A review of the manufacturing techniques for developing
chiral media based on the inclusion of cranks is presented.
Chirality is usually obtained by a randomdistribution of helices
in a host medium. Here the chiral elements are obtained by
bending thin metal-wires in three segments. We will show that a
random distribution of cranks is able of rotate the polarization
angle of the transmitted linearly polarized wave at microwave
frequencies. This effect can be enhanced by the precise location
of cranks forming a 2D periodic lattice. Several structures are
analyzed looking for isotropy, reciprocity and homogeneity.Ingeniería, Industria y Construcció

García Collado, Ángel Joaquín

Margineda Puigpelat, Jose

Martín Rodríguez, Ernesto

Molina Cuberos, Gregorio José

Núñez Trigueros, María Jose

Repositorio Digital de la Universidad Católica San Antonio de Murcia

Developing Chiral Media Based on the Inclusion of Metallic Cranks

Institutional Repository UCAM

3RD CONGRESS OF PORTUGUESE COMMITTEE OF URSI, LISBON, 3RD AND 4TH OF NOVEMBER 2009 1Developing Chiral Media Based on the Inclusion ofMetallic CranksGregorio J. Molina-Cuberos1, Angel J. Garcı´a-Collado2, Jose´ Margineda1, Marı´a J. Nu´n˜ez1, Ernesto Martı´n1.Abstract—A review of the manufacturing techniques for devel-oping chiral media based on the inclusion of cranks is presented.Chirality is usually obtained by a randomdistribution of helicesin a host medium. Here the chiral elements are obtained bybending thin metal-wires in three segments. We will show that arandom distribution of cranks is able of rotate the polarizationangle of the transmitted linearly polarized wave at microwavefrequencies. This effect can be enhanced by the precise locationof cranks forming a 2D periodic lattice. Several structures areanalyzed looking for isotropy, reciprocity and homogeneity.Index Terms—Chiral media, Materials science and technology,Microwave measurements.I. INTRODUCTIONELECTROMAGNETIC activity is the property of somematerials to rotate a linearly polarized incident wave.These media are composed by elements with chiral symmetry,and the phenomena occurs at frequencies depending on thesize of the elements. In such material the electric and magneticfields are coupled, which can be macroscopically describedthrough the following constitutive relations [1]:~D = ² ~E − jκ ~H~B = µ ~H + jκ ~Ewhere ² = ²0²r is the permittivity, µ = µ0µr is thepermeability and κ is the chirality parameter.For a linearly polarized incident wave, the transmittedwave passing through such medium is rotated and ellipticallypolarized. This is a consequence of the differences on phasevelocities and on absorption for the left -and right- circularlypolarized components. These propagation constants can bedetermined by:k± = ω√µ² (1± κr)where + and − subscripts are related with the right- and leftcircularly polarized waves, respectively, and κr is the relativechirality κr = (²rµr)−1/2.For homogeneous and isotropic media, the chirality param-eter is a complex number and its real part is related to therotation angle by:θ = 2dω√²0µ0κ′This work was supported by the Direccio´n General de Investigacio´n ofthe Spanish Ministerio de Educacio´n y Ciencia, under the projects/grantsTEC2006-13268-C03-01. TEC2006-13268-C03-02 and TEC2006-13268-C03-03.1 Grupo de Electromagnetismo, Facultad de Quı´mica, Universidad deMurcia, Campus Espinardo, E-30100, Murcia, Spain.2 Dpto. de Ciencias Polite´cnicas, Universidad Cato´lica San Antonio,Guadalupe, E-30107, Murcia, Spain.therefore the experimental determination of the rotation angleprovides information about the real part of the chirality.Materials with electromagnetic activity at microwave fre-quencies are usually made by spreading helical inclusions intoa host medium. The helices must be randomly oriented withno special direction in order to assure isotropy, otherwise theresult is a macroscopically bianisotropic material. We havedeveloped a new kind of materials based on the inclusion ofthree segment wire hooks, “cranks”.In a previous paper, we show that a random distributionof cranks produces girotropy, and the rotation angle dependson the frequency following a Condon model, with only onefrequency [2]. However, a helix is a much compact structure,and for the same total wire length helix are smaller thancranks, which makes the number density of cranks to be lowerthan the one using helices and increases the inhomogeneity.Therefore, the material can present both local density varia-tions and accidental alignments of the cranks, which causesfluctuations of the transmitted wave when the sample is rotatedor when a different sample area is illuminated by the incidentbeam. To