Microwave Electronics Lab

Analysis and Design of Left-Handed MetamaterialLenses Using Ansoft HFSS

Anthony Lai1, Kevin M.K.H. Leong1, Christophe Caloz2, and Tatsuo Itoh1

1University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, CA 90095, USA2École Polytechnique, Montréal, 3333 Queen Mary, H3V1A2, QC, Canada

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Microwave Electronics Lab

Introduction: Left-Handed Metamaterials

UCSD, 2D-LH

Historical Milestones• 1968 : theoretical analysis of hypothetical LH materials by Veselago• 1996/9 : introduction of electric (ε<0) / magnetic (μ<0) plasmon by Pendry• 2000 : experimental demonstration of LH structure by Smith

• approach: no simple/rigorous analysis& no design method

• structures: RESONANTlossy & narrow bandwidth& highly dispersive

LH definition: → materials with→ unit-cell << λ effective / macroscopic / homogeneous

0 and 0 0 and ||p gv vnε μ << < ⇒ −

• approach: Transmission line analysis& circuit design methods

• structures: NON-RESONANTlow loss & broad bandwidth& moderate dispersion

“BACKWARD WAVES”(e.g. Brillouin, Pierce)

( )CjZ ′=′ ω1

high-pass( )LjY ′=′ ω1

Resonant Structure Approach Transmission Line Approach

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Microwave Electronics Lab

Negative Refractive Index Lenses

RH medium LH medium

θLH –θRH

refractive index nLH refractive index nRH ( < 0)

kLH

kRH

sLHsRH

phase

power

phasepower

Plane Wave Cylindrical Wave

HFSS Simulations: Effective Medium (ε < 0, μ < 0)flat lens parabolic lens

magnitude phase magnitude phase

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Microwave Electronics Lab

Practical Realization of LHMs

Composite Right/Left-Handed TLω

β

ωsh

ωse

ω

β

ωsh

ωse

+βc-βc

1-D unit cell

CRLH metamaterial includes

LH and unavoidable

RH parasitic effects.

LH at low frequencies

RH at high frequencies

CL LR

CR LL

CLLR

CR LL

patch

ground plane

via

2-D unit cell

pperiod of unit cell

p

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Microwave Electronics Lab

HFSS Characterization of 2-D CRLH TL

0

2

4

6

8

10

12

Μ ΓΓ

Freq

uenc

y (G

Hz)

βp (rad)

TM mode (LH) TE mode TM mode (RH) air mode

Χ

Dispersion Diagram (HFSS)(p=5.0 mm, g=1.0 mm, h=1.27 mm, εR=10.2)

5.50 GHz 6.50 GHz 6.90 GHz

RH

3.55 GHz 3.75 GHz 4.00 GHz

LH

Measured E-Field Phase Atop 17x17 Array

17x17 Mushroom Array

coaxial feed

HFSS Eigenmode Simulation w/PBCs

RH: λg~1/fLH: λg~ f

PML

CRLH unit cell

master/slave boundaries on

all 4 sides

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Microwave Electronics Lab

RH/LH Interface Matching Conditions

Dispersion Diagram Refractive Index

dielectric line

nCRLH = -3.2 @ f = 3.77 GHzneed nRH = - nCRLH=3.2

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Microwave Electronics Lab

HFSS Simulation of NRI Lenses

* CRLH and RH regions interchanged for simulation

magnitude phase

magnitude phase

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Microwave Electronics Lab

Measured Results

SourceMagnitude Phase

SourceSourceMagnitude Phase

Source

Magnitude PhaseSourceSource

Magnitude Phase

~ Mushrooms (23x16 cells) in outlined area

Mushrooms (21x10 cells)* Entire structure built on εR=10.2 substrate

f0 =3.79 GHz

f0 =3.77 GHz

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