Treating linear antenna arrays as sampled continuous source distributions

Linear antenna arrays are usually described by the product of an array factor and a single element pattern. For certain configurations, such as the uniform linear array, the array factor can be obtained analytically by summing up the corresponding polynomial representation. The alternative of treating an array of finite extent as sampled continuous source distribution has been introduced many years ago, where however, the not very intuitive z-transformation approach has often been utilized in order to obtain closed form representations for many linear array configurations. In this paper, we work with sampled continuous source distributions and discuss their representation with Fourier transforms rather than with z-transforms. The relation to dispersion diagrams is shown and sampling with alternating sign is discussed. Particular focus is on leaky-wave antennas, where radiating TEM-waveguides, rectangular hollow waveguides, and composite right/left-handed waveguides together with the corresponding leaky-wave antennas are considered.