Unit structure

In the design of the unit cell, the distance between rectangular conductor wires is set to h = 0.5λ around 10 GHz. Thus, the metamaterial structure acts as effectively homogeneous [Reference Ramaccia, Scattone, Biotti and Toscano11]. Three-layer grid wire with d = 6.8 mm between each grid layer is used. The width and thickness of the single rectangular conductor wire are 1 mm × 1 mm.

The plasma frequency of the unit cell is linked with the effective density of electron and mass influenced by the electromagnetic interaction between unit cell layers [Reference Pendry, Holden, Stewart and Youns28]. Drude-like model defines the equivalent epsilon of the unit cell as

(6)$$\varepsilon _r( \omega ) = 1-\displaystyle{{\omega _p^2 } \over {\omega ^2}}, \;$$

where ω_p and ω represent the plasma frequency of the grid wire and operation frequency, respectively.

To investigate the scattering performance (reflection and transmission), the unit structure shown in Fig. 2 is numerically simulated under normal incidence plane wave illumination. The perfectly electric conducting and the perfectly magnetic conducting boundary conditions are set parallel to the z-direction, and the open boundary condition is set along the z-direction.

Fig. 2.

A unit structure of a three-layer grid-wire metamaterial. (a) Top view; (b) perspective view.

Simulated reflection and transmission spectra are shown in Fig. 3. The reflection coefficient poses two perfect reflection dips around 9.7 and 14.11 GHz. The designed unit structure provides an ultra-wide 3 dB transmission band from 8.5 to 17 GHz. Indeed, by studying (6), one can conclude that the plasma frequency overlaps with the first perfect reflection dip frequency (9.7 GHz), where the magnitude of the transmission coefficient is 1. When the ratio of ω ²_p/ω ² is close to 1, the refractive index n, i.e. the equivalent electrical permittivity ɛ_r, will be very close to zero, and the metamaterial starts to act as a perfect transmissive medium. Therefore, we can expect a rise in gain of the antenna just after 9.7 GHz when integrated with the grid-wire-based metamaterial lens. On the other hand, although the transmission is interrupted just above 17 GHz, the metamaterial lens works up to 18 GHz as shown in Fig. 3.

Fig. 3.

Simulated reflection and transmission spectra of the designed wire-based metamaterial lens under normal incidence.

The dynamic range of the equivalent effective permittivity is ~0–0.9ɛ ₀, corresponding to 9.7–16.5 GHz broad transmission band. Furthermore, the reflection and transmission spectra are same for both TE (transverse electric) and TM (transverse magnetic) polarizations due to the symmetrical geometry, and hence, the unit structure indicates polarization insensitivity.

A plane wave source at distance d _source = 2λ excites the entrance face of the grid-wire medium with the length of d_MM = λ/2 in air as shown in Fig. 4(a). In Fig. 4(b), the instantaneous electric field (E_y) amplitude is plotted for the case ω = ω_p, i.e. at 9.7 GHz. It can be seen that the reflection coefficient is zero with the satisfied perfect impedance matching condition between air and ENZ medium. Electric field distributions at the entrance and exit faces of the ENZ medium are identical, showing the ENZ medium is perfectly transmissive. It is worth noting that the electrical field strength is strongly enhanced in the ENZ medium as expected, in line with (3). According to the conservation of energy, the Poynting vector (S _ENZ) also significantly increases, which indicates the electromagnetic energy concentration skill of the ENZ medium. Furthermore, after passing the three grids of crossed metal wires, the net phase shift is zero, and the unit structure transmits the incident plane wave without phase change [Reference Li, Liu and Aydin29]. These outcomes reveal that grid-wire medium operates in the ENZ regime at 9.7 GHz. Indeed, the grid-wire metamaterial shows similar field characteristics up to 17 GHz, and therefore the ENZ regime is active over an ultra-wide band involving 9.7–17 GHz.

Fig. 4.

Simulated electric field profile for plane wave propagation through the epsilon-near-zero grid-wire medium. (a) The concept showing a TE-polarized plane wave impinges from air to ENZ medium. (b) The electric field distribution in all regions for the case ω = ω_{p .}

Pyramidal horn antenna design

A pyramidal horn antenna given in Fig. 5 is designed. Parameters of the antenna are shown on the E-plane and H-plane cut views of the antenna. The blue dashed line shows the long horn antenna with L length. The black solid line shows a horn antenna with a shorter length. The gain of the long horn antenna is obtained by adding the three-layer grid-wire metamaterial structure with d thickness to the aperture of the short horn antenna. The metamaterial lens structure is demonstrated with red in Fig. 5. As the electromagnetic wave propagates along the axis of the antenna, the phase distribution is deteriorated due to the side walls. By adding a metamaterial grid-wire structure whose relative permittivity is nearly zero at the aperture of the horn antenna, more homogenous distribution is obtained. Thus, the metamaterial consisting of two regions acts as a lens that focuses the energy. WR90 waveguide with H_WG = 22.86 mm and W_WG = 10.16 mm aperture dimensions and L_WG = 35 mm length is used to guide the source energy. The aperture of the horn antenna has W = 107 mm and H = 138 mm dimensions.

