# 3-D-Printed Two-Dielectric Rectangular Waveguide TE-TE Mode Converter

Germán Torregrosa-Penalva, Benjamin Potelon, Paula Viudes-Pérez, Héctor García-Martínez, Enrique Bronchalo, Ernesto Ávila-Navarro, Cédric Quendo

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Germán Torregrosa-Penalva, Benjamin Potelon, Paula Viudes-Pérez, Héctor García-Martínez, Enrique Bronchalo, et al.. 3-D-Printed Two-Dielectric Rectangular Waveguide TE-TE Mode Converter. IEEE Access, 2024, 12, pp.189191-189201. 10.1109/access.2024.3516323. hal-05073199

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Distributed under a Creative Commons Attribution 4.0 International License
Received 11 November 2024, accepted 9 December 2024, date of publication 12 December 2024, date of current version 23 December 2024.

Digital Object Identifier 10.1109/ACCESS.2024.3516323

RESEARCH ARTICLE

3-D-Printed Two-Dielectric Rectangular
Waveguide TE₁₀–TE₂₀ Mode Converter

GERMÁN TORREGROSA-PENALVA<sup>1</sup>, BENJAMIN POTELON<sup>1,2</sup>, (Member, IEEE),
PAULA VIUDES-PÉREZ<sup>1</sup>, HÉCTOR GARCÍA-MARTÍNEZ<sup>1</sup>, (Member, IEEE),
ENRIQUE BRONCHALO<sup>1</sup>, ERNESTO ÁVILA-NAVARRO<sup>1</sup>,
AND CÉDRIC QUENDO<sup>1,3</sup>, (Senior Member, IEEE)

Corresponding author: Germán Torregrosa-Penalva (gtorregrosa@umh.es)

This work was supported by the Conselleria de Educación, Universidades y Empleo (Generalitat Valenciana) joint project grant
CIAICO/2022/068, by grant PID2022-6101397830B-I00 funded by Ministerio de Ciencia, Innovación y Universidades (MICIU), Agencia
Estatal de Investigación (AEI) MICIU/AEI/10.13039/501100011033 and by European Regional Development Fund (ERDF) “ERDF A
way of making Europe”.

**ABSTRACT** In this work a novel TE₁₀–TE₂₀ mode converter for rectangular waveguide (RW) is presented. The proposed structure is conceived as a device that can be inserted in an empty straight section of a RW to yield the desired mode conversion. The converter is formed by a single ‘V’ shaped two-dielectric compact solid that can be scaled according to the frequency of operation and to fit inside the targeted RW section. It is a very low-cost light structure easy to fabricate compared to conventional alternatives of mode converters. To demonstrate the advantages of the proposed design and show its performance, a RW TE₁₀–TE₂₀ mode converter has been designed, simulated and measured at a center frequency of 10.7 GHz in a WR-137. It has been implemented by using additive manufacturing techniques and two materials with different dielectric permittivity. Simulated results show a mode conversion efficiency higher than 85% for a frequency bandwidth between 10.1 GHz and 11.7 GHz, and a mode purity higher than 98% for a frequency range between 9.5 GHz and 11.6 GHz. Back-to-back conversion measurements performed using WR-90 to WR-137 adapters and two of the proposed converter designs, are used to demonstrate the response of the novel TE₁₀–TE₂₀ mode converter. Also, the measurement of the *H*-plane radiation pattern of a TE₂₀ fed WR-137 aperture is provided to corroborate the good performance of the proposed mode converter. The comparison between these measurements and electromagnetic simulations are in good agreement and show a band of operation between 10.1 GHz and 11.1 GHz.

Additive manufacturing, mode converter, rectangular waveguide, slab waveguide.

# I. INTRODUCTION

Communication systems normally require single-mode oper-
ation of the transmission media, since the appearance of
higher order modes is associated with dispersion of the
signals to be transmitted. However, rapid advancement
in microwave technology has led to an increasing inter-
est in higher order modes and their applications. Mode
converters used for generating higher order modes are

The associate editor coordinating the review of this manuscript and
approving it for publication was Hussein Attia.

employed in high-power microwaves both for defense and
civil applications [1], [2]. They are also extensively found in
power-combining systems [3], [4], [5], in vacuum electron
devices [6], [7], [8], [9] and for antenna [10], [11], [12], [13]
and radar systems [14], [15], [16]. Mode converters are
employed in [17] for the design of an overmoded waveg-
uide oscillator. In the engineering measurement field, mode
converters are needed for the cold test of vector network
analyzers [18]. They are also necessary as intermediate
stages for transforming the propagating electromagnetic field
inside a waveguide in order to launch a particular mode

<footnote n="1">¹Elche Microwave Laboratory (EMwLab), Engineering Research Institute of Elche (13E), Miguel Hernández University of Elche, 03202 Elche, Spain</footnote>

<footnote n="2">²IMT Atlantique, Lab-STICC, UMR CNRS 6285, F-29238 Brest, France</footnote>

<footnote n="3">³Lab-STICC, UMR CNRS 6285, Université de Bretagne Occidentale, 29238 Brest, France</footnote>
(typically the circular TE₀₁ mode) [7], [18], [19], [20], [21], [22]. The TE₀₁ circular mode constitutes a most sought-after alternative due to its low losses, which is essential for example in additive manufactured waveguides, where the metallization of the structures remains a challenging factor [23].

