Metamaterials - Concept and Applications

March 2006

Dr Vesna Crnojević-Bengin

Faculty of Technical SciencesUniversity of Novi Sad

Overview

Microwave passive circuits

Metamaterials Definition Examples

LH metamaterials Idea Phenomena Realization

LH microstrip structures Resonant and non-resonant structures Applications

Microwave Passive Circuits

Rationale

Problem

Dimensions Performances

End-coupled ms resonator:

Antennas: narrow beam with only one source element? Classical theory: large source

Metamaterials: ENZ substrate

rrf

cL

22

Metamaterials

CharacteristicsDefinitionTypesExamples

Material Characteristics

Rel. permitivity εr

Rel. permeability μr

Rel. index of refraction

Rel. characteristic impedance

rrrn

r

rrZ

Hr, TanD

w

t

mikrostrip

substrat

uzemljenje

10-6 10-4 10-2 100 102 104 106

106

104

102

100

10-2

10-4

10-6

Extreme values of εr and μr

Metamaterials: EVL – Epsilon Very Large ENZ – Epsilon Near Zero MVL – Mu Very Large MNZ – Mu Near Zero MENZ – Mu and Epsilon

Near Zero HIMP – High Impedance LIMP – Low Impedance HIND – High Index LIND – Low Index

εr

μr

Definition

Metamaterials are artificial structures that exhibit extreme values of

effective εr i μr.

Metamaterials Do Not Exist

Artificial materials

Periodic structures

Period much smaller then λ

Homogenization of the structure

Effective values of εr and μr

Examples of Metamaterials

Left-Handed MM

First IdeasDevelopmentRealizationApplications

Other Quadrants?

Single-negative MM: εr<0 or μr<0

εr

μr

evanescentmode(ferrites)

evanescentmode

(plasma,metals@THz)

propagationmode(isotropic dielectrics)

j

eArE r)(

Veselago’s Intuition

Double-negative MM: εr<0 and μr<0 ?

εr

μr

evanescentmode(ferrites)

propagationmode(isotropic dielectrics)

j

eArE r)(

?

evanescentmode

(plasma,metals@THz)

No law of physics prevents the existence of DN MM

Generalized entropy conditions for dispersive media must be satisfied ( )

Conditions of Existence

)( 2f

Veselago’s Conclusions

Propagation constant β is real & negative

Propagation mode exists

Antiparalel group and phase velocities

Backward propagation (Left-hand rule)

Negative index of refraction

242

2

cCLvvCLv

CLvLHLHgp

LHLHg

LHLHp

00, nvv

cn p

p

Synonyms

Double-Negative (DN)

Left-Handed (LH)

Negative Refraction Index (NRI)

(Metamaterials)

Left-Handed Metamaterials

Double-negative MM: εr<0 and μr<0

εr

μr

evanescentmode(ferrites)

propagationmode(isotropic dielectrics)

propagationmode(Left-Handed MM)

evanescentmode

(plasma,metals@THz)

Consequences of LH MM

Phenomena of classical physics are reversed :

Doppler effect

Vavilov-Čerenkov radiation

Snell’s law

Lensing effect

Goss-Henchen’s effect

0

sinsin

sin

sinsin

1

t

iLH

RHt

tLH

tLHiRH

n

n

n

nn

Snell’s Law

!!!

But Alas...

Everything so far was “what ifwhat if””...

Can single- or double-negative materials really be made?

First SN MM – J. B. Pendry

εr<0 - 1996. μr<0 - 1999.

Why is r negative?

Plasmons – phenomena of excitation in metals Resonance of electron gas (plasma) Plasmon produces a dielectric function of

the form:

Typically, fp is in the UV-range

Pendry: fp=8.2GHz

0,12

2

effpp

eff fff

f

Why is μr negative?

E

H

22

2

1m

effff

fF

Experimental Validation

Smith, Shultz, et al. 2000.

LH MS Structures

Resonant and non-resonant structuresApplications

Resonant LH Structures

Split Ring Resonator (SRR)

Very narrow LH-range

Small attenuation

Many applications, papers, patents

Super-compact ultra-wideband (narrowband) band pass filters

Ferran Martin, Univ. Autonoma de Barcelona

Wide Stopband

Garcia-Garcia et al, IEEE Trans. MTT, juni 2005.

Complementary SRR

Application of Babinet principle - 2004. CSRR gives ε‹0

LH BPF – CSRR / Gap

November 2004. Gaps contribute to μ‹0 Low attenuation in the right stopband

BPF – CSRR / Stub

August 2005. 90% BW Not LH!!!

Three “Elements”

CSRR/Gap – steep left side CSRR/Stub – steep right side 2% BW

Multiple SRRs and Spirals

Crnojević-Bengin et al, 2006.

Fractal SRRs

21 2

21 2

Crnojević-Bengin et al, 2006.

