# An Overview of Design Techniques for Two-Dimensional Leaky-Wave Antennas
## 2 Classification of Leaky-Wave Antennas
A key advantage of 1-D periodic LWAs over the abovementioned types is their ability to scan from the backward to the forward quadrant. However, it is important to note that the antenna performance significantly deteriorates when the main beam approaches broadside. This issue, caused by  
Figure 1: **(a)** Pictorial representation of a 1-D LWA. The electromagnetic field is partially guided in the \(x\) direction in the gray structure. The amount of transmitted power has an exponential decay due to radiation and expressed by the leakage constant \(\alpha_{x}\), generating a far-field radiation pattern pointing in the \(\theta_{0}\) direction. **(b)** Schematic view of a 2-D LWA. As in **(a)**, the electromagnetic field is partially guided in the gray structure, undergoing an exponential decay of the transported power related to the leakage constant \(\alpha\) in the radial direction. the presence of an _open stopband_, has been extensively studied, and various strategies have been proposed to mitigate its negative effects (see, e.g., [41; 50; 51; 52]). The definition of LWAs based on the working principle of 1-D structures can be extended to the 2-D case. Two-dimensional _uniform_ and _quasi-uniform_ LWAs are indeed 2-D partially open waveguiding structures able to support a _cylindrical leaky wave_ which radially propagates outward from the central source [53]. This type of LWA can, typically by varying the frequency, generate a directive pencil beam at broadside or a conical beam with its axis aligned with the vertical direction. Interestingly, by considering an array feeding scheme, a directive pencil beam can be achieved off broadside [54], even with a circular polarization if a proper polarization-conversion metasurface is employed [55; 56; 57]. As for their 1-D counterpart, the radiation features of 2-D uniform and _quasi-uniform_ LWAs are commonly related to the fundamental leaky mode, which is a _fast wave_. One of the most important examples of 2-D uniform LWAs is a grounded dielectric slab (GDS) with a PRS on top, constituting an FPCA (see Figure 2d) [16]. Similarly to the distinction among 1-D _periodic_ and _uniform_ or _quasi-uniform_ LWAs, it is possible to define a _2-D periodic leaky-wave antenna_ when a 2-D partially open waveguiding structure presents a periodic modulation capable of propagating higher-order Floquet modes. If the periodicity occurs in only one dimension, which is a common case study, the radiating device is referred to as a _1-D periodic 2-D LWA_. A typical example in this context, which corresponds to the structure analyzed in this work, is the case of an annular metal strip grating printed on top of a GDS (see, e.g., [7]) where the periodicity is only present in the radial direction (see Figure 2e). If the periodicity occurs in two directions, as in the case of a metal-patch array printed on a GDS studied in [58], the radiating device is referred to as a _2-D periodic 2-D LWA_. This work deals with the numerical methods and the design rules that can be efficiently used for characterizing 2-D uniform and quasi-uniform LWAs (FPCAs) and 1-D periodic  
Figure 2: Pictorial representation of (**a**) a slitted rectangular waveguide (uniform 1-D LWA), (**b**) a rectangular waveguide with closely spaced holes (quasi-uniform 1-D LWA), (**c**) a grounded dielectric slab (GDS) with relative permittivity \(\varepsilon_{r}\) and with a metal strip grating supporting periodicity \(p\sim\lambda\) on top (1-D periodic LWA), (**d**) a GDS supporting a 2-D periodic screen with periodicity \(d\ll\lambda\) (quasi-uniform 2-D LWA), and (**e**) a GDS supporting annular concentric microstrip rings (radially periodic 2-D LWA). 2-D LWAs. These approaches can also be profitably exploited for the design of their 1-D counterparts [43; 59].