# Three-dimensional metal-only phoenix cell and its application for reflectarrays

Zhihang An<fnref n="1" /> ID
Raphaël Gillard<fnref n="1" />

Tony Makdissy<fnref n="2" />

María Garcia Vigueras<fnref n="1" />

Sébastien Vaudreuil<fnref n="3" />

**Correspondence**

Zhihang An.
Email: Zhihang.An@outlook.com

**Abstract**

A 3D metal-only waveguide-based phoenix cell for reflectarray is presented. The proposed cell consists of two concentric square waveguides and a metallic block in the centre, which offers two operation modes. The first mode uses its cross section to tune reflection phase while the second mode varies the heights of two waveguides to manipulate reflection phase. The principle of the two different modes is analysed in detail. A metal-only reflectarray antenna at 20 GHz is designed based on the first mode of the phoenix cell. It is fabricated using selective laser melting 3D printing technology. A good agreement between simulations and measurements is achieved. The measured gain at 19.75 GHz is 30.25 dBi with an aperture efficiency of 51.17% respectively. Also, the measured 1-dB gain bandwidth is 15% (19–22 GHz). A dual band metal-only reflectarray operating at 20 and 25 GHz is designed based on the second mode of the phoenix cell. The two metal-only reflectarray antennas fully demonstrate the capabilities of the proposed 3D metal-only phoenix cell.

**KEYWORDS**

antenna arrays, reflectarray antennas, waveguides

## 1 INTRODUCTION

Reflectarray antennas (RAs) can be seen as a combination of antenna arrays and reflector antennas with the advantages of high gain, low profile, low cost and easy manufacturing. They are usually implemented in microstrip technology, by printing metallic resonators on top of a dielectric substrate backed by a ground plane. Among other possible solutions, the Phoenix Cell (PC) is a topology of RA cell with high potential [1–8]. In its original version [1], it consists of two square concentric rings enclosing a square patch. The geometrical variation over the RA aperture is smoothen owing to the rebirth ability of the PC. In the literature, PCs are typically implemented using dielectric materials, which makes them not optimal for some applications operating in severe environments, such as satellite communications in space. In such situations, metal-only RAs

(MORAs) are preferable, as they avoid the intrinsic problems brought by the dielectric materials, such as outgassing, losses, and temperature-dependent dielectric constant [9].

Unit cells in MORA can be subdivided into three main categories: slot type, metallic blocks, and waveguides. The simplest form uses one or more metal sheets with slot apertures [10–13]. While this basic configuration has been widely studied, recent advancements in three-dimensional (3D) structures have offered increased flexibility in achieving a complete 360° phase range and enabled advanced functionalities. Several studies [14–20] have explored the use of metallic blocks and waveguides for precise control over the reflection phase. In the case of unit cells composed of metallic blocks, the reflection phase is solely determined by their heights, which imposes limitations on the performance of designed MORA. Conversely, waveguide-type cells provide numerous degrees of

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2023 The Authors. *IET Microwaves, Antennas & Propagation* published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.

<footnote n="1">¹IETR, INSA Rennes, Rennes, France</footnote>

<footnote n="2">²TICKET Research Laboratory, Antonine University, Hadat-Baadba, Lebanon</footnote>

<footnote n="3">³Euromed University of Fès, Fès, Morocco</footnote>
freedom for manipulating their characteristics. The reflection phase of these cells is influenced by both their cross sections and lengths, allowing for more versatile phase control.

The present paper is based on the original concept of three-dimensional (3D) MORA PC that was proposed in ref. [21] and is a direct extension of the RA design in ref. [22]. Such a concept consists of concentric square metal waveguides. Thanks to its 3D configuration, it offers more flexibility and new possibilities compared to slot-type cells. However, in order to fully benefit from these possibilities, a comprehensive study of its different operating mechanisms is needed, which is the first contribution of the present paper compared to ref. [22].

Indeed, there are two operation modes for the 3D PC. One is to fix the height of the waveguides and tune the reflection phase by varying their cross section. The other one is to fix the cross section and tune the reflection phase by varying the heights of both waveguides independently. A single band MORA operating at 20 GHz was synthesised in ref. [22]. Here, a dual band MORA operating at 20 and 25 GHz is also designed, which is the second contribution of the present paper.

Nowadays, the fabrication of such 3D waveguide-based structures is easier and cheaper thanks to the development of 3D printing technology. Many 3D printed MO microwave devices have been reported in refs. [23–27]. Here, as an experimental demonstration, the MORA operating at 20 GHz is fabricated using selective laser melting 3D printing technology and measured. This is the third contribution of this paper compared to ref. [22] that only provided simulation results.