Mode converters are normally devised as metallic devices that are connected to standard waveguide components to produce the desired mode conversion. The majority of the converter designs reported in the literature require complex structures to yield the targeted response [1], [6], [7], [8], [16], [18], [19], [21], [22], [23], [24], [25]. Some works refer as a desirable geometric characteristic for these converters that the normal to the input/output ports of the device (in the center of the ports) are aligned in a common plane for practical reasons [6], [24], [26]. Other works stress the importance of a compact configuration along with easiness of manufacture [6], although this feature should be regarded in terms of the operating wavelength. Also, some converters reported in the literature do yield the desired mode conversion at the expense of having to modify the input signal, like splitting it into different output ports [24].

Many reported mode converters address the TE₁₀–TE₂₀ mode conversion [1], [6], [18], while most converters start from RW modes due to the simplicity for manufacturing this type of waveguide [23]. The TE₂₀ mode is used in radar systems to simplify the feeding network of slot antenna arrays [27], [28] and for multimode beamshaping and polarization diversity [13]. In order to verify the correct performance of the proposed converter designs, published works normally compare electromagnetic simulations with measured responses of real manufactured devices in a back-to-back configuration [3], [6], [7], [18], while other researchers use the radiation pattern of an aperture fed with the desired mode for determining the performance of their converter designs [29], [30].

Due to the complex structures that mode converters generally present, additive manufacturing techniques have been suggested and recently employed for their implementation, mainly to reduce the weight of the fabricated structures [2], [15], [23], [26], [31]. Few published works present converter designs based on loading empty waveguide structures with metallic, dielectric or mixed loads, like periodic metallic inclusions [29], fin lines [4], [5], metallic sheets and dielectric wedges [32], dielectric rods [33] and metagratings [30].

In this work we present a novel TE₁₀–TE₂₀ mode converter in RW that is very simple to design and manufacture, low-cost and lightweight, and straightforward to use. The converter is made up of a single compact structure composed of two dielectric materials that is inserted into an empty straight section of RW to produce the desired mode conversion. Following the theoretical observations included in the work, a proof-of-concept TE₁₀–TE₂₀ mode converter is designed for a standard WR-137 at a working frequency of 10.7 GHz. The converter prototype is fabricated using additive manufacturing techniques [34], and its performance is analyzed

by comparing electromagnetic simulations with both back-to-back measurements using [S] parameters, and H-plane radiation pattern measurements in an anechoic chamber.

The work is organized as follows. In Section II, the proposed converter structure is studied divided in three different parts, and theoretical considerations for the design of each part are indicated. Section III is devoted to the particular proof of concept TE₁₀–TE₂₀ mode converter design, regarding specific materials, standard waveguide sections and frequency requirements. Next, the fabrication of the mode converter prototype is presented in Section IV, along with the measurements and the comparison with electromagnetic simulations. Section V outlines the final conclusions of the work.

## II. MODE CONVERTER THEORY

The proposed mode converter structure can be divided into three parts as shown in Fig. 1. Part 1 is formed by a slab rectangular waveguide (SRW) whose central slab section width increases in a taper-like way. In part 2, the electric field distribution is transformed from a single-maximum to a double-maximum distribution (similar to the TE₂₀ mode of the RW) by splitting the central slab of the SRW into two branches. In part 3, each branch is completed by taper-like sections where the branches respective widths decrease to zero at the positions where the TE₂₀ electric field reaches its maxima: $x = a/4$ and $x = 3a/4$.

<figure><img src="image_2.png" /><figcaption>FIGURE 1. Proposed mode converter outline divided into three different parts.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>FIGURE 2. Cross-section view of the SRW in part 1 of the proposed converter divided into three regions. Metallic walls are shown in dark gray color, the high permittivity region in light gray color, and the empty regions in white color.</figcaption></figure>

A SRW cross-section is shown in Fig. 2. This waveguide is studied in [35] and [36]. Part 1 of the converter structure
shown in Fig. 1 consists of a SRW whose central dielectric slab widens gradually along the waveguide axis. The main objective of this first section of the converter is to accommodate in the SRW central slab of width c as much power as possible compared to the power transmitted in the same central width c in an empty RW. From [36] it is straightforward to determine the ratio between the power transmitted in region II of Fig. 2 (P<sub>II</sub>) with respect to the total power P transmitted in the SRW of Fig. 2 (P = P<sub>I</sub> + P<sub>II</sub> + P<sub>III</sub>):

$$ \frac{P_{II}}{P} = \frac{1}{1 + \left(\frac{q(a-c)}{pc}\right)^2 \left(\frac{1}{\cos p} - 1\right)}, \quad (1) $$

where p and q are frequency-dependent parameters determined by the boundary conditions [36].

Eq. (1) is used to determine the width c that maximizes the power transmitted in the central slab of a SRW, with respect to the power transmitted in the same section of an empty RW. Fig. 3 shows this power ratio for a SRW with a central slab with ε<sub>r</sub> = 2.73, for three different frequencies. At 10 GHz the maximum power concentrated in the SRW central slab of width c with respect to the power transmitted in the same region of an empty waveguide is reached when c = 6.1 mm.

