Dual and broadband power dividers at microwave frequencies based on composite right/left handed (CRLH) lattice networks

Transcription

1 Dual and bradband wer divider at micrwave frequencie baed n cmite right/left handed (CH) lattice netwrk P. Vélez*, J.Bnache, F. Martín GEMMA/CIMITEC, Deartament d Enginyeria Electrònica, Univeritat Autònma de Barcelna, Bellaterra (Barcelna), Sain. *Crrending authr ( ): ari.velez@uab.cat Phne Number: Abtract Thi aer re a dual-band wer divider erating at GHz frequencie and imlemented by mean f imedance tranfrmer (al called inverter) baed n lattice netwrk and tranmiin line ectin. The dual-band functinality f the red device i achieved thank t the cmite right/left handed (CH) behavir f the imedance tranfrmer, able t rvide 90 and +90 hae hift at the firt and ecnd deign frequencie, reectively, f the divider. By uing uch cmbinatin f tranmiin line ectin and lattice netwrk, the characteritic imedance f the imedance tranfrmer i rughly cntant ver wide bandwidth, with the reult f brad erating band. T demntrate the ibilitie f the arach, a rttye device i deigned, fabricated and characterized. Keywrd: metamaterial; lattice netwrk; CH tranmiin line; wer divider; 1. Intrductin The imlementatin f micrwave device able t exhibit their functinality at everal frequencie ha been a ubject f an intenive reearch in recent year. One f the arache fr the imlementatin f dual-band, tri-band and (even) quad-band cmnent ue artificial line baed n metamaterial cncet, al knwn a metamaterial tranmiin line [1-3]. Such line are tranmiin line laded with reactive element, that i, inductr, caacitr, renatr, r a cmbinatin f them. Thank t the reence f thee reactive element the line exhibit enhanced deign flexibility, and micrwave device with uerir erfrmance r with nvel functinalitie can be imlemented by mean f uch artificial line. Multiband cmnent are examle f thee new functinal micrwave device. Tyically, the multiband micrwave cmnent baed n metamaterial tranmiin line are cmed f multiband imedance tranfrmer, namely, tranmiin line exhibiting 90 hae hift at the deign frequencie [4,5]. The key aect t achieve uch multiband functinality i the ibility t tailr the dierin diagram f the cnidered artificial line. Such cntrllability i nt ible in rdinary line. Indeed, metamaterial tranmiin line have ened the ath t the deign f micrwave cmnent n the bai f imedance and dierin engineering. By lading the line with reactive element, the dierin diagram and the characteritic imedance f the

2 line can be adjuted, that certain ecificatin nt eaily achievable with cnventinal line can be atified with metamaterial tranmiin line. The imlet realitic artificial line baed n metamaterial cncet are the -called cmite right/left handed (CH) line [6]. Thee line can be imlemented by lading a ht line with erie caacitr and hunt inductr (C-laded arach) [7-9], r by lading a ht line with renant element, uch a lit ring renatr (S) [10] r cmlementary lit ring renatr (CS) [11], and ther reactive element (hunt inductr r erie caacitr). The latter arach ha been deignated a the renant tye arach [1-14]. et u nw fcu the attentin n the C-laded arach. The equivalent T-circuit mdel f the unit cell f thee line i deicted in Fig. 1. The dierin diagram and the Blch imedance (r rati between vltage and current fr the Blch wave cnidering a eridic tructure cmed f uch cell) f thi tructure can be inferred frm the circuit mdel accrding t [15] Z B Z ( ) c l 1 (1) Z ( ) Z ( )[ Z ( ) Z ( )] () where Z and Z are the imedance f the erie and hunt branch, reectively, f the T-circuit, i the hae cntant and l the unit cell length. If nly ne cell r few cell are cnidered, then exrein () i identified with the image imedance, but bth the Blch and the image imedance are the equivalent f the characteritic imedance in rdinary line. The reulting dierin diagram exhibit a regin (at lw frequencie) where the hae and gru velcitie are antiarallel (left handed band), and a regin (at higher frequencie) where bth velcitie have the ame ign (right handed band). Hence thee line exhibit a CH behavir. In the left handed band, wave ragatin i backward, wherea in the right handed band wave ragatin i frward (i.e., a in rdinary line). Tyically, a band ga aear between the backward and frward tranmiin band, unle the line i balanced. The balanced cnditin i achieved when the erie and hunt renance frequencie are identical [], namely 1 1 C C (3) In thi cae, the tranitin between the left handed and the right handed band i cntinuu, the hae velcity i infinite at the tranitin frequency, and the gru velcity exhibit a finite value at that frequency. CH tranmiin line decribed by the mdel f Fig. 1 exhibit a banda behavir. Interetingly, it i ible t deign the line in rder t exhibit the ame ablute value f hae hift at tw different frequencie (f1 and f), with the ame value f the characteritic imedance. Cnidering that a ingle unit cell i ued (in rder t reduce dimenin), the cnditin t univcally determine the fur reactive element f the circuit f Fig. 1, fr an imedance tranfrmer, are:

3 ( 1 ) (4.a) Z A ( 1 ) (4.b) Z A ( ) (4.c) Z A ( ) (4.d) Z A where Z = j, Z = j, 1 = f1, = f, ZA i the required characteritic imedance f the tranfrmer (a real quantity) at the deign frequencie, and the hae f the tranfrmer i 90 at f1 and +90 at f. Fig. deict the dierin and characteritic imedance f the tranfrmer with ZA = at f1= 1GHz and f = GHz. Fig. 1.Equivalent T-circuit mdel f the unit cell f a cannical CH tranmiin line. a) b) 150 l Z B () ,5 1,0 1,5,0,5 3,0 0,5 1,0 1,5,0,5 3,0 Frequency (GHz) Frequency (GHz) Fig..Dierin diagram (a) and characteritic imedance (b) f a dual-band imedance tranfrmer with Z A= 70.71, imlemented by mean f the circuit f Fig. 1. The erating frequencie are f 1 = 1GHz and f = GHz. The element value that reult by lving (4) are: = 5.6nH, =.5 nh, C = 0.56F, C =.5F. Many dual-band cmnent have been imlemented fllwing thi trategy [5,16], and by increaing the number f reactive element, quad-band cmnent have al been rerted (uch cmnent are baed n the -called extended, r generalized, CH tranmiin line cncet [17-19], and everal rttye are rerted in [0-]). An imrtant difference between CH line and rdinary line i the frequency deendence f the characteritic imedance. Wherea it i cntant in cnventinal line, it trngly deend n frequency in CH tranmiin line. Nte hwever that it i carcely deendent n frequency in the vicinity f the tranitin frequency in balanced line []. Fr thi rean, many device have been deigned with multi-cell balanced tructure, each ne exhibiting a mall hae hift at the required frequencie. Tyically, the firt (left handed) band in CH line i narrw and the characteritic imedance in the vicinity f the frequency where the hae hift i 90 varie ubtantially with frequency. The reult, when thee line are ued fr the

4 imlementatin f dual-band device baed n imedance tranfrmer, i a narrw band at the firt erating frequency [5,16]. In thi aer, dual-band imedance tranfrmer are imlemented fllwing a different arach: the ue f lattice netwrk cmbined with tranmiin line ectin. Thrugh a rer deign, thee artificial line can be deigned t exhibit a CH behavir with a nearly frequency indeendent characteritic imedance. A will be hwn, the deigned dual-band device (a wer divider) exhibit tw erating band with imedance matching ver brad bandwidth, a cmared t ther rerted dual-band cmnent.. attice netwrk exhibiting CH behavir: thery and tate f the art The CH and the generalized CH tranmiin line mentined in the reviu ectin urt wave ragatin in a limited frequency band. All-a tructure exhibiting left handed, right handed r CH wave tranmiin can be imlemented by uing the -called lattice netwrk [3]. Indeed, all-a CH tranmiin line with arbitrary rder can tentially be yntheized with thee lattice netwrk tructure [4]. Hwever, the ractical imlementatin f thee lattice (r X-tye) netwrk i nt traightfrward, a will be later dicued. et u nw cnider an X-tye unit cell like the ne hwn in Fig. 3(a), i.e., a lattice netwrk, with imedance Z in the erie branche and Z in the cr diagnal arm. By calculating the element f the imedance matrix, thi tw-rt netwrk can be tranfrmed t it equivalent T-circuit mdel, deicted in Fig. 3(b). Uing (1) and (), the hae cntant and characteritic imedance f the generalized lattice netwrk f Fig. 3(a) are given by: Z Z c( l) (5) Z Z Z a) b) B Z Z Z (6) (b) Z Z Z Z (Z - Z )/ Z Fig. 3.attice-netwrk unit cell (a) and it equivalent T-circuit mdel (b). et u nw cnider that the element f the erie and cr branche i an inductr (Z = j) and a caacitr (Z= j/c), reectively (Fig. 4a). Evaluatin f (5) and (6) give: 1 C c( l) (7) 1 C

