Theoretical model: patch antenna with supersubstrate
Figure1 shows that a unit cell based supesubstrate is placed above a traditional patch antenna. The distance between patch antenna and supersubstrate is denoted by d in free space. The patch antenna is printed on a grounded substrate of thickness, h1, having effective permeability, εeffe1 and permittivity, µeffe1. At distance d from the substrate is the superstrate layer of thickness, h2 having effective permeability µeffe2 and permittivity, εeffe2.
Theoretical model of a patch antenna with supersubstrate.
To compute the far-field, there are many techniques to solve the problem. Here, first the MPA is modelled as a dielectric-loaded cavity20 and reciprocity theorem are applied to the whole structure (the antenna with the superstrate).
Consider E1, H1 and E2, H2 fields are generating inside the same medium with sources, J1, M1 and J2, M2, respectively. The Lorentz Reciprocity Theorem is given by,
$$\int {\int\limits_{S} {\left[ {E_{2} \times H_{1} - E_{1} \times H_{2} } \right]{\text{d}}S} } = \int {\int {\int_{V} {\left[ {E_{1} \cdot J_{2} + H_{2} \cdot M_{1} - E_{2} \cdot J_{1} - H_{1} \cdot M_{2} } \right]{\text{d}}V} } }$$
(1)
Here the fields (E1, H1 and E2, H2) and sources (J1, M1 and J2, M2) inside a medium is surrounded by a sphere of infinite radius. Therefore, (1) reduces to,
$$\int {\int {\int_{V} {[E_{1} \cdot J_{2} + H_{2} \cdot M_{1} - E_{2} \cdot J_{1} - H_{1} \cdot M_{2} ]} {\text{d}}V} } = 0$$
(2)
The patch antenna can be replaced by J1, an electric current source and M1 a magnetic current source. There are radiating an electric field, E1, H1 at point P(r, Ɵ, Φ). Similarly, a dipole with electric current J2 at same point P(r, Ɵ, Φ), radiates a far-field of E2 and H2. Assume M2 is equal to zero.
Now the far-field of the patch antenna can be derive using (2), there it is reduces to
$$\int {\int {\int_{V} {\left[ {E_{1} \cdot J_{2} } \right]{\text{d}}V} } } = - \int {\int {\int_{V} {\left[ {H_{2} \cdot M_{1} } \right]{\text{d}}V} } }$$
(3)
The (3) can further reduce as the reciprocity source J2 is,
$$J_{2} = \delta \left( {\vec{r} - \overrightarrow {{r_{p} }} } \right) \cdot \hat{u}$$
where, \(\hat{u} = \hat{\theta }\) for TM—parallel polarization and \(\hat{u} = \hat{\emptyset }\) for TE—perpendicular polarization.
Therefore (3) becomes,
$$E_{1} \left( {\vec{r}_{p} } \right) \cdot \hat{u} = - \int {\int {\int_{V} {\left[ {H_{2} \cdot M_{1} } \right]{\text{d}}V} } }$$
(4)
This equation can be used to obtain the radiation field radiating from the patch antenna to the above supersubstarte.
Unit cell: structural design and analysis
This section introduces the geometry of the proposed unit cell. The cell’s characteristics have been studied in CST Microwave Studio using PEC and PMC boundary conditions. Additionally, the analysis of the vector surface current density has been presented and discussed.
Unit cell model and characterization
A novel planar unit cell has been designed on a dielectric substrate for applications in millimeter-wave communication. Figure2 shows a single element as part of a periodic arrangement, which has been implemented and evaluated in CST full-wave electromagnetic simulator28. To characterize the unit cell, a waveguide with perfect electric conductor (PMC) and perfect electric conductor (PEC) boundaries is employed, within which the unit cell is situated, as shown in Fig.2a. The faces parallel to the yz-plane are designated as PMC boundaries, whereas those parallel to the xz-plane (i.e., perpendicular to the yz-plane), are designated as PEC. Subsequently, a linearly polarized TEM wave is introduced from waveguide port 1. This setup enables the evaluating the transmission and reflection coefficients at both Port 1 and Port 2.
Geometry and computational model of the proposed unit cell using PMC and PEC boundary walls: (a) perspective view with boundary walls setup in CST, (b) front view, (c) side view.