<figure><img src="image_4.png" /><figcaption>FIGURE 3. Ratio between the power being transmitted in the central slab of width c in a WR-137 SRW (ε<sub>r</sub> = 2.73), and the power being transmitted in the same central region width c in an empty WR-137 (ε<sub>r</sub> = 1), at 9 GHz (dashed line), 10 GHz (continuous line), and 11 GHz (dotted line).</figcaption></figure>

Part 2 of the proposed mode converter of Fig. 1, is formed by two branches that split the single maximum of the TE<sub>10</sub> transversal electric field distribution into the two maxima present in the TE<sub>20</sub> mode. Additionally, one of the branches accounts for the 180° phase shift between maxima necessary for yielding the TE<sub>20</sub> transversal electric field distribution. This can be easily performed in SIW structures with two probe feeds in a differential arrangement [27], [36], but is not so simple in commercial RW. Obviously, for the mode converter of Fig. 1 to work properly, the selected working frequency must be above the cut-off frequency of the TE<sub>20</sub> mode in the empty waveguide. This implies a rather linear dispersion diagram for the TE<sub>10</sub> mode around the converter

design frequency (similar to that of a TEM mode). For a TE<sub>10</sub> mode, the length of a RW filled with ε<sub>r2</sub> that provides an additional 180° phase shift with respect to the same length of a RW filled with ε<sub>r1</sub> is given by:

$$ l = \frac{1}{\sqrt{\varepsilon_{r2} \left(\frac{2f}{c_0}\right)^2 - \left(\frac{m}{a}\right)^2} - \sqrt{\varepsilon_{r1} \left(\frac{2f}{c_0}\right)^2 - \left(\frac{m}{a}\right)^2}}, \quad (2) $$

where c<sub>0</sub> is the speed of light in vacuum. Table 1 shows this length l when ε<sub>r1</sub> = 2.73 and ε<sub>r2</sub> = 7.52 employing eq. (2) in different scenarios for a 10 GHz frequency (where a<sub>WR-137</sub> is the width of the WR-137 waveguide given in Table 2).

For comparative purposes, let us consider TEM propagation in two transmission lines of the same length l and respective dielectric permittivities ε<sub>r1</sub> and ε<sub>r2</sub>. For the phase difference between both lines to be 180° at a frequency f, the value of l can be readily calculated as:

$$ l = \frac{\pi}{\frac{2\pi f}{c_0} \left(\sqrt{\varepsilon_{r2}} - \sqrt{\varepsilon_{r1}}\right)}. \quad (3) $$

<table><caption>TABLE 1. Length for additional π phase shift.</caption><thead><tr><th></th><th>a = a<sub>WR-137</sub></th><th>a = 0.5a<sub>WR-137</sub></th></tr></thead><tbody><tr><td>m = 1</td><td>13.5 mm</td><td>12.6 mm</td></tr><tr><td>m = 2</td><td>12.6 mm</td><td>—</td></tr></tbody></table>

<table><caption>TABLE 2. Standard waveguide characteristics.</caption><thead><tr><th>Waveguide</th><th>a (mm)</th><th>b (mm)</th><th>f<sub>c</sub> (GHz)</th><th>BW (GHz)</th></tr></thead><tbody><tr><td>WR-137</td><td>34.85</td><td>15.80</td><td>4.301</td><td>5.85 – 8.20</td></tr><tr><td>WR-90</td><td>22.86</td><td>10.16</td><td>6.557</td><td>8.20 – 12.40</td></tr></tbody></table>

For ε<sub>r1</sub> = 2.73 and ε<sub>r2</sub> = 7.52 eq. (3) gives l = 13.8 mm at 10 GHz, which is a similar value to the ones provided in Table 1. So, an initial tentative designing length for the high permittivity section of Fig. 1 could be l ~ 13 mm. The propagation of TE modes in an infinitely long RW with a constant transversal cross section similar to that of part 2 in Fig. 1 has been studied in [37]. However, the cross section in part 2 is not constant and the dielectric slabs have different permittivities. This is why this more qualitative analysis is used to determine the starting length l in Fig. 1.

Finally, the main purpose of part 3 in Fig. 1 is to ease the TE<sub>20</sub> electric field distribution transfer to the empty RW. This is accomplished by employing taper-like sections for each branch which end at the TE<sub>20</sub> maxima positions.

### III. MODE CONVERTER DESIGN

A TE<sub>10</sub>-TE<sub>20</sub> mode converter is designed for the WR-137 at 10.7 GHz. The converter frequency of operation and working bandwidth are determined by available standard commercial RW and their own frequency limitations, as given in Table 2. Since the TE<sub>20</sub> mode needs to propagate in the selected
waveguide, the WR-137 must be excited at a frequency above its single-mode bandwidth. Commercial coaxial to RW transitions are designed to properly work within the single-mode bandwidth, which prevents the possibility of launching the TE₁₀ mode above the TE₂₀ mode cut-off frequency. Thus, in order to circumvent this issue, coaxial to WR-90 transitions are employed to allow the generation of the TE₁₀ mode at 10.7 GHz, which falls inside the single-mode bandwidth of this waveguide as shown in Table 2. WR-90 to WR-137 taper transition sections are then employed to introduce the desired TE₁₀ mode inside the WR-137 waveguide at 10.7 GHz. Additionally, the total length *L* of the converter is limited under 60 mm in order to fit inside WR-137 3-inch-long sections.