5 Z B (8) C Inectin f (7) and (8) reveal that the netwrk f Fig. 4(a) i an all-a tructure (the characteritic imedance i real and frequency indeendent, like the ne f an rdinary tranmiin line), and that wave ragatin i frward frm DC u t (theretically) unlimited frequencie (the dierin diagram i al deicted in Fig. 4a). If the inductr and caacitr are interchanged (Fig. 4b), the characteritic imedance i al cntant and given by (8), wherea the hae cntant i fund t be: 1 C c( l) (9) 1 C and wave ragatin i backward in the whle electrmagnetic ectrum (ee the dierin diagram deicted in Fig. 4b). If the hae hift i mall enugh, the netwrk f Fig. 4(a) and (b) mimic a cnventinal line and a urely left-handed line, reectively. By adequately ching the reactive element f the erie and cr arm f the X- netwrk, all-a CH tructure f arbitrary rder can be btained [4]. Fr intance, Fig. 4 (c) and (d) hw the lattice netwrk crrending t rder- all-a CH and dual-ch line, reectively. T btain all-a tructure, it i neceary that the zer and le f the reactance f the erie branch cincide with the zer and le f the ucetance f the cr branch. Fr the ecific cae f rder- lattice netwrk, the cnditin i imilar t the balance cnditin fr T- r -tye CH tranmiin line: 1 C 1 C (10) where, C and, C are the reactive element f the erie branch and cr branch, reectively, and i the tranitin frequency. Fr the netwrk f Fig. 4(c), exrein (5), ubjected t (10), rewrite a: 1 1 C c( ) l (11) 1 1 C wherea the dierin relatin fr the netwrk f Fig. 4(d) i: 1 1 C c( ) l (1) 1 1 C

6 The dierin curve are al deicted in Fig. 4(c) and (d). In bth cae, the characteritic imedance i given by (8), with = and C = C. (a) C C l (b) C l C (c) C C C l C (d) C C C l C Fig. 4.Examle f lattice netwrk and their crrending dierin curve. (a) rder-1 right handed; (b) rder-1 left handed; (c) rder- CH; (d) rder- dual CH.

7 Frm a ractical viewint, the hyical imlementatin f the rder- lattice netwrk f Fig. 4(c) and (d) i nt traightfrward. An alternative t imlement all a rder- CH line i t cmbine urely left handed and urely right handed X-tye cell, a deicted in Fig. 5(a). In thi cae, the fllwing cnditin mut be atified: C Z (13) B C which give the characteritic imedance f the whle all-a netwrk. The tranitin frequency i given by that frequency atifying: arcc 1 1 C C arcc 1 1 C C 0 (14) namely: 1 1 (15) C C In articular, if C=C (which, accrding t 13, mean that = and C = C), the tranitin frequency can al be exreed a: 1 1 (16) C C crrending t the frequency where the urely left handed cell and the right handed cell exerience a hae hift f l = 90 and l = +90, reectively (thu rviding an verall hae hift f l = 0 ). Fig. 5(b) hw the dierin diagram crrending t the tructure f Fig. 5(a) fr the indicated element value. (b) (a) C C C l C Fig. 5. CH artificial tranmiin line unit cell cniting f tw cacaded rder-1 X-tye right handed and left handed cell (a), and dierin diagram (b). Element are: C = C = F and = =.65 nh (f = 3GHz, and it i indicated by a bld circle in b). It i wrth mentining that, in ite that the netwrk f Fig. 4(c) and 5(a) exhibit imilar dierin curve; there i nt an element tranfrmatin that make them equivalent. Ntice that the dierin relatin (with the frequency variable in the x-axi) fr the tructure f Fig. 5(a) i a cncave functin at all frequencie. Hwever, fr the

