A Wideband Millimeter-Wave Corrugated Horn at 30–50 GHz Taking Advantage of All-Metal 3-D Printing Fabrication

The development of commercial all-metal 3-D printing technology provides a new fabrication method for wideband millimeter-wave corrugated horns up to 50 GHz. Compared with conventional fabrication techniques, such as direct machining, electroforming, or recently developed methods relying on the assembly of platelets, all-metal 3-D printing has advantages of low cost, fast delivery, possibility of mass production, flexibility in fabrication of complicated geometries, and good mechanical robustness. In this letter, we report the development of a wideband millimeter-wave corrugated horn at 30–50 GHz (50% fractional bandwidth) based on commercial all-metal 3-D printing technology. Measurement results reported in this letter show good performance in terms of both return loss and cross polarization.


I. INTRODUCTION
C ORRUGATED horns have been widely used as feeds for reflector antennas from microwave to submillimeter wavelengths. The basic theory of corrugated horns was established in the 1970s [1], [2], [3]. After a decade of development, the early design methods of corrugated horns are well summarized in [4]. Because corrugated horns have good beam symmetry, low sidelobes, and low cross-polarization (XsP) level, they have important applications in the field of radio astronomy, satellite communications, and Earth observation.
For astronomical applications, wideband receivers are an important development direction, because they have the capability to capture celestial signals from a wider range of electromagnetic spectrum and increase the overall efficiency of these instruments. For this reason, wideband receivers have been proposed in the next-generation millimeter-wave (mm-wave) interferometer Manuscript  projects, such as the Atacama Large Millimeter/submillimeter Array 2030 [5] and the next-generation Very Large Array [6].
On the other hand, for large single-dish mm-wave telescopes, several Q-band wideband receivers have also been developed [7], [8].
Commonly, mm-wave corrugated horns are fabricated by machining [9] or electroforming [10], but these fabrication techniques require medium to high costs and long delivery times. Recent development suggests the use of assembly of platelets to fabricate wideband mm-wave corrugated horns as a way to reduce costs [11], [12]. However, the mechanical robustness of the assembly during thermal cycling is one of the main concerns of this technique. Owing to the active development of the all-metal 3-D printing technology, especially powder bed fusion (PBF) [13], a metal 3-D-printed mm-wave corrugated horn at 35-50 GHz is reported in [14]. The measurement results in [14] show that the corrugated horns fabricated by commercial PBF machine can operate up to 50 GHz, and the corrugated horns have very similar performance compared with directly machined corrugated horns. Because metal 3-D-printed horns are onepiece components, they have good mechanical robustness during thermal cycling. The cost can also be further reduced compared to the platelet technique, because the 3-D printing procedure is highly automatic and requires fewer human resources.
In this letter, we report the development of a wideband mmwave corrugated horn at 30-50 GHz based on commercial PBF technology. This corrugated horn has a fractional bandwidth of 50% that is wider than the state-of-the-art corrugated horn based on PBF technology, which has a fractional bandwidth of 35% [14]. Metal 3-D-printed corrugated horns have advantages in terms of low cost, fast delivery, possibility of mass production, flexibility in fabrication of complicated geometries, and good mechanical robustness. Therefore, they are attractive for the development of the next-generation large-array astronomical receivers, where a large number of feed horns will be needed. A similar corrugated horn design can be further applied in Q-band satellite communication [15] and remote sensing for meteorology [16], where the combination of reflector antennas and feed horns is the dominant design solution.

