modelado de metamateriales para aplicaciones en...

ModeladoModelado de de MetamaterialesMetamateriales paraparaAplicacionesAplicaciones en en AntenasAntenas

Raj MittraElectromagnetic Communication Laboratory

Penn State UniversityE-mail: rajmittra@ieee.org

TITLES, TITLESTITLES, TITLES——POSSIBLE POSSIBLE CHOICESCHOICES

META 101ALL YOU WANTED TO KNOW ABOUT

METAMATERIALS BUT WERE AFRAID TO ASKWHAT’S NEW ABOUT METAMATERIALSMETAMATERIALS—THE HOLY GRAIL!METAMATERIAL MODELING FOR ANTENNAS

FINALLY, WE SETTLE ON:

A CASE FOR METAMATERIAL MODELING

CLASSIFICATON OF METAMATERILS

Loughborough Antennas and Propagation Conference – 2006 F. Bilotti – Potential Applications of Matamaterials in Antennas

εRe[ ]

μRe[ ]

DPS∈ℜk

DNG∈ℜk

ENG

k ∈ℑMNG

∈ℑkMNZMNZ

ENZ

ENZ

RegularDielectricsDPS

Taxonomy of Metamaterials

Double Negative (DNG) materials (Periodicity d << λ)

Elements and distances between them are much smaller than a wavelength (Effective medium concepts, simultaneous effective negative permittivity and permeability)

Have several names including left-handed materials, backward-wave materials, Negative Index of Refraction (NIR) materials, etc.

Electromagnetic Band Gap (EBG) materials (Periodicity d ~ λ)

Element Distances are on the order of half a wavelength or more (Periodic medium concepts)

Photonic crystals, Photonic Band Gap materials (PBG), Artificial Magnetic Conductors (AMC), High Impedance Surfaces (HIS)

Electromagnetic Communication Lab

Acknowledgement:

The viewgraphs 5-22 are from Prof. Yang Haoof Queen Mary College, University of London

In a paper published in 2001, Rodger Walser from the University of Texas, Austin, coined the term 'metamaterial' to refer to artificial composites that '...achieve material performance beyond the limitations of conventional composites.' The definition was subsequently expanded by Valerie Browning and Stu Wolf of DARPA (Defense Advanced Research Projects Agency) in the context of the DARPA Metamaterials program that started also in 2001. Their basic definition:– Metamaterials are a new class of ordered composites that

exhibit exceptional properties not readily observed in nature. These properties arise from qualitatively new response functions that are: (1) not observed in the constituent materials and (2) result from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneities.

Periodic Structures in Nature and Daily Life

A bending light under the conservatory roof

Natural Periodic Structures

Bee hive

Crystal structure

Butterfly wings

Artificial DielectricsThe first ever known metamaterials, which mimic natural materials: high contrast lossless dielectrics and absorbers Usually consist of artificially created 'molecules': dielectric or metallic inclusions of certain shape. These 'molecules' can be distributed and oriented either regularly or randomly.The dimensions of the 'molecules' and characteristic distances between neighboring ones is much smaller than wavelength.Can be described in terms of material parameters (permittivity) The first artificial dielectric was invented by W.E. Kock and used in design of low-weight dielectric lenses at microwaves

[1] W. Kock, “Metallic delay lenses”, Bell Syst. Tech. J., vol. 27, pp. 58-82, 1948.

[2] R. Collin, Field Theory of Guided Waves. IEEE Press, Piscataway, NJ, 1990.

Wire Mediumplasma-like frequency dependent permittivity

negative below plasma frequencypositive but less than unity above omega0

2

201)(

ωωωε −=

J. Pendry, A. Holden, W. Steward, and I. Youngs, “Extremely low frequency plasmonsin metallic mesostructures”, Phys. Rev. Lett., vol. 76, no. 25, pp. 4773-4776, 1996.

Permittivity of Artificial Dielectrics

[1] J. Brown, “Artificial dielectrics," Progress in dielectrics, vol. 2, pp. 195-225, 1960.[2] W. Rotman, “Plasma simulations by artificial dielectrics and parallel-plate media," IRE Trans. Ant. Propag., vol. 10, pp. 82-95, 1962.

Artificial Magnetics

Magnetic inclusions: a) split-ring-resonator, b) swiss rollJ. Pendry, A. Holden, D. Robbins, W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena”, IEEE Trans. Microwave Theory Techn., vol. 47, no. 11, pp. 195-225, 1999.

