Eur. Phys. J. Appl. Phys. (2013) 61: 30501DOI: 10.1051/epjap/2013120320

THE EUROPEANPHYSICAL JOURNAL

APPLIED PHYSICS

Regular Article

Resonant features of planar Faraday metamaterial with highstructural symmetry

Study of properties of a 4-fold array of planar chiral rosettes placed on a ferrite substrate

Sergey Y. Polevoy1, Sergey L. Prosvirnin2,3, Sergey I. Tarapov1,a, and Vladimir R. Tuz2,3

1 Usikov Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12, Proskura St., Kharkiv 61085,Ukraine

2 Institute of Radioastronomy, National Academy of Sciences of Ukraine, 4, Krasnoznamennaya St., Kharkiv 61002, Ukraine3 School of Radio Physics, Karazin Kharkiv National University, 4, Svobody Square, Kharkiv 61077, Ukraine

Received: 8 August 2012 / Received in final form: 15 November 2012 / Accepted: 8 January 2013Published online: 26 February 2013 – c© EDP Sciences 2013

Abstract. The transmission of electromagnetic wave through a planar chiral structure, loaded with thegyrotropic medium being under an action of the longitudinal magnetic field, is studied. The frequencydependence of the metamaterial resonance and the angle of rotation of the polarization plane are obtained.We demonstrate both theoretically and experimentally a resonant enhancement of the Faraday rotation.The ranges of frequency and magnetic field strength are defined, where the angle of polarization planerotation for the metamaterial is substantially higher than that one for a single ferrite slab.

1 Introduction

It is known, that bulk chiral artificial structures [1,2] man-ifest a reciprocal optical activity. The typical constructiveobject of 3D chiral media is a spirally conducting cylin-der. The concept of chirality also exists in two dimensions.A planar object is said to be 2D chiral if it cannot be su-perimposed on its mirror image unless it is lifted from theplane. For instance, an array of metallic rosettes is an ex-ample of such an object. Hetch and Barron [3,4], Arnautand Davis [5,6] were the first who introduced planar chiralstructures into the electromagnetic research. However, 2Dchirality does not lead to the same electromagnetic effectswhich are conventional for 3D chirality and, so, it becamea subject of special intense investigations [7–9].

Planar chiral materials are quite simple structures inmanufacturing. However, in contrast to traditionalfrequency-selective surfaces, they provide an additionaltwist parameter to control electromagnetic properties. Be-sides, in some particular cases, quasi-2D planar chiralmetallic structures can be asymmetrically combined withisotropic substrates to distinguish a reciprocal opticalresponse inherent to true 3D chiral structures. In suchmetamaterials, at normal incidence of the exciting wave,an optical activity appears only in the case, when theirconstituent metallic elements have finite thickness, whichprovides an asymmetric coupling of the fields at the airand substrate interfaces [10].

a e-mail: tarapov@ire.kharkov.ua

From the viewpoint of possible applications in micro-wave and THz frequency bands, it is known that the thin-ner metallic elements of planar structures are easier infabrication. Thus, knowledge about optical properties ofmetamaterials based on the thin planar structures isespecially important.

The results of a detailed study of polarization trans-formations caused by an array of the perfectly conductinginfinitely thin planar chiral elements are presented in [11].In this work, the optical response of planar metamaterialswith 4-fold symmetry was studied in the case, when thearrays are placed on an isotropic dielectric substrate. Oneof the results obtained in this study is an argument thatthe 2D chiral planar structures do not change the polar-ization state of the normally incident wave in the main dif-fraction order. This theoretical conclusion was confirmedwith numerical data obtained by a simulation in the caseof arrays made of infinitely thin metallic rosettes placedon a dielectric substrate.

From both fundamental and application points of view,the planar metamaterials placed on a ferrite substrate [12]and layered ferrite-dielectric structures [13,14] are quiteinteresting objects because they can be used successfullyto design non-reciprocal magnetically controllablemicrowave devices based on the Faraday effect. On theother hand, magneto-optically active substrate can serveas a sensitive element for THz magnetic near-field imag-ing in metamaterials [15]. The polarization rotation of anear-IR probe beam revealed in the substrate measuresthe magnetic near-field.