The paper is organised as follows. Part 2 provides a detailed analysis of the two different operating modes of the proposed PC. Part 3 describes the design and the simulation of two different MORAs. Then, in part 4, the MORA operating at 20 GHz is fabricated and measured to further validate the proposed PC. Finally, a conclusion is drawn in part 5.

## 2 | UNIT CELL ANALYSIS

The general 3D PC is shown in Figure 1. It consists of two concentric square waveguides with short-circuit termination and a square metallic block at the centre. The presence of the inner square waveguide decreases the cut-off frequency of the fundamental TE₁₀ and TE₀₁-like modes in the external waveguide so that they can propagate at the operating frequency [22]. Also, the presence of the central metallic block decreases the cut-off frequency of the modes in the inner waveguide. The two different operation modes of the PC are introduced in this section.

### 2.1 | Phoenix cell with fixed height

For the first operation mode, the height of the waveguides is the same for both ($h_{in} = h_{ex}$) and fixed. The size of inner waveguide ($L_r$) is varied to control the cell behaviour. Since this

<figure><img src="image_1.png" /><figcaption>**FIGURE 1** The proposed phoenix cell (a) 3D view and (b) Sectional view.</figcaption></figure>

first operation mode of the PC has been analysed in ref. [22], it will not be repeated here.

### 2.2 | Phoenix cell with fixed cross section

For the second operation mode of the PC, the cross-section of the cell is fixed, and the reflection phase is tuned by varying the heights of both waveguides independently ($h_{in} \neq h_{ex}$). In this paper, these two degrees of freedom will be used to control the reflection phase at 20 and 25 GHz in order to design a dual-band RA. The detailed parameters of the PC are tabulated in Table 1. The size of the external waveguide ($L_c$) is fixed at 6 mm (half wavelength at 25 GHz) to prevent from grating lobes. The size of inner waveguide ($L_r$) must be large enough so it propagates the incident wave at 25 GHz. At the same time, it should not be too large as a too small gap between inner and external waveguides may increase fabrication error. Therefore, a medium value (4.5 mm) is selected for $L_r$. The propagation of the wave in the inner waveguide is also dependent on $L_p$. A large enough value is needed to allow propagation but, once again, the gap between inner waveguide and metallic block must be sufficient to make fabrication easier. As a trade-off, the value of $L_p$ is set to 2.7 mm.
The two waveguides are simulated, and their detailed characteristics are tabulated in Table 2. It can be seen that only the external waveguide operates in propagative mode at 20 GHz while both waveguides allow propagation at 25 GHz. Therefore, the reflection phase at 20 GHz is mainly controlled by the external waveguide while both waveguides are influent at 25 GHz.

The unit cell is simulated using HFSS® assuming stainless steel (with a conductivity of $1.33 \times 10^6$ S/m) for metals. Periodic boundary conditions are used to mimic a cell in a periodic infinite environment.

Figure 2 shows the simulated reflection phase of the unit cell from 20 to 25 GHz as a function of $h_{in}$ and $h_{ex}$. As expected, the response of the cell at 20 GHz is independent from $h_{in}$ (see Figure 2a). It can be observed from Figure 2b,c that the phase response is similar to that at 20 GHz when the frequency is close to 20 GHz, where the reflection phase is primarily controlled by $h_{ex}$. In this scenario, the inner waveguide still operates below cutoff. However, as depicted in Figure 2c,d, with the increase in frequency, the reflection phase can be affected by $h_{in}$, as these frequencies are close to the cutoff frequency of the inner waveguide. With further increase of the frequency, as shown in Figure 2f, a complete 360° phase range is achieved by varying $h_{in}$ whatever $h_{ex}$, except for the value of $h_{ex}$ that causes resonances. Note that the resonance occurs when $h_{in}$ or $h_{ex}$ equals one quarter wavelength of the quasi TE$_{10}$ mode.

Now, Figure 3 shows the simulated reflection magnitude from 20 to 25 GHz as a function of $h_{in}$ and $h_{ex}$. It can be seen from Figure 3a that the loss is less than 1.2 dB at 20 GHz. The maximum loss occurs at resonance. Since the incident wave also propagates in inner waveguide at 25 GHz, resonances at this frequency are observed for both $h_{in}$ and $h_{ex}$ (horizontal and vertical white areas in Figure 2f). As a consequence, the number of configurations with high losses is increased (see Figure 3f). As will be seen later, the synthesis process eliminates such lossy configurations.