Permeability of Resonant Magnetics

Characteristic sizes giving negative μ–PendryJ et al IEEE Trans MTT472075 1999–a ~ λo/ 2

Left-handed Medium (LHM): Material with Simultaneous

Negative ε and μ

V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Physics Uspekhi, vol. 10, pp. 509-514, 1968.

Right-handed VS Left-handed

Right-handed medium: vectors E, H and k form right triple of vectors

Left-handed medium: vectors E, H and k form left triple of vectors

Backward waves at beginning of 20th century

H. Lamb [1] may have been the first person who shown theexistence of backward waves (the waves which phase moves inthe direction opposite from that of the energy flow) in mechanical systems. Seemingly, the first person who discussed the backwardwaves in electromagnetism was A. Schuster [2]. On pp. 313-318 Schuster gives a speculative discussion of its implications foroptical refraction. H.C. Pocklington in [3] showed that in a specific backward-wave medium, a suddenly activated sourceproduces a wave which group velocity is directed away from thesource, while its velocity moves toward the source.[1] H. Lamb, “On group-velocity”, Proc. London Math. Soc., vol. 1, pp. 473-479, 1904.[2] A. Schuster, An Introduction to the Theory of Optics, Edward Arnold, London, 1904.[3] H. Pocklington, “Growth of a wave-group when the group velocity is negative”, Nature, vol. 71, pp. 607- 608, 1905.

Backward waves in left-handed transmission lines in 50ths

[1] G.D. Malyuzhinets, “A note on the radiation principle”, Zh. Tekh. Fiz., Vol. 21, pp. 940-942, 1951. [2] A. Grbic and G. Eleftheriades, “Periodic analysis of a 2-D negative refractive index transmission line structure,” IEEE Trans. Antennas Propagation, vol. 51, no. 10, pp. 2604-2611, 2003.

Positive and Negative Refraction

Positive refraction: from ordinary dielectric to ordinary dielectric

Negative refraction: from ordinary dielectric to left-handed medium

Negative Refraction in 40s

Academician L.I. Mandelshtam

(1879-1944)

Imaging by Pendry’s Perfect Lens

far field

near field

Photonic (electromagnetic) CrystalsPeriodical structures with lattice periods comparable to wavelengthsBand gaps: frequency bands where the material does not support propagating wavesSpatial and frequency dispersion: material parameters depend on the wave vector as well as on the frequencyStrong localization of photons and inhibited spontaneous emission due to photonic bandgaps

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics andelectronics,” Phys. Rev. Lett., vol. 58, no. 20, pp. 2059–2062, 1987.[2] S. John, “Strong localization of photons in certain disordered dielectric superlattices,”Phys. Rev. Lett., vol. 58, no. 23, pp. 2486–2489, 1987.

Example of Photonic Crystal with Complete Bandgap

E. Yablonovitch, T. Gmitter, and K. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett., vol. 67, no. 17, pp. 2295–2298, 1991.

QUESTION, QUESTIONQUESTION, QUESTION

Q. SO WHAT EXOTIC THINGS WOULD YOU DO WITH METAMATERIALS, IF YOU HAD THEM?

Inductive Coupling: Inductive Coupling: the author, the author, AmalAmal GraafstraGraafstra, , and his girlfriend, and his girlfriend, Jennifer Jennifer TomblinTomblin, , have matching RFID have matching RFID implants.implants.

BAN & MonitoringBAN & Monitoring

hearing

implant

Blood pressure

Vision

EEG

NE

TWO

RK

Heartmonitoring

Glucose

HandsetHandset evolutionevolutionSizeWeightPrice

FunctionalityDesign

1990 2000Antennas:

• Size reduction: effect on polarisation, bandwidth, efficiency and manufacturing tolerances

• Reduced ground plane: effect on matching, bandwidth, patterns and user interaction

• Price reduction: low cost elements

Antennas for mobile terminalsAntennas for mobile terminals

Customised antennas forspecific applications

Internal mobile phoneantennas

Antennas forPCMCIA cards

AAppplicaplicattionsions• Mobile phones

• GSM modules for customised applications

• PCMCIA

• Special terminals- Emergency phones- Code bars readers- Credit cards terminals…

• Mobile phones

• GSM modules for customised applications

• PCMCIA

• Special terminals- Emergency phones- Code bars readers- Credit cards terminals…

Effect of the componentsEffect of the components• Limited available volume

• Circuits and components

• Antenna: only component with physical limitations for miniaturisation!