II. WIDEBAND CORRUGATED HORN DESIGN
In general, corrugated horns consist of two sections, namely, the throat section and the flare section. The functions of the throat section are broadband impedance matching and the circular waveguide mode to the hybrid HE 11 mode conversion. The hybrid HE 11 mode is preferred in high-performance astronomical receivers, because it has a high coupling efficiency with the fundamental Gaussian mode and low XsP. The flare section guides the hybrid HE 11 mode to the aperture of the corrugated horn, and this section is important for a low XsP. For a compact corrugated horn design, an input circular waveguide with a radius of 3.65 mm and a 24 mm diameter aperture are used. All the corrugations have a constant pitch of 2.16 mm, and the corrugated horn has 34 corrugations in total with a flare angle of 6.5 • and a length of 79.3 mm.
As discussed in [17], the impedance of a corrugated waveguide does not only depend on the ridge radius (r) and slot depth (s), but also on the slot width (b). Corrugated waveguides with a high ratio between the slot depth and the slot width have good broadband impedance matching. In other words, relatively thin and deep slots at the throat section are needed in the design. In [17], a linear taper of both the slot depth and the slot width at the throat section is used to realize broadband impedance matching. Thanks to the development of modern electromagnetic simulation software, the commercial software WASP-NET [18] is used to fully optimize the depths and widths of the slots at the throat section instead in our design. This software is based on a hybrid algorithm of method of moment and mode matching, and it supports fast optimization of corrugated horn parameters. In our design, the first five corrugations are used to realize impedance matching and mode conversion. The optimized slot depths are between 3.27 and 2.65 mm, which correspond to 0.44λ and 0.35λ at 40 GHz. The optimized slot widths are between 0.67 and 1.34 mm with a largest depth/width ratio of 4.0, which is quite challenging for conventional fabrication techniques.
To improve the XsP performance, profiled slots with a constant width of 1.44 mm at the flare section are applied in the design. As discussed in [4], the slot depth of the minimum XsP of the hybrid HE 11 mode changes with the radius of the corrugated waveguide. It is further found that the slot depth of the minimum XsP can be fitted by a function of three parameters as follows: where r is the radius of the corrugated waveguide and λ is the wavelength. Because a corrugated horn consists of corrugated waveguides with different radii, the XsP performance of the corrugated horn can be improved by using a slot profile with the form of (1). Therefore, the three parameters a 1 , a 2 , and a 3 in (1) were first optimized, and a maximum XsP lower than −30.7 dB has been achieved in the whole frequency band. Then, a brute-force optimization is continued to further improve the XsP performance by fine-tuning the high-order modes. Finally, the maximum XsP was reduced to −32.0 dB in the final design. The final optimized slot depths vary from 2.88 to 2.17 mm at the flare section, which correspond to 0.38λ to 0.29λ at 40 GHz. The final slot profile and the corresponding maximum XsP are shown in Fig. 1.

III. FABRICATION BASED ON PBF
The designed corrugated horn has been fabricated by an EOS M290 metal 3-D printer with EOS AlSi10Mg material at the Advanced Technology Center of the National Astronomical Observatory of Japan. This metal 3-D printer uses laser-based PBF technology with a laser focus diameter about 100 µm, which results in fabrication tolerances around 50-100 µm. The average surface roughness (R a ) [19] of the as-built component is around 20 µm, which is determined by the material powder size (∼ 30 µm), the laser power, and other printing parameters. The current average surface roughness (R a ) is an optimal value after optimizations of the fabrication process. Regarding the electrical conductivity of EOS AlSi10Mg material, the noise temperature measurements of a high-performance astronomical receiver in [14] proved that the electrical conductivity of this 3-D-printed AlSi10Mg alloy is comparable with usual aluminum at Q-band frequencies, including the effect of surface roughness. As a result, the conduction loss of the corrugated horn fabricated with EOS AlSi10Mg material is not expected to be higher than that of a corrugated horn fabricated by direct machining of traditional aluminum.
The build orientation of the component is at 45 • with the build platform, and both the internal and external support structures are used in the printing process to improve the fabrication accuracy of the corrugations. The as-built corrugated horns are shown in Fig. 2(a), and the cross section of one horn cut into two halves is shown in Fig. 2(b). It clearly shows that the first several thin corrugations are well fabricated by the metal 3-D printer. The circular waveguide to WR-22 rectangular waveguide transition has also been fabricated to provide the necessary connection between the corrugated horn and the measurement equipment. Fig. 2(c) presents the flange parts of both the fabricated corrugated horn and the WR-22 waveguide transition, which are postprocessed by a milling machine to ensure the tight connection and the accurate alignment between different waveguide components. These factors are important to avoid extra reflection loss between these components.
In terms of delivery time, the 3-D printing and annealing of the horn takes around one week, and the postprocessing, including making flange parts, takes another one week; therefore, it is possible to deliver the corrugated horn within two weeks, which is very attractive for fast prototyping of new designs. In contrast, machining and electroforming require fabrication by an external contractor and take at least several months to deliver the component. The EOS M290 printer has a build volume of 250 mm × 250 mm × 325 mm; thus, it can produce around ten corrugated horns with similar sizes in two weeks in the case of mass production. The latest advanced metal 3-D printers can provide a much larger build volume with similar fabrication tolerances, which can further improve the fabrication efficiency. For machining, a Q-band corrugated horn costs at least a few thousand USD, and for metal 3-D printing, most of the cost comes from the labor cost. Although it is difficult to give an exact cost value, metal 3-D printing has significant advantages in terms of cost in the case of mass production.

