## 1 Introduction  
Over the past decade, there has been an increased interest in quasi-optical antenna solutions with the development of new millimeter-wave applications, such as terrestrial and satellite wireless communications, as well as surveillance and automotive radar systems. Quasi-optical antenna solutions [1] are generally simpler than alternative high-gain antennas, such as arrays using circuit-type beamforming networks [2], and are thus more robust to manufacturing and assembly tolerances at higher frequencies. A wide variety of quasi-optical beamforming solutions has been reported in the literature. They may be categorized into three-dimensional (3-D) and two-dimensional (2-D) solutions, producing a planar aperture and a line source, respectively. Some solutions, such as the well-known Luneburg lens [3], may be designed as a 3-D [4,5] or a 2-D solution [6, 7, 8]. A variant, known as the Rinehart-Luneburg lens or geodesic lens [9], is a 2-D quasi-optical beamformer providing a continuous curved aperture and wide scanning range. More compact geodesic lens designs implementing a folded profile were reported recently [10,11]. AlternativePPW beamformers using mechanically simple ridges have also been proposed for space applications [12; 13; 14; 15] and 5G communications [16]. Although slightly more complex in implementation due to the discretization of their aperture, constrained lenses [17] are better adapted to feed planar or linear arrays, enabling the integration of amplifiers at the element level to produce active antennas [18; 19]. A particular case of interest is the Rotman lens [20], which may be used to feed a linear array, possibly extended into a planar array [21; 22; 23], achieving wide scanning in the beamforming plane ranging from about \(\pm 30^{\circ}\) with a standard focal arc [24] to \(\pm 50^{\circ}\) with an improved focal curve design [25; 26]. The Rotman lens designs reported in the literature mostly use printed circuit board (PCB) technology, with substrate-integrated transmission lines [27]. Designs in stripline technology are reported in [28; 29] for space applications. At millimeter-wave frequencies, waveguide technology is often preferred to avoid excessive insertion losses. Few examples of Rotman lenses in waveguide technology are reported in the literature [30; 31]. They use E-plane waveguides to reduce the spacing between adjacent ports to half-a-wavelength, with the drawback that the parallel plate waveguide (PPW) section operates in a dispersive transverse electric (TE) mode, thus limiting the operating bandwidth. More recently, a double-ridged waveguide Rotman lens design was proposed and manufactured in two mechanical parts using selective laser sintering [32]. This configuration provides a port spacing small enough to maintain good performance of the lens over a wider frequency band while enabling the PPW section to operate in a transverse electromagnetic (TEM) mode leading to a true time delay design with better overall RF performance [33]. A ridge-gap waveguide design has been reported at 60 GHz, with similar benefits [34]. A double-ridged waveguide design has also been proposed by simultaneously covering the uplink and downlink frequencies allocated to satellite communications in the K/K\({}_{\text{a}}\)-band [35]. This work reports on a similar wideband double-ridged waveguide Rotman lens design in the K/K\({}_{\text{a}}\)-band adapted to be additively manufactured as a single part. This monolithic implementation could be extended in future works to produce a compact dual-stack planar array design as in [29]. Monolithic designs of quasi-optical beamformers in additive manufacturing (AM) have already demonstrated reduced mass and improved performance by removing issues resulting from assembly tolerances [36]. Similar benefits are obtained with the proposed Rotman lens design. The paper is organized as follows. Section 2 details the design of the double-ridged waveguide Rotman lens and associated linear array.