Beruete, M.

Navarro-Cia, Miguel

Orazbayev, B.

Pacheco-Peña, V.

Torres, V

English

Here we present numerical and experimental results of a zoned fishnet metamaterial lens with dual-band response. Good performance is demonstrated at frequencies 54 GHz and 55.5 GHz at which the fishnet metamaterial behaves as a medium with refractive indexes n1 = -0.78 and n2 = -0.43, respectively. Experimental focal lengths are FL1=8.4λ1 and FL2=9.4λ2. The dual-band response of zoned fishnet metamaterial lens shows potential for application in non-mechanical zoom millimeter-wave imaging system

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  University of BirminghamZoned fishnet metamaterial lens with millimetre-wave dual-band responseOrazbayev, B.; Pacheco-Peña, V.; Torres, V; Beruete, M.; Navarro-Cia, MiguelLicense:None: All rights reservedDocument VersionPeer reviewed versionCitation for published version (Harvard):Orazbayev, B, Pacheco-Peña, V, Torres, V, Beruete, M & Navarro-Cia, M 2015, Zoned fishnet metamaterial lenswith millimetre-wave dual-band response. in 2015 9th European Conference on Antennas and Propagation(EuCAP). Institute of Electrical and Electronics Engineers (IEEE), pp. 1-3.Link to publication on Research at Birmingham portalGeneral rightsUnless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or thecopyright holders. 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Mar. 2020Zoned fishnet metamaterial lens with millimetre-wave dual-band response  B. Orazbayev1, V. Pacheco-Peña1, V. Torres1, M. Beruete1, M. Navarro-Cía2 1 TERALAB (MmW—THz—IR & Plasmonics Laboratory), Universidad Pública de Navarra, Campus Arrosadía, 31006 Pamplona, Spain. miguel.beruete@unavarra.es 2 Optical and Semiconductor Devices Group, Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2BT, UK; Centre for Plasmonics and Metamaterials, Imperial College London, London SW7 2AZ, UK; and Centre for Terahertz Science and Engineering, Imperial College London, London SW7 2AZ, UK. m.navarro@imperial.ac.uk  Abstract—Here we present numerical and experimental results of a zoned fishnet metamaterial lens with dual-band response. Good performance is demonstrated at frequencies 54 GHz and 55.5 GHz at which the fishnet metamaterial behaves as a medium with refractive indexes n1 = -0.78 and n2 = -0.43, respectively. Experimental focal lengths are FL1=8.4λ1 and FL2=9.4λ2. The dual-band response of zoned fishnet metamaterial lens shows potential for application in non-mechanical zoom millimeter-wave imaging system. Index Terms—fishnet metamaterial, millimiter waves, metallic lenses. I.  INTRODUCTION  Since the dawn of civilization the possibility of controlling transmission of light has been of great interest for researchers. The best-known devices, the conventional dielectric lenses have been successfully used for this purpose even before Maxwell´s equations were reported. However, such lenses are limited to the electromagnetic parameters of natural materials. By introducing metallic lenses [1] Kock demonstrated new possibilities of lens design based on artificial dielectrics. A further advance has been recently witnessed with the appearance of metamaterials, which allow manipulation both permittivity (ε) and permeability (μ), and have made possible perfect lenses, superlenses, hyperbolic lenses, chiral lenses, ε-near-zero (ENZ) lenses, etc. [2]–[7]. The fishnet metamaterial has shown good performance for higher frequencies, because of its lower losses and frequency-robust magnetic response. Hence, lenses based on the fishnet metamaterial have also shown good performance [8]–[10], although they are still relatively bulky to be integrated in compact systems. The time-honored zoning technique can help to solve this problem. Although such a technique reduces even more the frequency range of the fishnet