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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011
Chiral Metamaterials With Negative Refractive Index Composed by an Eight-Cranks Molecule Gregorio J. Molina-Cuberos, Ángel J. García-Collado, Member, IEEE, Ismael Barba, and José Margineda, Member, IEEE
Abstract—A chiral medium constituted by a two-dimensional lattice of eight cranks of the same handedness is studied and found that it exhibits a huge electromagnetic activity, circular dichroism, and negative refraction index. Using a free-wave experimental setup and numerical simulations, the transmission and reflection coefficients for a thin slab of such metamaterials were determined, and the effective values for the refractive index, electric permittivity, magnetic permeability, and chirality parameter were calculated. The obtained results by means of the simulation agree quite well with the ones calculated from the experimental measurements. Index Terms—Chiral media, materials science and technology, metamaterials, microwave measurements.
I. INTRODUCTION
C
HIRAL media generate two possible effects on a linearly polarized propagating wave: rotation of polarization angle, known as rotatory dispersion, and polarization change from lineal to elliptical, known as circular dichroism [1]. Since it was predicted that materials with strong electromagnetic activity can also possess a negative refractive index [2], several chiral metamaterials (CMs) designs have been proposed and probed to produce such negative refractive index [3]. During the last years, different techniques to build materials with electromagnetic activity at microwave frequencies have been developed. They are mostly based on the periodical distribution of planar or quasi-planar particles, so they may use printed circuit board (PCB) technology. A review of some of those techniques may be found in [4]. García-Collado et al. [5] made use of solid metallic cranks placed in a foam host medium to design a unit cell composed by four metallic elements forming a cross. They experimentally demonstrated that a two-dimensional distribution of such Manuscript received October 13, 2011; revised November 21, 2011; accepted December 09, 2011. Date of publication December 21, 2011; date of current version January 30, 2012. This work was supported by the Dirección General de Investigación of the Spanish Ministerio de Educación y Ciencia (TEC 201021496-C03-02) and the Fundación Séneca Región de Murcia (11844/PI/09). G. J. Molina-Cuberos and J. Margineda are with the Departamento de Electromagnetismo y Electrónica, Universidad de Murcia, Campus Espinardo, Murcia 30100, Spain (e-mail:
[email protected];
[email protected]). A. J. García-Collado is with the Departamento de Electromagnetismo y Electrónica, Universidad de Murcia, Campus Espinardo, Murcia 30100, Spain, and also with the Departamento de Ciencias Politécnicas, Universidad Católica San Antonio, Murcia 30107, Spain (e-mail:
[email protected]). I. Barba is with the Departamento de Electricidad y Electrónica, Universidad de Valladolid, Valladolid 47002, Spain (e-mail:
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2011.2181306
Fig. 1. (right) Crank condensed node and (left) picture of the experimental mm, sample. The geometric parameters are given by mm, mm, mm, and mm.
cells is able to rotate a linear polarized wave, with homogeneous, isotropic, and reciprocal behavior for normal incidence. However, the material produced a strong absorption, especially around resonance. Barba et al. [6] designed an eight-cranks unit cell in PCB, and by using numerical time-domain simulations, they concluded that the structure works as a gyrator, and the rotation angle is basically proportional to the number of layers. Here, we present the experimental and numerical characterization of the structure proposed by Barba, and we show that, choosing the appropriate dimensions, the material exhibits a negative refractive index for one of the two propagation modes in the CM. Fig. 1 shows the schematic of the unit cell and a photograph of the experimental sample. The CM possesses symmetry on the perpendicular axis and, consequently, presents uniaxial chirality for a normal incident TEM wave. The unit cell is composed of eight same-handedness cranks and is patterned on an FR4 board with copper metallization 30 m thick, using both sides and connecting the segments through vias. The dimensions of the structure were chosen to resonate into the experimental frequency band (X-Band, 8.2–12.4 GHz), and the experimental sample is formed by a single layer of PCB. II. EXPERIMENT AND SIMULATION The macroscopic behavior of chiral media can be described by including a coupling parameter into the constitutive relations. Here, we make use of [1]
1536-1225/$26.00 © 2011 IEEE
(1) (2)
MOLINA-CUBEROS et al.: CHIRAL METAMATERIALS WITH NEGATIVE REFRACTIVE INDEX
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Fig. 2. (top) Electric and (bottom) magnetic fields in the incidence face of the crank condensed node shown in Fig. 1. The incident wave is polarized parallel to the -axis and is monochromatic, with a frequency of 12 GHz. The color scale is different for every component.