Figure2b presents the parameterized architecture of the unit cell. The cell comprises a metal ring with inner and outer radii labeled as ri and ro, respectively, along with a gap width, g1. Furthermore, there is a strip line positioned between the ring with a thickness t and a gap g2. The entire cell topology is printed on both sides of a dielectric substrate, here, Rogers RO4003C (lossy) material, with a relative permittivity of 3.38, a tangent loss of 0.0027, and a thickness, d of 0.508mm. The overall dimensions of the unit cell, including the substrate, is 3.4 × 3.4 mm2.
Figure3 depicts a vector surface current distribution at a frequency of 28GHz for a single unit cell. The cell is a part of an infinitely periodic arrangement of identical units. The illustration reveals strong currents aligned along the x and y directions within the upper and lower sections of the ring near the strip line junction, indicating substantial inductance effects. Conversely, in the central region of both the ring and strip, a weaker current distribution can be observed. This is indicative of a cancellation of currents within this central area. This behavior might be attributed to the introduction of a gap within the ring and strip, which induces higher capacitance effects.
Vector surface current density calculated at 28GHz on the top surface of the proposed element.
Figure4 illustrates the results of the parametric study of the unit cell. The cell characteristics are primarily determined by the metallic ring shape. The S-parameter plot indicates that the unit cell exhibits wideband transmission-type response across the millimeter-wave frequencies. With only the metal ring, the S21 bandwidth (at the level of –10dB transmission) is 50% (19–38GHz). However, the bandwidth can be further enhanced by adding a middle strip inside the ring. Consequently, the unit cell S21 bandwidth increases to 52% (21–43GHz). The other two parameters, metal ring gap, g1 and strip line gap, g2 play a crucial role in fine-tuning the responses to adjust the effective permittivity, effective permeability, and refractive index, as elaborated in the next section. Table 1 shows the optimized parameters of the proposed unit cell.
Parametric study of proposed unit cell.
Unit cell negative refractive index behavior
A material is considered to have a negative index when it exhibits both negative effective permittivity and negative effective permeability within a specific frequency range20. Figure5, which shows all possible combinations of signs of ε and µ. The first quadrant corresponds to the materials with positive refraction, third quadrant corresponds to the materials with negative refraction, but the second and fourth quadrant corresponds to materials that do not permit electromagnetic wave propagation, i.e., that will simply electromagnetic waves without energy dissipation. The real part of the refractive index influences the phase velocity of electromagnetic waves propagating through the medium, affecting the phase shift experienced by the waves as they interact with the antenna structure. This phase shift can impact the constructive or destructive interference patterns of the radiated electromagnetic field, thereby influencing the overall gain of the antenna. Additionally, the imaginary part of the refractive index, representing the absorption or attenuation of electromagnetic waves within the medium, affects the propagation losses experienced by the waves as they travel through the material. Higher absorption leads to greater energy loss, reducing the overall efficiency of the antenna system and potentially limiting the achievable gain. Real part of the positive refractive index can control the propagation speed and direction of electromagnetic waves. Positive real parts of the refractive index are commonly associated with dielectric materials used in antenna design. These materials help shape the radiation pattern, impedance matching, and overall performance of antennas by controlling the electromagnetic field distribution and wave propagation within the antenna structure.
All possible combinations of ε and µ.
Negative index materials (NIMs) offer unique advantages in enhancing antenna performance, particularly in terms of gain. NIMs enable focusing of electromagnetic waves in the ways not achievable with positive index materials. This property allows antennas to concentrate the radiated energy in a specific direction, thereby enhancing gain in that direction. To understand the behavior of metamaterial Snell’s law is revised here,
Snell’s law describes the relationship between the angles of incidence and refraction when an electromagnetic wave passes from one medium to another with different refractive indices. It can be mathematically expressed as:
$$n_{1} \sin \left( {\varphi_{1} } \right) = n_{2} \sin \left( {\varphi_{2} } \right)$$
(5)
where, n1 = refractive index of Medium 1, n2 = refractive index of Medium 2, φ1 = angle of incidence measured from the normal to the interface, φ2 = angle of refraction measured from the normal to the interface.
Figure6 shows the phenomena of NIMs, wherein the refraction angle (φ2) maintains a negative orientation with respect to the surface normal. The electromagnetic wave diverging from the source, which has an incident angle φ1, will converge effectively after passing through the NIMs leading to improved wave collimation 13. In other words, when a patch antenna impinges electromagnetic waves onto a metamaterial-based superstrate, Snell’s law dictates the relationship between the angle of incidence, φ1 of the electromagnetic wave and the angle of refraction, φ2 as it enters the superstrate. The refractive index, n2 of the superstrate material profoundly influences the degree to which the wave is refracted or bent. Moreover, Snell’s Law governs how the wavefronts propagate through the superstrate, impacting factors such as phase velocity and wavefront curvature.