8 rder- CH X-tye cell f Fig. 4(c), the dierin relatin i cnvex fr frequencie belw, and cncave abve that frequency (i.e., there i an inflexin int at ). Althugh the ynthei f a cacaded rder-1 left handed and right handed X-tye cell i imler than an rder- CH lattice netwrk, the frmer tructure may reent certain limitatin due t the curvature f it dierin relatin. Fr intance, it i nt ible t imlement dual-band cmnent baed n dual-band (90 ) imedance inverter imlemented with ingle unit cell (like the ne deicted in Fig. 5a) with a rati f erating frequencie maller than 3. The rean i that, due t the curvature f the dierin diagram (ee Fig. 5b), the ecnd eratin frequency (indicated by a triangle in Fig. 5b) i alway abve the ne indicated by a quare, thi ne being the ecnd erating frequency if the dierin curve wa a traight line (dahed line in Fig. 5b). Ntice that thi frequency i exactly three time the ne indicated by a tar (the firt erating frequency). Hence the abve tatement i grahically demntrated. The ynthei f CH all-a artificial line can be further imlified by cacading an X-tye left handed unit cell with a tranmiin line ectin with identical characteritic imedance, a deicted in Fig. 6(a), r with a air f tranmiin line ectin (at the inut and utut rt f the left handed X-tye cell). A tyical dierin curve fr the tructure f Fig 6(a) i deicted in Fig. 6(b). In thi cae, due t the reence f a ditributed element, the hae f the tructure grw indefinitely. (a) (b) C l C Fig. 6. CH artificial tranmiin line unit cell cniting f an rder-1 X-tye left handed cell cacaded t an rdinary tranmiin line ectin with hae cntant k and characteritic imedance Z. Cncerning the imlementatin, X-tye netwrk are differential tructure with cr branche. Therefre, a mentined abve, their ynthei i nt imle. CH artificial line were imlemented by Bngard et al. [5-7] by cmbining X-tye left handed cell and tranmiin line ectin. The tructure rerted in [7] utilize aired tri technlgy with tw additinal metal level t imlement the erie caacitance f the left handed X-tye cell, and via hle t imlement the cr inductance. The tructure, deigned t exhibit a tranitin frequency at f=6ghz, exhibit very brad band at bth ide f f. Uing the unit cell tructure f Fig. 6(a), a brad-band (matched frm DC t millimeter wave) ilicn-integrated CH tranmiin line uing a mnlayer CPW ht line wa red in [8]. The meaurement carried ut in [8] demntrate a balanced CH behavir frm 5GHz u t 35 GHz, with a tranitin frequency at f = 0 GHz.

9 The intereting aect f the tructure f [8] i that it i imlemented uing a ingle metal layer. Since the erie caacitance mut be imlemented in bth cnductr f the tranmiin line, the grund cnductr f the ht CPW mut be f finite width. The required caacitance were realized by interdigital caacitr, wherea fr the imlementatin f the cred inductr, the lutin red in [8] wa t imlement each f the inductance in a different lt f the CPW. Since the reulting tructure i trngly aymmetrical, the excitatin f the dd araitic mde wa revented by the ue f the bridge. Thu, the tructure indeed ue tw metal level. Other X-tye left handed, right handed and CH lanar tructure imlemented by uing tw metal level are rerted in [9]. It i wrth mentining that frm the equivalence between terminated culed line ectin and lattice netwrk [30], anther arach fr the hyical imlementatin f lattice netwrk baed artificial CH line wa reented in [4]. The unit cell i baed n the culed-micrtri Schiffman ectin [31], which i an eaily imlementable tructure that de nt require the ue f via-hle r air bridge, a ed t the cell reented in [5-9]. Indeed, culed-line ectin were earlier ued in [3,33] t btain CH tranmiin line, but with limited erfrmance due t the different even- and dd-mde hae velcitie f the culed line. Thi iue wa atifactrily lved in [4]. Thu, terminated culed line ectin ffer a imle arach fr the imlementatin f lattice netwrk CH tranmiin line. Obviuly, thi i a fully ditributed arach that inherently increae line ize a cmared t lattice netwrk CH line baed n lumed r emilumed (lanar) element. 3. Dual-band wer divider baed n left handed lattice netwrk and tranmiin line ectin The dual-band wer divider reented in thi aer i imlemented with a air f dualband imedance tranfrmer baed n the CH tructure f Fig. 6, i.e., a cmbinatin f a urely left handed lattice netwrk and a tranmiin line ectin. The chematic f thi divider i deicted in Fig. 7. The imedance f the imedance tranfrmer (ZA = 70.71) ha been et t thi value in rder t achieve gd inut matching, cnidering reference imedance f Z = 50 at the rt. At the deign frequencie the hae hift f the imedance tranfrmer i 90, and hence the imedance een at the inut rt f each tranfrmer, given by [15] Z A Zin, T (17) Z i 100, and the imedance een frm rt 1 i Zin= 50 at the deign frequencie.

