Eur. Phys. J. Appl. Phys. (2013) 63: 10502DOI: 10.1051/epjap/2013130023

THE EUROPEANPHYSICAL JOURNAL

APPLIED PHYSICS

Regular Article

Design of a novel negative refractive index material basedon numerical simulation

Muhammad Rizwan1, Yan-Kun Dou1, Hai-Bo Jin1,a, Zhi-Ling Hou2, Ling-Bao Kong2, Jing-Bo Li1,Faheem K. Butt1, and Fida Rehman1

1School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, P.R. China2School of Science, Beijing University of Chemical Technology, Beijing 100029, P.R. China

Received: 11 January 2013 / Received in final form: 7 April 2013 / Accepted: 26 June 2013Published online: 26 July 2013 – c© EDP Sciences 2013

Abstract. This paper presents a novel metamaterial constructed with wires, spheres and hollow slabs(WSHS), which simultaneously exhibits negative permittivity and permeability. An electromagnetic wavesimulation is performed based on the proposed metamaterial and shows that a negative refractive index isachieved for this metamaterial. Adjusting the lattice constant of the unit cell is an easy way to manipulatethe frequency of negative index of this structure. A left-hand material prism is designed composed ofmetamaterial unit cells and the simulation on the proposed prism proves the left-hand behavior of thedesigned metamaterial.

1 Introduction

Left-hand metamaterials have attracted significant inter-est in recent years due to their fascinating applicationsin invisibility cloaks, perfect lens, sensors, waveguides andresonators. These are artificially designed materials withnegative refractive index and do not exist naturally. Theidea of simultaneous negative permittivity and permeabil-ity was theoretically given by a Russian scientist Veselagoin 1967, who analyzed plane-wave propagation in aleft-handed medium [1,2]. His analysis provided the ideaof double negative (DNG) materials, i.e., a material inwhich both permittivity and permeability are simultane-ously negative and the Poynting vector of a plane wave isanti-parallel with its phase velocity [3]. Shelby et al. [4]went ahead with the work of Pendry et al. [5], and re-ported an anomalous refraction in a left-hand mediumcomprised of arrays of small metallic wires and split ringresonators [6,7]. To make a successful design of a left-hand material, the shape and geometry of the unit cellare the critical parameters. Up to date, designing new unitcells remains an active area for exploiting novel left-handmaterials and broadening the application of the left-handmaterials. In this regard, numerous methods have beenproposed to investigate and probe the design of struc-ture of the left-hand materials and their potential appli-cations [8–23]. Due to potential applications in antennareflectors and high gain compact antenna [24,25], perfectlens [26,27], multi-band absorber [28] and many others,the wire, fishnet and spherical left-hand material struc-tures gained considerable attention in past few years.

a e-mail: hbjin@bit.edu.cn

The purpose of this work is to take a step toward a newleft-hand material with unique unit-cell structure. We in-troduced a novel unit-cell structure which was composedof wires, spheres and hollow slabs and presented simula-tion results on this structure. The simulation showed thatthe proposed structure exhibited left-hand behavior re-gardless of the change of unit cell size. However, the start-ing values of the negative refractive index changed as thesize of unit cells was different. The parametric efficiency ofthe proposed left-hand material unit cell depends on thereflection and transmission coefficients. A left-hand ma-terial prism was constructed with the proposed unit cell.Electromagnetic wave simulation on the prism confirmedthe left-hand behavior of the present structure.

2 Unit-cell structure

A cubic unit cell is designed with cell dimension of d =4.0 mm, as shown in Figure 1. It is constructed based ona substrate with the thickness of 0.25 mm, of which thedielectric constant (ε′) is set to 3.8 and the loss tangentfactor (tg δ) 0.0015. There are two different copper struc-tures on two sides of the substrate, which are combined tomake a single unit cell. The thickness of copper wires onboth sides is 0.0017 mm whereas the upper side wires are0.15 mm in width and the lower side wires are 0.1 mm inwidth. The wires and hollow slabs have the same lengthof 3.3 mm on the upper side, whereas the total width oftwo hollow slabs is 3.1 mm as same as the length of wireson the lower side. The gap between the hollow slabs is0.6 mm. Spheres of 1.0 mm diameter are placed on the

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(a) (b)

Fig. 1. (a) Upper side of unit cell; (b) three-dimensional viewof unit cell, behind each hole there is a sphere of exactly samediameter on the lower side of the substrate.

lower side, exactly behind each hole of same diameter onthe upper side.