<table><caption>TABLE 1 Detailed parameters of the second mode of the phoenix cell.</caption><thead><tr><th>Parameter</th><th>L<sub>c</sub></th><th>L<sub>r</sub></th><th>L<sub>p</sub></th><th>h<sub>in</sub></th><th>h<sub>ex</sub></th></tr></thead><tbody><tr><td>Value (mm)</td><td>6</td><td>4.5</td><td>2.7</td><td>0–16.5, step = 0.25</td><td>0–12, step = 0.2</td></tr></tbody></table>

<table><caption>TABLE 2 Detailed parameters of two waveguides in the second mode of the phoenix cell.</caption><thead><tr><th></th><th></th><th></th><th>Inner waveguide</th><th>External waveguide</th></tr></thead><tbody><tr><td rowspan="4">20 GHz</td><td rowspan="2">γ = α+jβ</td><td>α (NP/mm)</td><td>0.26</td><td>0.0015</td></tr><tr><td>β (deg/mm)</td><td>0.12</td><td>15.75</td></tr><tr><td rowspan="2">Z<sub>c</sub> = R<sub>c</sub> + jX<sub>c</sub></td><td>R<sub>c</sub> (Ω)</td><td>1.09</td><td>51.91</td></tr><tr><td>X<sub>c</sub> (Ω)</td><td>97.90</td><td>0.08</td></tr><tr><td rowspan="4">25 GHz</td><td rowspan="2">γ = α+jβ</td><td>α (NP/mm)</td><td>0.0035</td><td>0.0013</td></tr><tr><td>β (deg/mm)</td><td>10.20</td><td>23.90</td></tr><tr><td rowspan="2">Z<sub>c</sub> = R<sub>c</sub> + jX<sub>c</sub></td><td>R<sub>c</sub> (Ω)</td><td>192.59</td><td>42.46</td></tr><tr><td>X<sub>c</sub> (Ω)</td><td>3.62</td><td>-0.01</td></tr></tbody></table>

## 3 | ANTENNA DESIGN

In this section, two different MORAs are designed to validate the capability of the proposed PC.

### 3.1 | Single-band reflectarray operating at 20 GHz

First, a RA operating at 20 GHz is designed to validate the PCs with fixed height. The illumination is achieved by a linearly polarised horn antenna with an offset angle of 25° with respect to the normal of the panel. The radiating aperture is

<figure><img src="image_2.png" /><figcaption>FIGURE 2 Simulated reflection phase (normal incidence) (a) Phase at 20 GHz (°), (b) Phase at 21 GHz (°), (c) Phase at 22 GHz (°), (d) Phase at 23 GHz (°), (e) Phase at 24 GHz (°), and (f) Phase at 25 GHz (°).</figcaption></figure>
13λ₀ × 13λ₀ (λ₀ is the wavelength at the centre frequency). The overall dimension is chosen to make full wave simulations possible and also to comply with the maximum size achievable with the fabrication process. The *f/D* ratio is 1.183. It is chosen to provide an edge taper less than -10 dB. The direction of the main beam has a tilt angle of 25°, opposite to the offset angle of the horn antenna. The synthesis process derives from the one used in [28]. It consists in selecting the geometry for each cell in the RA in order to achieve best the desired phase. The desired phase law at frequency *f* is defined by the following:

$$ \phi_m^{\text{des}}(f) = \frac{2\pi f}{c} [R_m - (x_m \sin \theta_0 \cos \varphi_0 + y_m \sin \theta_0 \sin \varphi_0)] + \phi^{\text{off}}(f) \quad (1) $$

where $R_m$ is the distance between the feed phase-centre and cell *m* in the RA, ($x_m, y_m$) are the coordinates of this cell, ($\theta_0, \varphi_0$) the direction of the main beam and *c* is the speed of light. $\phi^{\text{off}}$ is a phase offset that is optimised during the synthesis process to minimise the average phase error $\bar{\epsilon}$:

$$ \bar{\epsilon} = \frac{1}{N_f} \sum_{i=1}^{N_f} \sum_{m=1}^{N_c} \frac{I_m(f_i)}{\sum_{m=1}^{N_c} I_m(f_i)} \left| \phi_m^{\text{ach}}(f_i) - \phi_m^{\text{des}}(f_i) \right| \quad (2) $$

<figure><img src="image_3.png" /><figcaption>**FIGURE 3** Simulated reflection magnitude (normal incidence) (a) Mag at 20 GHz (dB), (b) Mag at 21 GHz (dB), (c) Mag at 22 GHz (dB), (d) Mag at 23 GHz (dB), (e) Mag at 24 GHz (dB), and (f) Mag at 25 GHz (dB).</figcaption></figure>

where $N_f$ is the number of frequencies ($f_i$) for which the optimisation is done, $N_c$ is the number of cells, $\phi_m^{\text{ach}}$ and $I_m$ are the achieved phase and the illumination intensity for cell *m*. This latter one is the magnitude of the electric field from the feed antenna impinging on the cell.

