Split ring resonator-based left-handed coplanar waveguide

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. 1V. G. Veselago, So . Phys. Usp. 10, 509 共1968兲. 2D. R. Smi h and N. K oll, Phys. Re . Le . 85, 2933 共2000兲. 3C. Caloz, C.-C. Chang, and T. I oh, J. Appl. Phys. 90, 5483 共2001兲. 4D. R. Smi h, W. J. Padilla, D. C. Vie , S. C. Nema -Nasse , and S. Schul z, Phys. Re . Le . 84, 4184 共2000兲. 5J. B. Pend y, A. J. Holden, D. J. Robbins, and W. J. S ewa , IEEE T ans. Mic owa e Theo y Tech. 47, 2075 共1999兲. 6R. Ma que ´s, J. Ma el, F. Mesa, and F. Medina, Phys. Re . Le . 89, 183901 共2002兲. 7A. G bic and G. V. Ele he iades, J. Appl. Phys. 92, 5930 共2002兲. 8R. Ma que ´s, F. Medina, and R. Ra ii-El-Id issi, Phys. Re . B 65, 144440 共2002兲. 9R. Ma que ´s, F. Mesa, J. Ma el, and F. Medina, IEEE T ans. An ennas P opag. 5, 2572 共2003兲. 10G. V. Ele he iades, O. Siddiqui, and A. K. Iye , IEEE Mic owa e Wi e- less Componen s Le . 13,51共2003兲. 11 M. Poza , Mic owa e Enginee ing 共Addison–Wesley, Reading, MA兲, 1993. 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.