10 Fig. 7.Schematic f the dual-band wer divider. By ching the erating frequencie a f1 = 1.7GHz and f = 5.4GHz, the cnditin t imlement the imedance tranfrmer are: Z A (18) C 1 C 1 arcc T ( 1 1 C 1 arcc T ( 1 C 1 C ) 90 ) 90 (19) (0) wheret() i the hae f the tranmiin line ectin, given by T( ) klt l (1) T v v and lt being the hae velcity and length f the tranmiin line ectin, reectively. Ntice that equatin (18)-(0) have three unknwn (, C and lt) that can be univcally determined. Slving (18)-(0) with the deign frequencie given abve, the unknwn are fund t be: =.09nH, C = 0.419F, and lt/v= (bviuly, the hae velcity deend n the effective dielectric cntant f the cnidered line). Fr the imlementatin f the divider uing the inferred CH imedance tranfrmer, we have cnidered the tlgy deicted in Fig. 8. Baically, the erie caacitance f the left-handed lattice netwrk are imlemented by mean f metallic ga, wherea the cred inductance are imlemented by mean f narrw tri with via (with 0.15mm radiu) in rder t cnnect the uer metal with the lwer metal. Tranmiin line ectin with the required value (ZB=70.71 and lt/v= 9.59 ) are added at bth ide f the X-tye left handed unit cell t rvide the needed hae hift. Thi tranmiin line ectin are imlemented by mean f duble ided arallel tri line (DSPS) [34] with an ffet equal t 0.66 mm (thi give the required imedance) and cnnected t the X-tye left handed lattice netwrk with taered line ectin, that have been timized t achieve the required hae rene (the taer line are neceary t

11 cnnect the line t the X-tye netwrk, which ha the indicated hae in rder t accmmdate the inductive via, and t rvide the required caacitive value). P1 (a) P (b) W P1 P1' l T T l S c l W c c Via W T P P' Fig.8. 3D view f the dual-band imedance inverter baed n an X-tye left handed lattice andwiched between tw tranmiin line ectin (a), and t view with rt and relevant dimenin indicated (b). The lwer metal i deicted in grey. Dimenin are: W = 6.6 mm, = 8.4 mm, W c =.6 mm, c = 0.75 mm, S c = 0.16 mm, l T =. mm, T = 1.13 mm, W T = 1.43 mm, l = 1. mm and l = 0.95 mm. The width f the narrw tri i 0.16 mm. Fig. 9 deict the dierin diagram and Blch imedance f the dual-band inverter f Fig. 8 inferred frm the chematic f Fig. 6 (by cnidering the element value and tranmiin line arameter f the tructure) and al frm the electrmagnetic rene (btained by mean f the Agilent Mmentum cmmercial ftware). The cnidered ubtrate i the ger O3010 with dielectric cntant r=10. and thickne h=1.7mm. A exected, the required hae hift at the erating frequencie i achieved. Since the tructure in nt erfectly balanced, a ingularity i berved arund the tranitin frequency (3.4GHz). Thi ingularity aear al in the characteritic imedance, but it i nearly frequency indeendent in the vicinity f the erating frequencie. l (a) f Circuit Sim. EM Sim. f Z B () 0 0,5 1,0 1,5,0,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 0,5 1,0 1,5,0,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 Frequency (GHz) Frequency (GHz) Fig. 9. Dierin diagram (a) and characteritic imedance (b) f the dual-band imedance tranfrmer, with Z A= 70.71, imlemented by mean f the tlgy f Fig. 8. The deigned and fabricated dual-band wer divider with final dimenin i deicted in Fig. 10. Ntice that the 50 acce line in rt 1 i imlemented by mean f a duble ided arallel tri line (b) Circuit Sim. EM Sim.