With respect to the dielectric materials employed to implement the converter, Figs. 4 and 5 show their dielectric properties $ε = ε_0(ε' - jε'')$ for our particular printing technology measured by means of the transmission/reflection method [38], for different samples fabricated for the WR-137 and WR-90. The average of their dielectric properties, over

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Measured dielectric properties of materials Preperm-dk3 (light gray) and Preperm-dk10 (dark gray) using the Baker-Jarvis method using samples for the WR-137.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 5. Measured dielectric properties of materials Preperm-dk3 (light gray) and Preperm-dk10 (dark gray) using the Baker-Jarvis method using samples for the WR-90.</figcaption></figure>

the recommended frequency bandwidth (BW) of the waveguides shown in Table 2, is given in Table 3 for both materials.

<table><caption>TABLE 3. Materials dielectric characteristics.</caption><thead><tr><th rowspan="2">Waveguide</th><th colspan="2">WR-137</th><th colspan="2">WR-90</th></tr><tr><th>ε'</th><th>ε''/ε'</th><th>ε'</th><th>ε''/ε'</th></tr></thead><tbody><tr><td>Preperm-dk3</td><td>2.75</td><td>0.0056</td><td>2.72</td><td>0.0052</td></tr><tr><td>Preperm-dk10</td><td>7.50</td><td>0.0055</td><td>7.52</td><td>0.0052</td></tr></tbody></table>

The different samples of each material are manufactured using fused deposition modeling (FDM) techniques with the Tumaker NX PRO dual direct drive HR×2 3D printer. It is a printer with a double independent head whose printing volume is 270 × 185×200 mm³, and allows the use of a wide variety of materials. The diameter of the nozzles employed is 0.4 mm and the printer has a safety closure that guarantees a stable temperature of the printing environment. The printer provides ±10 mm precision in the *xy* horizontal plane, and 50 mm resolution in the *z*-axis (the different layers are 200 mm high linked to the printing materials employed). The same printer and materials are used for the implementation of the different converter prototypes.

Taking into account the different theoretical considerations made in Section II, the initial proposed converter layout is shown in Fig. 6. It should be noted that, in order to allow a smooth transition between dielectric materials in the branch accounting for the 180° phase shift, instead of introducing a cuboid-like high permittivity section, a rhombohedron-like section is used. Also, this first concept design, apart from the inclusion of the high permittivity material, is strictly symmetrical with respect to the plane $x = a/2$.

<figure><img src="image_7.png" /><figcaption>FIGURE 6. Preliminary converter concept prototype. The different dimensions (mm) are: *L* = 60, *l* = 13, and *c* = 6.1.</figcaption></figure>

Some preliminary simulation results of the converter prototype of Fig. 6 are shown in Fig. 7, where the magnitude of the electric field distribution along the structure is provided. It is possible to observe that the device works as expected. The TE₁₀ mode is excited in the left port of the structure, while the TE₂₀ mode field distribution is formed on the other end of the converter. The first dielectric tapering section of the mode converter allows the field to concentrate in the middle part of the waveguide. Next, the field is split into two paths of high dielectric permittivity regions with respect to the surrounding air regions. In the top path, two half wavelength
lobes can be well observed, whereas in the bottom one three half wavelength lobes are appreciated. Thus, the bottom path provides the required electrical length for half a wavelength phase shift with regard to the top path. As previously stated, this is possible thanks to the $ε_{r2} = 7.52$ region inserted in the bottom path, which gives the needed extra electrical length.

<figure><img src="image_8.png" /><figcaption>FIGURE 7. Top view of the converter prototype showing the magnitude of the transversal electric field distribution at 10.7 GHz.</figcaption></figure>

A close look to the field distribution of Fig. 7 reveals that the TE₂₀ mode distribution at the output port is slightly unbalanced towards the branch in the converter with the high permittivity region. Thus, in order to properly balance the behavior of the structure for it to yield a pure TE₂₀ mode at its output, some modifications were introduced in the layout. Fig. 8 shows the proposed final converter layout. With respect to its simplest version in Fig. 6 two more degrees of freedom were added to the design.

<figure><img src="image_9.png" /><figcaption>FIGURE 8. Final converter prototype layout with the variables included in the optimization process: L, $W_{d1}$, $W_{d2}$, $W_{d3}$, DP₁, and DP₂.</figcaption></figure>

To balance the converter, $ΔP₁$ is used to control the amount of power which is carried in the low permittivity branch, when compared to the power propagating in the high permittivity section. Additionally, $ΔP₂$ adjusts the amount of power through the branch with the high permittivity rhombohedron-like section. Since electromagnetic fields tend to concentrate in the high permittivity regions, the idea behind these two additional degrees of freedom is to allow the optimization process to widen the low permittivity branch and make narrower the high permittivity one. With regard to

the $ε_{r2} = 7.52$ region, $W_{d1}$ is centered with respect to the whole converter length L, and the final tips of this region are located equidistant in a z plane, from the surfaces that limit this branch. Also, some asymmetry is permitted in this region since $W_{d2}$ and $W_{d3}$ can be different.

<table><caption>TABLE 4. Optimized converter dimensions.</caption><thead><tr><td>Parameter</td><td>Dimension (mm)</td></tr></thead><tbody><tr><td>L</td><td>56.65</td></tr><tr><td>w<sub>d1</sub></td><td>6.86</td></tr><tr><td>w<sub>d2</sub></td><td>9.97</td></tr><tr><td>w<sub>d3</sub></td><td>10.57</td></tr><tr><td>ΔP<sub>1</sub></td><td>2.03</td></tr><tr><td>ΔP<sub>2</sub></td><td>0.43</td></tr></tbody></table>

All six variables indicated in Fig. 8 were optimized to fulfill two requested goals. The objectives to be met were, on one side, a TE₁₀–TE₁₀ reflection coefficient smaller than -20.0 dB for the frequency range 10.2 GHz – 11.7 GHz, and a TE₁₀–TE₁₀ transmission coefficient smaller than -30.0 dB for the same frequency range. S-parameter simulations and optimization were carried out using the commercial electromagnetic software Ansys HFSS. The optimized dimensions are shown in Table 4.

