# An Overview of Design Techniques for Two-Dimensional Leaky-Wave Antennas
## 3 Fabry-Perot Cavity Antennas
### Theoretical Background  
Fabry-Perot cavity antennas are constituted by a grounded dielectric slab with a partially reflecting sheet on top. These devices are usually fed through dipole-like sources in the center (see Figure 3a). If a vertical electric dipole (VED)--which can be easily implemented through a coaxial cable [60; 61]--or a vertical magnetic dipole (VMD)--commonly realized through a loop antenna [62; 63]--is exploited, a cylindrical leaky wave with a pure transverse magnetic (TM) or electric (TE) polarization is excited, thus generating an omni-directional conical beam (see the results shown in Section 3.5). However, radiation at broad-side is prevented in this case by the null enforced by the source geometry [16]. With the aim of achieving a broadside pencil beam, a horizontal magnetic dipole (HMD)--commonly implemented through a slot on the ground plane excited by a microstrip [17] or a rectangular waveguide [64; 65; 66]--or a horizontal electric dipole (HED)--typically realized through an L-probe, bent coaxial feed [67; 68]--has to be employed. Such sources excite both TE and TM cylindrical leaky waves [53] and, thus, some difficulties in producing omnidirectional conical beams may arise due to possible TE-TM disequalization [16]. Figure 3: **(a)** Schematic representation of an FPCA (constituted by a grounded dielectric slab—in gray—with a PRS on top), its source (realized through dipole-like feeders), and its far-field radiation pattern (which can be a broadside pencil beam or a scanned conical beam). The red box on the left represents the possible implementations of the PRS unit cells through simple isotropic metasurfaces based on metallic lattices (black regions) printed on top of the dielectric slab (gray areas). **(b)** Transverse equivalent network of the FPCA. \(Y_{0}\) and \(Y_{d}\) represent the wave admittances of the free space and the dielectric constituting the cavity, respectively, and \(Y_{s}\) is the equivalent sheet admittance of the PRS. Once the feeder has been properly chosen, physically implemented, and matched (as discussed in the following, Section 3.4), the goal is to properly design the FPCA to achieve the desired performance in terms of directivity, pointing angle, working frequency, bandwidth, and efficiency. This objective can be achieved by simultaneously designing the PRS with the GDS characteristics, viz., the cavity height \(h\), the lateral dimension \(L\), and the dielectric-filling permittivity \(\varepsilon_{r}\) (see Figure 3a). On the one hand, the electrical thickness of the cavity mainly determines the beam angle [69]. On the other hand, the reflectivity of the PRS controls how much power leaks during propagation. For this reason, the beamwidth mainly depends on the PRS design [1]. These intuitive physical concepts can be rigorously described through the _leaky-wave theory_[16] or the _reciprocity approach_[70], obtaining, in both cases, closed-form design equations for FPCAs. The first parameter which can be easily chosen is the minimum lateral dimension \(L\) of the FPCA (see Figure 3a). This parameter has to be designed to ensure that the radiating characteristics of an infinite structure remain nearly unchanged when implemented in a practical device, thereby achieving high radiation efficiency (assuming the structure has low material losses). In other words, this means that \(L\) has to be designed to avoid significant edge effects. The design goal to achieve a very high aperture efficiency is thus to reach the lateral aperture with the power as low as possible or, in other terms, to let almost all the transmitted power radiate before reaching the FPCA's lateral boundaries.