*2.1. 1* × *4 Linearly Polarized Metasurface Array*

The array designs considered in this paper are based on the structure proposed in [11]. The radiator within the metasurface (RWMS) is extended due to its wide matching bandwidth and stable unidirectional radiation. The mechanism of this design depends on the excitation of the radiating elements' mode (TM11) and the surface-wave modes in such a way that their resonances are closely spaced in order to enhance the overall antenna performance in terms of gain and bandwidth. For brevity, this paper does not cover the analysis and the design of RWMS; the readers can refer to [11] to develop an understanding of the RWMS design. A one-dimensional (1-D) array is designed, as illustrated in Figure 1a. The array has four square-ring elements utilized to launch surface waves, in addition to their resonances. The inter-element spacing is *s* = 37.5 mm, which is about 0.56*λ<sup>o</sup>* at 4.5 GHz. The substrate is Rogers RT/Duroid-5880 (*ε<sup>r</sup>* = 2.2, tan*δ* = 0.0009) with a thickness *h* = 5.08 mm. The ring elements and the metasurface patches are printed on the top face of a single substrate with length *l<sup>s</sup>* = 191.5 mm and width *w<sup>s</sup>* = 62 mm. The remaining parameters are detailed in the caption of Figure 1. Since the design relies on the excitation of surface waves, it would be of interest to shed insight on the isolation between the ports. Therefore, the ring elements are individually fed with four coaxial probes, as presented in Figure 1a. For optimum broadside radiation, all elements are excited with the same magnitude and phase.

(**b**)RWMS with feed network

**Figure 1.** The 1 × 4 square ring elements embedded within metasurface and excited with (**a**) four coaxial probes and (**b**) feed network. The RWMS parameters are: *w<sup>i</sup>* = 10 mm, *w<sup>o</sup>* =20 mm, *l* = 16 mm, *w* = 9 mm, *g<sup>x</sup>* = 4.5 mm, and *g<sup>y</sup>* = 3.5 mm. The feed network parameters are: *l*<sup>1</sup> = 96.3 mm, *l*<sup>2</sup> = 10 mm, *l*<sup>3</sup> = 11.85 mm, *l*<sup>4</sup> = 25.65 mm, *l*<sup>5</sup> = 10 mm, *l*<sup>6</sup> = 11.85 mm, *l*<sup>7</sup> = 9.29 mm, *l*<sup>8</sup> = 6.9 mm, *g<sup>s</sup>* = 2.74 mm, *v* = 1.143 mm, *w*<sup>50</sup> = 1.1 mm, and *w*<sup>70</sup> = 0.7 mm.

The reflection coefficients and the mutual coupling between the coaxial ports are simulated and presented in Figure 2a. The −10 dB reflection coefficient bandwidth for all ports (dotted red line) is about 28% from 3.9–5.2 GHz, which is the same as attained with a single RWMS [11]. The isolation between two adjacent elements (e.g., *S*12) is low at lower frequencies and reaches up to −10 dB at 5.2 GHz. This is attributed to surface waves along the y-axis, which begin to resonate above 5 GHz [11], and they disturb both the port isolation and the broadside radiation. The isolation can be improved by increasing the spacing between the square-ring elements; however, this approach will introduce undesired sidelobes.

Once the port isolations are examined, a parallel feeding network, presented in Figure 1b, is designed for the implementation of the RWMS array. The feeding network is also designed on Rogers RT/Duroid-5880 substrate whose thickness *h<sup>f</sup>* = 0.38 mm. The feed is stacked below the 1 × 4 array, and the outputs of the feed are coupled to the ring elements by metallic vias. The dimensions of the feed network are detailed in the caption of the figure. For comparison purposes, the S-parameters investigated for the feed network when it is connected to the RWMS and a conventional square element array (in the absence of metasurface). As illustrated in Figure 2a, when the feed is connected to the RWMS array, the −10 dB fractional bandwidth is comparable to that obtained with coaxial ports; however, poor matching is attained when the feed is integrated with a conventional 1 × 4 square ring array.

**Figure 2.** (**a**) S-parameters and (**b**) the broadside realized gain of the 1 × 4 RWMS array.

To further examine the influence of coupling on the radiation behavior, the broadside realized gain is examined and plotted in Figure 2b. At lower frequencies, the gain is the same when the RWMS is excited either by the feed network or the multiple coaxial probes; however, the two results begin to deviate slightly around 4.7 GHz, which is attributed to the more pronounced effect of coupling.

The simulated realized gain, when the RWMS is excited with a feed network, ranges from 13.5 dB at 4 GHz and reaches up to 14.8 dB at 5 GHz. This observed high gain for the RWMS is attributed to the use of metasurfaces, as displayed in Figure 2b. The aperture efficiency at 4.5 GHz is about 83% for the RWMS array, while it is only 52% for a conventional square ring array. The impact of the metasurface in enhancing the efficiency is demonstrated by plotting the surface current distribution at 4.5 GHz in Figure 3. As observed, both the ring elements and the periodic patches contribute to the total radiation; this justifies the higher achieved efficiency compared to the conventional array.

**Figure 3.** Surface current distribution at 4.5 GHz for the 2 × 2 metasurface array.
