## 2 Very Compact Waveguide OMT  
### Design Description  
When compared to a symmetrical four-probe waveguide OMT, the asymmetric geometry of a two-probe waveguide OMT typically degrades the port-to-port coupling and/or cross-polarization discrimination (XPD), which is defined as the ratio of the co-polarized to cross-polarized electric fields in the common waveguide. This problem was solved in [21] by using a dual-pin matching element and in [22] by using a cross-shaped matching element. However, the small features of these matching elements have an impact on manufacturing lead times and costs when using standard computer numerical control (CNC) milling techniques. They also make them particularly sensitive to manufacturing errors in millimeter-wave frequencies, independently of the manufacturing technique used, which is not desirable for the design of large closely spaced array antennas considered for future broadband communication satellites [12]. There is an interest in simplifying the design of compact dual-probe waveguide OMTs while maintaining simultaneously low port-to-port coupling and high XPD values. A similar issue is observed in two-probe waveguide OMTs with longitudinal slots, and it was solved in [23; 24] by using a waveguide cross-section with twofold rotational symmetry. This feature is mechanically simple and provides additional degrees of freedom, enabling the fine-tuning of the response of the OMT. This approach is applied here to the design of a very compact dual-probe waveguide OMT in the K-band. A common waveguide with a square cross-section chamfered on two opposite corners provides the twofold rotational symmetry illustrated in Figure 1. As detailed in [24], this twofold rotational symmetry produces two slant fundamental modes in the common waveguide with slightly different propagation characteristics, enabling the introduction of a phase correction between them. This is a well-known feature used in the design of polarizing screens where the phase difference is set to \(\pm 90^{\circ}\) or \(\pm 270^{\circ}\) to produce circular polarization [25; 26; 27]. In linearly polarized OMT designs, only a small phase correction is required to compensate for the cross-polarized electric field component produced by the asymmetric junction design. It was found that this feature may also be used within the probing area to control the port-to-port coupling, although the two effects are antagonistic in the OMT configuration discussed in [24], i.e., reducing the cross-polarized electric field component in the common waveguide leads to increased port-to-port coupling while reducing port-to-port coupling results in higher cross-polarized electric field component. Interestingly, the design reported here is observed to have slightly different operations when compared to the design in [24]. The key difference between two-probe waveguide OMTs having either longitudinal or transversal ports is that the latter requires matching elements in the probing area to achieve low reflection, while the former may be designed without any matching element. The combination here of a simple and symmetric two-step matching element, implemented in the centre of the waveguide OMT and combined with the twofold rotationally symmetric common waveguide cross-section, enables simultaneously controlling the port-to-port coupling and the cross-polarized electric field component. For comparison, the linearly polarized OMT design in [24] having similar characteristics requires two common waveguide portions with different asymmetric cross-sections, one providing port-to-port coupling reduction and the other correcting for the cross-polarized electric field component. This configuration results in a less compact design with about twice the length of the waveguide's broad wall dimension along the longitudinal direction. Thus, the waveguide OMT design reported here has some clear advantages for single-band microwave systems.