A two-component NZRI metamaterial based rectangular cloak Open Access

In the recent years, a great deal of interest has been reported in the literature on the physics and engineering of metamaterial. Metamaterials are naturally unavailable artificially constructed uncommon materials that may have some exciting electromagnetic properties. These exotic properties may include, negative permittivity (ε < 0) or permeability (μ < 0), negative refractive index, inverted Snell’s law etc. Victor Veselago $i ¯ n$ 1967,¹ depicted a concept of materials of such reversed characteristics but the matter was not much interesting to the researchers due to the unavailability of such natural materials. Around 30 years later Smith et al.² in the year 2000, practically presented a composite material of such negative properties and using such material they also successfully designed a first invisibility cloak in the microwave range in the year of 2006.³ Metamaterial that display both negative permittivity (ε) and negative permeability (μ) simultaneously are called double negative (DNG) or left handed (LH) metamaterial. Metamaterial with either negative permittivity or permeability is called single negative (SNG) metamaterial. In this regard, according to V. Veselago, the sign of refractive index will be negative as well, if both the permittivity and permeability is found to be negative. However, because of these unconventional features of metamaterial, it can be utilized in many important applications like electromagnetic absorption reduction, antenna design, filter design, invisibility cloaking, absorber design etc.^3–7 There are many metamaterial structures have been proposed in the literatures for specific applications but metamaterial with near zero refractive (NZRI) properties in the three axis are rarely found. For example, O. Turkmen et al. in Ref. 8, presented a single axial nested–U type metamaterial for C-and X-band applications but they used multiple ring for producing multi-band functionality and their metamaterial did not show near zero refractive (NZRI) property. Abdallah Dhouibi et al. in Ref. 9, designed a Z-shaped metamaterial for C-band applications but their metamaterial was not demonstrated for near zero refractive (NZRI) property and for z-axis wave propagation. In addition currently, a metamaterial unit cell structure was reported in Ref. 10 for S-band applications but it was showing epsilon negative property in conjunction with NZRI property for the x-axis wave propagation only. Similarly, there are some double negative metamaterials found in the literature like, T. D. Karamanos et al. in Ref. 11, proposed a dual frequency metamaterial in the C-band for the single axis wave propagation but they used two different metamaterial structures in the two sides of the substrate. S. S. Islam et al. in Ref. 12, claimed a metamaterial for the C-band but it’s effective medium properties were calculated for the z-axis wave propagation only. However, recently one of prominent applications of NZRI metamaterial is invisibility cloak design. The cloak of invisibility is a form of alteration that makes an object hidden. An object will be invisible if it prevents to scatter waves in any direction from it. By using metamaterial shell, the scattering from an object can be reduced. For ensuring the cloaking operation, usually the scattering cross section (SCS) of an object is reduced to zero.¹³ After the first design that was mentioned in Ref. 3, very few works are found in the literature in this field. For example, P. Alitalo et al. in Ref. 13 designed a single layer cylindrical cloak that works in 3.3 GHz. They also demonstrated a cloak in Ref. 14 for X-band but it was a cylindrical type cloak. Ladislau Matekovits et al. in Ref. 15 constructed a single layer cylindrical cloak as well using a metasurface of width modulated unit cell but it works in the K-band only.

In this paper, a new pi-shaped NZRI metamaterial is proposed that shows NZRI properties for x and z-axis wave propagation in the microwave regime. The metamaterial is then used for designing a rectangular invisibility cloak and it works well in the C-band of microwave spectra. Commercially available CST Microwave Studio simulation software was utilized to obtain all the reflection and transmission parameters of the unit cell and the cloak.

The design parameter and the schematic view of the proposed unit cell structure are given in Fig. 1(a). The unit cell structure is designed with two metal parts of copper and they are placed in such a way that it forms a pi-shape with all of them having thickness of 0.035mm. Each part has two arms that are joined orthogonally. The two joined arms are not equal in size. There is a gap between the two parts where upside gap is denoted by ‘g’ and its value is 0.33mm. Similarly, the lower side gap is denoted by ‘s’ and its value is 0.5mm. In this design, each arm of the unit cell acts as inductance and each gap of the unit cell are responsible for generating capacitance. The equivalent circuit is given in Fig. 1(b). As the length of each arms and the gaps in the unit cell are not equal, the inductances and capacitances are marked as L1, L2, C1, and C2 respectively.

However, the structure is designed over a square shaped FR-4 substrate material with dielectric constant of 4.2, dielectric loss-tangent of 0.002. The side length and width of the substrate is of 10 mm and thickness of 1.6 mm. The rest of the design parameters are seen in the Table I. In this study, the commercially available Finite-integration-technique (FIT)-based computer simulation technology (CST) Microwave Studio software is used to obtain the transmission and reflection parameter of the unit cell. To show the operation of the unit cell initially the z-axis wave propagation is executed and then the x-axis wave propagation will be performed. For z-axis wave operation, the unit cell was placed between positive and negative wave-guide ports at the z-axis and the electromagnetic wave was propagated in the z-axis. The perfect electric and perfect magnetic conductor boundary conditions were applied in the rest of the axis. For simulation, frequency domain solver was used for simulation and 1001 frequency samples were taken. The simulation was executed for frequency range between 5 to 9 GHz. The simulation geometry for z-axis wave propagation is seen in the Fig. 2(a).