12 (a) P1 P1 W (b) P P (c) P3 P3 Fig. 10. Tlgy (a) and htgrah, t (b) and bttm (c), f the fabricated dual band wer divider. Dimenin are: W = 9.9 mm, = 19. mm. The circuit imulatin, electrmagnetic imulatin and meaured inertin l (S31 i very imilar t S1 and i nt deicted) and return l (S11) are deicted in Fig.11. The agreement between circuit, electrmagnetic imulatin and meaurement i reanable. The meaured inertin l (ntice that the ideal value i 3 db) and return l at the deign frequencie are I(f1) = 3.6 db, (f1) = 1.3 db, I(f) = 3.7 db, and (f) = 0.7 db. Device dimenin are 0.14g 0.8g, where g i the guided wavelength at f1. A it wa mentined befre, thi tye f tructure exhibit (ideally) frequency indeendent characteritic imedance, reulting in brader bandwidth, a cmared t ther CH baed circuit. Indeed, the deigned device exhibit a rughly cntant imulated inertin l and the matching level i better than 10dB in very brad frequency band in the vicinity f the deign frequencie. 0 S 1 (db), S 11 (db) S 1 S 11 Circuit Sim. EM Sim. Meaure -50 0,5 1,0 1,5,0,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 Frecuency (GHz) Fig. 11. Frequency rene f the fabricated dual-band wer divider deigned t erate at f 1=1.7GHz and f =5.4GHz (b). S 31 ha nt been included ince thi i imilar t S 1.

13 4. Cncluin In thi aer, the tentiality f lattice netwrk unit cell fr the imlementatin f enhanced bandwidth micrwave cmnent ha been demntrated. Thee all-a netwrk can be deigned t exhibit left handed, right handed r cmite right/left handed (CH) behaviur. Secifically in thi wrk, t eae deign and ynthei, the authr have cmbined a left handed lattice unit cell with a air f rdinary tranmiin line ectin in rder t imlement a dual-band imedance inverter with brad erating bandwidth. Thi inverter ha been then ued fr the imlementatin f a dual-band T-junctin wer divider. Thank t the nearly cntant characteritic imedance f the inverter in the vicinity f the deign frequencie, the divider ha been fund t exhibit gd matching level and wer litting ver wide band. T the authr knwledge, thi i the firt dual-band wer divider imlemented by mean f CH tructure (imedance inverter) that cmbine X-tye netwrk and tranmiin line ectin. 5. Acknwledgement Thi wrk ha been urted by MINECO-Sain (rject TEC and CSD ), and by AGAU-Generalitat de Catalunya, thrugh rject 014SG-157. Pari Vélez i in debt t MINECO (Sain) fr urting hi wrk thrugh the FPU grant AP eference 1. G.V. Eleftheriade and K.G. Balmain, Negative refractin metamaterial: fundamental rincile and alicatin, Jhn Wiley & Sn, Inc, New Jerey C. Calz and T. Ith, Electrmagnetic Metamaterial: Tranmiin ine Thery and Micrwave Alicatin, Jhn Wiley & Sn, Marqué, F. Martín and M. Srlla, Metamaterial with negative arameter: thery, deign and micrwave alicatin, Jhn Wiley & Sn, Inc, New Jerey I.H. in, M. De Vincenti, C. Calz and T. Ith, Arbitrary dual-band cmnent uing cmite rigth/left handed tranmiión line, IEEE Tran. Micrwave Thery and Technique, vl. 5, , Aril J. Bnache, G. Sió, M. Gil, A. Inieta, J. García-incón and F. Martín, Alicatin f cmite right/left handed (CH) tranmiin line baed n cmlementary lit ring renatr (CS) t the deign f dual band micrwave cmnent, IEEE Micrwave and Wirele Cmnent etter, vl. 18, , Augut C. Calz and T. Ith, Nvel micrwave device and tructure baed n the tranmiin line arach f metamaterial, IEEE-MTT Int l Micrwave Sym, vl. 1 Philadelhia, PA, , June A. K. Iyer and G. V. Eleftheriade. Negative refractive index metamaterial urting -D wave, in IEEE-MTT Int l Micrwave Sym., vl., Seattle, WA, , June A. A. Oliner. A eridic-tructure negative-refractive-index medium withut renant element, in USI Diget, IEEE-AP-S USNC/USI Natinal adi Science Meeting, San Antni, TX,. 41, June C. Calz and T. Ith. Alicatin f the tranmiin line thery f left-handed (H) material t the realizatin f a micrtri H tranmiin line, in Prc.IEEE-AP-S USNC/USI Natinal adi Science Meeting, vl., San Antni, TX, , June J.B. Pendry, A.J. Hlden, D.J. bbin and W.J. Stewart, Magnetim frm cnductr and enhanced nnlinear henmena, IEEE Tranactin Micrwave Thery Tech., vl. 47, , Nv

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