• Limited available volume

• Circuits and components

• Antenna: only component with physical limitations for miniaturisation!

iPoDsiPoDs and Implants and Implants Future of Future of body centricbody centric communicationscommunications

RFID (Radio Frequency Identification ) RFID (Radio Frequency Identification ) SystemSystem

* Technology for automatic identification of objects

* Application : logistics,security system,animal tracking transportation and manufcacturing process control

Why are Metamaterials interesting?They require combining expertise in the fields of electrical engineering and materials science.Artificial Dielectrics and their Applications:– Explore Metamaterials and – Investigate their viability in enhancing antenna

performance.Antennas and Metamaterials:– Size Reduction– Other Improvements, e.g., bandwidth, directivity

and pattern shape.– They can make objects dissapear (cloaking)*Fine print—That’s the promise anyway!!

HOW DID WE GET STARTED ON THEDNG STUFF? WHAT WOULD THEY DO FOR US ONCE WE HAVE THEM?

V.G.Veselago, SOV. Phys, 10, 5091968

Engineered media that have a negativeindex of refraction ( negative permittivity andPermeability)

Perfect reconstruction, High Transverse Wave vectors Imaginary Longitudinal component Evanescent Fields

The ‘Perfect Lens’

LET’S BEGIN WITH A LITTLE HISTORY

• Metamaterials are artificial materials that

exhibit electromagnetic responses generally

not found in nature.

• Engineered media that have a negative index

of refraction ( negative permittivity and

permeability )

• Predicted in 1968 by V.G.Veselago

• E,H and K form a left-handed system of

vectors Composite Metamaterial (CMM)

D.R.Smith and S.Schultz, UCSD

V.G.Veselago, SOV. Phys, 10, 509,1968

Realization of Metamaterials

Realization of Conventional Metamaterial

Negative ε• Thin metallic wires are arranged periodically• Effective permittivity takes negative values below plasma frequency

Negative μ• An array of split-ring resonators (SRRs) are arranged periodically

( Koray Aydin, Bilkent University, Turkey Sep 6 , 2004 )

Realization (contd.)

Extraction of constitutive effective Extraction of constitutive effective parameters from Sparameters from S--parameters for parameters for

normalnormal incidenceincidence

Effective ParametersEffective Parameters

Inversion Method

• Can be applied to both simple and complex structures

• Can use both numerical and experimental data

• S-parameters for metamaterials are more complex

• Ambiguities in the inversion formulas

Equations used in the inversion approachEquations used in the inversion approach

Compute Z:

Compute n:

Compute effective μand ε:

221

211

221

211

)1()1(

SSSSZ

−−−+

±=

Conditions used: Z’ > 0 and

<= 1-

})]'[ln(]2)]"{[[ln(100 dinkdink

oeime

dkn −− −+−= π

210 XiXe dink −±=−Y =

( 2 different roots )

( 2 different roots )

( )221

211

21

11 SSS

X +−=2

(branches with different m)

n”<=0, ε”<= 0 and μ” <= 0

Iterative approach to pick n such that n is continuous

zneff /=ε nzeff =μ and

Example 1: 2Example 1: 2--D infinite array of dipoles for normal incidenceD infinite array of dipoles for normal incidence

X

Y

Z

Plane wave source EY

Plane of reflection

Plane of transmission

Unit cellBC used

X and Y: PBCZ: PML

Ei, Et and Er are the contributions from the zerothFloquet mode measured on the corresponding planes.

(1) By enforcing ε” <0 and μ” <0, only m=0 can be solution.

(2) By enforcing n”<0, the correct root can be determined.

(1)(1)

(2)

Solutions for all branches ( m=0, Solutions for all branches ( m=0, --1 and +1) and 2 roots1 and +1) and 2 roots

Determine the solutionby using ref. (1):

Extracted parameters: 2Extracted parameters: 2--D infinite array of dipolesD infinite array of dipoles

X

Y

Z

Plane wave source EY

Plane of reflection

Plane of transmission

Unit cellBC usedX and Y: PBC

Z: PML

Example 2: 2Example 2: 2--D infinite array of splitD infinite array of split--rings for normal incidencerings for normal incidence

Extracted parameters: 2Extracted parameters: 2--D infinite array of splitD infinite array of split--ringsrings

Note: The shaded area represents the non-physical region, where ε” or μ” > 0. In this region, we choose the branch that best connect n just before and after this band.

