesAlù, Bilotti, Engheta, Vegni, IEEE IMS 2005, Long Beach, USA, June 2005Bilotti, Alù, 1st EU Ph.D. School on Metamaterials, San Sebastian, Spain, July 2005Alù, Bilotti, Engheta, Vegni, IEEE AP/URSI Symp., Washington, USA, July 2005Alù, Bilotti, Engheta, Vegni, ICEAA’05, Turin, Italy, September 2005Alù, Bilotti, Engheta, Vegni, ICECom’05, Dubrovnik, Croatia, October 2005