In the calculation of $I_m$, the field from the feed is approximated by $\cos^q$ with $q = 19.574$ at 20 GHz. Also, two frequencies are used for optimisation: $f_1 = 19.5$ GHz and $f_2 = 20.5$ GHz in order to increase the bandwidth.

As a trade-off between antenna thickness and achieved phase range, the height of the PC is fixed to 6 mm for all cells. Then, the reflection phase is only controlled by $L_r$.

A database is first established to characterise the response of the cell versus $L_r$. The used parameters of the PC are tabulated in Table 3. The cell response is calculated with HFSS assuming oblique incidence and y-polarisation for the incident wave. The incident angle is set to the value at the array centre (25°) where the illumination is the highest. The simulated reflection coefficient at $f_1$ and $f_2$ is summarised in Figure 4. A complete 360° phase cycle is achieved at both frequencies and the maximum loss is less than 0.25 dB. Note that the jump in magnitude when $L_r = 7.1$ mm is due to the disappearance of the external waveguide when the value of $L_r$ reaches that of $L_c$ (also accounting for metal thickness).

For the sake of completeness, the reflection coefficient is also evaluated for incident angles different from the one at the array centre. In these additional simulations, $\phi_{inc}$ is fixed at 90° while $\theta_{inc}$ is varied from 0 to 40°. These angles correspond to the cells in the central row along *y* axis. Both TE and TM cases are considered. As shown in Figure 5, the maximum phase deviation is less than 31°, which is completely acceptable for synthesising a RA.

The RA is then synthesised using the database in Figure 4. To limit fabrication issues, cells where the gap between two metal walls is less than 0.2 mm are not accepted in the final design. Cells with such a narrow gap between the inner and external waveguides are simply removed from the database. For those where the narrow gap is located between the inner

<table><caption>**TABLE 3** Detailed parameters of the first mode of the phoenix cell.</caption><thead><tr><td>Parameter</td><td>L<sub>c</sub></td><td>L<sub>r</sub></td><td>L<sub>p</sub></td></tr></thead><tbody><tr><td>Value (mm)</td><td>7.5</td><td>1–7.5 (step = 0.05)</td><td>1</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**FIGURE 4** The reflection phase (y-polarization, $\phi_{inc} = 90^\circ$, $\theta_{inc} = 25^\circ$) (a) 19.5 GHz and (b) 20.5 GHz.</figcaption></figure>
waveguide and the metallic block, the treatment is different because the associated phase is not so sensitive. Consequently, in this case, the gap is suppressed (filled with metal).

The variation of cell geometry over the RA panel is shown in Figure 6. Having in mind that cells with either a small or a large $L_r$ have a quite similar geometry, it can be said that a smooth variation is achieved. Figure 7 depicts the 3D radiation pattern of the antenna at 20 GHz, simulated with HFSS®. It shows that the main beam points to the desired direction, which verifies the design process. The simulated radiation patterns and gain response are summarised in Section 4 for comparison with the measured results.

## 3.2 | Dual-band reflectarray operating at 20 and 25 GHz

A dual band RA is now designed to validate the PC with fixed cross-section. The operating frequencies are 20 and 25 GHz. The radiating aperture is $15\lambda_{up} \times 15\lambda_{up}$ ($\lambda_{up}$ being the free space wavelength at 25 GHz) with an element spacing of

$0.5\lambda_{up}$. The illumination is achieved by a linearly polarised horn antenna with an offset angle of 15° with respect to the normal of the panel. The $f/D$ ratio is 1. The direction of the main beam at both frequencies has a tilt angle of 15°, opposite to the offset angle of the horn antenna.

The design process is similar to that of the single band MORA but two offset phases are now optimised to minimise the average phase error at two target frequencies. During the synthesis process, the cell geometries ($b_{in}$ and $b_{ex}$) are selected simultaneously. The required phase shift distributions at both frequencies are calculated by Equation (1). The used database is shown in Figure 8.