X

Z

Y

Plane wave source EY

Plane of reflection

Plane of transmission

Unit cellBC used

X and Y: PBCZ: PML

Example 3: 2Example 3: 2--D infinite array of splitD infinite array of split--rings + dipoles for normal incidencerings + dipoles for normal incidence

Extracted parameters: 2Extracted parameters: 2--D infinite array of splitD infinite array of split--rings+dipolesrings+dipoles (1(1--layer)layer)

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

22--D Infinite array of splitD Infinite array of split--rings + dipoles ( 2rings + dipoles ( 2--layer )layer )

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

Extracted parameters: 2Extracted parameters: 2--D infinite array of splitD infinite array of split--rings+dipolesrings+dipoles (2(2--layer)layer)

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

22--D Infinite array of splitD Infinite array of split--rings + dipoles ( 3rings + dipoles ( 3--layer )layer )

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

Extracted parameters: 2Extracted parameters: 2--D infinite array of splitD infinite array of split--rings+dipolesrings+dipoles (3(3--layer)layer)

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

22--D Infinite array of splitD Infinite array of split--rings + dipoles ( 4rings + dipoles ( 4--layer )layer )

Extracted parameters: 2Extracted parameters: 2--D infinite array of splitD infinite array of split--rings+dipolesrings+dipoles (4(4--layer)layer)

Note: The shaded area represents the non-physical region, where ε” or μ” > 0.

Comparison of effective parameters for 1 to 4Comparison of effective parameters for 1 to 4--layer splitlayer split--ring + dipolering + dipole

Note: The effective parameters for 1-4 layers are almost the same, except that more resonant peaks can be seen for more layers.

Refraction in DNG Prisms

DNG DPS

Metamaterial Design using Metamaterial Design using SRRsSRRs and Dipolesand Dipoles

Front view Top view

Top view of a metamaterial prism

L1 L2

g

d

w

z

x

t

y

x

�w

y

x

LeLe--Wei Li, Wei Li, HaiHai--Ying Yao, and Wei Ying Yao, and Wei XuXuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQunQun WuWuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China

IWAT’05, March 7, 2005, Singapore

Simulation ResultsSimulation Results

Distribution of electric field component Ez(r,t) in rectangular linear around a metamaterial prism at f=16.21 GHz

LeLe--Wei Li, Wei Li, HaiHai--Ying Yao, and Wei Ying Yao, and Wei XuXuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQunQun WuWuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China

IWAT’05, March 7, 2005, Singapore

Simulation ResultsSimulation Results

Electric field component Ez(r,t) distribution due to a metamaterial prism

LeLe--Wei Li, Wei Li, HaiHai--Ying Yao, and Wei Ying Yao, and Wei XuXuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQunQun WuWuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China

IWAT’05, March 7, 2005, Singapore

Scattering PatternScattering Pattern

Distribution of electric field component Ez(r,t) in polar plot due to a metamaterial prism at f=16.21 GHz

LeLe--Wei Li, Wei Li, HaiHai--Ying Yao, and Wei Ying Yao, and Wei XuXuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQunQun WuWuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China

IWAT’05, March 7, 2005, Singapore

Negative Refraction in a Slab

Plane wave

θ ??DNGDNG

SLABSLAB

Comprising Comprising of Periodicof Periodic

Structures Structures

EBG Array Settings: Oblique incidence (EBG Array Settings: Oblique incidence (TMzTMz))

Array settings:Ele. Separation: 2.25 mm x 5 mm x 4 mEle. Separation in λ: 0.1125 x 0.25 x 0.20Total number: 38 x 17 x 6 = 3876Total number falls within beam width = 34 ( X: 10, Y

85.5 mm = 4.3 λ85 mm = 4.3 λ

24 mm = 1.2 λ

22 mm = 1.1 λ

FDTD Computational domainPhsyical size: 85.5 mm x 85 mm x 67 mm

Cell number: 680 x 684 x 536 = 2.5 x 108 cells

λ = wavelength at 15.0 GHz

Guassian beam

θ = 30o

Vertical Field Distribution Vertical Field Distribution at 14.4 GHzat 14.4 GHz

Free space Dielectric Slab EBG Array

P1P2

P4Array ( 6 layers )