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A general theoretical approach is used in [2] to predictelectromagnetic properties of uniaxial composites with4-fold inclusions in the form of planar chiral gammadionscombined with ferrite ellipsoids. It needs two pseudo-vectors to describe the system. The first vector is a biasmagnetic field and the second one is a vector defining thehandedness of the gammadion shape. They are pseudo-vectors (axial vectors) because being time-odd. As a resultof the theory, these composite systems are bi-anisotropicnon-reciprocal media described by specific constitutiveequations of the same kind as those ones used in themoving chiral media.

However, it is necessary to clarify the effect of the par-ticles handedness (and the corresponding pseudo-vectorin the theory) on the system properties and the degreeof reciprocal rotation. As it has been mentioned above, itis important at least in the case of metallic planar chiralparticles which have small thickness in comparison withthe wavelength. The theoretical and experimental stud-ies of the particle handedness effect are extremely im-portant in this point and are the subject of the presentresearch.

Thus, the purpose of this paper is to study both the-oretically and experimentally the resonant properties ofplanar gyrotropic metamaterials (arrays of metallicrosettes placed on a ferrite substrate) depending on thevalue of static magnetic field strength. The field is appliednormally to the structure plane, i.e., the systems are con-sidered in the Faraday geometry. The periodic cell sizeof the studied metamaterials is chosen in such a way thatthe high-quality factor resonances appear in the structuresspectra in the millimeter waveband. We consider metama-terials based on a 4-fold symmetry array which consistedof thin metallic rosettes. As a main result of our study theessential resonant enhancement of the Faraday rotation isdemonstrated both theoretically and experimentally forthe metamaterial. This effect is substantially higher thanthat one for a single ferrite slab.

2 Structures under study and theoreticalapproach

The metamaterial being under investigation is designedas a layered structure, which consists of a planar chiralperiodic structure placed on a ferrite plane-parallel slabwith thickness 0.5 mm. The chiral structure is made offiberglass (ε′ = 3.67, tan δ = 0.06) with a thickness of1.5 mm, one side of which is covered with copper foil. Thefoil side of this layered structure is patterned with a peri-odic array whose square unit cell consists of a planar chiralrosette (see Fig. 1). The ferrite slab is leaned against thisarray of metallic elements. Two samples of each kind (i.e.,right-handed and left-handed elements) of gyrotropic pla-nar metamaterial 60 × 60 mm2 which are differed by theperiod of the rosette array have been performed. Sample 1of both right-handed and left-handed kinds has the periodd = 5 mm and the radius of rosette arcs a = 1.66 mm,whereas sample 2 has d = 4 mm and a = 1.33 mm, re-spectively. The angular size φ and the width w of the

(a)

(b)

Fig. 1. The periodic array of planar chiral elements placed ona dielectric substrate: (a) the photograph; (b) the square unitcell of the periodic array (d is the period of the structure) witha metallic element shaped as the planar chiral right-handedrosette (a is the radius of arc, φ = 120◦ is its angular size,w = 0.267 mm is the width of copper strips which form therosette).

copper strips which form the rosettes for all samples areidentical.

We applied the “resonant model” of “saturated” fer-rite [16,17] to calculate the ferrite constitutive parame-ters in the case when the static magnetic field H0 is morestronger than the field of the saturation magnetization4πMS, and the “non-resonant model” of “non-saturated”ferrite [18,19] if the field H0 is less than 4πMS.

When the field strength is larger than 4πMS, we usecommon expressions for permittivity and permeability forz-axis biased ferrite [16,17], assuming that the ferrite ma-terial is magnetically saturated and taking into accountthe dielectric and magnetic losses

εf = ε, μ̂f =

⎛⎝

μ iβ 0−iβ μ 00 0 μz

⎞⎠ , (1)

where

μ = 1 + 4π(χ′ − iχ′′), β = 4π(K ′ − iK ′′), μz = 1,(2)

χ′ = ω0ωm[ω20 − ω2(1 − α2)]D−1,

χ′′ = ωωmα[ω20 + ω2(1 + α2)]D−1, (3)

K ′ = ωωm[ω20 − ω2(1 + α2)]D−1,

K ′′ = 2ω2ω0ωmαD−1, (4)

D = [ω20 − ω2(1 + α2)]2 + 4ω2

0ω2α2,

ωm = γ4πMS, (5)

ω0 is the frequency of ferromagnetic resonance (FMR), αis the dimensionless damping constant, γ is the gyromag-netic ratio andMS is the saturation magnetization. We usethe Gaussian system of units. The ferrite material of brandL14H is characterized by the following set of parameters:ε = 13.2 − i0.0697, α = 0.0285, ωm/2π = 14.2 GHz.The value ωm corresponds to the saturation magnetiza-tion field of 4πMS = 4800 Oe.

