Cut wires grating –– single longitudinal wire” planar metastructure to achieve microwave magnetic-type resonance in a single wire

Here we present new metastructures consisting of a cut-wire grating and a sing le nonmagnetic longitudinal cu t-wire orthogo nal to grating’s wires. Experimental i nvestigations at m icrowaves show that th ese str uctures can pro vide str ong magnetically-induced re sonant res ponse of t he longitudinal cut-wire depending on the geometry in the case when a m etastructure is oriented along the direction of the wave propagation and the cut-wires of the grating are parallel to the electric fie ld of the incident plane electromagnetic wave. It is supposed that this response is due to the excitation of resonant currents by magnetic field of s urface polaritons in many equivalent spatial LC-circuits for med by cu t-wire p airs of th e gr ating and sections of th e longitudinal c ut-wire. Three res onant e ffects ha ve been separately obser ved and i dentified by measurements in waveguides, cutoff waveguides and free s pace. T hese effects a re conne cted with the grating, LC-circuits and the longitudinal cut-wire. To distinguish and tune the resonances we use split cut-wires loaded with varactor diodes.


Introduction
We kno w, at microwaves metamaterals with cond uctive nonmagnetic chiral i nclusions, c an possess a n e ffective magnetic p ermeability, which depends on the orien tation o f the in clusions with resp ect to th e m agnetic field h of t he incident el ectromagnetic wa ve. R esonance phe nomena are caused by the excitation of resonance currents by the field h. Presently ex tensive i nvestigations are d irected toward the development o f m agnetic m etamaterials co ntaining technologically si mple lin e non magnetic wires to ap ply in dispersion engineering [1]. The main attention is devoted to a cut-wire pair that posse sses both t he electric and m agnetic responses due to the possibility of parallel currents induction by the electric field and a ntiparallel currents, by the magnetic field [2,3].
Since the m agnetic a nd el ectric res onance responses are generated practically at the same frequency, it is difficult to separate these sign als and ev aluate th e m agnetic contribution. Term "parallel currents" means that induced currents i n parallel wires flow in th e sa me d irection in contrast to "antiparallel currents", when induced currents flow in the opposite directions.
In paper [4 ] it is sugg ested a n ew way to create sep arately a strong m icrowave m agnetically-induced resonance response using nonmagnetic cut-wires. Magnetic nature, magneticallyinduced re sonant re sponse or m agnetic-type res onance m ean that reson ance is due to th e ex citation of cu rrents by electromotive fo rce wh ich is caused by th e altern ating magnetic fi eld with acc ordance of F araday's l aw of electromagnetic in duction. Red uctive ex pression "ex citation of c urrents by magnetic fi eld", i s used rat her often, e .g. [2] and references. Electric-type resonance means that resonance currents are induced by electric microwave field. In [4] it was found in waveguides that a line nonmagnetic wire of length l m ( fig. 1 a), which is orien ted alo ng wav eguide ax is p arallel to the direction of propagation of an electromagnetic wave (and perpendicularly to its electric field E) a nd a rranged asymmetrically near a grating of cu t-wires l p (Grating), can exhibit a res onance res ponse of m agnetic nat ure. Grating (wires l p are parallel to the incide nt electric field E) fo rms surface polaritons bell ow the res onance freque ncy i n dependence on leng th l p . W ithout the Grating there is not response of longitudinal wir e l m . Asymmetrical location corresponds to th e position of lon gitudinal cut-wire l m , when distance t 1 ≠ t 2 in contrast to symmetrical location when t 1 = t 2 . A giant resonance is observed in longitudinal single cut-wire l m of a definite (resonance) length in a certain frequency range corresponding to the existence o f surface polaritons. In this paper we i nvestigate ex perimentally th is v ery in teresting phenomenon in waveguides (WG), cutoff waveguides (cutoff WG) and free space depending on the geometry. We suggest and verify a concept of magnetically-induced response based on possibility of resonant currents induction by magnetic field of s urface polaritons i n m any spatial LC-circuits fo rmed by Grating's cu t-wire l p pairs an d section s of th e l ongitudinal cut-wire l m . I n LC-circuits an tiparallel cu rrents flow in adjacent wi res l p w hile lik e-directed cu rrents f low along th e longitudinal cu t-wire l m . I n this pa per we dem onstrate and identify three separately ob served res onant effects. The first resonance is due to p arallel cu rrents i nduction in Grating's wires, the second resonance effect is due to the excitation of resonance currents in LC-circuits and t he t hird res onance i s due t o t he resonance cu rrent al ong l ongitudinal c ut-wire l m. Varactor-loaded sp lit cu t-wires are app lied to tun e an d distinguish the resonances.