P4: YZ Plane

Free space Dielectric Slab EBG Array

P4: Transmission region

Transverse Field distribution P4 and P5 at 15.0 GHz

Free space Dielectric slab EBG Array

P5: ~1 wavelength behind the array

P4: ~2/3 wavelength behind the array

Transverse Field distribution P2 and P3 at 16.0 GHz

Free space Dielectric slab EBG Array

P3: ~1/3 wavelength behind the array

P2: Right behind the slab/array

Transverse Field distribution P4 and P5 at 17.5 GHz

Free space Dielectric slabEBG Array

P5: ~1 wavelength behind the array

P4: ~2/3 wavelength behind the array

Vertical Field Distribution Vertical Field Distribution at 15.6 GHzat 15.6 GHz P1

P2

P4Array ( 6 layers )

Free space Dielectric Slab EBG Array

P4: YZ Plane

Free space Dielectric Slab EBG Array

P4: Transmission region

Ring DimensionsSide length – 3mm Thickness - 0.25mmGap - 0.5mm

Waveguide DimensionsX-band waveguideWidth – 19.25mmHeight – 10.625mm

Terminated by PML walls to avoid reflections

The SRR was placed vertically with the gap-bearing side parallel to the direction of propagation.

Voltage Measurementpoints

y

z

x

RingField Planes

SINGLE & MULTIPLE LAYER SRR

Before theresonance

After theresonance

Amplitude

Amplitude

Phase

Phase

Field Distributions Confirm the Resonant Permeability Behavior

Ring DimensionsSide length – 3mm Thickness - 0.25mmGap - 0.5mm

Waveguide DimensionsX-band waveguideWidth – 19.25mmHeight – 10.625mm

Terminated by PML walls to avoid reflections

The SRR was placed vertically with the gap-bearing side perpendicular to the direction of propagation.

Voltage Measurementpoints

y

z

x

RingField Planes

SRR Design : Perpendicular Orientation

• Comparison of reflection and transmission coefficients obtained from measurements and simulations (Dimensions Scaled)

• Comparison of real parts of effective permittivity and effective permeability

S-parameters and Effective Parameters: Parallel Orientation

Comparison of reflection and transmission coefficients obtained from measurements and simulations (Dimensions scaled)

Comparison of real parts of effective permittivity and effective permeability

Perpendicular Orientation - Results

• Comparison of real parts of effective permittivity and effective permeability

• Comparison of reflection coefficients obtained from simulations for the three cases

Composite Unit Cell - Results

Distance d of the points from the source

Increase in phase ( phase advance) for points away from the source in the frequency range where the effective parameters are simultaneously negative.

Phase of the field measured at three different points along the waveguide inside the DNG unit cell

Sourced

y

z

Confirmation of Backward Wave Propagation

Verification

x

y

Pass Band below cutoff

Waveguide BC-SRRS

Coaxial feed

37600

8.4 GHz 8.6 GHz

62000

76300

8.8 GHz

74000

8.7 GHz

79400

9.1 GHz

68700

8.9 GHz

Ez in XY-plane

Hz in YZ-plane

x

y

• SRRs are coupled as seen from the magnitude and phase distributions of the E and H fields

• The axial magnetic moment does not exist and so cannot cause negative permeability.

• Wave tunneling might be due to a resonance wave propagation along the SRR chain

z

y8.7Ghz

Simulation and Field Analysis

Waveguide DimensionsWidth – 10.66mmHeight – 4.2mmCut off – 14.07GHz

Ring DimensionsSide length – 1.7mm Thickness - 0.25mmGap - 0.48mm

Cut Off

Pass Band below Cutoff

Regular Half-wavelength Resonance of the SRR ( Negative Permeability)

z

y

Magnitude Phase

Magnitude and Phase of Ex nearthe SRR

Transmission Coefficient

K – Band Wave Guide

Ex (13.65GHz) Ex(13.95GHz)

Hx(13.65GHz) Hx(13.95Ghz)

• Components of E and H fields normal to theSRR plane

z

y

Half wavelength Resonance Full wavelength Resonance

• Magnitude of the fieldsis more than 3 times higher than that at other frequencies

• Separation ~ 0.35Ghzand the fact that the Half-wavelengthresonance occurs at twofrequencies indicates thata slow wave modepropagates through theSRR waveguide below cutoff

