A New Paradigm in Electromagnetics - University of … New Paradigm in Electromagnetics Prof. Fan Yang Department of Electrical Engineering, University of Mississippi [email protected]

The University of Mississippi Department of Electrical EngineeringC

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http://www.ee.olemiss.edu

Metamaterial Surfaces: A New Paradigm in Electromagnetics

Prof. Fan YangDepartment of Electrical Engineering, University of Mississippi

[email protected]


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OUTLINEOverview of metamaterial surfaces

Characterizations and designs

Various EM applications

A simple and efficient FDTD/PBC algorithm

Basic idea: constant kx method

Numerical examples

A low profile surface wave antenna

Antenna concept

Designs and verifications

Conclusions


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Meta-Materials

Meta: a prefix means “beyond”Meta-materials: engineered materials with superior electromagnetic properties

Double negative (DNG) materials

Left handed materials

Magneto-materials

Electromagnetic band-gap (EBG) structures

Artificial magnetic conductor

Volumetric structure (3D) and Planar structure (2D)


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Meta-material Surfaces

Meta-material surfaces such as frequency selective surfaces (FSS), soft and hard surfaces, and electromagnetic band gap structures have unique EM properties due to the inherent periodicity.

Electromagnetic band gap structures have been presented recently and extensive research has been conducted in this topic.

It exhibits a stop band for surface wavesand an in-phase reflection coefficient.

The meta-material surfaces have been widely used in various EM applications to improve the performance of RF devices.Mushroom-like EBG surface

Top view

Cross view

C

L


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Introduction of EBG Ground Plane

EBG ground plane:

PEC ground

Dielectric substrate

Periodic patches

Connecting vias

y

x Top View

x

z

Cross View

Geometry of an EBG ground plane

W=0.12 λ

g=0.02 λ

h=0.04 λ

εr=2.20

EBG ground planes can be easily fabricated by the PCB (Printed Circuit Board) technique.

They are analyzed using the finite different time domain (FDTD) method.


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Band Gap for Surface Wave Suppression

0.0 4.0 8.0 12.00.0

4.0

8.0

12.0

X (cm)Y

(cm

)

-20.0 0.0 20.0 40.0 60.0

20*log|E| (dB)

40

30

20

0.0 4.0 8.0 12.00.0

4.0

8.0

12.0

X (cm)

Y (

cm)

-20.0 0.0 20.0 40.0 60.0

20*log|E| (dB)

40

30

2010

EBG case PEC case


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In-Phase Reflection for Plane Wave Incidence

PML

PBC

Plane wave incidence

Observational plane

0 5 10 15 20 25−200

−150

−100

−50

0

50

100

150

200

Freq (GHz)

Ref

lect

ion

phas

e (D

egre

e)

FDTDRef.PEC

PMCEBG

Reflection phase results

Observation: The phase of the reflection coefficient of an EBG structure changes from 180˚ to -180˚ with frequency, while it is 180˚for a PEC and 0˚ for a PMC surface. The simulated result agrees well with the data in a reference paper.


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Polarization Dependent EBG Surface Designs

Top view

Cross view

Top view

Cross view

Top view

Cross view

Square patch EBGIndependent of polarization

Top view

Cross view

Offset viasRectangular EBG

Slot loaded EBG


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Rectangular Patch EBG Surface

Remarks:

1. Rectangular patch dimensions: W=0.16λ3GHz, L=0.24λ3GHz.

2. The reflection phase is dependent on the wave polarization.

3. Z polarization: θ=90˚, f=3.07 GHz; θ=-90˚, f=4.09 GHz.

4. Y polarization: θ=90˚, f=2.41 GHz; θ=-90˚, f=2.99 GHz.

Top view

Cross view2 2.5 3 3.5 4 4.5

−200

−150

−100

−50

0

50

100

150

200

Freq (GHz)

Ref

lect

ion

phas

e (D

egre

e)

Z polY pol

y

z


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Slot Loaded Patch EBG Surface

Top view

Cross view

Remarks:

1. Square patch with slots: Ws=0.02λ3GHz, L=0.12λ3GHz, Ps=0.04λ3GHz.

2. The reflection phase is dependent on the wave polarizations.

3. Z polarization: θ =90˚, f=3.07 GHz; θ=-90˚, f=4.08 GHz.

4. Y polarization: θ=90˚, f=2.87 GHz; θ=-90˚, f=3.51 GHz.

y

z

2 2.5 3 3.5 4 4.5−200

−150

−100

−50

0

50

100

150

200

Freq (GHz)

Ref

lect

ion

phas

e (D

egre

e)

No slot Slot, Z polSlot, Y pol


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Square Patch with Offset Vias

2 2.5 3 3.5 4 4.5−200

−150

−100

−50

0

50

100

150

200

Freq (GHz)

Ref

lect

ion

phas

e (D

egre

e)

Via at 1/2 WVia at 3/8 WVia at 1/4 WVia at 0 Top view

Cross view

y

z

Remarks:

1. The vias move along the Y direction: 1/2 W, 3/8 W, 1/4 W, 0.

2. The reflection phase of Y polarized waves changes with vias’position while it remains the same for Z polarized waves.

3. Dual resonance is observed for Y polarized plane wave.


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With or Without Vias ?

Mushroom EBG ground planeWITH VIAS

y

x Top View

x

z

Cross View

y

x Top View

x

z

Cross ViewPatch loaded grounded slab

NO VIAS

W=0.10 λ

g=0.02 λ

h=0.04 λ

εr=2.94

λ=75 mm

r =0.005 λ


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Surface Wave Property

X M0

1

2

3

4

5

6

7

8

9

10

Fre

quen

cy (

GH

z)

Γ Γ

Band Gap

Light line Light line

First mode

Second mode

Wavenumber X M

0

1

2

3

4

5

6

7

8

9

10

Fre

quen

cy (

GH

z)

Γ Γ

No Band Gap

Light line Light line

First mode

Second mode

Wavenumber

No Band GapBand Gap

With vias No viasRemarks:1. The dispersion diagrams of both artificial complex ground planes

have been determined using the spectral FDTD method.2. When the vias in the mushroom structure is removed, the band gap

disappears. For the patch loaded grounded slab, the TM surface wave (the first mode) exists at all frequencies.


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Plane Wave Property

0 2 4 6 8 10 12−200

−150

−100

−50

0

50

100

150

200

Freq. (GHz)

Ref

lect

ion

phas

e (D

egre

e)

With viasNo vias

PML

PBC

Plane wave incidence

Observational plane

Reflection coefficients for normal incidence

Remarks: Reflection phases of both ground planes are almost identical to each other for normal incidence.


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Numerical examples


Antenna concept


Conclusions


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EBG Application in Microstrip Patch Antenna

−150 −100 −50 0 50 100 150−30

−25

−20

−15

−10

−5

0

Angle (Degree)

Pat

tern

(dB

)

EBG

Thick Sub.

Step−Like

Thin Sub.

A patch antennasurrounded by EBG structures E plane patternsRemarks:1. A compact microstrip antenna on a high dielectric constant substrate

usually suffers from severe surface waves2. The EBG structure can effectively suppress the surface waves,

resulting in a high antenna gain and low back radiation.


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EBG Application in Microstrip Patch Array

5.2 5.4 5.6 5.8 6 6.2 6.4−30

−25

−20

−15

−10

−5

0

Remarks: 1. Mutual coupling in phased antenna arrays needs to be reduced in order

to enhance the performance of the radar systems.2. When the EBG structure is inserted between antennas, the mutual

coupling is reduced from -16.8 dB to -24.6 dB.

Freq (GHz)

S (

dB)

No EBG With EBG

S11

S12


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Low Profile High Efficiency Antenna Designs

Options Efficiency Low Profile Antennas

PECJ

PECJ

PMCJ

Monopole

N/A

Microstrip

New frontier

M

PEC

Goal: Goal: To develop low profile and high efficiency antennas on PMC-like ground planes.


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Wire Antennas On Meta-Material Surfaces

Wire antennas, such as dipole, loop, curl, ...

Full wave numerical analysis tools, such as FDTD, MoM, …

Innovative antenna designs with versatile functionality for wireless communications

Artificial complex ground planes, such as EBG, soft/hard surfaces, FSS, ...


