Spli ing esona o -based le -handed coplana wa eguide
F. Ma ı
´n and J. Bonache
Depa amen d’Enginye ia Elec o
`nica, Uni e si a Au o
`noma de Ba celona,
08193 Bella e a (Ba celona), Spain
F. Falcone and M. So olla
Depa amen o de Ingenie ı
´a Ele
´c ica y Elec o
´nica, Uni e sidad Pu
´blica de Na a a,
31006 Pamplona (Na a a), Spain
R. Ma que
´s
Depa amen o de Elec o
´nica y Elec omagne ismo. Facul ad de Fı
´sica–Uni e sidad de Se illa,
A . Reina Me cedes s/n, 41012 Se illa (Spain)
共Recei ed 9 May 2003; accep ed 8 Oc obe 2003兲
In his le e , a plana le -handed p opaga ing medium consis ing o a coplana wa eguide 共CPW兲
induc i ely coupled o spli ing esona o s 共SRR兲and pe iodically loaded wi h na ow me allic
wi es is p oposed. The wi es make he s uc u e beha e as a mic owa e plasma wi h a nega i e
e ec i e pe mi i i y which co e s a b oad equency ange. The nega i e pe meabili y equi ed o
achie e le -handed wa e p opaga ion is p o ided by he ings in he icini y o hei esonan
equency. The esul is a s uc u e which allows nega i e wa e p opaga ion in a na ow equency
band. The ansmission coe icien measu ed in a ab ica ed p o o ype de ice exhibi s e y low
inse ion losses in he pass band and high- equency selec i i y. Since ings a e much smalle han
signal wa eleng h a esonance and can be easily uned, SRR-CPW-based s uc u es a e o in e es
o he design o e y compac mic owa e ci cui s based on le handedness. © 2003 Ame ican
Ins i u e o Physics. 关DOI: 10.1063/1.1631392兴
The de elopmen o a i icial ma e ials 共me ama e ials兲
wi h simul aneously nega i e pe meabili y and pe mi i i y,
o le -handed ma e ials 共LHMs兲, has been a subjec o g ow-
ing in e es in ecen yea s. Apa om i s exo ic elec ody-
namic p ope ies 共such as he e e sal o Snell’s law, Dopple
e ec , and Che enko adia ion兲, poin ed ou by
Veselago mo e han 30 yea s ago,1key o his in e es is he
po en ial applicabili y o hese me ama e ials o he ab ica-
ion o adio equency 共 兲and mic owa e componen s
based on le handedness. Due o nega i e alues o e ec i e
pe mi i i y and pe meabili y, LHMs a e nega i e e ac i e
index media wi h an ipa allel phase and g oup eloci ies.2,3
Namely, he wa e ec o k o ms a le -handed iple wi h
he ec o s Eand H共 he elec ic and magne ic ield in en-
si y兲and wa e on s o p opaga ing elec omagne ic 共EM兲
wa es a el owa d he sou ce, i.e., opposi e o he di ec ion
o ene gy low.
Due o he absence o anspa en LHMs in na u e, a
LHM medium has o be a i icially ab ica ed. This can be
achie ed by mic os uc u ing a ma e ial in a leng h scale
much sho e han he wa eleng h o EM adia ion, so ha a
con inuous medium wi h e ec i e elec omagne ic p ope ies
共pe mi i i y and pe meabili y兲is ob ained. An a i icial
LHM ope a ing in he mic owa e egion was epo ed by
Smi h e al.4The s uc u e was ab ica ed by combining a
pe iodic a ay o me al pos s wi h an a ay o nonmagne ic
spli ing esona o s 共SRRs兲. O iginally p oposed by Pend y,5
SRRs p o ide a nega i e e ec i e pe meabili y in he icin-
i y o he esonan equency, while me allic wi es beha e
like a wo-dimensional 共2D兲plasma wi h nega i e pe mi i -
i y up o he plasma equency. Le -handed wa e p opaga-
ion has been also demons a ed in a one-dimensional 共1D兲
con igu a ion consis ing o a hollow me allic wa eguide pe-
iodic loaded wi h SRRs.6Fo EM p opaga ion in he axial
di ec ion, he me allic wa eguide emula es a lossless plasma
whose dielec ic pe mi i i y is nega i e below he cu o e-
quency.
The ci ed s uc u es exhibi a le -handed side e ec bu
a e a om being conside ed as po en ial candida es o mi-
c owa e and wi eless componen sys ems. To his end, com-
pa ibili y wi h plana ci cui echnology is equi ed. LHMs
based on plana ansmission lines ha e been ecen ly e-
po ed. I is ema kable he wo k o G bic and Ele he iades,7
who demons a e he exis ence o backwa d wa e adia ion
共a cha ac e is ic analogous o e e sed Che enko adia ion兲
in a dual ansmission line, whe e a hos coplana wa eguide
is loaded wi h se ies capaci o s and shun connec ed induc-
o s. In his le e , a 1D LHM based on a coplana wa eguide
induc i ely coupled o SRRs and pe iodic loaded wi h na -
ow me allic wi es is p esen ed. F om he dispe sion ela ion
ob ained in a lumped elemen equi alen ci cui o he s uc-
u e, i is ound ha phase and g oup eloci ies a e an ipa -
allel in a na ow band jus abo e he esonan equency o
SRRs. This heo e ical e idence o le -hand sided wa e
p opaga ion is co obo a ed om ull wa e EM simula ions
and alida ed by measu ing he ansmission coe icien in a
ab ica ed p o o ype de ice.