Investigated metastructures. Concept of the magnetically-induced response
Investigated metastructures con sist of a gratin g of cu t parallel co pper wi res with len gth l p (Grating) an d a s ingle nonmagnetic (copper) l ongitudinal cut -wire (length l m ) which is pl aced per pendicularly to wi res l p on di stance s ( fig. 1a). One can imagine the metastructure as matter with many LC-circuits fo rmed by cut-wi re pair s of the Grating and sections of th e longitudinal cut-wire. In the case wh en metastructure is placed al ong propagation direction magnetic-type resona nce effects are observed. Obtained results allow to sugg esting a con cept of th e reson ance responses. Me tastructures " Grating -sing le lo ngitudinal cut-wire", " Wire pair -longitudinal c ut-wire", " Gratingparallel cut-wire" are investigated depending on geometry. Metastructures with varactor-loaded sp lit lo ngitudinal cutwire and split parallel cut-wire are also investigated.

Measurements methods (waveguides, free space)
We ha ve m easured fre quency de pendence of the transmission coefficient T of el ectromagnetic wa ve of metastructures wi th panoramic st anding-wave-ratio a nd attenuation meter s R2-5 3 (3 -6 GH z) an d R2-6 1 (8 -12 GHz). Metastruct ures are arranged along the a xis a nd oriented p arallel to t he side wall of a stand ard rectangu lar waveguide ( fig. 2a). B esides we h ave m easured frequency dependence of t he tran smission coe fficient T of electromagnetic wav e with metastructures arra nged i n below-cutoff rectangular sec tion. T he m easurements were performed in frequency range 3-6 GHz, in this case we used WG (48 x24 mm) an d a below-cutoff re ctangular section (16x24 mm ). W e have also u sed a standar d waveguide (23x10 mm ) an d a below-cutoff rectan gular sectio n (8x10mm) to measure transmission in frequency range 8-12 GHz. To prepare below-cuto ff rectangular section a fragment o f th e m ain WG (of th e length L= 25mm) is divided int o t hree se ctions by m etal spacers parallel to t he direction of wave propagation. Investigated metastructure is placed into a central cutoff rectangular section ( fig. 2b). A comparative analysis of the signal transmission spectra in the m ain and b elow-cutoff rectangu lar sectio n is an important m ethod of i dentification of t he type of exci ted resonance [ 5]. F or e xample, i n t he ca se o f m agnetic excitation (m agnetic-type resonance i n WG, MR) th e transparency band i n cutoff WG is observed above the MR frequency. In ad dition, t he m agnetic ex citation is characterized by the prese nce of s uper-forbidden ba nd below t he MR. In t he case of electric e xcitation (electrictype resonance, ER), the transparency band in cutoff WG is observed below the ER frequency. We ha ve al so measured t he fre quency dependence of t he transmission coefficient T of metastructures arranged in free space in the gap between transm itting and receiving waveguides for two cases . In the first cas e receivi ng a nd transmitting WG are plac ed along th e sam e ax is (Adirection). In the second case receiving WG is placed along transverse B-direction ( fig. 2c).