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Curl Antennas for Wireless Communication

Curl antenna features: Curl antenna features:

1. Simple structure.

2. Circularly polarized pattern.

Curl Antenna

PEC ground plane

Curl antennas on a PEC ground planeCurl antennas on a PEC ground plane::

When a curl antenna is positioned above a PEC ground plane, a relative large height (0.20 λ) is required to good CP pattern.

Research goal: Research goal: To design a low profile curl antenna with good CP pattern suitable for GPS, WLAN, and other wireless communications.


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Curl on EBG Ground: Experiment Results

52 mm

13 mm

4 5 6 7 8 9 10−20

−15

−10

−5

0

Freq (GHz)

S11

(dB

)

EBGPEC

Remarks:Remarks:1. An EBG ground plane is fabricated on a RT/duroid 5880 (εr=2.20, h=2 mm) substrate. The EBG patch width is 6 mm and gap width is 1 mm.2. The parameters of the curl are: R=5.5 mm, L=5 mm, h=3mm.3. The curl antenna exhibits a good return loss with the low profile configuration.


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Dipole Antenna on PDEBG: Circular Polarization

BASIC IDEASBASIC IDEAS

Low Profile:

PEC:

PMC:

Artificial ground:

0→kd

0, === Eyx

rπθθ

LINEAR polarization.

2,

2πθπθ −== yx

CIRCULAR polarization!

Dipole

PDEBG surface

Dipole

Ground plane

x

y

)ˆˆ(21

)ˆˆ(21

22 yx jkdjjkzjkdjjkz

jkzjkz

eyex

eyexE

θθ +−−+−−

−−

⋅+⋅+

⋅+⋅=r

jkzjkzyx ezexE −− ⋅+⋅=== ˆˆ,0

rθθ

)]ˆˆ()ˆˆ[(21 yxjyxeE jkz −⋅++= −

r

Direct

Reflected


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Dipole on EBG Ground: Experiment Results (1)

75 mm

34 mm

Remarks:Remarks:1. An PDEBG ground plane is fabricated on a RT/duroid 6002 (εr=2.94, h=6 mm) substrate. Rectangular EBG patches are used with 13 mm length and 8 mm width. The gap width is 2 mm.2. A dipole (L=34 mm, h=3 mm) is oriented along 45˚ direction.3. The antenna exhibits a good return loss (S11<-10 dB) from 3.25-4.14 GHz.

1 2 3 4 5−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

)


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Dipole on EBG Ground: Experiment Results (2)

1 2 3 4 50

2

4

6

8

10

Freq (GHz)

AR

(dB

)

−50 0 500

2

4

6

8

10

θ (Degree)

AR

(dB

)

xzyz

Axial ratio vs. frequency Axial ratio vs. θ

Remarks:Remarks:1. A good axial ratio of 2 dB is obtained at 3.56 GHz and the bandwidth (AR <3dB) is 5.6%.2. The axial ratio vs. elevation angle is measured at 3.56 GHz and the beamwidth (AR <3dB) is around 30˚.


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Reconfigurable Antennas with Switching Beams (1)

Single bent monopole

Feed x

y

z

1-D beam switch

Feedx

y

z

1 2

12

2-D beam switch

Feedx

y

z

1 2

3

4

1 23 4

Remarks:1. Reconfigurable radiation pattern is challenging for an antenna elementelement .

2. A bent monopole on EBG ground plane radiates a tilted antenna beam.

3. This property is utilized to construct reconfigurable antennas with 1-D or 2-D switching beams.


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Reconfigurable Antennas with Switching Beams (2)

−15 dB

−10 dB

−5 dB

0 dB 30°

−150°

60°

−120°

90°−90°

120°

−60°

150°

−30°

180°

0°

xz planeEBG

Bent monopole

75 mm

30 mm

Remarks:1. A reconfigurable bent monopole antenna on a EBG ground plane is

designed, fabricated, and tested. The antenna height is 0.02 λ.2. The antenna resonates at 4.32 GHz with 10.6% bandwidth (450

MHz, 4.04-4.49 GHz).3. The antenna beam switches between ±29˚ with a gain of 6.5 dB.


