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## Metamaterials - Concept and Applications

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### Metamaterials - Concept and Applications

### Microwave Passive Circuits

March 2006

Dr Vesna Crnojević-Bengin

Faculty of Technical Sciences

University of Novi Sad

Overview

- Microwave passive circuits
- Metamaterials
- Definition
- Examples
- LHmetamaterials
- Idea
- Phenomena
- Realization
- LHmicrostrip structures
- Resonant and non-resonant structures
- Applications

Rationale

Problem

- DimensionsPerformances
- End-coupled ms resonator:
- Antennas: narrow beam with only one source element?
- Classical theory: large source
- Metamaterials: ENZ substrate

Material Characteristics

- Rel. permitivityεr
- Rel. permeabilityμr
- Rel. index of refraction
- Rel. characteristic impedance

Extreme values ofεrandμr

- 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

μr

εr

Definition

Metamaterials are artificial structures that exhibit extreme values of effectiveεr i μr.

Metamaterials Do Not Exist

- Artificial materials
- Periodic structures
- Period much smaller thenλ

Homogenization of the structure

Effective values of εrandμr

Other Quadrants?

- Single-negative MM:εr<0 orμr<0

μr

evanescent

mode

(plasma,metals@THz)

propagation

mode

(isotropic dielectrics)

εr

evanescent

mode

(ferrites)

Veselago’s Intuition

- Double-negative MM:εr<0 andμr<0 ?

μr

evanescent

mode

(plasma,metals@THz)

propagation

mode

(isotropic dielectrics)

εr

?

evanescent

mode

(ferrites)

Conditions of Existence

- No law of physics prevents the existence of DN MM
- Generalized entropy conditions for dispersive media must be satisfied ()

Veselago’s Conclusions

- Propagation constant βis real &negative

Propagation mode exists

Antiparalel group and phase velocities

Backward propagation (Left-hand rule)

Negative index of refraction

Synonyms

- Double-Negative (DN)
- Left-Handed (LH)
- Negative Refraction Index (NRI)
- (Metamaterials)

Left-Handed Metamaterials

- Double-negative MM: εr<0 andμr<0

μr

evanescent

mode

(plasma,metals@THz)

propagation

mode

(isotropic dielectrics)

εr

propagation

mode

(Left-Handed MM)

evanescent

mode

(ferrites)

Consequences of LH MM

- Phenomena of classical physics are reversed :
- Doppler effect
- Vavilov-Čerenkov radiation
- Snell’s law
- Lensing effect
- Goss-Henchen’seffect

Snell’s Law

!!!

But Alas...

Everything so far was “what 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 ofexcitation in metals
- Resonance of electron gas (plasma)
- Plasmon produces a dielectric functionof the form:
- Typically, fpis in the UV-range
- Pendry: fp=8.2GHz

Experimental Validation

- Smith, Shultz, et al. 2000.

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 givesε‹0

LH BPF – CSRR/ Gap

- November 2004.
- Gaps contribute toμ‹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 SRRsandSpirals

Crnojević-Bengin et al, 2006.

Fractal SRRs

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

- Microstrip

LH TL

- Dual structure

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:

=

!!!

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

Applications of LH MM

- Guided wave applications
- Filters
- Radiated wave applications
- Antennas
- Refracted wave applications
- Lenses

Guided Wave Applications

- Dual-bandand enhanced-bandwidth components
- Couplers, phaseshifters, power dividers, mixers)
- Arbitrary coupling-levelimpedance/phase couplers
- Multilayer super-compactstructures
- Zeroth-order resonatorswith 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 CRLHTL :
- DC offset – additionaldegree of freedom

Arbitrary pair of frequenciesfor dual-band operation

- Applications:

Phaseshifters,

matching networks,

baluns, etc.

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

- Conventional BLC operates atfand3f
- RH TL replaced by CRLH TL

arbitrary second passband

CµS/CRLH DCCaloz, 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 atβ=0
- Resonance independentof the length
- Q-factor independent of the number of unit cells

SSSRCrnojević-Bengin, 2005.

- LZOR=λ/5
- LSSSR=λ/16
- Easier fabrication
- More robust to small changes of dimensions

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

- Operates at its fundamental mode
- Less complexand more-efficient feeding structure
- Continuousscanning from backward (backfire)to forward (endfire) angles
- Able to radiate broadside

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

Electronically Controlled LW Antenna

- Frequency-independent LWantenna
- Capable of continuousscanning and beamwidth control
- Unit cell:

CRLH with varactor diode

- βdepends 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...

- Subwavelengthfocusing:
- Grbic, Eleftheriades, 2003, (Pendry 2000):
- NRI lense with εr=−1 andµr=−1achieves focusing at an area smaller thenλ2
- Anisotropic CRLH metamaterials:
- Caloz, Itoh, 2003.
- PRI in one direction, NRI in the orthogonal
- Polarizationselective antennas/reflectors

Future Applications

- Miniaturized devices basedZOR
- MM beam-formingstructures
- Nonlinear MM devices for generationof ultrashort pulses forUWBsystems
- Active MM - dual-band matching networks for PA,high-gain bandwidth distributed PA, distributed mixers
- Refracted-wave structures – compact flat lenses, near-field high-resolutionimaging, exotic waveguides
- SN MM – ultrathin waveguides, flexible single-mode thick fibers, verythin cavity resonators
- Terahertz MMs – medical applications
- Natural LH MM – currentlynot 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 topten scientific breakthroughs of 2003.”

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

“MMs have a huge potential and may represent one of theleading edges of tomorrow’s technologyin high-frequencyelectronics.”

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

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