metamaterial lens [11], [12]. Therefore an optimization of the zoned lens profile is required, in order to have a dual regime. In this work we present simulation and experimental results for the dual-band zoned fishnet metamaterial lens [13]. II. LENS DESIGN The design procedure of the zoned fishnet metamaterial lens with dual band response consists of two steps: first, an application of the zoning technique in order to obtain a slim profile, and second, finding the optimal profile of the lens supporting the dual regime. A. Zoning technique In order to obtain a slim profile for the fishnet lens the zoning technique is applied, whereby redundant material is removed each time one wavelength phase shift is reached. The limit of the thickness t depends on the free-space wavelength λ0 and the index of refraction of the medium n [1]: nt10 , (1) From the general equation of an ellipse [10] we obtain the design equation of the lens profile [11]:  tnnxnFLnFLzlenslenslenslens,1)1()1()1(mod22222, (2) where nlens is the effective refractive index of the structure, FL is the focal length, and m is an integer (m = 0, 1, 2, 3) that represents the successive steps for the zoned lens profile. B. Final design The unit cell of the fishnet metamaterial, used in this work, has the following parameters: dx = 2.5 mm, dy = 5, dz= 1.5 mm and w = 0.5 mm (Fig. 1(a)). The effective index of refraction of the fishnet metamaterial evaluated from the dispersion diagram, using the Eigenmode solver of CST Microwave StudioTM [14], is shown in Fig. 1(a). For the chosen working frequencies f1 = 54 GHz and f2 = 55.5 GHz the effective refractive indices are nlens1 = -0.78 and nlens2 = -0.43 respectively. Due to the discretization imposed by dx and dz, the zoned profile is approximated by a staircase profile, which is outlined in Fig. 1(b) (black solid line), where also the curves for both frequencies defined by (2) for four successive steps (m = 0, 1, 2, 3) are plotted (dashed blue and red lines, respectively). The zoned fishnet metamaterial lens is optimized to work in the dual band regime by a minimization of the root-mean-square-error between (2) and the staircase approximation. As a result a slim dual-band zoned fishnet metamaterial lens with two focal lengths Work supported by the Spanish Government under contract Consolider Engineering Metamaterials CSD2008-00066 and contract TEC2011-28664-C02-01. V.P.-P. is sponsored by Spanish MECD under grant FPU AP-2012-3796. B. O. is sponsored by Spanish MINECO under grant FPI BES-2012-054909. V.T. is sponsored by UPNA. M.B. is sponsored by the Spanish Government via RYC-2011-08221. M. N.-C. is supported by the Imperial College Junior Research Fellowship. In memoriam of Professor Mario Sorolla. FL1=48.7 mm (8.8λ1) and FL2 = 55 mm (10.2λ2) is synthetized. The fabricated lens is demonstrated in Fig. 1(c). The final design has overall dimensions 111 mm × 135 mm × 8 mm (19.8λ1 × 24.1λ1 × 1.4λ1).   Fig. 1. a) Effective refractive index of an infinite fishnet metamaterial. (Bottom-right inset). The unit cell dimensions: dx = 3mm, dy = 5mm, dz = 1.5mm, metal thickness w = 0.5 mm and hole diameter a = 2.5 mm. b) Lens profiles and curves of the successive steps for: f1 = 54 GHz (dashed blue curve) and for f2 = 55.5 GHz (dotted red curve), the thickness limits, t1 and t2 (blue and red horizontal curves, respectively). c) Fabricated zoned fishnet metamaterial lens. III. RESULTS First, the zoned fishnet metamaterial lens is simulated with the transient solver of CST Microwave StudioTM. In order to reduce the computational effort, magnetic and electric symmetries are used at yz- and xz-planes respectively. A vertical polarized (Ey) plane-wave has been used as a source exiting the structures from their planar face. In Fig. 2(a, c) the numerical results for the field distribution on