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Numerical examples


Antenna concept


Conclusions


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FDTD Analysis of Periodic Structures

Many electromagnetic structures possess a periodicity in one or more directions, such as FSS, EBG, antenna array.

To alleviate the computational burden, one ways is to model only one individual element and use periodic boundary conditions to simulate the effect of periodic replication.


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Fundamental Challenge of PBC

)exp(),,(),,0()exp(),,(),,0(ajkzyaxzyxajkzyaxzyx

x

x

======

HHEE

:domain Frequency

PML

PML

PBC

Periodic structure

Ckkx /sinsin0 θωθ =⋅=

z

)/sin,,(),,,0()/sin,,(),,,0(CatyaxEtzyxECatyaxEtzyxE

θθ

+===+===

:domain Time

x

Fundamental challenge: Data at future time are needed.


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PBC in the kx-frequency Plane

Normal incidence method:1. θ=0, kx=0 no advance time data needed.2. Only calculate normal incident case.

Sine-Cosine method:1. f = constant kx=constant2. Limit: a single frequency per simulation.

Split-field method:1. Calculate oblique incidence2. Auxiliary fields P, Q, new updating scheme3. Limit: fails at large incident angle due to stability condition:

Dxtc θsin1−≤

∆∆


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New PBC in FDTD: Constant Kx Method (1)

Ckx /sinθω=

Fix kxmethod

Split field method

)exp(),,,(),,,0(

ajktzyaxEtzyxE

x===

:domain Time

Basic idea: Calculate along a vertical line in the kx-frequency domain.


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New PBC in FDTD: Constant Kx Method (2)

PML

PML

PBC

Periodic structure

z

Implementation:Implementation:1. In the main computational domain, standard

Yee’s algorithm2. A simple updating equation in the boundary

Advantages of the constant Advantages of the constant kkxx method:method:1. Simple to implement

Use (E, H) instead of (P, Q)Standard Yee’s updating schemeSame PML

2. Efficient in computationSame stability conditiondt independent of incident angle and kx

)exp(),,,(),,,0( ajktzyaxEtzyxE x===

x


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Example: A Dipole FSS (1)

Geometry:Geometry:

1. A dipole frequency selective surface mounted on a dielectric slab.

2. The length of the dipole is 12 mm and the width is 3 mm. The periodicity is 15 mm both along x and y directions.

3. The dielectric slab has a thickness of 6 mm and dielectric constant of 2.2.

4. A TEz plane wave incidents into the structure in the xz plane

Top view

Cross view

x

y

x

z


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Surface wave region

Reflection

Transmission

Reflection


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Surface wave region

6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1R

efle

ctio

n co

effic

ient

Frequency (GHz)

θ= 0°, Split−field

θ= 0°, Fix Kx

θ=15°, Split−field

θ=15°, Fix Kx


θ=30°, Fix Kx


θ=45°, Fix Kx


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Geometry of Periodic PEC Patches

1cm

0.5cm

Top view Side view

300

1cm 0.5cm

TE wave

Parameters:1. FDTD grid size: 0.5 mm=0.01λ6GHz. Each element includes 20×20

cells.2. Kx ranges from 0 to 838 (1/m) (~40 GHz).3. TE incidence case, extract the reflection coefficients for 0º, 30º,

60º, 85º.


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Reflection Coefficient in kx-frequency plane


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Constant kx Method vs. Split Field Method (1)

30º TE caseNormal incidenceRemarks:1. Reflection coefficient vs. angle is extracted from the kx-f plane and

the result is compared with the split field method.2. The results agree with each other for normal and 30º TE incident

cases.


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Constant kx Method vs. Split Field Method (2)

60º TE case 85º TE caseRemarks:1. The results of both method agree with each other for 60º TE

incident case. 2. For 85º TE incident case, the split field does not converge because

of stability reason. Only the result from the constant kx method is plotted.


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Numerical examples


Antenna concept


Conclusions


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Monopole Antenna and Pattern

Monopole antennas Pattern on a finite ground planeRemarks: Remarks: 1. Monopole antennas are widely used in wireless communications.2. A monopole antenna has an omni-directional pattern, a radiation null

along its axis, and is vertically polarized.3. λ/4 monopoles are popular because of efficiency considerations. But it is

NOT a low profile design!