Fig. 5.

Pyramidal horn antenna with L length (blue dashed line) and its shortened version (black solid line) with L′ = L/k (k is a constant) length and EPS-ENZ metamaterial. (a) E-plane, (b) H-plane.

The length of the short horn is set to L’ = 5λ ₀, λ ₀ is the free-space wavelength at 10 GHz. The gain of the short horn is enhanced to the gain of a long horn with L length by adding the grid-wire metamaterial. Thus, a more compact pyramidal horn antenna is obtained by adding conductor wires to the aperture of the antenna, which can easily be fabricated by standard manufacturing techniques.

Metamaterial lens design for pyramidal horn antenna

A metamaterial lens consisting of a grid-wire unit structure is placed at the aperture of the horn antenna to obtain more homogeneous phase distribution. Since the phase-shift is much lower in the ENZ slab compared to free-space, the phase velocity is higher in that region. More uniform phase distribution results in higher gain and directivity [Reference Chen, Ma, Zou, Jiang and Cui30]. The phase at the center and edge of the aperture can be expressed in terms of horn length L, metamaterial thickness d, and relative permittivity of metamaterial ɛ_MM [Reference Huang, Li, Sun, Sun and Tong12]:

(7)$$\theta _H = \displaystyle{L \over {\lambda _o}} + \displaystyle{{d\sqrt {\varepsilon _{MM, H}} } \over {\lambda _o}}, \;$$

(8)$$\theta _E = \displaystyle{L \over {cos\theta \lambda _o}} + \displaystyle{{d\sqrt {\varepsilon _{MM, E}} } \over {cos\theta \lambda _o}}, \;$$

where λ ₀ is the free space wavelength and ɛ_MM,H and ɛ_MM,E are the relative permittivity at the center and edge, respectively. θ is the angular variation starting from the side walls of the horn, as shown in Fig. 5. It may be θ_E or θ_H depending on the plane of the horn. To have homogenous phase distribution on the aperture, |θ _H − θ _E| should be equal to zero. However, this is not possible when θ variation is accounted. This results as the need to design an inhomogeneous metamaterial. By setting θ _H = θ _E, the relative permittivity of metamaterial can be obtained as follows:

(9)$$\sqrt {\varepsilon _{MM}} = L\left({\displaystyle{{1-{\rm cos}\theta } \over {d{\rm cos}\theta }}} \right) + \displaystyle{{\sqrt {\varepsilon _{MM, E}} } \over {{\rm cos}\theta }}.$$

This variation is demonstrated for the metamaterial with 2d thickness in Fig. 6 as the function of θ. Although the curve changes little for angles θ < 10°, it ascends rapidly above. ɛ_MM is greater than the free space effective permittivity for θ > 21°. This figure proves the necessity to use a metamaterial with varying dimensions to ensure homogenous phase distribution.

Fig. 6.

Effective permittivity variation of the metamaterial as the function of θ. Red dotted line demonstrates the free-space relative permittivity.

We designed the metamaterial lens consisting of two sections: (1) for θ_E < 6.5° and θ_H < 6.72°, three-layer metallic grids are used to ensure the ENZ characteristics; (2) above these angles, metamaterial is truncated and free space is left around the axis of the horn. The grids are truncated gradually at the corners due to the phase discontinuities at that region. The physical dimensions of the outermost layer of the grid-wire are shown in Fig. 7.

Fig. 7.

Metamaterial lens for the horn aperture. The dimensions are given for the outermost layer in mm.

The dimensions of the other two layers are downsized according to the slope of the horn using (10)–(13) where d is set to 6.8 mm.

(10)$${\rm tan}\left({\displaystyle{{H-H_{WG}} \over {2L}}} \right) = {\rm tan}\left({\displaystyle{{H^{\prime}-H_{WG}} \over {2L^{\prime}}}} \right), \;$$

(11)$$L^{\prime} = L-d, \;$$

(12)$$H^{\prime} = \displaystyle{{H_{WG}d + HL^{\prime}} \over L}, \;$$

(13)$$SF = \displaystyle{{H^{\prime}} \over H}.$$

Simulation results

The numerical analyses of the antennas are carried out using 3D full-wave electromagnetic simulator of CST Microwave Studio Transient Solver based on the finite integration technique [31]. The horn antenna and the metamaterial lens are assumed to be made of copper. Reflection coefficient (S ₁₁) variation of the 5λ horn and 5λ horn with metamaterial is demonstrated as the function of frequency in Fig. 9. In Fig. 9, the reflection coefficient variation of a horn with L = 10λ (k is set to 2) is also demonstrated.

Fig. 9.

Reflection coefficient variation of the horn antenna with EPS-ENZ metamaterial lens.