the xz-plane are plotted for the design frequencies f1 = 54 GHz and f2 = 55.5 GHz respectively. The focal length FL = 44.2 mm (7.9λ1) and 50.3 mm (9.3λ2), the depth of focus DF= 10 mm (1.8 λ1) and 10.7 mm (2λ2), and the FWHM along x is 2.8 mm (0.5 λ1) and 2.8 mm (0.5λ2) for f1 and f2 respectively. Finally, in Fig. 2(b, d) experimental results for spatial power distribution in xz-plane are shown for f1 and f2 respectively. Agreement between simulation and experimental results is evident. The focal length FL = 47 mm (8.4λ1) and 51 mm (9.4λ2), the depth of focus DF= 13.7 mm (2.5 λ1) and 14.2 mm (2.6λ2), and the FWHM along x is 3.3 mm (0.6 λ1) and 3.4 mm (0.6λ2) for f1 and f2 respectively. The numerical and experimental values of the focal lengths coincide with the design values. IV. CONCLUSIONS The dual-band zoned fishnet metamaterial lens has been designed, fabricated and measured at the V-band of millimeter-waves. Experimental and simulation results are in good agreement. The low-profile and weight of the zoned lens with millimeter-wave dual-band response demonstrates a possibility to work in integrated systems with good competition to other conventional diffractive optical devices.   Fig. 2. The spatial power distribution on the xz-plane for f1 = 54GHz (a, b) numerical and measured respectively, and for f2 = 55.5 GHz (c, d) numerical and measured respectively.  REFERENCES [1] W. E. Kock, “Metal-Lens Antennas,” Proc. IRE, vol. 34, no. 11, pp. 828–836, Nov. 1946. [2] J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett., vol. 85, no. 18, pp. 3966–3969, Oct. 2000. [3] N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens.,” Science, vol. 308, no. 5721, pp. 534–7, Apr. 2005. [4] Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects.,” Science, vol. 315, no. 5819, p. 1686, Mar. 2007. [5] V. V. Shevchenko, “The geometric-optics theory of a plane chiral-metamaterial lens,” J. Commun. Technol. Electron., vol. 54, no. 6, pp. 662–666, Jun. 2009. [6] A. Demetriadou and Y. Hao, “A Grounded Slim Luneburg Lens Antenna Based on Transformation Electromagnetics,” IEEE Antennas Wirel. Propag. Lett., vol. 10, pp. 1590–1593, 2011. [7] M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B, vol. 86, no. 16, p. 165130, Oct. 2012. [8] M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Planoconcave lens by negative refraction of stacked subwavelength hole arrays,” Opt. Express, vol. 16, no. 13, p. 9677, 2008. [9] M. Navarro-Cía, M. Beruete, M. Sorolla, and I. Campillo, “Converging biconcave metallic lens by double-negative extraordinary transmission metamaterial,” Appl. Phys. Lett., vol. 94, no. 14, p. 144107, Apr. 2009. [10] M. Navarro-Cía, M. Beruete, I. Campillo, and M. S. Ayza, “Beamforming by Left-Handed Extraordinary Transmission Metamaterial Bi- and Plano-Concave Lens at Millimeter-Waves,” IEEE Trans. Antennas Propag., vol. 59, no. 6, pp. 2141–2151, Jun. 2011. [11] V. Pacheco-Peña, B. Orazbayev, V. Torres, M. Beruete, and M. Navarro-Cía, “Ultra-compact planoconcave zoned metallic lens based on the fishnet metamaterial,” Appl. Phys. Lett., pp. 1–12, 2013. [12] V. Pacheco-Peña, B. Orazbayev, M. Beruete, and M. Navarro-Cía, “Zoned Near-Zero Refractive Index Fishnet Lens Antenna : Steering Millimeter Waves,” J. Appl. Phys., pp. 1–8, 2014. [13] B. Orazbayev, V. Pacheco-Peña, M. Beruete, and M. Navarro-Cía, “Exploiting the Dispersion of the Double-Negative-Index Fishnet Metamaterial to Create a Dual-Band Low-Profile Metallic Lens,” Sci. Rep. [14] CST Computer Simulation Technology AG, “CST Microwave Studio.” http://www.cst.com, 2015.   

Zoned fishnet metamaterial lens with millimetre-wave dual-band response

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Zoned fishnet metamaterial lens with millimetre-wave dual-band response

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