"
Grating -single longitudinal cut-wire" metastructure Below we presen t resu lts of in vestigation of m etastructure "Grating -sing le lo ngitudinal cu t-wire" (Fig.1a), lik e [4 ], placed along propagation direction of electromagnetic wave and engineered to have magnetic resonance properties using only c ut-wires, l p an d l m are lengths o f gr ating's wi re and longitudinal cu t-wire, sdi stance between Grating l p a nd single wire l m Grating (w ires l p are parallel to the E-field) exhibits a r esonance r esponse, wh ich is man ifested by resonance I of the electric-type an d cha racterized by a resonance dependence of the transmission coefficient with a minimum at a cert ain frequency de pendent o n t he wi re l p length. This Grating is ex cited by the E-field (induction of parallel curre nts) and generates surface wa ves (polaritons ) near res onance I (below the resonance fr equency). Local transverse magnetic fi eld of polaritons i nduces electromotive forces and resonance currents in many spatial LC-circuits (such as abghefa and cdehgbc created from cutwire pairs of Grating and sectio ns of longitudinal cut-wire) and resonance current along longitudinal cut-wire. These Gratings a re used in metastructures to ac hieve re sonance effects in range 3 -6 GHz. Grating with l p = 21mm al lows t o o bserve re sonance effects conn ected with both Grating, LC-circuits an d longitudinal cu t-wire l m . Grating with l p =16mm is selec ted so as to sh ift r esonance I to hi gh-frequency edge of the interval of measurements and do not overlap with resonance connected wit h longitudi nal cut-wire l m . Fig. 3a shows th e frequency de pendences of t ransmission T measured in t he presence of Grating of wires l p =21mm, for which resonance I is observed in the WG at 6 GHz and pass-band is observed in th e cu toff WG section at frequ encies b elow th is resonance. Fig. 3b shows cor responding frequency dependences o f T measured in th e pr esence of G rating of wires l p =16mm, for which resonance I and pass-band (below I) a re ob served ab ove 6 GHz in the WG an d cu toff WG. Position of pass-band below th e reson ance I specifies electric excitation a nd el ectric-type re sonance of the Grating. Now let u s co nsider t he results of m easurements in th e presence of metastructure " Grating -si ngle l ongitudinal cut-wire". In fig. 4ab we s ee fre quency dependences of transmission T measured in WG, cut off WG and in free space i n t he presence of m etastructures " Grating -single longitudinal cu t-wire" with th e same l p =21mm, s=0.2mm, t= l p /4 and l m =26mm. In this case in addition to resonance I  The position of reso nance MR III depends on leng th l m . The resonance III is observed at frequency 3.4 GHz in the case of l m1 = 26mm ( fig. 4a). W ith decreasing l m to l m2 = 24mm resona nce MR III shifts to hi gher f requencies and observed at 4 GHz (Fig. 4c). Fig. 5 shows frequency depe ndences of transmission measured in WG a nd cut off WG (a ,b) a nd i n f ree s pace (c,d) in t he presence of m etastructure " Grating -sin gle longitudinal cut-wire" with th e same l p =16mm, l m =23mm, t= l p /4 but different distance s. W ith l p =16mm it is easy to observe h ow t he res onance III shifts in dependence on s because resonance I and corresponding pass-band in cutoff WG would shift to the high-frequency edge of the interval of m easurements a nd do not o verlap with m agnetic-type resonance III related to the l m wire. Re sonance III was excited at 5.1 GHz for a distance of s 1 =2.7mm an d sh ifted to lo wer frequen cies (4 .7 GHz) when s 2 was d ecreased to 1.1mm ( fig. 5a). When s 3 =0.2mm resonance III of l m wire was observed at f requency 3.5 GH z ( fig. 5b). Th e belowcutoff section ex hibited t he co rresponding pa ss-bands (above frequency of t he m agnetic-type re sonance III of l m wire and supper-forbidden bands (below III, which occur at about 5 a nd 4.4 G Hz a nd fol low behind t he s hifting resonance III. Resonance II related to th e LC-circuits was depicted at fre quency 5.2 GHz in WG a nd free space ( fig.  5b,c).
Resonance III of l m is not depicted in free space in Adirection, but one can obse rve resonance resp onse in Bdirection by measurement of cross-polarized reflected wave from l m wire, fig. 5d. In this case electric field of reflected wave is parallel to longitudinal cut-wire l m and is orthogonal to the E -field of incident wave. A stro ng reson ance III is obs erved when t he l m wire is arranged asymme trically (t = l p /4), its in tensity d ecreases when l m wire shifts to symmetrically location. In the case of t=l p /2 resonance response III is absent. Strong MR III is ob served i f th e l m value i s close t o halfwavelength i n t he f requency re gion a djoining re sonance I from t he si de of l ower f requencies, w hich i s t he regi on of existence of surface polaritons generated by Grating l p . It is easy to prepare like structures to achieve magnetic-type resonance re sponse of a si ngle l ongitudinal wi re l m in different frequency ranges. Thereto it takes only to choose necessary lengths of wires l m and l p . Fig. 7 sh ows th e resonance III and dependence on wire l m length in range 8 -13 GHz. In the case of l p =6mm and l m1 =11mm resonance III is o bserved at 8 G Hz. The resonance MR III shifts toward higher frequencies (8.8 GHz) with decreasing l m1 to l m2 =9mm. Pass-band of the below-cutoff section in this case exhibits th e correspo nding shift an d is observed ab ove th e resonance MR III. In the case of metastructure with two longitudinal cut-wires l m1 and l m2 two MRs III are excited at different frequencies and t wo co rresponding pass-bands (in c utoff WG sect ion) appear above the resonances III ( fig. 6).
Resonance MRIII at f requency 4 .1GHz is prov ided b y wire l m1 = 25mm and resonance at fre quency 5 .3GHz i s provided by w ire l m2 = 21mm. Thi s expe riment al so co nfirms con nection a nd dependence o f res onance III on w ire l m length. P osition of pass-bands confirms magnetic excitation and magnetic-type of the resonances III.
It is easy to prepare like structures to achieve magnetic-type resonance response of a si ngle l ongitudinal cut -wire l m in different frequency ranges ( fig. 7). Thereto it takes only to choose necessary lengths of wires l m and l p . Fig. 7 shows the resonance III and dependence on wire l m length in range 8 -12 GHz. In the case of l p =6mm and l m1 =11mm resonance III is o bserved at 8 G Hz. The resonance MR III shifts toward higher frequencies (8.8 GHz) with decreasing l m1 to l m2 =9mm. Pass-band of the below-cutoff section in this case exhibits th e correspo nding shift an d is observed ab ove th e resonance MR III.