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(a)

(b)

Fig. 2. (a) Theoretical dependencies of the componentsof permeability tensor for the thin ferrite slab versus thenormally applied static magnetic field at f = 30 GHz;(b) the same dependencies detailed for small static fields by“non-resonant” ferrite model.

When the field strength H0 is smaller than 4πMS, theexperiment can be well described using the non-resonant“non-saturated” ferrite model [18,19]. Let us note thatin the non-saturated model, the current magnetization Mis a function of the static magnetic field strength M =M(H0). The elements of the tensor μ̂f ( 1) are representedby empirical expressions [19]:

μ = μdem + (1 − μdem)(M/MS)3/2,

μz = (μdem)P , P = (1 −M/MS)5/2, (6)β = −γ4πM/ω, μ′′ = μ′′

z = β′′ = 0,

where μdem is the permeability of completely demagne-tized ferrite, whose properties can be calculated using thetwo-domain model [18] for frequencies ω > γ(Hr +4πMS):

μdem =13

+23

√(ω/γ)2 − (Hr + 4πMS)2

(ω/γ)2 −H2r

, (7)

where Hr is the strength of field matched to the rema-nent magnetization. For the used ferrite brand, it is Hr =3500 Oe. The dependence of the components of the per-meability tensor of ferrite versus the static magnetic field

Fig. 3. Theoretical dependence of the metamaterial resonancedip frequency on the static magnetic field strength for twovalues of period of the planar chiral structure. The solid linedenotes the dependence of FMR frequency of the ferrite on thestatic field according to the expression (8). The same depen-dence but corrected in the region of small field is presented bythe dashed line.

strength is presented in Figure 2 for the frequency f =ω/2π = 30 GHz.

For a thin ferrite slab magnetized normally to its plane,the FMR frequency ω0 is defined by the well-knownformula [17]:

ω0 = γ|H0 − 4πMS|. (8)

The dependence of FMR frequency versus the static mag-netic field strength is shown in Figure 3. Note that theformula (8) is rigorous when the field strength H0 is largerthan 4πMS. When the field strength is less than 4πMS,the frequency of FMR may be somewhat lower due to thefact that the ferrite changes in the multidomain state anda violation of its magnetic order grows as the static fieldstrength decreases (see the dashed line in Fig. 3). For thesame reason, the FMR linewidth should grow as the fieldstrength decreases.

As the field strength decreases below 4πMS, the do-main structure appears in the ferrite and its magneticstate demonstrates a certain disorder. Note that in thiscase, the values of the diagonal components of the μ̂f ,i.e., the value μ, tend to permeability of completely de-magnetized ferrite μdem (7). This value is not equal tozero (Fig. 2b). The latter is reasonable, because whendomains disorder, then their contribution to the integralmagnetization decreases. However, the magnetization ofeach domain is a positive value, in spite of the externalfield being directed along the domain magnetic momentor against it. Contributions to the diagonal componentsμ from all domains are added and it tends to some con-stant when the field strength decreases. A quite differentbehavior is observed for the off-diagonal component β. Asthe field strength decreases, the domains, whose magneticmoment is directed along the external field, and domains,whose magnetic moment is directed opposite to the field,give a different sign for the contribution to the β (the

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(b)

(a)

Fig. 4. Experimental setup: (a) the overview; (b) the schemeof experiment.

non-reciprocal Faraday effect). Thus, contributions of alldomains to the off-diagonal components β are subtractedand β tends to zero as the field strength decreases. Notethat when the field strength is less than 4πMS, the correctcount of the magnetic disorder of domain structure in theferrite should lead to the gradual change of the compo-nents μ and β.

The fields, intensities and polarization characteristicsof the electromagnetic waves diffracted by the array ofrosette-shaped elements were calculated using the fullwave method described earlier in [12]. This approach isbased on the method of moments for solution of the vec-tor integral equation for surface currents induced by theelectromagnetic field on the array elements [20]. The lastones are assumed to be perfectly conducting and infinitelythin. The equation was derived with boundary conditionsthat demand a zero value for the tangential componentof the electric field on metal strips. In our calculations,we used the Fourier transformations of fields and surfacecurrent distributions.