The p oposed implemen a ion o he le -handed s uc-
u e is depic ed in Fig. 1共a兲. This consis s o a hos coplana
wa eguide 共CPW兲wi h a cen e conduc o 共signal s ip兲and
wo g ound planes on ei he side sepa a ed by slo s. SRRs
a e symme ically placed in he back side o he subs a e
while hin me al wi es connec he signal o he g ound a
hose posi ions coinciden wi h he cen e o he SRRs. Com-
pa ed o he SRR-wi e medium o Smi h,4o he SRR-
hollow me allic wa eguide,6 he p oposed LHM is plana
and he ab ica ion p ocedu e simply equi es a s anda d
mask/pho oe ching echnique 共an A lon 250-LX-0193-43-11
APPLIED PHYSICS LETTERS VOLUME 83, NUMBER 22 1 DECEMBER 2003
46520003-6951/2003/83(22)/4652/3/$20.00 © 2003 Ame ican Ins i u e o Physics
subs a e—dielec ic cons an
⑀
⫽2.43, hickness h⫽0.49
mm—has been used兲. By placing he SRRs pa allel o he
CPW, he main componen o he elec ic ield in he ings is
pa allel o he ing plane, while he magne ic ield is pola -
ized along he ing axis. These a e necessa y condi ions o
achie e a nega i e e ec i e pe meabili y. On he o he hand,
connec ing wi es ac as he me al pos s in he 2D LHM o
Smi h,4and p o ide he e ec i e nega i e pe mi i i y which
is equi ed o ob ain le -handed wa e p opaga ion in he
line. In Fig. 1, he dimension o he uni cell is ᐉ⫽5mm
while he cen e conduc o and slo wid hs a e W⫽5.4 mm
and G⫽0.3 mm, espec i ely. These la e al dimensions ha e
been de e mined o ob ain a cha ac e is ic impedance o he
hos line o Zo⫽50 ⍀共 he impedance o measu ing p obes兲,
and hence op imize ansmission in he pass band. The ings
ha e an in e nal adius o ⫽1.3 mm, wid hs o c⫽0.2 mm,
and a sepa a ion o d⫽0.2 mm 关see Fig. 1共b兲兴. Wi h his
geome y, he esonan equency o he ings is expec ed o
be o⫽7.7 GHz.8,9 Finally, he wid h o connec ing wi es is
0.2 mm.
Le us now ocus on he p opaga ion cha ac e is ics o
he p oposed s uc u e h ough he analysis o he dispe sion
ela ion. This is in e ed om he lumped elemen equi alen
ci cui o he elemen al cell 关Fig. 2共a兲兴, which is alid in he
long-wa eleng h egime 共
␤
ᐉⰆ1, whe e
␤
is he p opaga ion
cons an o guided wa es兲. Due o symme y, he magne ic
wall concep has been used so ha he equi alen ci cui
ac ually co esponds o one hal he basic cell. Land Ca e
he pe -sec ion induc ance and capaci ance o he line. These
pa ame e s model he induc ance associa ed wi h he cen al
conduc o o he hos CPW and he capaci i e coupling be-
ween his conduc o and g ound planes 共slo capaci ance兲,
espec i ely. Lpis he equi alen induc ance o connec ing
wi es and SRRs a e modeled as pa allel esonan ci cui s
共wi h induc ance Lsand capaci ance Cs) which a e induc-
i ely coupled o he line h ough a mu ual induc ance, M.
To ob ain le handedness, i is necessa y ha he shun ad-
mi ance is domina ed by he induc ance o he wi es a he
esonan equency o he ings. This condi ion depends on
he wid h and dis ance be ween connec ing wi es and is eas-
ily achie able p o ided ois no e y high. By ob aining he
equi alen impedance o he se ies b anch, he ci cui can be
simpli ied o ha shown in Fig. 2共b兲共which is o mally iden-
ical o ha p oposed in Re . 10 o he SRR/wi e medium o
Smi h兲,4whe e Cs
⬘and Ls
⬘a e gi en by
Cs
⬘⫽Ls
␻
o
2M2,共1兲
Ls
⬘⫽
␻
o
2M2Cs,共2兲
wi h
␻
o
2⫽1/(LsCs)⫽1/(Ls
⬘Cs
⬘). The dispe sion ela ion o
he ci cui o Fig. 2共b兲can be easily ob ained om s anda d
calculus:11
cos共
␤
ᐉ兲⫽1⫺
Lp
␻
⫺1
C
␻
4Lp/C
冉
2L
␻
⫺Ls
⬘/Cs
⬘
Ls
⬘
␻
⫺1
Cs
⬘
␻
冊
.共3兲
Figu e 3 shows he p e ious exp ession in a
␻
–
␤
ep esen-
a ion, whe e he scale o he e ical axis has been limi ed o
ew GHz o app ecia e he dispe si e beha io in he egion
o in e es . The alues o Land Cha e been ob ained by
means o a ansmission line calcula o ; Lphas been es i-
ma ed om he simula ed equency esponse o he wi ed
CPW 共SRRs emo ed兲, whe e he plasma equency is gi en
by he esona o composed by Cand Lp;10 Mhas been
in e ed om he ac ional a ea, F, o he slo s occupied by
he ings (M⫽F•L); inally, Lsand Csha e been ob ained
acco ding o he model desc ibed in Re . 9. Acco ding o Fig.