To mitigate the impacts of resonances on the performances of the designed RA, all cells with a loss greater than 1 dB are removed from the database before the synthesis of the dual band RA.

The synthesised dual band MORA with its 3D radiated fields are shown in Figure 9 as a preliminary illustration of its behaviour. It can be seen that the main beams are pointing to the desired directions at 20 and 25 GHz. The detailed performances in the lower frequency band are summarised in Figure 10.

It can be seen from Figure 10a,b that the achieved side lobe and cross polarization at 20 GHz are below -20.21 dB and -33.4 dB, respectively. In addition, Figure 10c shows that the gain at 20 GHz is 28.11 dBi with an aperture efficiency of 35.74% and the 1-dB gain bandwidth is about 5%.

Now the performances in the upper frequency band, as shown in Figure 11 are analysed. It can be seen from Figure 11a,b that the achieved side lobe and cross polarisation

<figure><img src="image_5.png" /><figcaption>**FIGURE 5** The reflection phase under oblique incidence (y-polarisation, $\phi_{inc} = 90°$, freq = 20 GHz) (a) TM case and (b) TE case.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**FIGURE 6** The cell geometry of RA (value of $L_r$ in mm).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**FIGURE 7** Radiation field of the designed RA at 20 GHz.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**FIGURE 8** Simulated reflection coefficient (x-polarization, $\phi_{inc} = 90^\circ$, $\theta_{inc} = 15^\circ$) (a) Phase at 20 GHz (°), (b) Phase at 25 GHz (°), (c) Mag at 20 GHz (dB), and (d) Mag at 25 GHz (dB).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**FIGURE 9** Dual band RA with radiation fields (a) 20 GHz and (b) 25 GHz.</figcaption></figure>

at 25 GHz are below –24.56 dB and –36.06 dB, respectively. In addition, Figure 11c shows that the gain at 25 GHz is 30.94 dBi with an aperture efficiency of 43.94% and the 1-dB gain bandwidth is about 5%.

These results can demonstrate that the designed RA can operate in two different frequency bands.

## 4 | FABRICATION AND MEASUREMENT

The MORA operating at 20 GHz is fabricated and measured to further demonstrate the capabilities of the proposed PC. The RA and a horn antenna are fabricated layer by layer using selective laser melting 3D printing technology. During the fabrication, the RA is under nitrogen atmosphere at 100/ 240 W (border/volume) laser power ($\lambda$ = 1075 nm). The

<figure><img src="image_10.png" /><figcaption>**FIGURE 10** Performances in lower frequency band (a) Radiation pattern in xoz' plane (20 GHz), (b) Radiation pattern in y'oz' plane (20 GHz), and (c) Gain response and aperture efficiency.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**FIGURE 11** Performances in upper frequency band (a) Radiation pattern in xoz' plane (25 GHz), (b) Radiation pattern in yoz' plane (25 GHz), and (c) Gain response and aperture efficiency.</figcaption></figure>

material used is a 316 L stainless steel powder with a diameter distribution between 10 and 45 µm. Some preliminary tests have shown that the minimum achievable wall thickness is 0.3 mm. The wall thickness of the PC is chosen to mitigate potential fabrication errors. As shown in Figure 1b, the thickness of the inner wall is 0.3 mm, while the external wall is 0.2 mm. Since the two adjacent cells share the same external wall, the thickness of the external wall is equivalent to 0.4 mm.

The RA with horn antenna is shown in Figure 12. The gain response and aperture efficiency are summarised in Figure 13. The discrepancy in gain between theory and experience is less
than 0.53 dB from 18 to 22 GHz, which is completely acceptable. The measured realised gain at 19.5 GHz is 30.25 dBi with a maximum aperture efficiency of 51.17%. The measured 1-dB gain bandwidth is 15% (from 19 to 22 GHz).

The direction of maximum beam in the target frequency range is tabulated in Table 4. The deviation from the desired direction (25°, 270°) is caused by two reasons. The first is the fabrication and assembly, which can directly vary the location of phase centre of the feed antenna. The second is the fabrication of the RA itself, which may produce additional phase errors. However, the deviation is less than 2° demonstrating the feasibility of such an antenna.