where and are the electrical permittivity and magnetic permeability, respectively, and is the chirality parameter. The characterization of the material requires the determination of the three constitutive parameters in (1) and (2). The experimental determination of the usual reflection and transmission coefficients do not provide enough information to describe the changes in the polarization needed to characterize the material. At least one additional measurement is required, and therefore magnitude and phase of three parameters are needed. Two transmission coefficients corresponding to polarization parallel and perpendicular of the incident wave one, and , and the reflection coefficient parallel to the incident wave, , were measured by using two standard rectangular horn antennas and a PNA-L N5230A network analyzer. A description of the experimental setup and the adaptations to measure electromagnetic activity can be found in [7] and [8]. In order to verify the experimental results, we have performed different simulations using a commercially available simulator in time domain, CST Studio Suite. We have modeled the normal incidence of a plane wave over one layer of CM formed by a distribution of cells, identical to our experiment, and obtained the same transmission and reflection coefficients, so we may compare the results obtained by means of both methods (experimental and numerical). The numerical modeling also makes possible the examination of the field distribution inside the node (see Fig. 2 for example). The electric field is consistent with the induction of an electric charge in the ends of every metallic crank, while the magnetic field rotates around the cranks due to the induced currents. The linear incident wave can be split into the two circular polarizations, i.e., right- and left-circularly polarized waves, RCP and LCP, which are the propagation modes in unbounded chiral media [9]. As a consequence, the electromagnetic coupling is overcome, and each propagation mode verifies a constitutive equation without the coupling parameter . Each mode propagates through the chiral media as if it were in an isotropic one. The transmission coefficients for the RCP and LCP modes can be calculated from and by (3)
Fig. 3. (left) Experimental and (right) simulation results of the reflection and transmission coefficients for (top) RCP and RCL waves, (middle) rotation angle , and (bottom) circular dichroism .
(4) The differences in magnitude and phase between are described by the rotatory power and ellipticity
and [10] (5) (6)
where the first one provides the rotation angle for a linearly polarized incident wave, and the last one describes the difference between the amplitudes of the two propagation modes. III. RESULTS AND DISCUSSION Fig. 3 shows the experimental (left) and simulation (right) results of the reflection and transmission coefficients for the RCP and LCP waves, the rotation of the polarization angle, and the ellipticity of the transmitted wave. The calculated results agree quite well with the experimental results. A clear resonance at 11.8 GHz is found for all the parameters, both measured and simulated. At resonance, the transmission coefficient of the LCP wave is higher than that of RCP, shown in Fig. 3(a) and (b), and therefore the transmitted wave is left-handed elliptical polarized. At the resonance, the transmitted wave is perpendicular to the incident one, and the linearly polarized incident wave is distorted after transmission and becomes elliptical. Far from the resonance, the transmission coefficients and are similar, and the incident wave remains linearly polarized after transmission, but the polarization plane is rotated by an angle . As typically occurs in chiral media, and experimentally tested here, the sign of the rotation angle changes if the handedness of the cranks is inverted in the unit cell. Fig. 4 shows the retrieval results of the effective medium parameters for the refraction index , chirality parameter, electric permittivity, and magnetic permeability obtained
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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011
Fig. 4. (left) Experimental and (right) simulation results of the effective medium parameters for (top) refractive index , (middle) chirality parameter , and (bottom) relative permittivity and relative permeability.