3 Experiment and data analysis

The experimental setup [14] consists of the structure un-der study, which is placed between two matching rec-tangular horns (transmitting and receiving ones) fittedto the Vector Network Analyzer Agilent N5230A. Hornsare situated on the axis passed normally to the plane ofthe structure (Fig. 4a). Using the Network Analyzer the

S-parameters, namely S21 – the transmission coefficientfor the structure in the frequency range 22–40 GHz, can bedetected and analyzed by the special computersoftware.

For measurements in a longitudinal static magneticfield, the structure and horns are positioned between thepoles of the electromagnet to provide the orientation ofthe components of electromagnetic field (E,H) and staticfield (H0) as it is shown in Figure 4b. The electromagnetpoles have axial holes, that allow one to place horns insidethe magnetic system. The poles diameter is 120 mm andthe distance between them is less than 30–90 mm. Notethat due to such sufficiently large poles diameter, the in-homogeneity of the static magnetic field in the structurearea does not exceed 3–5 %, which is quite enough to pro-vide experiments with high quality. The static magneticfield strength is controlled by a computer. A more detailedtechnique of such a kind fully automated experiment onecan find in [14].

First of all, let us mention that the experimental studyof transmission of normally incident wave through twokinds of planar chiral arrays which differed by sign of chi-rality was carried out in both cases of free standing arraysand arrays placed on ferrite substrate. It was shown thatthere is not any difference in the intensity of transmittedfield and polarization transformations obtained for thesetwo samples. Thus the experimental evidence of indistin-guishability of these properties has been demonstratedbetween two enantiomorphous kinds of planar chiralsamples which consisted of right-handed and left-handed thin metallic rosettes in the case of normallyincident wave. This property was argued theoreticallybefore in [11,12].

Thus, at the normal incidence of the exciting wave,the complex layered structure being a thin planar chiralmetallic array placed on the normally magnetized ferritesubstrate (or the isotropic dielectric substrate) does notmanifest any appearance of the property related to 3Dchiral objects. It is an impressive observation because thesymmetry is broken in the direction orthogonal to thestructure plane and we deal with the object which hasa volume chiral geometry. The reason lies in a very smalldifference between the fields existed on the array inter-faces with free space and the substrate in the case, whenthe considered array has a small thickness in comparisonwith a wavelength. A finite thickness of metallic elementsof the array is a prerequisite to make asymmetrically cou-pling fields at the air and substrate interfaces and to ob-serve an effect of volume chirality of such structure [10].

On the basis of the theoretical approach describedabove, we have defined numerically the transmissionspectrum of the structure under study. The characteris-tic frequency ranges where the transmission demonstratesa minimum and the resonant behavior exists (the metama-terial resonance dip frequency fr) were determined. Theseresonances are caused by metallic elements of the struc-ture. In the case of linearly y-polarized normally incidentplane electromagnetic wave, the dependence of fr on thestatic magnetic field strength has been calculated for two

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values of the planar chiral structure period d (see Fig. 3).Besides that, the dependence of the FMR frequency onthe static magnetic field strength for the thin ferrite slabused in experiments (f0(H0) = ω0/2π) is plotted in thesame figure.

One can see that: (i) the variation of the metamate-rial resonant dip frequency (dfr/dH0) is as stronger asthe frequency of this resonance is closer to the FMR fre-quency f0. This fact is caused, obviously, that near theFMR the value of the real part of the diagonal compo-nents of the permeability μ considerably increases. In turn,μ is uniquely connected with the value of the resonant fre-quency related to array; (ii) in the range of magnetic fieldstrengths from 12 500 Oe up to 15 000 Oe, two resonantdips (i.e., two values of resonant frequency for the samevalue of the magnetic field strength) are observed. Suchscenario is caused by the effect of resonance of not onlydiagonal components of the permeability but off-diagonalones as well. In particular, it is known [16,17], that inthe vicinity of FMR frequency, the eigenwave propagationconstant of the longitudinally magnetized ferrite can ac-quire more than one value (in the given case, it is two).To be specific, let us call the area, where the resonant fre-quency of array and FMR frequency are close enough toeach other as an “interaction area”; (iii) as the structureperiod increases, the resonant frequency of response dipsdecreases.