9.97e+005 4.89e+005

1.03e+003 3.07e+002

Field Distributions

Electromagnetic Communication Lab

Next 3 Slides are courtesy of Prof. HosseinMossallei of Northeastern University

1 layer and 3 Layer Periodic Array of Spheres1 layer and 3 Layer Periodic Array of Spheres

h=2.5 cm

3-Layer with h=2.5 and d=1.5 cmx

yz

d

Diameter = 1 cmεr=40

Tripod FSS Tripod FSS –– Layered StructuresLayered Structures

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0frequency (GHz)

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

% o

f Pow

er R

eflec

ted

normal incidenceTE at 30

o

TM at 30o

Ty

L1

L2

Tz

mmTmmTmmLmmLangleflare

z

y

44.240.148.040.0

240

2

1

=

===

o

d=0.02 mm

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0frequency (GHz)

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

% o

f Pow

er R

eflec

ted

normal incidenceTE at 30

o

TM at 30o

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0frequency (GHz)

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

% o

f Pow

er R

efle

cted

normal incidenceTE at 30

o

TM at 30o

D=1 mm

1-Layer

2-Layer2 of 2-Layer

Sphere Dielectric and Coupling PerformanceSphere Dielectric and Coupling Performance

Coupling and Resonance Behavior

εr=20

x

yz εr=10

260

nm520 nm

160 nm

εr

H-Field in y-x plane

Mag

netic

Dip

ole

Elec

tric

Dip

ole

Normal Mode

Elec

tric

Dip

ole

Mag

netic

Dip

ole

Reverse Mode

TIME TO RAISE A FEW ??TIME TO RAISE A FEW ??

THE PERFECT LENS?

Refraction in DNG Prisms

DNG DPS

Equivalent Medium ApproachIt is a Common practice to replace an artificial dielectric with its equivalent ε and μperform an analysis of composite structures (antenna + medium) using the equivalent medium.

But this can lead to significant errors and wrong conclusions

Single layer

R T...

Multiple layers

Exit angle?

.

.

.

.

.

.

.

.

.

Floquetharmonics

Negative Retraction in a Slab

Plane wave

θ ??DNGDNG

SLABSLAB

Imaging with DNG Lens

Field distribution along z in the RHS of Lens

or ?

0 ZIsource

DNG LENS

Field Distribution

0 ZI 0 7 Z

Field Distribution

Question?

Images?

Can we resolve two longitudinally-spaced sources with a DNG lens?

DNGDNG

LensLens

NEXT ?NEXT ?

SMALL ANTENNAS WITH VERY HIGH DIRECTIVITIES?

DPS

ENG

Performance Enhancement of Small Antennas

Small Antenna

(length << λ)

Thin shell,

Radius << λ

Big Q?? Can we violate

Chu limit?

Artificial Magneto-Dielectric Substrates

Performance Enhancement of Wire and Patch Antennas Using Artificial MaterialsPekka Ikonen(1), Stanislav Maslovski(1), Kostantin Rozanov(2), Murat Ermutlu(3), and Sergei Tretyakov(1)(1)Radio Laboratory / SMARAD Center of Excellence Helsinki University of Technology(2)Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow, Russia(3)Nokia Networks, Finland

Clockwise from top right:– A single unit-cell design.– A two unit-cell design.– Fabricated single unit-cell BW

TL.

1.2mm

Multilayered Loop Inductors

Parallel-Plate Capacitors

Transmission Line Approach

Based on Transmission Line (TL) circuit models:

RH-TL– Regular microstrip line– Lowpass in nature

LH-TL– Inductance/Capacitance interchanged– Series/Parallel arrangements inverted– Highpass in nature

Loading a MPA

Microstrip Patch Antenna (MPA):

– Normally λ/2 a side.– TL structure loads sides.– Size reductions.

Antennas tested:– 7.55 GHz λ/4 (69% area

savings).– 485 MHz λ/6 (87% area

savings).– 348 MHz λ/8 (93% area

savings).

