## 2 Unit Cell Design and Proposed FPC Antenna  
The goal is to design a stacked combination of layers of FSS elements, in a unit cell configuration, which when paced as a grid above the patch antenna (excitation source) in an FPC configuration, should realize the following four functionalities/objectives in parallel:  
1. Wideband monostatic RCS reduction. 2. Appropriate gain enhancement. 3. Off-broadside peak radiation. 4. Reduced cavity height (\(\lambda/4\)). Where \(\lambda\) is free space wavelength at operating frequency. Conventionally, the FP cavity, with an excitation source within, resonates when a PRS is placed at a height of \(\sim\)\(\lambda/2\) above the ground plane reflector, and results in an enhanced gain radiation of the source antenna. The cavity height (h) at wavelength (\(\lambda\)) corresponding to the operating frequency can be calculated as [35]:  
\[\mathrm{h}=\left(\varphi_{\mathrm{PRS}}+\varphi_{\mathrm{G}}\right)\lambda/4 \pi+\mathrm{N}\lambda/2, \tag{1}\]  
where \(\varphi_{\mathrm{PRS}}\) is the phase of reflection coefficient of PRS, \(\varphi_{\mathrm{G}}\) is reflection phase of ground reflector, and N defines the resonance order. \(\varphi_{\mathrm{G}}\) is further estimated as:  
\[\varphi_{\mathrm{G}}=\pi-2\ \mathrm{tan}^{-1}\left(Z_{\mathrm{d}}\ \mathrm{tan}\ ( \beta\mathrm{d})/Z_{0}\right), \tag{2}\]  
where \(Z_{\mathrm{d}}\) and \(Z_{0}\) are characteristic impedances of the dielectric and air, respectively, \(\beta\) represents the dielectric phase constant (given as \(2\pi/\lambda\)), and \(\mathrm{d}\) is the dielectric thickness over which the ground plane is lying. For the metallic reflector only (i.e., without the dielectric), the reflection phase is \(\pi\). For N = 0, the resonant cavity height turns out to be \(\lambda/2\) if \(\varphi_{\mathrm{PRS}}\) is assumed to be of \(\pi\) rad. If a PRS can be designed to exhibit a 0 reflection phase, the cavity height can be reduced to \(\lambda/4\). The unit cell with port designations is shown in Figure 1a. To obtain wideband RCS reduction, the top surface of the unit cell, as shown in Figure 1b, was constructed from a closed metallic ring of square shape, with four RF resistors (100 \(\Omega\) each) soldered on four sides. Such a resistive periodic surface (AFSS) mounted on a perfect electric conductor (PEC) plane with a dielectric sandwiched in-between serves as a wideband RAM for an impinging electromagnetic (EM) wave [36]. However, for the proposed objectives, the backing PEC plane has to be replaced with an appropriate PRS, so that all our four objectives can be simultaneously achieved. A survey of literature [37; 38; 39] shows various designs of reflective surfaces; however, the appropriate PRS to be conjoined with the selected AFSS should be:  
1. Symmetric in design, so that wideband RCS reduction can be achieved for both polarizations of the incident radar wave, i.e., transverse electric (TE) and transverse magnetic (TM), and
2. It should give 0 reflection phase so that once mounted above patch antenna, the cavity height can be reduced to \(\lambda/4\). Such a surface can be designed if a dual-sided PRS dielectric is constructed with an inductive mesh (aperture) grid on its top and a capacitive patch grid on its bottom [40]. AFSS of periodic square rings when backed by such a surface would achieve wideband RCS reduction, gain enhancement, and reduce cavity height; however, to also achieve radiation beam deflection, a gradient of phase has to be implemented within this composite PRS. To achieve this, a gradation in the size of mesh aperture was kept, as an inductive gradient achieves higher beam deflection than a capacitive gradient [40]. The proposed constituent unit cell elements of the PRS are shown in Figure 1c,d. Therefore, the designed final unit cell consists of resistive ring on the top, followed by air gap, and followed by gradated aperture on top of a constant patch element.