Non-Resonant LH Structures

June 2002. Eleftheriades Caloz & Itoh Oliner

Transmission Line (TL) approach

Novel characteristics: Wide LH-range

Decreased losses

Conventional (RH) TL

MicrostripH

r, TanD

w

t

mikrostrip

substrat

uzemljenje

LH TL

Dual structure

L

L

LjY

CjZ

1

1

A Very Simple Proof

Analogy between solutions of the Maxwell’s equations for homogenous media and waves propagating on an LH TL

Materials: LH TL:

01

)(1

2

CC

jY

jZ

LjY

CjZ

1

1

=

!!!01

)(1

2

LL

Microstrip Implementation

Unit cell

Dispersion Diagrams

RH TL LH TL

Is This Structure Purely LH?

Unit cell

CRLH TL

Real case – RH contribution always exists

LH TL Characteristics

Wide LH-range

Caloz, Itoh, IEEE AP-S i USNC/URSI Meeting, juni 2002.

2-D LH Metamaterials

Applications of LH MM

Guided wave applications Filters

Radiated wave applications Antennas

Refracted wave applications Lenses

Guided Wave Applications

Dual-band and enhanced-bandwidth components Couplers, phase shifters, power dividers,

mixers)

Arbitrary coupling-level impedance/phase couplers

Multilayer super-compact structures

Zeroth-order resonators with constant field distribution

Lai, Caloz, Itoh, IEEE Microwave Magazin, sept. 2004.

Dual-Band CRLH Devices Second operating frequency:

Odd-harmonic - conventional dual-band devices Arbitrary - dual-band systems

Phase-response curve of the CRLH TL : DC offset – additional degree of freedom

Arbitrary pair of frequencies for dual-band operation

Applications:Phase shifters,

matching networks,

baluns, etc.

Dual-Band BLC Lin, Caloz, Itoh, IMS’03.

Conventional BLC operates at f and 3f RH TL replaced by CRLH TL

arbitrary second passband

CµS/CRLH DC Caloz, Itoh, MWCL, 2004.

Conventional DC: broad bandwidth (>25%) loose coupling levels (<-10dB)

CRLH DC: 53% bandwidth coupling level −0.7dB

ZOR Sanada, Caloz, Itoh, APMC 2003.

Operates at β=0 Resonance independent of

the length Q-factor independent of the

number of unit cells

SSSR Crnojević-Bengin, 2005.

LZOR=λ/5

LSSSR=λ/16 Easier fabrication More robust to small changes of dimensions

outputinput

g Lstub

L

wstub

Radiated Wave Applications

1-D i 2-D LW antennas and reflectors ZOR antenna, 2004. - reduced dimensions Backfire-to-Endfire LW Antenna Electronically controlled LW antenna CRLH antenna feeding network

Backfire-to-Endfire LW Antena

Liu, Caloz, Itoh, Electron. Lett., 2000.

Operates at its fundamental mode Less complex and more-efficient feeding structure

Continuous scanning from backward (backfire) to forward (endfire) angles

Able to radiate broadside

Electronically Controlled LW Antenna

Frequency-independent LW antenna

Capable of continuous scanning and beamwidth control

Unit cell:

CRLH with varactor diode

β depends on diode voltage

Antenna Feeding Network

Itoh et al, EuMC 2005.

Refracted Wave Applications

Most promising

Not much investigated - 2-D, 3-D Negative focusing at an RH–LH interface Anisotropic metasurfaces Parabolic refractors...

Current Research...

Subwavelength focusing: Grbic, Eleftheriades, 2003, (Pendry 2000):

NRI lense with εr=−1 and µr=−1 achieves

focusing at an area smaller then λ2

Anisotropic CRLH metamaterials: Caloz, Itoh, 2003. PRI in one direction, NRI in the orthogonal Polarization selective antennas/reflectors

Future Applications Miniaturized devices based ZOR MM beam-forming structures Nonlinear MM devices for generation of ultrashort

pulses for UWB systems Active MM - dual-band matching networks for PA,

high-gain bandwidth distributed PA, distributed mixers

Refracted-wave structures – compact flat lenses, near-field high-resolution imaging, exotic waveguides

SN MM – ultrathin waveguides, flexible single-mode thick fibers, very thin cavity resonators

Terahertz MMs – medical applications Natural LH MM – currently not known to exist SF MM - chemists, physicists, biologists, and

engineers tailor materials missing in nature

Main Challenges

Wideband 3-D isotropic LH meta-structure

Main Challenges

Development of fabrication technologies(LTCC, MMIC, nanotechnologies)

Development of nonmetallic LH structures for applications at optical frequencies

Miniaturization of the unit cell

Development of efficient numerical tools

Conclusion

“LH materials … one of the top ten scientific breakthroughs of 2003.”

Science, vol.302, no.5653, 2004.

“MMs have a huge potential and may represent one of the leading edges of tomorrow’s technology in high-frequency electronics.”

Proc. of the IEEE, vol.93, no.10, Oct.2005.