Above cut-off frequency of the waveguide, low reflection is observed. Although the presence of a metamaterial lens on the aperture of the antenna has negative effect on the reflection behavior, it is still below −15 dB in the whole frequency band. In Fig. 10, broadside gain of the horn antenna with a metamaterial lens is reported as the function of the frequency. The gain variation of the conventional horn is also exhibited together with long horn antenna. Horn antenna loaded with a metamaterial lens exhibits gain improvement at the frequencies above 9.7 GHz. Gain enhancement up to 3 dB is obtained. Loading the horn aperture with the metamaterial lens has a positive effect on the sidelobes, especially on θ = 0 plane. At 13.4 GHz, 5λ horn antenna with metamaterial has very close gain value to that of 10λ horn.

Fig. 10.

Gain variation of the horn antenna with a metamaterial lens with respect to frequency.

The E- and H-plane patterns of the horn antenna are compared to that of horn antenna with a metamaterial lens at the 12, 14, and 16.5 GHz frequencies in Fig. 11. Solid lines belong to 5λ horn, whereas dash-dotted lines are that of horn antenna with a metamaterial lens. The patterns of the long horn are exhibited in the figure with black dotted lines, as well. The 1.89, 2.61, and 3.03 dB gain enhancements are achieved by loading EPS-ENZ metamaterial lens to the aperture of 5λ horn antenna at 12, 14, and 16.5 GHz, respectively.

Fig. 11.

E-and H-plane gain patterns of the horn antenna and horn antenna with metamaterial at (a) 12, (b) 14, and (c) 16.5 GHz. At 16.5 GHz, 3.03 dB gain enhancement is obtained compared to the conventional horn antenna with the same size.

Fabrication of the horn antenna with metamaterial lens

The fabrication process is illustrated in Fig. 12. The proposed fabrication is a hybrid method, and based on two different non-metallic 3D printing techniques: FDM and SLS. First, the 5λ horn antenna prototype is fabricated with FDM technique with polylactic acid (PLA) material using a commercially available 3D printer (Formiga-P 110 Velocis).

Fig. 12.

Fabrication process involving fused deposition modeling and selective laser sintering.

The density of the print is set to 100%, and the diameter of the filament is 1.75 mm. The second step is the fabrication of EPS-ENZ metamaterial lens. Since the grids are too small (width × thickness: 1 mm × 1 mm) for manufacturing with FDM, SLS technique is used in lens fabrication. Polyamide material in powder form is the host material instead of PLA in the SLS process. After 3D printing, postprocessing, i.e. surface smoothing, is required to prevent decrease and fluctuations in the antenna gain, and increase the surface energy [Reference Garcia, Rumpf, Tsang and Barton32, Reference Byford, Ghazali, Karuppuswami, Wright and Chahal33].

The roughness on the inner surface of the antenna is removed with the help of aplastic sandpaper. Then, both the inner side of the horn antenna and the surface of the metamaterial lens are coated by a commercial nickel-based conductive aerosol (841AR) providing effective shielding over the operating frequency band. It is observed that the surface roughness decreases with metal deposition as expected [Reference Jun, Elibiary, Sanz-Izquierdo, Winchester, Bird and McCleland34]. After metallization, the metamaterial lens is integrated into the horn aperture via an applied adhesion layer. Due to the angular plane of the horn, a strong adhesion is achieved. The resulting prototype is demonstrated in Fig. 13. The horn with L = 5λ-d length is fabricated following the previous procedure.

Fig. 13.

Prototype of 5λ horn with a metamaterial lens.

Measurement results

The experimental verification of the antennas was performed with the measurement setup given in Fig. 14. WR-90 waveguide to the coaxial adapter is used for transition. The measured reflection coefficient of the two antennas is shown in Fig. 15. Reflection coefficient for the horn antenna shows good impedance matching performance with S ₁₁ lower than −10 dB within 7.3–14.8 GHz (1:2.02 BW) band. A 1:2.1 BW is observed for horn with a metamaterial lens.

Fig. 14.

Measurement setup for the experimental verification of horn antennas.

Fig. 15.

Measured reflection coefficient of the antennas as the function of frequency.

From the gain variation of the reference antenna, gain values of the antenna under test are determined. The measured and simulated gain variations of the 5λ horn with and without a metamaterial lens are plotted as the function of frequency in Fig. 16. The measured peak gain of the horn with a metamaterial lens is 23.59, 21.9, and 21.5 dBi at 12, 14, and 16 GHz, respectively. In the measurements, maximum gain enhancement is observed at 12 GHz which is about 3.5 dB. The discrepancy between gain values of simulation and measurement might come from fabrication uncertainties. Due to the physical dimension and fabrication technique of the grids, the lens profile does not remain planar. There are small bends at the inner corners of the grids. Although the printed lens has some deformations in its structure due to the unperfect manufacturing, the gain enhancement can be clearly observed in the measurements for a wide frequency band.

Fig. 16.

Measured gain variation of the 5λ horn antenna with and without metamaterial as the function of frequency.

The gain improvement starts at 9 GHz in measurement. It was at 9.7 GHz in simulations. This is attributed to the deformation of the lens, as well. However, the results clearly show that deformations do not have a great impact on the radiation performance of the horn antenna.