Patch

via to ground plane

Loading Strip

Width=2.25 ”Length=0.125”

@ 4303.5" 0.4 f MHzλ ==

Height = 0.01875” = 18.75 mils

via = 0.04375” = 43.75 mils

Y

X

Ground PlaneY

X

Z9=rε

Size-Reduction of MPA:

(a)(a) (b)(b)

(c)(c)

Ez field distribution between patch and ground @ f=430 MHz(a)(a)

Ex field distribution between patch and ground @ f=430 MHz

Ey field distribution between patch and ground @ f=430 MHz

(b)(b)

(c)(c)

via

loading stripProbe feed

YX

2 22

1 1

2

1 tan( )

2 ( )

r yy

r y

r

kY k h

k

Y

εε

γ ε

=

=

8.232 ≈rε

L

b

x

y

z

PMC

PMC

PMC

PMCPMC

PMC1rε

3rε

2rε

Partially filled Cavity

d

a’

a

h

(1)

(3)

(2)

Simulation results based on theoretically calculated effective dielectric constant:

Directivity Enhancement of a Class of Patch

Antennas using Metamaterial Superstrates

Directivity Enhancement of a Class of Patch Directivity Enhancement of a Class of Patch

Antennas using Metamaterial Antennas using Metamaterial SuperstratesSuperstrates

Motivation

◈ In the past, array antennas had been widely used for applications requiring high directive antennas.

◈ However, array antennas require a complex feed network, and it makes difficulty in fabrication of array antennas and cause losses.

◈ A simple way to obtain high directivity with one or a few radiators is necessary. Metamaterial superstrates

BeamArray and complex feed network Superstrate

Patch

High Directivity

Candidates for Metamaterial Superstrates

◈ Periodic structures such as FSSs and EBGs act as spatial angular filters with transmission and reflection pass and stop bands, and can be used to enhance directivity of a class of antennas being placed above them.

Woodpile EBGStacked

dielectric layerDielectric rod

EBG FSS

◈ Two approaches for the analysis of antennas with metamaterial superstrates1. Fabry-Perot Cavity (FPC) Antenna Partially Reflecting Surface (PRS)

2. Leaky Wave Antenna

11.76cm

9.66cm

1.00 cm

εr=2.2, t=20mil

L1=1.33cm, dl=1.0cm

Fabrication and Measurement Results of the 7×28 Strip Dipole FSS Composite

Measured Maximum Directivity: 19.5dB

FSS superstrate printed on a commercial available dielectric material

11.5 12 12.5 13 13.5Frequency(GHz)

10

12

14

16

18

20

22

Gai

n(dB

)

simulationmeasurement

-80 -60 -40 -20 0 20 40 60 80angle(degree)

-40

-35

-30

-25

-20

-15

-10

-5

0

pow

er(d

B)

E-plane(12.5GHz)H-plane(12.5GHz)E-plane(simul)H-plane(simul)

20×10 Thin FSS Superstrate

Fabrication and Measurement Results of the 20×10 Thin FSS Composite (1)

εr = 2.2,

t = 2.0828 mm

< top view > < back view >

< side view >

The design parameter valuesFSS array size: 10 × 20a = 12, b = 6dl_l = 8.7, dl_u = 11.2dw_l =1, dw_u = 4h = 16, Lg=2.0828

h = 13

8.41 and 11.67 GHz

Two FSS layer are etched in same substrate whose thickness is only 2.0828 mm

Must we use DNG superstrate and other metamaterials and look for focusing effects for directivity enhancement?

DNG

Ground planeMicrostrip patch

DNG

Ground plane

Ground plane Microstrip patch

Metamaterials with frozen modes and other Special Characteristics

Q. Can we achieve higher directivity than is possible for a uniformly illuminated aperture of the same size as that of the antenna + superstrate composite?

Ground planeMicrostrip patch

FSS

TE mode E-field when θ=1, φ=90

TM mode E-field when θ=1, φ=0

S11 ~ -1.4 dB at 13 GHz

Phase ~ 360 deg at 13 GHz

S21 ~ -6 dB at 13 GHz Phase ~ -90 deg at 13 GHz

Can’t find any resonant mode at 13 GHz but reflection phase

Dual-layer simulation

Single-layer (red line) dipole compare to dual-layer (blue line)

L = 1.2

L = 1.3L = 1.4

Geometry of a fabricated dipole strip FSS composite and its unit cell.

Comparison of the simulated and measurement results: (a) directivity and (b) radiation pattern

EBG SUBSTRATESEBG SUBSTRATES

DO THEY ENHANCE ANTENNA PERFORMANCE?

REF: EuCAP’06 PAPER BY LIVERPOOL U

CONVENTIONAL MSACONVENTIONAL MSA

SLOT ANENNA ABOVE HISSLOT ANENNA ABOVE HIS

RETURN LOSS CHARACTERISTICS OF RETURN LOSS CHARACTERISTICS OF ANTENNA ABOVE HIS ANTENNA ABOVE HIS

ALTERNATIVE TO VESELAGO ALTERNATIVE TO VESELAGO LENS?LENS?