"Wire-pair -longitudinal cut-wire" metastructure
One ca n im agine Grating l p as com position of m any wi repairs and confirm suggested conception by investigation of metastructure consisting one wire pair and longitudinal cutwire. We investigate metastructure (see fig. 8), created from one pai r of cut-wires AB in co mposition with asymmetrically lo cated lon gitudinal cu t-wire CD orthogonal to AB (wires AB are parallel to the electric fiel d of i ncident el ectromagnetic wav e). We show t hat t his metastructure can al so possess m agnetic-type res onance of longitudinal cu t-wire CD a t fre quencies di fferent f rom electric resona nce of c ut-wires AB. Conditions t o ach ieve magnetically-induced response and resonance properties are similar to th e case of m etastructure "Grating-longitudinal cut-wire". In Fig. 9a we see f requency dep endences of transmission T measured in WG a nd c utoff WG i n the presence of metastructure "Cut-wire pair -l ongitudinal cutwire", distance d between wires AB is 20mm.   We observe in WG electric resonance I related to the wire pair AB without longitudinal w ire CD at 6 GHz a nd corresponding pass-band in cutoff WG (below resonance I).
In add ition with "Cu t-wire-pair -lon gitudinal cu t-wire" metastructure we o bserve m agnetic-type res onance III related t o wire CD a nd c orresponding pass-band i n cut off WG (above the resonance III), fig. 9a. W ith decreasing of the length l AB resonance I shifts to the high-frequency edge of the i nterval of m easurements an d do not ov erlap with magnetic-type resonance III related to the CD wire (Fig. 9  b,c).

. "Grating -parallel cut-wire" metastructure
Let u s co nsider " Grating -sing le parallel cu t-wire" metastructure created from grating of wires l p and a cut-wire (marked l e ) located parallel l p on distance s (Fig. 10.) In this case electric-dipole resonance (ER) is excited, which depends on t he wi re l ength (l e ) an d ca n b e ob served both with and without Grating l p . Th e b elow-cutoff sectio n exhibits a p ass-band, whi ch si tuated bel ow the ER frequency and is characteristic of t he electric excitation. In the case of strong c hange of distance s resonance frequency related to l e wire is no t practically sh ifted (Fig. 11) in contrast to MR frequency related to l m wire (Fig. 5a,b). In the case of using two wires with different lengths l e1 and l e2 two ERs ( ER 1 and ER 2 ) a re e xcited at di fferent frequencies an d t wo pass-bands (in cut off WG) a ppear bellow resonances ER that are characteristics of the electric excitation (Fig. 12).

