Comment on "electromagnetic resonances in individual and coupled split-ring resonators"

Commen on ‘‘Elec omagne ic esonances in indi idual and coupled spli - ing esona o s’’ †J. Appl. Phys. 92, 2929 „2002…‡ R. Ma que ´s,a) F. Medina, and R. Ra ii-El-Id issi 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 3 Decembe 2002; accep ed 28 May 2003兲 I is poin ed ou ha he ecen ly epo ed esonances appea ing in spli - ing esona o s a e explained by he ecen ly epo ed heo y abou he magne oelec ic coupling 共o bianiso opy兲in he enso pola izabili y o hese pa icles. © 2003 Ame ican Ins i u e o Physics. 关DOI: 10.1063/1.1592317兴 Gay-Balmaz and Ma in ha e p esen ed a de ailed and indep h nume ical and expe imen al analysis o he so-called spli - ing esona o s 共SRRs兲.1These pa icles we e ecen ly p oposed by Pend y and co-wo ke s2as sui able elemen a y b icks o build up a i icial media wi h special elec omag- ne ic p ope ies, such as nega i e magne ic pe meabili y2 and/o nega i e e ac i e index3,4 when combined wi h a i- icial plasma media 共conduc ing wi e media兲. The analysis and expe imen s epo ed in Re . 1 con i m he p edic ions in Re . 2 abou he beha io o an indi idual SRR when i is placed in an ex e nal ime- a ying magne ic ield. Apa om he con i ma ion o he p edic ions o Pend y e al.,2some in e es ing esul s conce ning he beha io o hese pa icles a e also epo ed in Re . 1. Among hese esul s, i can be ound he exci a ion o a esonance when he SRR is illumi- na ed by an ex e nal elec omagne ic wa e wi h he magne ic ield pe pendicula o he pa icle axis 关 he so-called ‘‘pe - pendicula ’’ pola iza ion in Fig. 1共a兲o Re . 1兴. Since, in his case, he magne ic lux ac oss he ings anish, his beha io is no expec ed om he heo y epo ed in Re . 2 and de- se es a commen in o de o cla i y he unde lying physics. In ac , some mon hs be o e he publica ion o Re . 1, he au ho s o his commen published a heo y abou he ele an pola izabili ies o he SRR pa icle5in oducing some e inemen s on p e iously epo ed models. This heo y—which could no be known by he au ho s o Re . 1 a he da e o he submission—comple es he o me model o Re . 2 by aking in o accoun magne oelec ic couplings in he pa icle. In b ie , i can be said ha ou esonan pola - izabili ies a e p edic ed in:5 he so-called magne ic, ␣ zz mm , elec ic, ␣ yy ee , and magne oelec ic, ␣ yz em⫽⫺ ␣ zy me , pola iz- abili ies 共see Re . 5 o no a ion and coo dina e axis de ini- ions兲. The i s o hese pola izabili ies is accoun ed o in he heo y epo ed in Re . 2 and i is esponsible o one o he esonances shown in Fig. 2 o Re . 1 共 he one co e- sponding o pa allel pola iza ion兲. Al hough he emaining pola izabili ies a e no p edic ed in Re . 2, hey do lead o physical e ec s. In pa icula , he ␣ yy ee pola izabili y should p oduce a esonan abso p ion peak when he pa icle is placed in an ex e nal elec ic ield pola ized as in Fig. 1共a兲o Re . 1 共i.e., pe pendicula o he pa icle axis and o he s aigh line in he plane o he ing passing h ough he ing sli s兲. The ␣ zy me and ␣ yz em pola izabili ies also yield a esonan abso p ion peak o bo h ‘‘pa allel’’ and pe pendicula pola - iza ions o he inciden wa e shown in Fig. 1共a兲o Re . 1. All hese esonances a e epo ed in Re . 1, Figs. 2–5, as a esul o bo h expe imen s and compu e simula ions. I is also o in e es he ac ha no esonan abso p ion was ob- se ed o inciden wa es wi h he pe pendicula pola iza ion shown in Fig. 1共b兲o Re . 1. This ac is also consis en wi h he heo y epo ed in Re . 5, since no esonan pola izabil- i ies a e p edic ed in such a heo y ha could be exci ed by inciden wa es wi h his ield pola iza ion. The ela i e s eng h o he esonances 共which a e weake o pe pendicu- la pola iza ion兲can be also explained om he nume ical alues o he di e en pola izabili ies compu ed wi h he model in Re . 5. The e o e, i can be concluded ha he esul s epo ed in Re . 1 p o ide an expe imen al and nume ical e i ica ion o he heo y epo ed in Re . 5. Al hough in Re . 5, indi ec nume ical and expe imen al e idence o he heo y was gi en, we hink ha he expe imen s and nume ical simula- ions in Re . 1 p o ide a much mo e di ec e i ica ion o such a heo y. The aim o his commen is o poin ou his ac and o ecognize he con ibu ion o he au ho s o Re . 1 o his pa icula p oblem. 1P. Gay-Balmaz and O. J. F. Ma in, J. Appl. Phys. 92, 2929 共2002兲. 2J. 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. 3D. 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. 4R. A. Shelby, D. R. Smi h, and S. Schul z, Science 292,77共2001兲. 5R. Ma que ´s, F. Medina, and R. Ra ii-El-Id issi, Phys. Re . B 65, 144440 共2002兲. a兲Elec onic mail: [email p o ec ed] JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 4 15 AUGUST 2003 27700021-8979/2003/94(4)/2770/1/$20.00 © 2003 Ame ican Ins i u e o Physics