For measurement purpose, a fabricated prototype was built using 14 × 23 unit cells as seen in Fig. 2(b). The dimension of the prototype was 140 × 230 mm². The measurements were performed in an open space region using two broadband horn antennas placed 1.5 m apart. The prototype was placed between the horn antennas in such a way, which ensure the z-axis wave propagation through the prototype. A vector network analyzer N5227A was used to calculate the S-parameters of the unit cell. Moreover, for calibration purpose, measurement with and without prototype were performed as well.

The current distribution of the unit cell at the frequency of 8.29 GHz is showed in the Fig. 2(c). Unlike the split ring resonator, the current is following opposite direction in the two arms of the unit cell because of the dissimilar geometry of the unit cell.

The Fig. 3(a) displays the simulated and measured S-parameters magnitude of the unit cell for the z-axis electromagnetic wave propagation. It depicts that, the transmission parameter (S₂₁) exhibits one broad resonance in the frequency of 8.29 GHz in the microwave region. These resonance are also belongs to the X-band of the microwave spectra. However, the measured result is presented where the transmission coefficient shows bit left shifted resonance at the frequency of 8.21 GHz than the simulated amplitude. This shift usually happens due to open space measurement process or fabrication errors.

The effective medium parameters permittivity, permeability, refractive index can be determined from the simulated complex parameter S₁₁ (reflection coefficient) and S₂₁ (transmission coefficient) by the method mentioned in Refs. 16 and 17. The Fig. 3(b) reveals the real magnitude of effective permittivity against frequency. The permittivity curve shows negative magnitude at the frequency of 8.29 GHz with a value of ε = − 1.15. The Fig. 4(a) and 4(b), displays the real magnitude of effective permeability and the real value of refractive index consecutively. It is seen from the Fig. 4(a) that, at the frequency of 8.29 GHz, the permeability curve have clear positive magnitude. Usually, in the varying magnetic field, the gap between the arms of the unit cell forms charge density. Although, at low frequency the current of the oscillator can remain in phase with the applied field but at the higher frequency it fails to cope. It then produces negative permeability at that frequency. Similarly, in the Fig. 4(b), it is evident that, the refractive index (η) curve has near zero peaks from the frequency of 5 GHz to 8.48 GHz that covers almost 2 GHz frequency bandwidth in the microwave spectra. However, it is notable here that, at the frequency of 8.29 GHz the refractive index curve displays positive near zero refractive index peak as well with the value of η = 0.89. Therefore, according to z-axis wave propagation the material can be characterized as NZRI metamaterial at the frequency of 8.29 GHz.

The further investigation was done by placing the metamaterial between the two positive, negative wave-guide ports at the x-axis to ensure x-axis wave propagation. The perfect electric and perfect magnetic conductor boundary conditions were applied in the rest of the axis. The Fig. 5(a) and 5(b) displays the simulation arrangement and the S-parameters magnitude of the unit cell for the z-axis wave propagation consecutively.

In the Fig. 5(b) it is visible that, for the x-axis wave propagation the reflection coefficient (S₁₁) exhibit maximum resonances at the frequency of 7.39 GHz which are in the range of C-band of microwave spectra. The Fig. 6(a) and 6(b), reveals the real curve of effective permittivity and permeability of the unit cell due to the x- axis wave propagation. The permittivity curve at Fig. 6(a) displays zero positive magnitude at the frequency of 7.39 GHz with a real value of ε = 0.006. Equally, in the Fig. 6(b), the effective permeability curve exhibits negative peaks at the frequency of 7.39 GHz with a real value of μ = − 0.85. Usually, the properties of permittivity and permeability are most likely affected by the polarization due to internal architecture of the material. When electromagnetic waves enter in anisotropic materials, which have unequal lattice axes, it is affected by the polarization inside the material. As a result, the value of permittivity and permeability changes due to changes in the design. In the same way, the refractive index curve is also affected by the polarization.

However, the real magnitude of refractive index is seen in the Fig. 7 for x-axis wave propagation. At the frequency of 7.39 GHz, in the Fig. 7 the refractive index curve displays positive near zero refractive index magnitude with the real value of η = 0.47. Moreover, it is remarkable that, it shows near zero refractive index property from the frequency of 5 GHz to 5.70 GHz and 6.32 GHz to 7.79 GHz that covers more than 1 GHz bandwidth, which has potential applications in the high gain directional antenna design and electromagnetic cloaking operation.