In addition, the comparisons of normalised radiation patterns between full wave simulations and measurements are shown in Figure 14. The agreement is globally very good. Higher discrepancy can be seen when theta is greater than 25°, due to blockage from the horn antenna and arm. Figure 14b and c show that the measured side lobe and cross-polarization

<figure><img src="image_12.png" /><figcaption>FIGURE 12 Photographs of manufactured RA and its measurement setup.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 13 Gain response (left) and aperture efficiencies (right) of the single band RA.</figcaption></figure>

<table><caption>TABLE 4 Direction of maximum beam.</caption><thead><tr><th>f (GHz)</th><th>18</th><th>19</th><th>20</th><th>21</th><th>22</th></tr></thead><tbody><tr><td>(theta, phi)</td><td>(25.88°, 269.80°)</td><td>(26.35°, 270.03°)</td><td>(26.09°, 270.82°)</td><td>(26.18°, 271.44°)</td><td>(26.05°, 271.44°)</td></tr></tbody></table>

at 20 GHz are about 21.15 and 25.20 dB below the main beam, respectively. These levels stay lower than 13.57 dB/24.39 dB in the frequency range from 19 to 22 GHz. The degradation of the side lobe level at 22 GHz (see Figure 14e) is mainly due to the gradual increase in phase error as the frequency moves away from the optimised frequency.

Table 5 compares the proposed MORA with state-of-the-art MORAs. Globally, only 3D cells (either metallic blocks [14, 15, 20] or this work) can achieve an aperture efficiency higher than 50% while allowing dual polarisation.

## 5 | CONCLUSION

In this work, a 3D MO PC with two different operating modes is proposed. The cross section of the PC or the heights of two waveguides in the PC is used to control the reflection phase. The principle and performance of both modes of the PC are analysed in detail. A single band MORA using the first mode of the PC is designed, fabricated and measured. A good

<figure><img src="image_14.png" /><figcaption>FIGURE 14 Normalised radiation patterns of the single band RA (a) yoz plane (19 GHz), (b) xoz' plane (19 GHz), (c) yoz plane (20 GHz), (d) xoz' plane (20 GHz), (e) yoz plane (22 GHz), and (f) xoz' plane (22 GHz).</figcaption></figure>
<table><caption>TABLE 5 Comparison of state-of-the-art MORA.</caption><thead><tr><th></th><th>Type (2D or 3D)</th><th>Polarization</th><th>Freq (GHz)</th><th>Gain (dBi)</th><th>1-dB gain bandwidth (%)</th><th>3-dB gain bandwidth (%)</th><th>Aperture efficiency (%)</th><th>3D printing</th></tr></thead><tbody><tr><td>[10]</td><td>Slot (2D)</td><td>Single linear</td><td>12.5</td><td>33.9</td><td>12.8</td><td>-</td><td>53.8</td><td>No</td></tr><tr><td>[11]</td><td>Slot (2D)</td><td>Dual linear</td><td>12.5</td><td>32.5</td><td>8.3</td><td>-</td><td>-</td><td>No</td></tr><tr><td>[12]</td><td>Slot (2D)</td><td>Circular</td><td>20</td><td>31.4</td><td>6.85</td><td>10.15</td><td>35</td><td>No</td></tr><tr><td>[13]</td><td>Slot (2D)</td><td>Dual linear</td><td>10</td><td>29.6</td><td>6.6</td><td>10.1</td><td>35.7</td><td>No</td></tr><tr><td>[14]</td><td>Metallic block (3D)</td><td>Dual linear</td><td>12.2</td><td>33.2</td><td>-</td><td>-</td><td>50</td><td>No</td></tr><tr><td>[15]</td><td>Metallic block (3D)</td><td>Dual linear</td><td>100</td><td>28</td><td>-</td><td>-</td><td>50.1</td><td>No</td></tr><tr><td>[16]</td><td>Metallic block (3D)</td><td>Circular</td><td>24/32</td><td>24.3/24.5</td><td>-</td><td>10/9.3</td><td>38/26</td><td>Yes</td></tr><tr><td>[17]</td><td>Waveguide (3D)</td><td>Single linear</td><td>75</td><td>42.3</td><td>-</td><td>-</td><td>30.2</td><td>No</td></tr><tr><td>[18]</td><td>Waveguide (3D)</td><td>Single linear</td><td>60</td><td>27.9</td><td>-</td><td>-</td><td>40.5</td><td>Yes</td></tr><tr><td>[19]</td><td>Waveguide (3D)</td><td>Single linear</td><td>25/32/37</td><td>23.7/24.3/23.8</td><td>-</td><td>-</td><td>-</td><td>Yes</td></tr><tr><td>[20]</td><td>Waveguide (3D)</td><td>Circular</td><td>41</td><td>-</td><td>-</td><td>40.96</td><td>55.4</td><td>Yes</td></tr><tr><td>This work</td><td>Waveguide (3D)</td><td>Dual linear</td><td>20</td><td>30.25</td><td>15</td><td>-</td><td>51.17</td><td>Yes</td></tr></tbody></table>

