# An Overview of Design Techniques for Two-Dimensional Leaky-Wave Antennas
## 2 Classification of Leaky-Wave Antennas  
In this section, a widely accepted [1; 18] classification of LWAs is provided with the aim of introducing the different working principles and radiating features of the devices discussed in this work. The first distinction among LWAs is related to the _geometry_ of the radiating device. Specifically, LWAs can be classified as one-dimensional (1-D) or two-dimensional (2-D), depending on whether the guiding structure is mainly linear or planar, respectively. In other words, a principal fixed direction of propagation can be easily identified in 1-D LWAs (see Figure 1a), whereas 2-D LWAs are, in general, radial devices commonly fed in the center, and are characterized by a partially guided wave propagating along a plane (see Figure 1b). This aspect influences the radiation properties of the device; a 1-D structure typically generates _fun beams_, whereas a 2-D structure produces _pencil beams_ or _conical beams_, depending on the operating frequency [18]. The other classification concept, which affects the scanning behavior of the antenna, is related to the _working principle_ of the device and it allows us to define uniform, quasi-uniform, and periodic LWAs. When the cross section of the radiator remains constant along the propagation direction, the structure is usually referred to as _1-D uniform LWA_. A classic historical example is a rectangular waveguide with a longitudinal slit (see Figure 2a), which enables power to leak as it propagates [45; 46; 47]. The radiation is usually related to the perturbation of the fundamental guided mode, which is, in general, a _fast wave_. In the _transmission_ mode, 1-D LWAs are commonly fed from one side of the input waveguidelaunching the traveling leaky wave. By properly varying the working frequency, the main beam is scanned from nearly broadside to nearly endfire, with some intrinsic problems for the generation of a beam exactly at broadside or endfire [18]. It is worthwhile to point out that 1-D LWAs can also be fed in the center to generate leaky waves that propagate in both, opposite, directions. Such 1-D LWAs are commonly referred to as _bidirectional_[18]. When there is a periodic modulation of the geometry in the longitudinal direction of the radiating structure with a period \(d\) much lower than the operating wavelength \(\lambda\), the device is referred to as _1-D quasi-uniform LWA_. The radiation properties of this kind of antenna are similar to those of 1-D uniform LWAs since both of them work with only the fundamental mode in propagation. The performance, however, can significantly be improved with respect to the uniform case by properly engineering the periodic modulation. For instance, the idea proposed in [48] to reduce the leakage rate and achieve a more directive antenna with respect to the uniform, slotted, rectangular waveguide was to consider closely placed holes rather than a continuous, longitudinal slit responsible for cutting the current lines on the metal walls of the guide (see Figure 2b). When there is a periodic modulation of the geometry along the longitudinal direction of the radiating structure with a period \(p\) approximately larger than half of the operating wavelength \(\lambda\), the device is referred to as _1-D periodic LWA_. The difference with respect to the 1-D quasi-uniform LWA is given by its working principle. While in the quasi-uniform case there is only the fundamental, basically _fast_ mode in propagation, in 1-D _periodic_ LWAs the guided wave is represented by an infinite number of _Floquet modes_ (or _space harmonics_) due to the larger periodicity. A typical example of 1-D periodic LWAs is a dielectric waveguide or a microstrip that is loaded by perturbations with periodicity comparable to the wavelength [49] (see Figure 2c). As is common in this kind of structures, the fundamental Floquet mode is usually _slow_. For this reason, LWAs are typically designed so that the \(n=-1\) harmonic is fast, enabling the device to radiate.