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Low Profile Circular Patch Antenna

2 3 4 5 6−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

)

MeasurementFDTD simulation

Return loss resultsCenter fed circular patch

Remarks:Remarks:1. Low profile design: a center fed circular patch antenna on a thin

substrate.2. The antenna has a similar pattern as a monopole antenna: symmetric

patterns with a null in the broadside direction, polarized along θ direction. 3. Problem: the return loss is poor due to the inherent high impedance.


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Patch Fed Surface Wave Antenna: Geometry

y

xTop View

x

z

Cross View

Antenna structure:

1. Grounded substrate: εr = 2.94, t = 3mm, the radius R of the circular ground plane size is 75 mm.

2. Periodic square patch loading: 8 ×8 square patches, w = 7.5 mm, g = 1.5 mm.

3. Center fed circular patch : h = 1.5 mm, r = 21 mm. A feeding probe is connected to its center.


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Input Impedance and Return Loss

3 3.5 4 4.5 5 5.5 6−100

−50

0

50

100

150

200

250

Freq. (GHz)

Impe

danc

e (Ω

)

Patch

SWA

3 3.5 4 4.5 5 5.5 6−30

−25

−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

)

PatchSWA

Input impedanceRemarks:Remarks:1. A center fed patch antenna has an inherent high impedance, resulting in

a poor return loss .2. Because of efficient launching of surface waves, the SWA has a lower Q

factor and the impedance is around 50 Ω at the resonant frequency. Therefore, a very good return loss is observed.

Return loss


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Near Field Distributions

Patch antennaRemarks:Remarks:1. The near fields distributions are calculated at the resonant frequencies

and normalized to the E field at the feeding port.2. The surface wave antenna shows stronger E fields than the patch

antenna. For example, near the edge of the ground plane, the E field level of the SWA is about 5 dB higher than that of the patch antenna.

Surface wave antennay (cm)

x (c

m)

|E| (dB)

−30−35

−40

−45−45 −40 −40

−45

−10 −5 0 5 10

−10

−8

−6

−4

−2

0

2

4

6

8

10

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

y (cm)

x (c

m)

|E| (dB)

−30

−35

−40−40 −35 −35

−40

−10 −5 0 5 10

−10

−8

−6

−4

−2

0

2

4

6

8

10

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0


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Radiation Patterns

−150 −100 −50 0 50 100 150−50

−40

−30

−20

−10

0

10

θ (Degree)

Dire

ctiv

ity (

dB)

Co−polX−pol

−150 −100 −50 0 50 100 150−30

−25

−20

−15

−10

−5

0

5

10

θ (Degree)

Dire

ctiv

ity (

dB)

φ=0φ=45

E plane pattern H plane pattern

Remarks:Remarks:1. Several important observations from the SWA pattern: broadside null,

symmetric patterns, Eθ polarization, low cross polarization.2. H plane pattern is omni-directional.3. The SWA pattern is similar to an actual monopole antenna.


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Parametric Study: Resonant Frequency Tuning

3 4 5 6 7−30

−25

−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

)

0.36

0.34

0.32

0.30 0.28

0.26

0.24

0.22

0.20 λ

y

xTop View

Radius r

Return loss results

xCross View

zRemarks:Remarks:1. The radius of the circular feeding patch can be used to tune the resonant

frequency of the antenna.2. A good return loss is achieved when the ratio of the patch radius to the

periodicity of the unit cell (0.12 λ) is between 2-3.


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Parametric Study: Beam Direction Control

−150 −100 −50 0 50 100 150−30

−25

−20

−15

−10

−5

0

5

10

θ (Degree)

Dire

ctiv

ity (

dB)

1.0 λ1.5 λ

y

xTop View

Radius R

Radiation patterns

x

z

Cross View

Remarks:Remarks:1. The radius of the ground plane is used to control beam direction.2. When R is increased from 1 λ4GHz to 1.5 λ4GHz , the return loss remains

similar.3. The antenna beam moves to a low elevation angle, from 46º to 52º. In

addition, more ripples occurs because of the interference of waves.


