## 2 Configuration and Mechanism  
The configuration and structural parameters of the developed antenna are given in Figure 1. The antenna has three basic layers: a bottom GGW as the transmission layer, a medium slotted ground layer for energy coupling, and a top patch layer for radiation. Additionally, a glued prepreg is used to bond the top layer and the ground layer, as shown in Figure 1a. For the bottom layer, a GGW is designed with two rows of square pin arrays on bilateral sides to form a waveguide in the Ka-band, and a tapered ridge array along the central line is used to excite a slow-wave, as shown in Figure 1b. For the top layer, a patch array with a circular split-ring-shaped unit is developed for circularly polarized radiation, as shown in Figure 1c. For the medium layer, a slotted ground with dielectric slab is designed for energy coupling from the waveguide to the patch array. A PIN diode array is arranged on the backside of the dielectric slab, to independently and electrically control the operating states of each slot and, furthermore, to reconfigure the period length of the patch array. The DC biasing network with the coupling slot is given in Figure 1d, which shows that the diodes are soldered under the slots through three pads on the back of the lower dielectric slab, with one in the center and two straddling on both sides of the slot. The bilateral rectangular pads shared by two neighboring slots are shorted to the ground layer by vias, and the central square one is used to load a biasing voltage through the biasing line with a fan-shaped choke to prevent the RF current from radiating. In this research, for low loss and, furthermore, to achieve high gain, a GGW is chosen as the transmission structure, where two rows of square pin arrays on bilateral sides are designed to form a waveguide, and then to produce a stopband in the Ka-band. Since a fundamental fast-wave (\(\beta<k_{0}\)) can only produce forward beam scanning, a slow-wave excitation should be designed for backward-to-forward beam scanning. Thus, a tapered ridge array along the central line in the GGW is then designed to suppress the fundamental wave. An important structural parameter of the stub arrays for the dispersion characteristic, height \(h_{s}\), is analyzed and optimized in a simulation. The dispersion curves of the GGW for different values of \(h_{s}\) are shown in Figure 2, which demonstrate that a slow-wave property is achieved with the stub array. It is found that a larger \(h_{s}\) will lead to a larger phase constant. Finally, \(h_{s}=1.5\) mm is chosen to produce a proper slow-wave performance in the desired band. Then a fixed-frequency beam scanning with \(-1\)th spatial harmonics can be realized with periodic radiation units. For CP radiation, a circular split-ring-shaped patch structure is properly designed and the structural parameters are optimized. As shown in Figure 3, the orientation of the surface currents features a circulation within a time period T, demonstrating a right-handed circular polarization. Thus, a RHCP LWA is achieved. Figure 1: Configuration and parameters of the CP FFBS LWA. (**a**) Side view; (**b**) perspective view; (**c**) top view; (**d**) DC biasing network and detailed structure. Dimensions (mm): \(r_{2}=1.1\), \(r_{1}=0.92\), \(w=0.2\), \(g_{0}=4\), \(P_{0}=1.75\), \(L_{\rm A}=1\), \(L_{\rm B}=2\), \(d=1\), s = 6, \(a_{1}=1.6\), \(w_{\rm g}=4\), \(w_{1}=1\), \(s_{1}=1.8\)\(h_{1}=0.762\), \(h_{2}=0.254\), \(h_{\rm g}=0.101\), and \(l_{1}\)= 0.8. Figure 2: Dispersion diagram of the GGW with and without the ridge array. The developed CP patch array of a total of 80 units arranged in two rows on the top layer is excited by the coupling slots on the ground, and each slot is independently and electrically controlled by a pair of PIN diodes. When the PIN diode is forward biasing, the slot is shorted and then the patch is OFF, corresponding to state \"0\". On the contrary, the patch works on state \"1\". Thus, the period length of radiating units can be manipulated.