by means of experimental and numerical studies. The simulation results agree quite well with the experimental ones—for example, the difference in the resonant frequency obtained from both studies are in the order of some megahertz. Using numerical and experimental data, the resonant frequencies of the refractive index and chirality parameters are and GHz, respectively. For a very narrow frequency range of around 100-MHz width above the resonance, the effective index obtained from experimental data seems to be negative, although this was not found in the numerical study. The chirality parameter depends on the frequency following a pattern that has been found previously by other authors—see, for example, [3] or [10]—with a maximum value of . The imaginary part of is close to zero except inside a 1-GHz-width band. The RCP and LCP waves spread through the medium as if it were an isotropic one with refractive indices , respectively. The effective refraction index presents a strong dependence with frequency (Fig. 5), and it becomes negative for a 0.3-GHz-width band above the resonance. This negative value is due to and , and not due to permittivity and permeability being both negatives, as in traditional metamaterials. Nevertheless, it is also possible that, as we have seen, in a narrow band, the medium have a “traditional” negative index. By contrast with the refractive index of RCP, the value of changes lightly with frequency. The peak in the imaginary part of near the resonance produces a strong absorption of the RCP wave, much higher than the absorption of the LCP one, and therefore the transmitted wave is left-handed elliptical polarized, which is in agreement with Fig. 3(a) and (b). IV. CONCLUSION This letter presents the electromagnetic characterization of a chiral metamaterial formed by a two-dimensional lattice of eight
Fig. 5. (left) Experimental and (right) simulation results of the refractive index for the RCP and LCP waves, and , respectively.
cranks of the same handedness by using experimental and numerical techniques. A very strong electromagnetic activity with a transmitted wave perpendicular to the incident one, as well as circular dichroism has been observed. Moreover, negative refraction index is achieved, at least for one of the two circularly polarized waves due to the relative large value of the chirality parameter. The results obtained by the simulation agree quite well with the experimental ones. REFERENCES [1] I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves on Chiral and Bi-Isotropic Media. Norwood, MA: Artech House, 1994. [2] J. B. Pendry, “A chiral route to negative refraction,” Science, vol. 306, pp. 1353–1355, 2004. [3] B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Non planar chiral metamaterials with negative index,” Appl. Phys. Lett., vol. 94, p. 151112, 2009. [4] I. Barba, A. C. L. Cabeceira, A. J. García-Collado, G. J. MolinaCuberos, J. Margineda, and J. Represa, “Quasiplanar Chiral materials for microwave frequencies,” in Electromagnetic Waves/Book 2. Rijeka, Croatia: InTech, 2011. [5] A. J. García-Collado, G. J. Molina-Cuberos, J. Margineda, M. J. Nuñez, and E. Martín, “Isotropic and homogeneous behavior of chiral media based on periodical inclusions of cranks,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 3, pp. 175–177, Mar. 2010. [6] I. Barba, A. C. L. Cabeceira, A. Gómez y, and J. Represa, “Chiral media based on printed circuit board technology: A numerical time-domain approach,” IEEE Trans. Magn., vol. 45, no. 3, pp. 1170–1173, Mar. 2009. [7] J. Muñoz, M. Rojo, A. Parreño, and J. Margineda, “Automatic measurement of permittivity and permeability at microwave frequencies using normal and oblique free-wave incidence with focused beam,” IEEE Trans. Instrum. Meas., vol. 47, no. 4, pp. 886–892, Aug. 1998. [8] G. J. Molina-Cuberos, A. J. García-Collado, J. Margineda, M. J. Núñez, and E. Martín, “Electromagnetic activity of chiral media based on crank inclusions,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 5, pp. 278–280, May 2009. [9] C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett., vol. 29, pp. 458–462, 1974. [10] R. Zhao, L. Zhang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Conjugated gammadion chiral metamaterials with optical activity and negative refractive index,” Phys. Rev. B, vol. 83, p. 035105, 2011.