experimentally determine the rotation angle, we hadto measure several samples and a mean value of the rotationangle was carried out.In order to enhance the isotropic degree, we have searchedthe chiral behavior by placing the cranks forming 2D periodicstructures. We have designed several lattices composed bycranks with different sizes and orientations. In this paper wemake a short review of some of our achievements in thedevelopment of chiral media based on metallic cranks.II. DESIGN OF CHIRAL MEDIAThe most widely used fabrication technique consists ondistributing, as randomly as possible, helices in a dielectrichost medium. Following this procedure, chiral media usingcranks instead of helices was manufactured, by first time [2].Chiral elements were produced from a 0.4 mm diameter and12.6 mm length copper wire. Wires are bent in three segmentsby two 90 degrees angles, all with the same handedness. Theelements were dispersed in an epoxy resin with a low curingtemperature. Special attention was paid to obtaining a randomand homogeneous distribution without privileged directions.The samples were 30 cm diameter and 1.5 cm wide disks,with an average inclusion number density around 2 cm−3. Thedensity results much lower than the inclusion number densityobtained when helices were used [3] and therefore a higherinhomogeneity degree.The homogeneity problem can be solved by locating thecranks forming 2D structures. For example, by introducing3RD CONGRESS OF PORTUGUESE COMMITTEE OF URSI, LISBON, 3RD AND 4TH OF NOVEMBER 2009 2one of the segments into the host medium, a 5 mm widthslab of foam with a relative permittivity close to one. Therest of the crank, two segments forming a 90 degrees angle,remains located on the front side of the host medium. Keepingthe back side of the medium completely free of metals. Thisis a quite laborious technique with some problems linked tothe manufacturing process, such us the lack precission in thelocation of the cranks.In order to increase the fabrication quality and to introducemore parameters for material design, we make use of printedcircuit boards, PCB. The three dimensional cranks are pro-duced by using conductive pathways in both sides of the PCBand metalized holes.A periodic lattice of cranks presents some adventages com-pared with the random distribution of helices. New parametersfor material design, such as the relative length of segmentsand lattice characteristic lengths are now available. However,it present also some disadventajes related with the alignmentsof the cranks, which produces anisotropic materials. We willprove that unwanted effects can be overcome by using differentcrank orientations.Fig. 1 shows pictures of three samples produced by follow-ing the manufacturing techniques before described: randomdistribution of cranks in an epoxy matrix, cross distributionof cranks in foam forming a 2D periodic structure, and aPCB based periodic structure, which are labelled as “RND”,“CROSS” and “PCB”, respectively.III. EXPERIMENTAL RESULTSThe electromagnetic activity has been measured by makinguse of an experimental set-up for X-band previously re-ported [3]. It is based on a free-wave system, initially designedfor permittivity and permeability measurements, and adaptedto measure the rotation angle of a linearly polarized wave. Anincident beam is focused by an ellipsoidal concave mirror sothat diffraction problems are minimized, even with relativelysmall samples. The transmitting antenna is placed at one ofthe mirror foci and the sample at the other one. The receivingantenna can rotate about the longitudinal axis, which allowsthe measurement of the scattering parameters (S parameters)corresponding to any polar transmission.Fig. 2 shows the angle of rotation for RND sample, theerror bars show the standard deviation of the mean for 10measurements at different sample regions [2]. The solid lineis the expected value of the rotaion angle obtained by fitting aone frequency Condon model [5] to the experimental data. Weobserve that the rotation angle depends on the frequency fol-lowing the typical chiral behavior, with a resonance frequencyat around 8.5 GHz. A similar frequency dependence was alsoobserved on composites formed by randomly oriented helix[6], [7] and [3].When 2D periodic structures of cranks are analyzed, wehave found, in most of cases, that the rotation angle dependson the relative orientation between the cranks and the incidentwave [4]. Fig. 3 shows an example of the rotation angle fortwo different orientations between cranks and incident wave.Clearly, the observed girotropy is a non-chiral effect. We haveFig. 