Source plane

Image plane

Imaging Device

Distribution of electric fieldDistribution of electric field

a) near the front interface b) near the back interface

Near field scan resultsNear field scan results

Distribution of electrical field at the source and image planes.Confirmation of λ/15 resolution and 18% bandwidth reported!

P.A. Belov, Y. Hao, S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens”, Phys. Rev. B, vol. 73, 033108, 2006.

Intensity distributionIntensity distribution

a) near the front interface b) near the back interfaceResolution is λ/15!

P.A. Belov, Y. Hao, S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens”, Phys. Rev. B, vol. 73, 033108, 2006.

AMC Ground DesignsAMC Ground Designs

Response of AMC GroundResponse of AMC Ground

AMC GroundAMC Ground

Antenna over AMC GroundAntenna over AMC Ground

SUMMARY QSUMMARY Q’’SSQ1.DNG’S ARE INTERESING CONCEPTUALLY, BUT IS THIS LENS BUSINESS REALY PRACTICAL? IT DOESN’T ACTUALLY WORK LIKE A CONVNTIONAL OPTICAL LENS; THE MATERIAL IS NOT ISOTROPIC; AND, LOSSES AND BANDWIDTH CAN BE PROBLEMS.

Q2.OK, SO EVEN IF WE PUT THE LENS BUSINESS ASIDE, HOW ABOUT THEIR USE AS SUBSTRATES, SUPERSTRATES ABD SHELL COVERS FOR SMALL ANTENNAS? SHOULD WE ONLY LOOK FOR DNG’S FOR THESE APPLICATIONS?

MORE QUESTIONSMORE QUESTIONS

Q3.CAN WE GET MORE DIRECIVITY FROM A SMALL ANTENNA COMPOSITE (ANTENNA + SUPERSTRATE) BY USING METAMAERIALS, THAN IS POSSIBLE TO REALIZE FROM THE APERTURE SIZE OF THE COMPOSITE?Q4.CAN WE GET GOOD BACKLOBE SUPPRESSION FROM A GROUNDPLNE, WHOSE SIZE IS COMPARABLE TO THAT OF THE ANTENNA (∼λ/2),BY USING METAMATERIALS?SHOULD ALL MANNER OF IMAGING SYSEMS BE LABELED AS LENSES?

A FEW MOREA FEW MOREQ5.DO THE EFFECTIVE PARAMETERS REMAINUNCHANGED WHEN WE VARY THE THCKNESS OF THE METAMATERIAL SLAB, OR CHANGE THE INCIDENT ANGLE?Q6.FOR SMALL ANTENNA/SUPESTRATE COMPOSITES, SHOULD WE BE LOOKING AT THE SIZE OF THE ANTENNA OR THA OF THE COMPOSITE WHEN COMPARING DIRECTIVITIES?Q7.IS THERE A SPECIFIC ADVANTAGE TO BE GAINED IN USING EBG’S WITH SMALL PERIODICIIES WHOSE CELL SIZE IS MUCH SMALLER THAN A WAVELENGTH?

BIG QUESTION(S)??BIG QUESTION(S)??

SO, WHERE DO WE GO FROM HERE?HOW DO WE REALIZE LOW LOSS, ISOTROPIC, ESSENTIALLY NON-DISPERSIVE METAMATERIALS THAT ARE LOW COST AND CAN BE INTEGRATED WITH SMALL ANTENNAS TO IMPROVE THEIR FUNCTIONALIY AND PEFORMANCE?

Resonator Array structures for Resonator Array structures for metamaterials?metamaterials?

Higher Frequencies pushing into the THz rangeSpherical resonators instead of cylindrical resonatorsFree space optical testing.

1 mm diameter silica spheres. Fabricated by Amanda Baker

W0RTH A LOOK?W0RTH A LOOK?COURTESY OF ELENA SEMOUCHKINA (PENN STATE)COURTESY OF ELENA SEMOUCHKINA (PENN STATE)

A WORD ABOUT SIMULATIONA WORD ABOUT SIMULATION

Antenna-metamaterial composites requireheavy duty computing power to model

(Note: We routinely simulate upward of billion-unknown-category problems)

1 mm diameter silica spheres. Fabricated by Amanda Baker

Resonator Array structures for metamaterials?

• Higher Frequencies pushing into the THz range

• Spherical resonators instead of cylindrical resonators

• Free space optical testing.