3, a na ow pass band jus abo e he esonan equency o
FIG. 1. 共a兲Layou o he SRR-based le -handed CPW s uc u e d awn o
scale. Ac ual de ice leng h is 3.5 cm and 共b兲geome ical pa ame e s o he
SRR.
FIG. 2. 共a兲Lumped elemen equi alen ci cui o he basic cell o he
p oposed s uc u e and 共b兲simpli ied ci cui wi h he se ies b anch eplaced
by i s equi alen impedance.
4653Appl. Phys. Le ., Vol. 83, No. 22, 1 Decembe 2003 Ma in
e al.
he ings is expec ed. Since
␤
dec eases wi h equency,
phase and g oup eloci ies a e an ipa allel. The e o e, nega-
i e wa e p opaga ion occu s and he s uc u e beha es as a
na ow band LHM. I connec ing wi es a e emo ed, e ec-
i e pe mi i i y is no longe nega i e and he pass band
beha io is expec ed o change o a s op band. The ansmis-
sion (S21) and e lec ion (S11) coe icien s o he le -hand
side s uc u e shown in Fig. 1 and o he same s uc u e
wi hou connec ing wi es, ha e been ob ained by means o
ull wa e EM simula ion 共using he comme cial so wa e CST
MICROWAVE STUDIO兲. The esul s, depic ed in Figs. 4 and 5,
con i m he p esence o a na ow pass band in he le -
handed de ice and a s op band beha io o he wi eless
s uc u e. These s uc u es ha e been ab ica ed in a A lon
250-LX-0193-43-11 subs a e by means o a s anda d mask/
pho oe ching echnique. A e solde ing 3.5 mm connec o s
a he inpu /ou pu po s, he ansmission and e lec ion co-
e icien s ha e been measu ed by means o a Agilen 8722ES
ec o ne wo k analyze 共 he esul s a e also depic ed in Figs.
4 and 5兲. Reasonable ag eemen be ween expe imen and
simula ion has been ob ained. The pass band shown in Fig. 4
共which is a consequence o he simul aneous nega i e pe -
mi i i y and pe meabili y兲is an ex ao dina y esul o a
SRR-based le -handed s uc u e: A high deg ee o equency
selec i i y has been achie ed wi h a ansmission coe icien
nea 0 dB. The sligh deg ada ion isible in he expe imen is
due o ohmic and dielec ic losses, no accoun ed o in he
simula ions.
In conclusion, le -handed wa e p opaga ion in a CPW,
coupled o spli ing esona o s and pe iodically loaded wi h
signal- o-g ound wi es ac ing as induc o s, has been demon-
s a ed. Since nega i e pe meabili y and pe mi i i y coexis
only in he icini y o he esonan equency o he ings,
signal p opaga ion in he s uc u e is limi ed o a na ow
equency band. This has been demons a ed in a ab ica ed
p o o ype de ice, whe e he measu ed ansmission coe i-
cien has been indica i e o negligible inse ion losses in he
allowed band. The p oposed s uc u e can be o in e es o
he ab ica ion o high selec i i y band pass il e s based on
le handedness. Compa ibili y wi h monoli hic mic owa e
in eg a ed ci cui o p in ed ci cui boa d ab ica ion ech-
nologies as well as compac ness 共de i ed om he ac ha
ing dimensions a e elec ically small兲, a e o he key aspec s
ha lead us o hink abou he applica ion o hese s uc u es
o he design o minia u ized mic owa e and millime e
wa e ci cui s.
This wo k has been suppo ed by DGI and CICYT by
p ojec Con ac Nos. BFM2001-2001, TIC2002-04528-C02-
01, and TIC2001-3163. Thanks o R. Pineda om Omic on
Ci cui s, s.l. o he ab ica ion o he p o o ypes.
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FIG. 3. Dispe sion diag am o he lumped elemen ci cui model o he
SRR-CPW s uc u e.
FIG. 4. Simula ed 共 hin line兲and measu ed 共bold line兲 ansmission S(2,1)
and e lec ion S(1,1) coe icien s o he le -handed SRR-CPW s uc u e.
FIG. 5. Simula ed 共 hin line兲and measu ed 共bold line兲 ansmission S(2,1)
and e lec ion S(1,1) coe icien s o he SRR-CPW s uc u e wi h he wi es
emo ed.
4654 Appl. Phys. Le ., Vol. 83, No. 22, 1 Decembe 2003 Ma in
e al.