An additional modification was also included in the design in order to make it resemble as much as possible the fabricated prototype. This involved rounding all the corners of the structure assuming a radius of curvature of 200 mm, according to the size of the nozzle used in the 3-D printer in the manufacturing process. Finally, in order to allow a simple insertion of the device inside WR-137 empty sections, some supporting elements were considered in the final prototype. These elements are used to ensure a steady position of the converter inside the waveguide. They are formed by two lateral 30 × 3×3 mm³ cuboids placed as rails at positions (0, 0, L/2) and (a, 0, L/2), and 5 transversal cuboids of different lengths $l_s$ and dimensions $l_s×3 × 2 mm³$ that hold the converter to the lateral rails. They also confer the converter additional mechanical strength and prevent the converter from changing its original position when placed inside the waveguide.

The simulated S-parameters for the optimized design are shown in Figs. 9 and 10, and are compared to the simulated S-parameters of the converter with rounded corners and supporting elements. The response of the proposed mode converter is limited at lower frequencies by the cut-off frequency of the TE₂₀ mode in the WR-137. At higher frequencies the converter's working bandwidth is compromised by the appearance of the TE₃₀ mode, as shown in Fig. 10. The converter's bandwidth could be increased by the inclusion of additional elements (like a metallic post at $x = a/2$ and close to $z = L$ as in [39]) to prevent this mode and the TE₁₀ mode to appear. In Fig. 9, the TE₁₀–TE₁₀ reflection coefficient is lower than -15 dB between 10.25 GHz and 12.02 GHz,
while the TE₂₀–TE₁₀ transmission coefficient is better than -0.6 dB between 10.38 GHz and 11.6 GHz. These transmission losses are directly related to the loss tangent (ε''/ε') shown in Table 3 of the materials employed in the design.

Fig. 10 shows that the TE₁₀–TE₁₀ transmission coefficient is lower than -15 dB between 9.32 GHz and 11.7 GHz. The introduction of the rounded edges and supporting structural elements do not alter notably the converter's behavior.

From the simulated S-parameters of Fig. 9 it is possible to calculate the TE₁₀ to TE₂₀ conversion efficiency response of the device (see Fig. 11). The mode conversion efficiency ($\eta_{mc}$) and the mode purity (mp) can be obtained as:

$$ \eta_{mc} = |S_{21}(TE_{10}-TE_{20})|^2 \quad (4) $$

$$ mp = \frac{|S_{21}(TE_{10}-TE_{20})|^2}{\sum_{m=1}^{5} |S_{21}(TE_{10}-TE_{m0})|^2} \quad (5) $$

<figure><img src="image_10.png" /><figcaption>FIGURE 9. Mode converter optimized design simulation (continuous line) compared to simulations of mode converter with rounded edges and supporting elements (dotted line). TE₂₀–TE₁₀ transmission coefficient (gray line), and TE₁₀–TE₁₀ reflection coefficient (black line). Inset shows the top view realistic design with rounded edges and supporting elements.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 10. Mode converter optimized design simulation (continuous line) compared to simulations of mode converter with rounded edges and supporting elements. TE₁₀–TE₁₀ transmission coefficient (black line), and TE₃₀–TE₁₀ transmission coefficient (gray line). Inset shows the magnitude of electric field distribution at the output port at 10.7 GHz.</figcaption></figure>

As shown in Fig. 11, the conversion efficiency has a peak value of 88.8% at 10.55 GHz, and it is better than 85% in the range between 10.1 GHz to 11.7 GHz. This efficiency could be improved by using dielectric materials with lower losses. As discussed in [11], an efficiency decrease from 95% to 90% corresponds to a magnitude difference of 0.23 dB in $S_{21}$. With respect to the mode purity parameter, mp is higher than 98% for a frequency range between 9.5 GHz and 11.6 GHz, and higher than 99% between 10.3 GHz and 11.5 GHz. At 10.7 GHz mp reaches its peak value. Rounding off the converter edges and the inclusion of supporting elements reduce slightly the aforementioned bandwidths, but do not modify significantly the simulated response of the optimized design, which implies robust behavior in the face of possible tolerances.

<figure><img src="image_12.png" /><figcaption>FIGURE 11. Mode converter optimized design simulated TE₁₀ to TE₂₀ conversion efficiency (continuous lines) compared to simulated TE₁₀ to TE₂₀ conversion efficiency of mode converter with rounded edges and supporting elements (dotted lines).</figcaption></figure>

Finally, Table 5 provides a comparison between the characteristics exhibited by the novel two-dielectric RW TE₁₀–TE₂₀ mode converter proposed in this work, and previous mode converters reported in the literature. The proposed mode