Negative refractive index effect (adapted from21).
The extracted values of refractive index neffe, effective permittivity εeffe, and effective permeability µeffe of the proposed unit cell have been illustrated in Figs. 7 and 8. These parameters are computed using the following equations22derived from the S-parameter matrix22,
$$n_{eff} = \frac{1}{kd}\cos^{ - 1} \left[ {\frac{1}{{2S_{21} }}\left( {1 - S_{11}^{2} + S_{21}^{2} } \right)} \right]$$
(6)
$$Z = \sqrt {\frac{{\left( {1 + S_{11} } \right)^{2} - S_{21}^{2} }}{{\left( {1 - S_{11}^{2} } \right)^{2} - S_{21}^{2} }}}$$
(7)
$$\varepsilon_{eff} = \frac{{n_{eff} }}{Z}$$
(8)
$$\mu_{eff} = n_{eff} Z$$
(9)
where k and d are the propagation constant and material thickness, respectively. In this work, the desired operating frequency is 28GHz.
Parametric study of proposed unit cell w.r.t refractive index.
Extracted constitutive effective parameters of unit cell (a) Effective permittivity, (b) Effective permeability, (c) Effective refractive index.
While the parametric study of S parameters depicted in Fig.4 illustrates that the combination of a metallic ring with a middle strip line increases bandwidth, it does not result in a negative refractive index, as can be seen by the refractive index parametric study shown in Fig.7. At 28GHz, the refractive index remains positive. However, Fig.7 shows that introducing gaps between the metallic ring and the middle strip line dramatically lowers the refractive index from zero to − 10.2 at 28GHz. This shift towards negative refractive index values offers significant advantages, particularly in enhancing the antenna gain.
In Fig.8a, it can be observed that the effective permittivity of the proposed unit cell is negative. Similarly, the effective permeability is negative at 28GHz. Consequently, the refractive index of the unit cell maintains a negative value at 28GHz. This indicates that the unit cell exhibits the property of negative refractive behavior. This characteristic is expected to enhance the incident wave focusing from the source, leading to improved antenna gain.
While the metallic ring structure is common in literature, the proposed unit cell design innovatively incorporates a middle line and two gaps, enhancing unit cell functionality for wideband performance and negative refraction. Extensive parametric studies and simulations optimized factors like bandwidth, gain, and impedance matching. We view our design as a significant advancement with potential to catalyze further research and development in metamaterial-based antenna systems.
Proposed unit cell as a superstrate—simulation results and discussion
The traditional patch antenna is designed in CST software. Patch antenna parameters such as dimensions, S parameters, directivity and efficiency are shown in Figs. 9, 10, and 11 respectively.
Patch antenna (all dimensions are in millimeters).
Patch antenna S-parameters and directivity.
Patch antenna efficiency.
A single layer of 5 × 5 unit cell array is designed and placed on a traditional MPA. The total size of the proposed 5 × 5 unit cell array is 1.59λ × 1.59λ. The MPA is designed to resonate at 28GHz. The optimal distance between MPA and the unit cell array is chosen as 15mm to obtain maximum gain at 28GHz. The obtained boresight gain of the single layer unit cell array is 7.33dBi at 28GHz, which corresponds to about 1.33dB gain enhancement. A careful study indicates that the boresight gain can be further increased by placing another layer of the unit cell array. The distance between two layers is 0.5mm; however, the distance between MPA and (original) unit cell array remains the same, i.e., 15mm. The two layers of the proposed unit cells working in synergy may lead to a significant enhancement of the gain of the source MPA. Figure12 shows the Cartesian gain plot of the MPA with single layer and double layers of unit cell. As it can be observed, application of the two unit cell layers result in a significant gain enhancement of about 7.9dBi; the value of the improved gain is as high as 13.9dBi.
Cartesian plots of MPA with single and double layers of 5 × 5 unit cell array: (a) the arrangement of the two identical unit cell layers (all dimensions in millimeters); (b) realized gain of the MPA with a single and double unit cell arrays.