Comparison of experimental data and theoretical con-clusions has been made in the field range 0–6500 Oe. Inparticular, the qualitative agreement between experimen-tal and calculated data for the dependence of metama-terial resonance dip frequency fr on the magnetic fieldstrength (for the d = 5 mm) is revealed (Fig. 5). When themagnetic field strength exceeds the value corresponding tothe saturation magnetization field (4πMS = 4800 Oe), thederivation dfr/dH0 changes sign. It is related to the men-tioned above effect, namely the presence of low-field mode(with df0/dH0 < 0) in the FMR spectrum [16], when thefield strength is less than 4πMS. However, as it was ex-pected, the slope of the experimental frequency depen-dence of the metamaterial resonance dip on the magneticfield strength is a bit smaller than that one predicted in thetheory. This difference can be explained by the fact thatthe magnetically disordered domains appear in the struc-ture. The maximal value of frequency shift of the metama-terial resonance on the magnetic field strength (trianglemarkers in Fig. 5) is about 900 MHz. The origin of thedivergence between theoretical and experimental data isnon-equality of actual and theoretical values of the ferriteconstitutive parameters and their frequency dispersion.

In order to verify the non-reciprocal properties of themetamaterials under study, the experimental analysis ofthe electromagnetic wave transmission was performed forthe case where the angle between the plane of polariza-tion of transmitting and receiving horn is ψ = 45◦. Itcan be seen (Fig. 6) that both character and magnitudeof the shift of metamaterial resonance dip frequency de-pend strongly on the static magnetic field direction. Thus,the non-reciprocal properties of the investigated planar

Fig. 5. The dependence of the metamaterial resonance dipfrequency on the static magnetic field strength for planar chiralstructure d = 5 mm.

Fig. 6. Measured metamaterial resonance dip frequency of gy-rotropic planar chiral metamaterial versus the static magneticfield strength for d = 5 mm and ψ = 45◦.

metamaterial are demonstrated. Let us note, that forψ = 90◦ this dependence has the symmetric form as wasexpected. The last observation is yet another proof of anindependence of the metamaterial response on the hand-edness of metallic rosettes.

For a more detailed study of the polarization proper-ties of the metamaterial under study, we have performedthe experimental and numerical analysis of the polariza-tion rotation (more exactly, of the rotation of main axis ofthe polarization ellipse) of the wave transmitted throughthe structure with respect to the linearly polarized inci-dent wave. Theoretical dependencies of the angle of po-larization rotation θr(H0) on the magnetic field strengthfor two resonant modes of the metamaterial and for twovalues of its period d are shown in Figure 7.

The points marked by squares correspond to the high-frequency modes (hf-modes, located to the left of depen-dency f0(H0) in Fig. 3), and the points marked by circlescorrespond to the low-frequency modes (lf-modes,

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Fig. 7. Theoretical dependencies of the polarization rotationangle of two different metamaterial resonant modes versus thestatic magnetic field strength for two values of the structureperiod d.

located to the right of dependency f0(H0)). It is easilyseen that the structure with a smaller period rotates theplane of polarization on the greater angle than the struc-ture with the large period. This may be caused by higherquality factor of resonant modes in the structure with thesmaller period that occurs due to increase of the summarysurface of metallic elements when the period decreases.

One can see while the field strength tends to zero, therotation angle decreases to zero as well for both modes.This fully coincides with used theoretical models of ferritepermeability (Fig. 2), where it was shown that the off-diagonal component β which is responsible for polariza-tion rotation tends to zero as the field strength decreases.

This occurs, as mentioned above, due to the compen-sation of the effect of multidirectional domains orienta-tion on the rotation angle. However, let us note, that inthe “interaction area” (where H0 is from 12 500 Oe upto 15 000 Oe) polarization rotation angles increase drasti-cally. It can be seen that for high-frequency modes (squaremarkers) the maximum of θ reaches θr ≈ −50◦. For low-frequency modes (circle markers), this dependence looksmonotone (under the given field strength) and reaches themaximum values at θr ≈ 50◦.

Such resonant-like behavior of θr occurs obviously inthe “interaction area” due to increasing the values of off-diagonal components of the ferrite permeability (Fig. 2a)in the vicinity of FMR.