<table><caption>TABLE 5. Comparison between simulated results of different rectangular mode converters.</caption><thead><tr><th>Ref.</th><th>[3]</th><th>[6]</th><th>[7]</th><th>[18]</th><th>[24]</th><th>This work</th></tr></thead><tbody><tr><td>Structure</td><td>SIW</td><td>WG</td><td>WG</td><td>WG</td><td>WG</td><td>WG*</td></tr><tr><td>Converted mode</td><td>TE<sub>10</sub>–TE<sub>30</sub></td><td>TE<sub>10</sub>–TE<sub>20</sub></td><td>TE<sub>10</sub>–TE<sub>m0</sub></td><td>TE<sub>10</sub>–TE<sub>20</sub></td><td>TE<sub>01</sub>–TE<sub>20</sub></td><td>TE<sub>10</sub>–TE<sub>20</sub></td></tr><tr><td>Freq. band</td><td>X–Ku</td><td>H</td><td>Q–W</td><td>Ka</td><td>Ka</td><td>X</td></tr><tr><td>Complexity</td><td>High</td><td>High</td><td>High</td><td>High</td><td>High</td><td>Low</td></tr><tr><td>mp (%)</td><td>&gt; 95</td><td>N.A.</td><td>~97</td><td>N.A.</td><td>N.A.</td><td>&gt; 98</td></tr><tr><td>BW (%) **</td><td>27.0</td><td></td><td>14.0</td><td></td><td></td><td>20.0</td></tr><tr><td>η<sub>mc</sub> (%)</td><td>&gt; 97</td><td>&gt; 95</td><td></td><td>97.7</td><td>97.5</td><td>&gt; 85</td></tr><tr><td>BW (%) **</td><td>25.0</td><td>39.4</td><td>N.A.</td><td>40.9</td><td>30.3</td><td>14.7</td></tr><tr><td>|S<sub>11</sub>| (dB)</td><td>&lt; -10</td><td>&lt; -15</td><td>&lt; -15</td><td>&lt; -20</td><td>&lt; -19</td><td>&lt; -15</td></tr><tr><td>BW (%) **</td><td>26.5</td><td>14.0</td><td>10.0</td><td>N.A.</td><td>30.3</td><td>16.0</td></tr></tbody></table>

<footnote>* Dielectric device inside an empty waveguide (WG).</footnote>

<footnote>** Relative bandwidth.</footnote>
converter is very simple to manufacture and integrate into a straight section of the desired RW. This implies a considerable reduction in cost, weight, and volume, when compared to other alternative mode converter designs. The simplicity, compactness, and ease of integration and implementation of the proposed mode converter comes at the expense of a smaller conversion efficiency figure of merit. This issue can be overcome with the use of low-loss dielectric materials.

The proposed mode converter design could benefit from the use of a single low-loss high-permittivity printing material. In this case the different permittivity regions could be achieved by selecting different printing densities. The inclusion of air gaps in the dielectric solid structure would reduce the losses of the converter, increasing the conversion efficiency. This, in addition to using more precise printing technologies, would permit a direct frequency scaling of the converter for higher operating frequency bands.

## IV. MODE CONVERTER FABRICATION AND MEASUREMENT

Fig. 12 shows some views of the fabricated prototype. The converter weighs 8.1 g (apart from the empty RW section necessary for it to work) and the 3D printer took 1 hour and 15 minutes to fabricate it.

<figure><img src="image_13.png" /><figcaption>**FIGURE 12.** Mode converter manufactured prototype. Left: top view. Right: isometric view.</figcaption></figure>

In order to validate experimentally the behavior of the device, two converter prototypes were fabricated, and back-to-back configuration measurements were carried out. Fig. 13 shows this configuration along with the simulated magnitude of the electric field distribution at two different frequencies when the converters are placed as indicated 38 mm apart (longest possible distance in our experimental setup).

Fig. 14 shows a picture of the measurement setup. It includes a 3.5-mm coaxial to WR-90 transition, a WR-90 to WR-137 75-mm long taper section, two WR-137 75-mm long sections with the back to back converters inside as in Fig. 13, and again symmetrically the elements back to the 3.5-mm coaxial connector. The different RW elements are fabricated by Flann Microwave. Measurements included a TRL calibration performed at the WR-90 ends.

Figs. 15 and 16 show the comparison between back-to-back measurements and simulations. It is possible to observe that there is a good agreement between measurements and simulations. When the converters are placed together the

<figure><img src="image_14.png" /><figcaption>**FIGURE 13.** Back-to-back configuration for TE₁₀ to TE₂₀ to TE₁₀ conversion (top). Magnitude of electric field distribution at 10.2 GHz (middle) and at 11.2 GHz (bottom).</figcaption></figure>

overall behavior does not seem as convenient as when the distance between them is 38 mm. When both converters are next to each other they seem to interact so as not to provide a satisfactory conversion in the working bandwidth. Meanwhile, when the distance between mode converters is 38 mm, the measured response is in accordance with the expected converter performance.

<figure><img src="image_15.png" /><figcaption>**FIGURE 14.** Measurement setup including coaxial to waveguide transitions and WR-137 to WR-90 taper adapters.</figcaption></figure>

In Fig. 16 the measured back-to-back S₁₁ parameter is under -15 dB for a frequency bandwidth between 10.1 GHz and 11.0 GHz, while measured transmission losses are in agreement with the TE₁₀-to-TE₂₀-to-TE₁₀ conversion simulation setup of Fig. 13. Some discrepancies in Figs. 15 and 16 between measurements and simulations might be ascribed to tolerances when placing the converter prototypes inside the waveguide sections (in the longitudinal z-axis), and to fabrication errors. The use of other 3D printing technologies that are more precise than FDM, printers with better printing resolution or the inclusion of support elements in the upper part of the converter, would mean a reduction in these differences between measurements and simulations. The frequency shift in some resonances suggests a relative error of 0.6%
<figure><img src="image_16.png" /><figcaption>**FIGURE 15.** Back-to-back S-parameter measurements (continuous lines) and simulations (dotted lines) with converters 0 mm apart. TE₁₀–TE₁₀ transmission coefficient (gray line), and TE₁₀–TE₁₀ reflection coefficient (black line).</figcaption></figure>

which falls within the printing resolution of the 3D printer used for manufacturing the devices, as detailed in Section II. Measurements confirm that the fabricated prototypes behave as shown in Section III.

