magnetic and electric excitations in split ring resonators -凯发官网入口

arxiv:0710.0812v2 [cond-mat.mtrl-sci] 7 jul 2008magnetic and electric excitations in split ring resonatorsjiangfeng zhou, 1,2 thomas koschny, 2,3 and costas m. soukoulis 2,31 department of electrical and computer engineering and microelectronicsresearch center, iowa state university, ames, iowa 500112 ames laboratory and department of physics and astronomy,iowa state university, ames, iowa 500113 institute of electronic structure and laser - forth,and department of materials science and technology, university of crete, greecewe studied the electric and magnetic resonance of u-shaped srrs. we showed that higher orderexcitation modes exist in both of the electric and magnetic resonances. the nodes in the currentdistribution were found for all the resonance modes. it turns out that the magnetic resonances arethe modes with odd-number of half-wavelength of the current wave, i.e. λ/2, 3λ/2 and 5λ/2 modes,and the electric resonances are modes with integer number of whole-wavelength of current wave, i.e.λ, 2λ and 3λ modes. we discussed the electric moment and magnetic moment of the electric andmagnetic resonances, and their dependence to the length of two parallel side arms. we show thatthe magnetic moment of magnetic resonance vanishes as the length side arms of the srr reducesto zero, i.e. a rod does not give any magnetic moment or magnetic resonance.pacs numbers: 160.4760,260.5740introductionthe idea of negative index materials (nims), i.e. ma-terials with both negative electrical permittivity, ǫ, andmagnetic permeability, µ, was f i rst introduced by vese-lago [1]. however, it was only recently that such ma-terials were investigated experimentally, [2, 3, 4, 5, 6].although it has been well known how to obtain ǫ < 0material easily (e.g. using lattice of metallic wires), therealization of µ < 0 (especially at high frequencies) re-sponse had been a challenge, due to the absence of nat-urally occurring magnetic materials with negative µ. in1999, pendry et al. [7] suggested a design made a twoconcentric metallic rings with gaps, called split ring res-onators (srrs), which exhibit a µ < 0 around the mag-netic resonance frequency ω m . immediately after smithet al. [8] fabricated the f i rst negative index materialat ghz frequencies. recently dif f erent groups observed[9, 10, 11, 12] indirectly negative µ at thz frequencies.in most of the thz experiments, only one layer of srrswere fabricated on a substrate and the transmission, t,was measured only for propagation perpendicular to theplane of the srrs, exploiting the coupling of the electricf i eld to the magnetic resonance of the srr via asymme-try [13]. it was realized that one only need the singlesrr to see the magnetic resonance ef f ects. this wayis not possible to drive the magnetic permeability neg-ative. one reason is that is very dif f i cult to measurewith the existing topology of srrs and continuous wiresboth the transmission, t, and ref l ection, r, along thedirection parallel to the plane of the srrs. so there isa need for alternative, improved and simplif i ed designsthat can be easily fabricated and experimentally char-acterized. this new design was recently achieved in theghz region [14, 15] and the thz region [16, 17, 18, 19]by the use of f i nite length of wires and the f i shnet topol-ogy. very recent work has moved the negative refractiveindex into optical wavelength [20, 21].in this manuscript we systematically studied the elec-tric and the magnetic resonance response of u-shapedsrrs for dif f erent propagating directions. the ef f ectiveelectric permittivity, ǫ, as well as the magnetic permi-ability, µ will be extracted by the retrieval procedure[22, 23, 24]. in addition, the current distribution alongthe sides of the u-shaped srr will be numerically cal-culated. we show that the magnetic resonance are themodes with odd-number of half-wavelength of the currentdensity wave, while the electric resonance are modes withinteger number of whole-wavelength the current densitywave. in addition we studied the dependence of the elec-tric and magnetic resonance as a function of the length ofthe side arms of the u-shaped srr. it is found that themagnetic moment of the u-shaped srr vanishes as thelength of side arms of srr reduces to zero. so there isno magnetic moment or magnetic resonance for a metal-lic rod. one needs the side arms of the u-shaped srrin order to have a magnetic moment.electric and magnetic responses ofsrrsa common constituent to provide magnetic responsein metamaterials is the split-ring resonator (srr). thesrr in its simplest form consists of a highly conductivemetallic ring which is broken in one (or several) loca-tion(s) by a non-conductive gap of air or other dielectricmaterials. if this ring is placed in a temporally varyingmagnetic f i eld an electric circular current is induced inthe metallic ring which in turn leads to charge accumu-lating across the gaps. the electric f i eld which builds dueto the charge at the gap counteracts the circular currentleading to energy stored (predominantly) in vicinity of