Split longitudinal cut-wire and parallel cut-wire loaded with varactor diodes
It is special interest to study a metastructure using varactor diodes. In [6] it has bee n demonstrated that the resonance frequency of sp lit ring resonators (SRRs) can b e tuned using v aractor diodes. Th e resulting p article has b een called a varactor-loaded sp lit ring reson ator (VLSRR). In this paper we use va ractor diodes in metastructures to tune resonance response related to cu t-wires and m atch th e resonance m inima of t ransmission T to con crete reson ant elements with certain ty wh at is im portant fo r m ultiresonance system. By an alogy with [7 ] we call resu lting cut-wire as varactor loaded sp lit lon gitudinal cu t-wire l m a nd varactor-loaded split parallel cut-wire l e .   (Fig. 14) and from 3.34 GHz to 3.49 GHz (Fig. 15) with the tuning voltage V DC from 0 to 10v. Corresponding pass-band in cutoff WG (above III) follows the shifting resonance III.
Positions of resonances I and II are practically not changed. Metastructure " Gratingv aractor lo aded split p arallel cu twire l e " consis ts of Grating l p and sp lit cu t-wire l e lo aded with varactor. This metastructure exhibits electric resonance response I related to Grating of w ires l p and electric resonance ER related t o varactor l oaded sp lit p arallel cutwire l e . Fig. 16 shows that the resonance ER shifts from 4.6 GHz to 4.86 GHz with the tuning voltage V DC from 0 to 10v corresponding to varactor tun ing cap acitance fr om 9.63 to 1.47 pF.

Discussion
Obtained results allo w t o su ggesting a con cept o f magnetically-induced re sonance re sponse (m agnetic-type resonance) based on e xcitation o f r esonant cu rrents by electromotive force which, w ith acc ordance of Faraday's law of el ectromagnetic i nduction, i s c aused by t he transverse m agnetic field of surface po laritons in m any equivalent s patial LC-circuits fo rmed by cut-wire pair s of the Grating a nd sections of the longitudinal cut-wire l m . Is there an y po ssibility o f t raditional electric ex citation of current in cut-wire l m ? Theoretically, yes, because near each cut-wire-end of the Grating the re a re electric fiel d's longitudinal c omponents i n m utually op posite di rections (parallel and an tiparallel to th e wave vector k). Th erefore these c omponents of t he field can i nduce curre nts i n opposite directions along the longitudinal cut-wire; so, total longitudinal cu rrent m ust be practically ab sent. Besi des practically exi stence of t he l ongitudinal electric field near the Grating has been not depicted [7] when double split ring was used as a pr obe f or d etermining t he ori entations of surface polaritons local fields. It has been s hown t hat m etastructure e xhibit electric-type resonance I of the Grating forming surface polaritons below the res onance fre quency depending on len gth l p . T his resonance is due to th e excitatio n of parallel reso nance currents in cut-wires l p by electric field. It has bee n sh own that metastructure exhibit magnetic-type resonance II of LC-circuits de pending on l ength l p and distance s between t he l ongitudinal c ut-wire l m an d th e Grating. It has bee n sh own that metastructure exhibit magnetic-type resonance III in range of surface polaritons ex istence, depending on length l m and distance s. This resonance is due to the excitation of resonance current in a single longitudinal cut-wire l m . 3. Concept of m agnetic-type res onances (m agneticallyinduced respon ses) is presen ted. Th e concep t is b ased on the ex citation of circu lar resonance curren ts in m any equivalent spa tial LC-circuits an d co rresponding ind uced magnetic m oments by th e tran sverse mag netic field of surface p olaritons (resonance II). In this case a ntiparallel currents flow in the Grating's adj acent cu t-wires l p wh ile like-directed currents flow along cut-wi re l m . C urrents contribution of many LC-circuits provides strong resonance current a nd electric dipole moment along cut-wire l m a nd strong resonance effect (resonance III).