<figure><img src="image_17.png" /><figcaption>**FIGURE 16.** Back-to-back S-parameter measurements (continuous lines) and simulations (dotted lines) with converters 38 mm apart. TE₁₀–TE₁₀ transmission coefficient (gray line), and TE₁₀–TE₁₀ reflection coefficient (black line).</figcaption></figure>

In order to further demonstrate experimentally the good performance of the proposed two-dielectric TE₁₀–TE₂₀ mode converter design, the *H*-plane radiation pattern of a WR-137 aperture was measured at different frequencies in the *X*-band. Two sets of measurements were performed: in one of them the aperture was fed by the TE₁₀ mode, while in the other one, the implemented TE₁₀–TE₂₀ mode converter design was used to yield the TE₂₀ mode which was next fed to the WR-137 aperture. Fig. 17 shows the *H*-plane radiation pattern measurement setup inside an anechoic chamber. It consisted in the different elements indicated by the dashed contour in the top diagram of Fig. 13: a coaxial to WR-90 transition, a

75-mm long WR-90 to WR-137 taper adapter device, and a WR-137 75-mm long open ended RW section. This open end acts as the antenna aperture under test.

<figure><img src="image_18.png" /><figcaption>**FIGURE 17.** H-plane radiation pattern measurement of TE₂₀ fed WR-137 aperture. Left: setup on polystyrene rotating platform and receiving horn probe. Right: closeup view with WR-137 aperture loaded with proposed TE₁₀–TE₂₀ converter.</figcaption></figure>

Fig. 18 shows the comparison between simulations and measurements of the WR-137 aperture *H*-plane radiation patterns at 10.7 GHz. The *H*-plane radiation pattern corresponding to the TE₁₀ mode feeding is provided to point out some minor measurement errors in the anechoic chamber setup, leading to a slight asymmetry in the expected radiation pattern. Simulations and measurements in Fig. 18 are in good agreement. On one hand, it should be highlighted the measured well defined null for the direction normal to the aperture surface (θ = 0°), and on the other the reasonable measured symmetry exhibited by the two beams generated by the aperture TE₂₀ field distribution. The measured beamwidth between the two maxima is 59°, while the simulated angle separation is 60°. These underlined characteristics corroborate once again the correct operation of the proposed mode converter, as well as the purity of the TE₂₀ mode generated with it at the design frequency.

<figure><img src="image_19.png" /><figcaption>**FIGURE 18.** Measurements (continuous lines) and simulations (dotted lines) of WR-137 aperture H-plane radiation patterns at 10.7 GHz. Radiation patterns of WR-137 aperture fed with TE₂₀ mode are shown in black color, while radiation patterns of WR-137 aperture fed with TE₁₀ mode are shown in gray color.</figcaption></figure>

Fig. 19 provides the measured *H*-plane radiation patterns of the WR-137 aperture at 10.2 GHz and 11.2 GHz, along with their corresponding simulations. It is possible to observe that at 10.2 GHz the level of the beam at θ < 0° is higher than the beam at θ > 0°. On the contrary, at 11.2 GHz the
<figure><img src="image_20.png" /><figcaption>FIGURE 19. Measurements (continuous lines) and simulations (dotted lines) of WR-137 aperture H-plane radiation patterns at 10.2 GHz (top graph) and 11.2 GHz (bottom graph). Radiation patterns of WR-137 aperture fed with TE₂₀ mode are shown in black color, while radiation patterns of WR-137 aperture fed with TE₁₀ mode are shown in gray color.</figcaption></figure>

behavior is exactly the opposite. This could suggest a correct optimization of the converter design at the target frequency of 10.7 GHz.

Simulations and measurements in Figs. 18 and 19 are normalized to their respective TE₁₀ fed radiation pattern maximum.

## V. CONCLUSION

In this work a new type of RW TE₁₀–TE₂₀ mode converter is presented. The proposed design is simple to implement and can be directly used as an inserted element inside an empty section of RW. The proposed mode converter represents a plain alternative to cumbersome and intricated heavy metallic devices for providing the desired mode conversion. It is formed by a single two-dielectric ‘V’ shaped structure, that turns the incoming TE₁₀ fundamental mode electric field distribution into that of the TE₂₀ mode, by means of two branches acting as a ‘splitter’ while producing the necessary 180° phase shift between the branches. Theoretical considerations are given to properly explain the behavior of the suggested converter design. A proof-of-concept RW TE₁₀–TE₂₀ mode converter is designed and manufactured at a target frequency of 10.7 GHz, using two materials with different dielectric characteristics and WR-90 and WR-137 standard sections. Simulated results show a TE₂₀ mode purity at the converter’s output higher than 98% for a frequency range between 9.5 GHz and 11.6 GHz, and a mode conversion efficiency higher than 85% for a frequency bandwidth between 10.1 GHz and 11.7 GHz, related to the loss tangent of the materials employed in the design. The implementation of the converter is carried out by means of additive manufacturing techniques. The final prototype weighs 8.1 g and fits easily inside an empty 6 cm long WR-137 section with the help of some supporting structural rails. The performance of the converter prototype is verified in two ways. On one

hand, back-to-back measurements (namely TE₁₀–TE₂₀–TE₁₀ conversion) have been carried out which are in good agreement with electromagnetic simulations of the same scenarios. On the other hand, the proposed mode converter has been employed for measuring the H-plane radiation pattern of a TE₂₀ fed WR-137 aperture, providing again a good agreement with simulated responses.