The results of experimental verification of dependen-cies θr(H0) (Fig. 7) and fr(H0) (Fig. 3) are summarizedin Figure 8. To provide clear demonstration of the ef-fect of geometrical parameters of the metamaterial un-der study on its polarization properties, experimental dataare shown for: (i) the polarization rotation angle θ of lin-early polarized wave transmitting through a ferrite slab(Fig. 8a); (ii) the polarization rotation angle θ of linearlypolarized wave transmitting through planar chiral struc-ture loaded with a ferrite slab when the period is chosento be d = 5 mm (Fig. 8b).

(a)

(b)

Fig. 8. Experimental dependencies of the polarization rotationangle θ as a function of frequency and static magnetic fieldstrength for: (a) ferrite slab; (b) ferrite loaded by planar chiralstructure with period d = 5 mm.

One can see that the surface plotted for the ferrite slab(Fig. 8a) is much smoother than that one for the arraystructure loaded with ferrite slab (Fig. 8b). The monotonicgrowth of θ from 0◦ to 15◦ with increasing field strengthfrom 0 Oe to 6500 Oe for all frequencies occurred for theferrite slab. A presence of moderate dips is caused by theimpossibility to provide the perfect matching of elementsof the experimental setup. Also, for the planar chiral arrayloaded with ferrite slab, a monotonic growth of θ on thefield strength takes place. However, near the frequencyof the metamaterial resonance dip (fr = 25.5 − 26.5 GHz(Fig. 5)), this dependence acquires a pronounced resonantcharacter, and for θ → θr achieves significantly highervalues than that one for the ferrite slab (up to θr ≥ 45◦).

It can be seen that the value θr (Fig. 8b) also de-pends on the magnetic field strength, and the maximumof θr is observed at H0 ≈ 4800 Oe (i.e., in the transitionarea from saturated ferrite model to unsaturated one).In this region the real part of permeability has extreme

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value (Fig. 2a), which explains the extremeness in thedependency of θr(H0).

Theoretical and experimental curves for the chiralstructure loaded with the ferrite slab are similar in shapeand exhibit a character extreme in the vicinity of the fieldstrength close to the saturation magnetization, as it is ex-pected from the general representations.

The distinct feature of the planar chiral Faraday meta-material (i.e., the resonant planar array loaded with fer-rite slab) is larger sensitivity of its polarization propertiesto the static magnetic field strength compared with thatone of the same ordinary ferrite slab. This phenomenoncan be explained by the fact that the resonant charac-ter of the magnetic permeability component of ferrite (ortheir strong frequency dispersion) is applied on the reso-nant character of oscillations in the planar chiral structure(strong frequency dispersion of the effective material pa-rameters of the chiral structure), which takes place in the“interaction area”. Note that a similar situation, known asthe amplification of the Faraday effect, has been detectedby the authors in the millimeter wave range before, but inmore simple resonant structures (the open resonator [21],the photonic crystal [14]). However, in the case consid-ered here, we are dealing with the structure being planarresonant metamaterial that promises the similar effect inthe very thin structure. The needed resonant properties ofthin metamaterial slab are imparted by complex shapedmetallic rosettes. The complex shape of array particles en-ables us to achieve resonant response of the structure inthe wavelength less than pitch of the array. The 4-foldsymmetry planar chiral rosettes are chosen to clear theway to design the polarization-insensitive array structureat least at normal incidence of the exciting wave. Thus wecan produce sub-wavelength resonant structures suitablefor such promising applications as planar metamaterialwhich is controllable by static magnetic field.

4 Conclusion

The transmission of electromagnetic waves of millimeterrange through the layered metamaterial formed by the res-onant planar chiral structure loaded with the gyrotropicmedium has been studied both experimentally and theo-retically. Namely: (i) the dependence of frequency of themetamaterial resonant response and the angle of polar-ization rotation on the longitudinal static magnetic fieldare detected, and a satisfactory agreement between thetheory and experiment is demonstrated; (ii) the range offrequencies and magnetic field strength where the angle ofpolarization rotation by the metamaterial appears essen-tially higher than that one related to a single ferrite slabis defined; (iii) at the normal incidence of the excitingwave, the independence of this metamaterial response on

handedness of its planar chiral thin metallic elements hasbeen verified; (iv) the usage of arrays with high structuralsymmetry based on planar chiral particles enables addi-tional means to produce sub-wavelength resonant meta-materials, which have small size of the periodic cell andcontrollable properties by static magnetic field.

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