agreement between simulations and measurements is achieved. The maximum realised gain and maximum aperture efficiency are 30.32 dBi and 51.17%, respectively. Also, the 1-dB gain bandwidth is about 15%. The performances of the proposed MORA are quite good compared with other published MORA s. A MORA using the second mode of the PC is designed. Simulation results show that it can operate in two different frequency bands. These two MORA s demonstrate the various capabilities of the proposed 3D MO PC. Further improvements are still possible since all available degrees of freedom have not been exploited yet (typically, h could be varied over the aperture of single band MORA as done in ref. [29], variations in $L_p$ could also provide more flexibility).

## AUTHOR CONTRIBUTIONS

Zhihang An: Data curation; Methodology; Validation; Writing – original draft; Writing – review & editing. Tony Makdissy: Supervision; Writing – review & editing. Maria Garcia-Vigueras: Supervision; Writing – review & editing. Sebastien vaudreuil: Resources; Supervision. Raphael Gillard: Supervision; Writing – review & editing

## ACKNOWLEDGEMENTS

The work was jointly funded by the Agence Universitaire de la Francophonie (Moyen-Orient) and the National Council for Scientific Research Lebanon (CNRS-L). This work was also supported by the European Union, the French Ministry of Higher Education and Research, Brittany Region and Rennes Metropole through CPER funding.

## CONFLICT OF INTEREST STATEMENT

None

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## ORCID

Zhihang An https://orcid.org/0000-0003-2979-5807

## REFERENCES

1. Moustafa, L., et al.: The Phoenix Cell: a new reflectarray cell with large bandwidth and rebirth capabilities. Antennas Wirel. Propag. Lett. 10, 71–74 (2011). https://doi.org/10.1109/lawp.2011.2108633

2. Deng, R., et al.: Single-layer dual-band reflectarray antennas with wide frequency ratios and high aperture efficiencies using Phoenix elements. IEEE Trans. Antennas Propagat. 65(2), 612–622 (2017). https://doi.org/10.1109/tap.2016.2639023

3. Li, X., Li, X., Yang, L.: Single-layer dual-band wide band-ratio reflectarray with orthogonal linear polarization. IEEE Access 8, 93586–93593 (2020). https://doi.org/10.1109/access.2020.2986040

4. Bornot, A., et al.: A Single-Layer Reflectarray Using Hexagonal Phoenix Cells for Ka-Band Applications,” in 2021 15th European Conference on Antennas and Propagation (EuCAP), pp. 1–5. IEEE, Mar., Dusseldorf (2021)

5. Richard, V., et al.: Spherical mapping of the second-order phoenix cell for unbounded direct reflectarray copolar optimization. PIER C 90, 109–124 (2019). https://doi.org/10.2528/pierc18102303

6. Salti, H., Gillard, R.: A statistical approach for gain bandwidth prediction of phoenix-cell based reflect arrays. Adv. Sci. Technol. Eng. Syst. J. 3(1), 103–108 (2018). https://doi.org/10.25046/aj030112

7. Makdissy, T., et al.: ‘Phoenix’ reflectarray unit cell with reduced size and inductive loading,” IET Microwaves. Antennas & Propagation 10(12), 1363–1370 (2016). https://doi.org/10.1049/iet-map.2015.0626

8. Guarriello, A., et al.: A general equivalent circuit model for Phoenix cells. IEEE Trans. Antennas Propagat. 69(11), 7982–7986 (2021). https://doi.org/10.1109/tap.2021.3076676

9. Coonrod, J., Davis, J.: Sending circuit materials into space. Microw. J. (2014)

10. Deng, R., et al.: A low-cost metal-only reflectarray using modified slot-type Phoenix element with 360° phase coverage. IEEE Trans. Antennas Propagat. 64(4), 1556–1560 (2016). https://doi.org/10.1109/tap.2016.2526258

11. An, W., Xu, S., Yang, F.: A metal-only reflectarray antenna using slot-type elements. Antennas Wirel. Propag. Lett. 13, 1553–1556 (2014). https://doi.org/10.1109/lawp.2014.2342376

12. Henderson, K.Q., Ghalichechian, N.: Circular-polarized metal-only reflectarray with multi-slot elements. IEEE Trans. Antennas Propagat. 68(9), 6695–6703 (2020). https://doi.org/10.1109/tap.2020.2993229

