5.2.1 Theoretical Background

Rectangular aperture antennas are routinely used for several applications, and the analysis of the basic radiating system has received considerable attention so far. Typically, for computational purposes, the presence of an infinite metallic flange has been considered because this hypothesis permits the use of free-space Green's functions, thus considerably alleviating the numerical effort. Moreover, the hypothesis is quite adherent to physical reality: in the majority of cases, the metallic flange's size fully justifies such an approximation.

A wide research effort has been produced on the subject. After the first pioneering works of [1 5], where only the contribution of the dominant mode in the aperture field was considered, several other works have been published, taking into account higher order modes or cross polarization [6 8]. A considerable variety of different numerical techniques has also been experienced (from integral equation to transverse operator techniques [9, 10]) and the relevance of the choice of different field expansions on the aperture has been studied [11].

The basic theory used to model the rectangular waveguide aperture, as well as aperture arrays, is illustrated in [12 15]. The field inside a rectangular waveguide is expressed as the sum of the modes of the waveguide (though, as extensively discussed later, this issue is open to alternative choices). Referring to transverse electric (TE) and transverse magnetic (TM) modes reported in Appendix C, and by imposing a correspondence between the variable p (or q) and the...