In the context of future wireless communication systems, antenna arrays stand out as promising candidates. To explore the versatility of the proposed unit cell regarding gain enhancement, a 2 × 2 MPA array incorporating the unit cell is implemented to operate at the frequency of 28GHz. The NIM unit cell array is strategically positioned at an optimal distance of 15mm above the 2 × 2 MPA array, resulting in gain improvement. In the following section, a of 2 × 2 MPA array with the integrated NIM unit cell is implemented and experimentally validated.
Experimental validation
The proposed unit cell array and 2 × 2 MPA antenna array has been fabricated on Roger’s substrate RO4003. The fabricated antenna components and 2 × 2 antenna array system with N-MTM is depicted in Fig.13. The MPA antenna and unit cell substrates are separated by an air gap of 15mm, which is maintained using 3D plastic spacers with relative permittivity 2.7. Likewise, the air gap of 0.5mm between two-unit cell layers are maintained by plastic spacers. Each array element is fed individually to maintain the overall system simple and easy to integrate. Consequently, the overall system contains four ports. The S parameters of the proposed designs has been measured at all ports using the vector network analyzer. The simulated and measured S parameters are plotted in Fig.14. During the s-parameter and radiation pattern measurements, the remaining ports were terminated by 50Ω connectors to maintain consistency and accuracy in the testing setup. The measurement result shows that MPA array elements with superstrate are resonating at 28GHz, and isolation between them is better than 20dB.
Fabricated array prototype: (a) 2 × 2 array, (b) unit cell layer, (c) 2 × 2 array with four ports, (d) perspective view of the 2 × 2 antenna array system with N-MTM.
Measured and simulated S-parameters of the proposed 2 × 2 antenna array system with N-MTM at four ports.
In Fig.15, the experimental setup of the proposed 2 × 2 antenna array with double metamaterial layer inside the anechoic chamber is depicted. The design of the four-port antenna system was intended to illustrate the concept of future millimeter-wave array systems, where multiple antenna elements are densely packed together on the same substrate. Although the prototype was connected to only two ports within the anechoic chamber for testing purposes, it is important to note that all ports were functional and tested. The realized gain of the proposed array system was measured in the chamber at the desired frequency of 28GHz, with the peak gain recorded at 13.5 dBi, as shown in Fig.16. Furthermore, simulations and measurements of the radiation patterns at the E-plane (XOZ) and H-plane (YOZ) were conducted. The CST setup simulation for the E-plane (XOZ) and H-plane (YOZ) is shown in the Fig.17. Furthermore, Fig.18 illustrates the polar plots of the simulated and measured radiation patterns at the XOZ and YOZ planes, respectively. Remarkably, a gain enhancement of 7.55dB in the E-plane and 7.25dB in the H-plane was achieved at the resonant frequency of 28GHz, demonstrating a strong agreement between the simulated and measured results.
Measurement setup for 2 × 2 antenna array system with N-MTM inside the anechoic chamber.
Broadside realized gain versus frequency of the 2 × 2 antenna array system with N-MTM.
CST Simulation Setup, (a) 2 × 2 antenna array system with N-MTM H—Plane (YOZ), (b) 2 × 2 antenna array system with N-MTM E—Plane (XOZ).
Radiation patterns at 28GHz: simulation (gray) versus measurement (black).
Benchmarking
The proposed antenna has been compared to recent state-of-the-art designs reported in the literature, and utilizing superstrate metamaterial unit cells for gain enhancement at millimeter-wave frequencies. The data gathered in Table 2 indicates that the proposed structure exhibits a superior combination of gain performance and small size. In particular, it offers significantly higher gain than antennas featuring similar physical dimensions. At the same time, it is considerable smaller than the benchmark structures of comparable gain. In the context of negative metamaterials, extensive research has indeed been conducted across various fields. However, there remain unexplored avenues, particularly in emerging technologies like 5G/6G communication systems. These metamaterials hold immense promise for applications such as reconfigurable intelligent surfaces and small base stations. By enhancing electromagnetic wave properties—such as gain and beam steering—our novel design showcases negative metamaterial behavior. Notably, it achieves an impressive wide bandwidth of 68.75%. The modifications introduced to the unit cell, including targeted adjustments to gaps in the metallic ring and the incorporation of middle slots, contribute to the realization of a negative refractive index. Our work contributes significantly to advancing the understanding and utilization of negative metamaterials, opening new possibilities for innovative communication applications and beyond.