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<figure><img src="image_21.png" /></figure>

**GERMÁN TORREGROSA-PENALVA** was born in Novelda, Spain, in 1976. He received the Graduate and Ph.D. degrees in telecommunications engineering from the Universidad Politécnica de Madrid, Spain, in 1999 and 2004 respectively. In 2002, he joined the Miguel Hernández University of Elche (UMH), where he is currently an Associate Professor. Since 2023, he has been part of the Elche Microwave Laboratory (EMwLab), UMH. His current research activities include the

conception and design of novel microwave circuits implemented with additive manufacturing techniques, the characterization of the dielectric properties of materials using high frequency techniques and circuits, the design of microwave sensors for different applications, and the design of microwave circuits for educational and industrial purposes.

<figure><img src="image_22.png" /></figure>

**BENJAMIN POTELON** (Member, IEEE) received the M.S. degree in telecommunication engineering from Nice Sophia-Antipolis University, Nice, France, in 2004, and the two Ph.D. degrees in electronics and peer-accreditation from Brest, France, in 2007 and 2016, respectively. Since 2008, he has been an Associate Professor with the Electronics Department, University of Brest, and the Laboratoire des Sciences et Techniques de l'Information, de la Communication et de la Connaissance (Lab-

STICC). In 2022, he joined the Microwave Department, IMT-Atlantique, as a Professor. His research interests include the modeling and design of passive devices for microwave and millimeter-wave sub-systems and systems. He is also involved in the development of microwave sensors for various application fields.

<figure><img src="image_23.png" /></figure>

**PAULA VIUDES-PÉREZ** was born in Elche, Spain, in 1999. She received the master’s degree in telecommunications engineering from the Miguel Hernández University of Elche (UMH), in 2024, where she is currently pursuing the Ph.D. degree in industrial and telecommunications technologies. She is currently a Predoctoral Researcher with Elche Microwave Laboratory (EMwLab), UMH. Her research interests include the implementation of novel microwave devices by using additive man-

ufacturing techniques, the design of microwave sensors, and the dielectric characterization of materials using microwave frequencies.
<figure><img src="image_24.png" /></figure>

**HÉCTOR GARCÍA-MARTÍNEZ** (Member, IEEE) was born in Albatera, Spain, in 1991. He received the M.S. degree in telecommunication engineering and the Ph.D. degree in industrial and telecommunication technologies from the Miguel Hernández University of Elche (UMH), Elche, Spain, in 2017 and 2021, respectively. He was a Visiting Scholar with the Microwave Laboratory, University of Pavia, Pavia, Italy, in 2019. He is currently an Assistant Professor with the Department of

Materials Science, Optics and Electronic Technology, and a member of Elche Microwave Laboratory (EMwLab). His research interests include the design of passive and active microwave circuits in complex structures through 3-D additive manufacturing techniques and the analysis of biological materials using microwave devices.

<figure><img src="image_25.png" /></figure>

**ERNESTO ÁVILA-NAVARRO** was born in Elche, Spain, in 1974. He received the M.Sc. degree in telecommunication engineering from the Polytechnic University of Valencia, Spain, in 1998, and the Ph.D. degree from the Miguel Hernández University of Elche, Spain, in 2008, with a doctoral thesis in printed antennas. In 2000, he joined the University Miguel Hernández of Elche, where he is currently an Associate Professor with the Department of Materials Science, Optics and Elec-

tronic Technology, and a Researcher with the Microwave Laboratory of Elche (EMwLab). His current research interests include printed antennas, passive and active microwave devices, bioelectronics, dielectric characterization of materials at microwave frequencies, and microwave imaging systems for tumour detection.

<figure><img src="image_26.png" /></figure>

**ENRIQUE BRONCHALO** was born Guadalajara, Spain, in 1963. He received the degree in Physics from the Complutense University of Madrid, in 1986, and the Ph.D. in physics from Alcalá University, in 1996. In 2001, he joined the Miguel Hernández University of Elche, Spain, where he holds an Associate Professor position with the Signal Theory and Communications Division. His current research is focused on passive microwave devices and microwave sensors.

<figure><img src="image_27.png" /></figure>

**CÉDRIC QUENDO** (Senior Member, IEEE) received the Graduate and Ph.D. degrees in electrical engineering from the University of Brest, Brest, France, in 1999 and 2001, respectively. From 2001 to 2010, he gave courses and conducted research in several institutes. Since 2010, he has been a Professor with the Electronic Department, University of Brest. From 2012 to 2016, he was the Vice-President with the University of Brest. Since 2018, he has been the Head of Lateral, a joint Lab-

oratory between Thales LAS-OME and Lab-STICC. His research interest includes the modeling and design of microwave devices for microwave and millimeter-wave applications.

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