IV. CORRUGATED HORN CHARACTERIZATION
The S-parameters of the fabricated corrugated horn have been measured by a Keysight N5225B vector network analyzer (VNA), and the measurement setup is shown in Fig. 3(a). The corrugated horn is connected to the VNA through a metal 3-D-printed WR-22 waveguide transition, and a microwave  absorber is placed in front of the measurement setup to reduce the multipath reflection from the environment. The measurement results of S 11 for both the vertical and horizontal polarizations are presented in Fig. 4(a), and the WASP-NET simulation results with the transition are also included for comparison. The maximum S 11 of both the polarizations is −23.9 dB.
The beam patterns of the fabricated corrugated horn have been measured by a planar near-field measurement system [20], as shown in Fig. 3(b). The corresponding far-field beam patterns were carefully calculated from the near-field measurement data based on the data reduction method reported in [21]. The copolarization (CoP) and XsP far-field beam patterns for the vertical polarization at three different frequencies are presented in Fig. 5. The measurement shows that the CoP beam patterns have good symmetric Gaussian shape. The maximum XsP is further presented in Fig. 4(b), which shows a maximum XsP of −26.1 dB in the whole frequency band. Although there is slight degradation compared with the simulation result, this value still means an excellent polarization performance for most of the applications.
The performance degradation compared with the ideal design of the corrugated horn is considered to be mainly due to the 3-D printing process. As shown in Fig. 6, to further investigate the fabrication errors, the nondestructive industrial X-ray computed tomography (CT) scan is used to obtain the dimensional errors of the 3-D-printed corrugated horn, and the results are summarized in Table I. The dimensional errors show an overall deviation from the design values and, therefore, lead to the degradation of the return loss. In addition, the data show different dimensional errors between the xz plane (horizontal) and the yz plane (vertical), which lead to the slightly different return losses for the two orthogonal polarizations shown in Fig. 4(a). On the other hand, the maximum XsP is less sensitive to the small deviation from the   [4], and the degradation of XsP is mainly due to a different kind of fabrication errors. In Fig. 6(b), it can be clearly seen that the bottom part of the corrugated horn is slightly smaller than the upper part, resulting in an internal offset around 50 µm at the yz plane of the corrugated horn. As explained in [4], this kind of discontinuities inside corrugated horns generate high-order modes, which mainly degrade the XsP performance. Therefore, the degradation of XsP shown in the measurements is considered to be due to the internal offset introduced by the 3-D printing process.
To summarize the discussion in the last paragraph, the 3-D printing process breaks the rotational symmetry of the corrugated horn in two ways. One is to introduce different deviations between the vertical and horizontal directions of the corrugated horn, resulting in the different return loss degradation for two orthogonal polarizations. The other is to introduce the internal offset, resulting in the XsP performance degradation. Therefore, by using the mechanical data obtained by the CT scan, it is possible to fine-tune the 3-D printing process to improve the performance of the corrugated horns in the future.

V. CONCLUSION
The successful development of an all-metal 3-D-printed wideband mm-wave corrugated horn at 30-50 GHz was reported in this letter. The fabrication process took the advantage of commercial all-metal 3-D printing technology to fabricate geometries, which are challenging for conventional techniques, and also to reduce both the cost and the delivery time. A return loss better than 23.9 dB and a maximum XsP lower than −26.1 dB were demonstrated by the measurements. The development of this Q-band wideband corrugated horn can promote the application of the wideband mm-wave corrugated horn in large-array astronomical receivers and also in other relevant fields.