In the further step, the material was then used to design an electromagnetic cloak. Cloak of invisibility is one kind of alteration that makes an object hidden from view to the nearby observer. An object can be made hidden if it does not scatter waves in any direction from it or it does not reflect waves back to source. Moreover, it prevents to create any shadow in the forward direction (i.e. no scattering takes place in the forward direction). Therefore, when the object will be hidden, it will not disturb the fields outside the object. To do this, now-a-days metamaterial shell is being adopted so that scattering from the object core and shell cancel each other. Usually, to cloak an object perfectly, the scattering cross section (SCS) from an object should be kept below one value. In this study, a very simple single layer rectangular cloak was designed using the proposed metamaterial. The designed cloak is seen in the Fig. 8(a). The designed metamaterial was used to build the wall of the cloak. Four walls were built and each wall was 400 mm² that was built by 2 × 2 unit cell. From the Fig. 8(a), it is seen that, a metallic (aluminium) cylinder was placed in the cloak as an object to be concealed. The inner radius of the cylinder was 3 mm and outer radius was 4 mm. The metallic cylinder was placed in the middle of the cloak in such a way that the distance from the centre of the cylinder to each of the metamaterial wall of the cloak was a = b = 10 mm. For simulation, a transverse electric wave was propagated through the cloak so that the electric field remains parallel to axis of the metal cylinder.

The Fig. 8(b) shows the numerical result of normalized scattering width of cloaked object normalized to scattering width of bare object. From the Fig. 8(b) it is evident that at the frequency of 5.18 GHz the normalized scattering width shows the lowest value below one with a value of 0.10, which indicates that the object is being cloaked at that frequency. It also exhibits value less than one from the frequency of 5 GHz to 5.35 GHz.

The Fig. 8(c) shows the cloak structure prepared for measurement purpose with the metal cylinder inside. Similar to the simulation arrangement, a cloak structure was prepared for measurement purpose. For the measurement of the cloaking performance two WR137, C-band rectangular waveguides were utilized. Moreover, a copper box with 44 mm long, 68.5 mm wide and 49.4mm height was prepared according to the size of the waveguide that was open at its two ends. The copper box was slight bigger than each waveguide so that two waveguides can be inserted into the box keeping them face to face. This box was placed between two waveguides and the cloak structure was placed inside the box for measurement. For measurement purpose metal cylinder with cloak structure and without cloak structure were measured. The waveguides were connected to the same vector network analyzer (N5227A) and the S-parameters were calculated.

In the Fig.9, the E-field distribution in the xy-plane for uncloaked (bare) object (Fig. 9(a)), object at uncloaked frequency (Fig. 9(b)) and object at cloaked frequency (Fig. 9(c)) are displayed. In the Fig. 9(a) a clear E-field distortion in the forward direction (behind the object) is visible which indicates forward scattreing from the object. Similar distortion (zero field) is also apparent behind the object within cloak shell but at uncloaked frequency in the Fig. 9(b). However, in the Fig. 9(c) it is evident that, at the cloaked frequency (at 5.18 GHz) the wave front is reconstructed and no zero field shadow is visible behind the object and forward scattreing is reduced perfectly. Therefore, it indicates the cloaking operation at that frequency (at 5.18 GHz). However, it is also evident from the above study that, in this region (5 GHz to 5.35 GHz) the proposed metamaterial shows near zero refractive index (NZRI) property for all the three principal axes wave propagation.

In the Fig. 10(a) and 10(b), the numerical and measured results of transmission parameter (S₂₁) for both uncloaked and cloaked state are shown respectively. In this study, the S-parameters are compared with the empty state. The ‘empty state’ refers to the measured free space transmittance (S₂₁) that was taken by usual free space measurement process using two horn antennas and network analyzer N5227A and the free space transmittance was found near zero line. The ‘Bare’ line refers to the characteristics of the bare cylinder only without cloak shell and the ‘cloak’ line defines the metal cylinder within the metamaterial cloak shell.

In the Fig. 10(a), the numerical result is presented where the transmission coefficient (S₂₁) has touched the free space line at the frequency of 5.25 GHz, which is in the C-band and it is far from the bare cylinder characteristics as well. Consequently, at this frequency, the S₂₁ and empty S₂₁ are nearly same and the object has been cloaked properly at this point of frequency. Therefore, if any outsider sees the object at this frequency, he will see the free space line instead of the object characteristics. Moreover, the normalized scattering width at this frequency exhibits less than one value as well. Similarly, in the Fig. 10(b), the experimental result is presented for the cloak where transmission characteristics are found nearly same as the numerical results. The experimental transmittance for the object within cloak shell displays the peak at the frequency of 5.29 GHz instead of 5.25 GHz of the simulated result. Therefore, the measured results display almost good conformity with the simulated results.

In this study, a novel near zero refractive index metamaterial was presented. The metamaterial exhibits near zero refractive index properties for all the two principal axes (x and z-axis) wave propagation in the microwave regime. For characterization of the metamaterial, the CST Microwave Studio simulation tool was utilized. The measured result agrees well with the simulated result as well. Later on, this metamaterial was used to design a single layer rectangular cloak. It was shown that, the proposed metamaterial-based rectangular cloak was able to cloak a cylindrical object in the C-band region of microwave spectra. The measured result for the cloak was also presented and it shows good agreement with the simulated result. The design, simplicity, NZRI characteristics and rectangular cloaking operation has made the metamaterial novel in the electromagnetic paradigm.

The authors declare no conflict of interest.

This work was supported by the Universiti Kebangsaan Malaysia, under the grand DLP-2014-003.