13. Huang, P.-L., Hsu, Y.-C., Ma, T.-G.: X-Band tile-based metal-only Reconstructible reflectarray with 3D printing support. Antennas Wirel.
Propag. Lett. 22(9), 1-5 (2023). https://doi.org/10.1109/lawp.2023.3275648

14. Chou, H.-T., Lin, C.-Y., Wu, M.-H.: A high efficient reflectarray antenna consisted of periodic all-metallic elements for the ku-band DTV applications. Antennas Wirel. Propag. Lett. 14, 1542–1545 (2015). https://doi.org/10.1109/lawp.2015.2411750

15. Deng, R., et al.: A 100-GHz metal-only reflectarray for high-gain antenna applications. Antennas Wirel. Propag. Lett. 15, 178–181 (2016). https://doi.org/10.1109/lawp.2015.2436824

16. Zhu, J., Liao, S., Xue, Q.: 3-D printed millimeter-wave metal-only dual-band circularly polarized reflectarray. IEEE Trans. Antennas Propagat. 70(10), 9357–9364 (2022). https://doi.org/10.1109/tap.2022.3184483

17. Cho, Y.H., Byun, W.J., Song, M.S.: High gain metal-only reflectarray antenna composed of multiple rectangular grooves. IEEE Trans. Antennas Propagat. 59(12), 4559–4568 (2011). https://doi.org/10.1109/tap.2011.2165479

18. Wu, G.B., Hou Chan, C.: Millimeter-wave filtering reflectarray for high-gain antenna applications. In: 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, pp. 1493–1494. IEEE, Jul., Atlanta (2019)

19. Zhu, J., et al.: Additively manufactured metal-only waveguide-based millimeter-wave broadband achromatic reflectarrays. IEEE Trans. Antennas Propagat. 71(7), 1–6190 (2023). https://doi.org/10.1109/tap.2023.3278799

20. Palomares-Caballero, Á., et al.: Wideband 3-D-printed metal-only reflectarray for controlling orthogonal linear polarizations. IEEE Trans. Antennas Propagat. 71(3), 2247–2258 (2023). https://doi.org/10.1109/tap.2023.3240583

21. Makdissy, T., et al.: Dual linearly polarised 3D printed Phoenix cell for wide band metal only reflectarrays. IET Microw., Antennas Propag. 14(12), 1411–1416 (2020). https://doi.org/10.1049/iet-map.2020.0265

22. An, Z., et al.: In: A Metal-Only Reflectarray Made of 3D Phoenix Cells," in 2022 16th European Conference on Antennas and Propagation (EuCAP), pp. 1–5. IEEE, Mar., Madrid (2022)

23. Zhang, B., et al.: Metallic 3-D printed antennas for millimeter- and submillimeter wave applications. IEEE Trans. Thz Sci. Technol. 6(4), 592–600 (2016). https://doi.org/10.1109/tthz.2016.2562508

24. Zhang, B., Zirath, H.: Metallic 3-D printed rectangular waveguides for millimeter-wave applications. IEEE Trans. Compon., Packag. Manufact. Technol. 6(5), 796–804 (2016). https://doi.org/10.1109/tepmt.2016.2550483

25. Zhang, B., Zirath, H.: A metallic 3-D printed E-band radio front end. IEEE Microw. Wireless Compon. Lett. 26(5), 331–333 (2016). https://doi.org/10.1109/LMWC.2016.2548982

26. Zhang, B., et al.: Investigation on 3-D-printing technologies for millimeter-wave and terahertz applications. Proc. IEEE 105(4), 723–736 (2017). https://doi.org/10.1109/jproc.2016.2639520

27. Zhang, B., et al.: Attempt of the metallic 3D printing technology for millimeter-wave antenna implementations. In: 2015 Asia-Pacific Microwave Conference (APMC), pp. 1–3. IEEE, Nanjing, China (2015)

28. Mao, Y., et al.: A novel phase synthesis approach for wideband reflectarray design. IEEE Trans. Antennas Propagat. 63(9), 4189–4193 (2015). https://doi.org/10.1109/tap.2015.2447004

29. An, Z., et al.: Bandwidth enhancement of a metal-only reflectarray based on the Phoenix cell. In: 2022 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI), pp. 587–588. IEEE, Denver (2022)

**How to cite this article:** An, Z., et al.: Three-dimensional metal-only phoenix cell and its application for reflectarrays. IET Microw. Antennas Propag. 18(4), 211–219 (2024). https://doi.org/10.1049/mia2.12431