1. Detailled image of the samples: a) Random distribution of cranks(RND), b) Cross distribution of cranks forming a 2D periodic structure(CROSS). c) PCB based periodic structure (PCB).7 8 9 10 11 12 13−30−20−100102030Frequency (GHz)Rotation angle (deg)Fig. 2. Rotation angle produced by the sample shown in Fig. 1a. Dotsand bars are, respectively, the mean value and standart deviation for 10measurements of different sample regions. Solid line is calculated by fitting aCondon model to the experimental data. Reproduced from IEEE-MCWL 19,278-280, 2009 [2].3RD CONGRESS OF PORTUGUESE COMMITTEE OF URSI, LISBON, 3RD AND 4TH OF NOVEMBER 2009 3also verified the sample is not reciprocal. Therefore the rota-tion due to chirality, if any, is hidden by other electromagneticeffects.However, it is possible to cancel the non-chiral effects by anadequate distribution of cranks and to build chiral media withhomogeneous, isotropic and reciprocal behavior at microwaverange for normal incidence. Fig. 4 show the rotation angleproduced by CROSS sample (dots) and the experimentaluncertainty on the angle determination (vertical bars). Wehave verified that the rotation angle does not depends on theorientation of the sample. It seems that the cross distributionof cranks cancells the non-chiral effects.The dependence with frequency of the rotation angle issimilar to the one obtained by using a random distribution ofcranks, Fig. 2. It also follows a Condon model with one reso-nance frequency at around 10 GHz. We also observe the samedependence for waves incident both from the front side andfrom the back side, i.e. the media is also reciprocal. We havealso experimentally confirmed the fact that a sample formedby elements with different handedness produce a change in thesign of the rotation angle, with the same resonance frequency.Finally, the typical chiral behavior can be also produced byPCB based materials. Fig. 5 shows the rotation angle producedby “PCB”, which does not depend on the relative orientation ofthe incident wave nor on the incident plane. Here the resonancefrequency looks to be outside our measurement range, and itcouldnot be determined.IV. CONCLUSIONSHere the state of the art for developing chiral media basedon conductive cranks is reviewed. We present it is possibleto produce a rotation in the polarization angle for a linearlypolarized wave at microwave frequencies by using differentstructures of cranks randomly dispersed or periodically local-ized in a host medium.REFERENCES[1] I.V. Lindell, A.H. Sihvola, S.A. Tretyakov, and A.J. Vitanen, “Electro-magnetic Waves in Chiral Media”. Boston, MA: Artech House, 1994.[2] G.J. Molina-Cuberos, A.J. Garcı´a-Collado, J. Margineda, M.J. Nun˜ez,E. Martı´n, “Electromagnetic Activity of Chiral Media Based on CrankInclusions”, IEEE Microwave and Wireless Components Letters, vol 19,pp. 278–280, 2009.[3] A. G’omez, A. Lakhtakia, J. Margineda, G.J. Molina-Cuberos, M.J.Nu´n˜ez, J.S. Ipin˜a, A. Vegas and M.A. Solano, “Full-Wave Hy-brid Technique for 3D Isotropic-Chiral-Material Discontinuities inRectangular Waveguides: Theory and Experiment”, IEEE Trans. Mi-crow. Theory Tech., vol. 56, num. 12, pp. 2815-2825, 2008. doi:10.1109/TMTT.2008.2007190.[4] A.J. Garcı´a-Collado, G.J. Molina-Cuberos, J. Margineda, M.J. Nun˜ez, E.Martı´n, “Isotropic and Homogeneous Behaviour of Chiral Media Basedon Periodical Inclusions of Cranks”, submitted to IEEE Microwave andWireless Components Letters, 2009.[5] E. U. Condon, “Theories of Optical Rotatory Power”, Rev. of ModernPhys., vol. 9, pp.432-457, 1937.[6] G. Busse, J. Reinert and A. F. Jacob, “Waveguide characterization ofchiral material. Experiment” IEEE Trans. Microw. Theory Tech., vol 47,No 3, 1999.[7] C.R. Brewitt-Taylor, P.G. Lederer, F.C. Smith and S. Haq, “Measurementsand predictions of helix-loaded chiral composites”, IEEE Trans. AntennasPropag., vol. 47, pp. 692-700, 1999.8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13−40−30−20−1001020304050Frecuency (GHz)Rotation angle (deg)Fig. 3. Girotropy produced by a 2D structure for two different orientationsbetween cranks and incident wave.8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13−30−20−100102030Frecuency (GHz)Rotation angle (deg)Fig. 4. Rotation angle produced by ”CROSS” sample. Dots and bars are,respectively, the experimental value and the experimental uncertainty. Solidline is calculated by fitting a Condon model to the experimental data.8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13−1001020304050Frecuency (GHz)Rotation angle (deg)Fig. 5. Rotation angle produced by ”PCB” sample.

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Developing Chiral Media Based on the Inclusion of Metallic Cranks

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