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Parametric Study: Number of Periodic Patches

3 3.5 4 4.5 5 5.5 6−30

−25

−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

) 4×4 patches

2×2 patches

6×6 patches

8×8 patches10×10 patches

y

xTop View

# of patches

Remarks:1. The center two rows have little effect on return loss. 2. The third and fourth rows, which locate near the edge of exciting

disk, have a significant effect on improving the return loss.3. Adding more rows of patches has little effect on the return loss.

x

z

Cross View


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Patch Fed Surface Wave Antenna (SWA): Photo

Middle layer: circular disk Top layer: periodic patches

Remarks:Remarks:1. A circular ground plane with a diameter of 150 mm.2. Middle layer: a circular disk with a center feeding probe.3. Top layer: 8 × 8 periodic square patches.4. RT/Duroid 6002 substrate is used in each layer with εr=2.94 and

thickness of 1.5 mm.


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Patch Fed Surface Wave Antenna (SWA): S11

3 3.5 4 4.5 5 5.5 6−30

−25

−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

)

MeasuredFDTD

3 3.5 4 4.5 5 5.5 6−30

−25

−20

−15

−10

−5

0

Freq. (GHz)

S11

(dB

)

PatchSWA

Patch antenna vs. SWA Measurement vs. FDTD

Remarks:Remarks:1. When the superstrate with periodic patches is stacked on the circular

disk, the resonant frequency shift down (5.12 4.76 GHz) and the return loss of the antenna is significantly improved (-7.9 -28.9 dB).

2. The measured result agrees well with the FDTD simulations.


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Patch Fed Surface Wave Antenna (SWA): Pattern

Measurement vs. FDTDMeasured patterns−150 −100 −50 0 50 100 150

−30

−25

−20

−15

−10

−5

0

5

10

θ (Degree)

Gai

n (d

B)

MeasuredFDTD

−150 −100 −50 0 50 100 150−30

−25

−20

−15

−10

−5

0

5

10

θ (Degree)

Gai

n (d

B)

φ=0, co−polφ=0, X−polφ=45, co−polφ=45, X−pol

Remarks:Remarks:1. The SWA generates a monopole type radiation pattern with a 5.6 dB

gain at θ=47º direction.2. The measured radiation pattern agrees well with the FDTD simulated

result.3. The relatively high cross-polarization in the back is due to the

diffraction of the feeding cable.


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Numerical examples


Antenna concept


Conclusions


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Meta-Material Surface

Properties of meta-material surfaces

Designs of meta-material surfaces

Surface wave Plane wave

Applications of meta-material surfaces

Patch element

and array

Low profile dipole

Surface wave

antennas

Low profile

monopole

Low profile

curl

Circularly polarized

dipole

Parameter analysis PDEBG designs Vias effects


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Various Antennas on Meta-Material Surfaces

Patch element Patch array Bent monopole

Low profile curl CP dipole Surface wave antenna


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A Simple and Efficient FDTD/PBC Algorithm

The idea of a novel periodic boundary condition (PBC) are presented for analysis of periodic structures.

By fixing the horizontal wavenumber, the periodic boundary condition can be easily formulated in the FDTD method.

The new approach is simple to implement and efficient for arbitrary incident angles.

The validity of the approach has been demonstrated through several numerical examples.


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Low Profile Surface Wave Antenna

Novel surface wave antennas excited by a dipole or a circular disk are introduced in this presentation.

It exhibits a monopole type radiation pattern and a good return loss within an attractive low profile configuration.

An antenna prototype was designed, fabricated, and tested. The antenna resonated at 4.76 GHz with a 5.6% bandwidth. A monopole type pattern with a 5.6 dB gain was obtained.

The proposed antenna has a good potential for wireless communications such as vehicle radio systems.


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Acknowledgement

The presenter would like to gratefully thank following colleagues for their collaborations:

• Prof. Yahya Rahmat-Samii, UCLA

• Prof. Ahmed Kishk, The University of Mississippi

• Prof. Atef Elsherbeni, The University of Mississippi

• Prof. Ji Chen, University of Houston

• Prof. Hossein Mosallaei, Northeastern University,

and many other colleagues in UCLA and The University of Mississippi.

Documents

A New Paradigm in Electromagnetics - University of … New Paradigm in Electromagnetics Prof. Fan Yang Department of Electrical Engineering, University of Mississippi [email protected]