3 Numerical results and discussions

The sample is illuminated by a plane wave at normalincidence with the electric field parallel to the y-axis (E ‖y-axis) and the magnetic field parallel to the z-axis (H ‖z-axis). The resulting propagation direction is along thex-axis (k ‖ x-axis). FDTD (finite difference-time domain)simulations were performed to calculate S parameters.Perfect electric conductor (PEC) boundary conditionswere assigned for the side walls (x-y planes) of the unitcell a horizontally polarized electric field. Perfect magneticconductor (PMC) boundary conditions were employed forthe top and bottom walls (z-x planes) for a vertically po-larized magnetic field. This corresponds to normal inci-dence (x) of a TEM plane wave.

We use S parameter’s retrieval method to calculate theeffective parameters of the structure in Figure 1. In theliterature, the S parameter’s retrieval method has beendemonstrated to be a valid method [29–33] to calculatethe S parameters and the effective parameters for unit cellsas in Figure 1. In simulation, the frequency band rangesfrom 0.1 to 25 GHz. The real and imaginary parts of S arepresented in Figure 2. The minimum wavelength (whenfrequency is 25 GHz) is four times larger than the unit-cell size. The starting value of negative refractive index isat 18 GHz as shown in Figure 3a. Negative refractive in-dex lies in the frequency band from 18 GHz to 22.5 GHz,while in the remaining part it has a positive real valuewhich meets the requirements of second law of thermo-dynamics and the energy conservation. The real part ofpermeability is about 1 when the frequency is less than18 GHz or more than 23 GHz, which indicates the classicfeature of nonmagnetic material, as shown in Figure 3b.The negative real parts of permeability and permittivityin Figures 3b and 3c are observed in the frequency bandfrom 18 GHz to 22.5 GHz, which contributes the negativerefractive index.

To validate the negative refractive index behavior ofthe proposed structure, a full electromagnetic wave simu-lation is performed based on a left-hand material prism.The left-hand material prism is designed in accordancewith the prism proposed in previously reports [34–36], as

Fig. 2. (a) The real part and imaginary part of S11 and(b) those of S21.

Fig. 3. Effective material parameters (a) refractive index(b) permeability and (c) permittivity.

shown in Figure 4. It contains nine unit cells along y-axisand nine unit cells along x-axis. A rectangular electromag-netic wave is guided normally on the prism from the bot-tom face of the prism during simulation. The 18 GHz fre-quency is taken in simulation, which is the starting valueof negative refractive index. The wave propagates at rightangle to the injected wave as shown in Figure 4. The prismsimulation proves the presence of the negative refractiveindex at 18 GHz and hence proves the left-hand behaviorof the proposed structure.

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M. Rizwan et al.: Design of a novel negative refractive index material based on numerical simulation

Fig. 4. Prism simulations for the verification of left-handmaterial.

Fig. 5. The starting frequency of negative n for various unitcell sizes.

Figure 5 shows the dependence of starting frequencyof negative index (SFNI) on unit-cell size. It is shown thatSFNI decreases with increasing the lattice constant of theunit cell, so we can achieve the aimed negative refrac-tion frequencies according to the dependence of SFNI onthe unit-cell size. The special electromagnetic response ofa metamaterial is usually described by a simple equiva-lent circuit composed of an inductor L and a capacitorC [36]. From Figure 3, it can be observed that the SFNIis consistent with the resonance frequency. The resonancefrequency can be expressed as f = 1

2π√

LCwhere L is the

inductance and C is the capacitance. In general, C = εAa ,

where A is the area of the structure and a is the distancebetween the wires and hollow slabs. As the size of the unitcell increases the area of the wires and the two hollow slabsalso increases, subsequently the capacitance increases andthe resonance frequency decreases. C strongly depends on

the dimension of structure. To increase f one has to de-crease C. The impact of unit-cell size on SFNI is clearlyshown in Figure 5. For the unit cell with d = 3 mm, SFNIis at 24 GHz, and for the 10 mm unit-cell size, SFNI is atabout 8 GHz.

4 Summary

In this article, a novel metamaterial was constructed withwires, spheres and hollow slabs and numerical simulationson the metamaterial were carried out. The designed struc-ture led to negative refractive index. The left-hand be-havior of the metamaterial was proved by using the prismsimulation. The simulation showed that the proposedstructure exhibited left-hand behavior regardless of thechange of unit cell size, while the starting value of thenegative refractive index decreased with increasing latticeconstant of the unit cell.

This work was supported by the National High TechnologyResearch and Development Program of China (863 program)and the Key grant Project of Chinese Ministry of Education(Grant No. 313007).

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