Ángel Palomares-Caballero

Carlos Molero
email: cmoleroj@ugr.es

Pablo Padilla
email: pablopadilla@ugr.es

María García-Vigueras
email: maria.garcia-vigueras@insa-rennes.fr

Raphaël Gillard
email: raphael.gillard@insa-rennes.fr

C Palomares-Caballero

P Molero

Padilla

Wideband 3-D-Printed Metal-only Reflectarray for Controlling Orthogonal Linear Polarizations

Keywords: unit cell, dual polarization, metal-only, millimeter-waves, polarization control, reflectarray antenna

This paper presents a metal-only reflectarray that enables the control of incident orthogonal polarizations in a large bandwidth. The proposed reflectarray is based on a unit cell whose tuning elements allow the independent control of the reflection phase value for the vertical and horizontal impinging polarizations. Due to the symmetry of the unit cell, the same performance is produced by each polarization when its reflection phase response is modified. The proposed unit cell provides a fairly linear phase response along the frequency with a phase variation in the orthogonal polarization of ±1 o . The performance under oblique incidence and the frequency limitation of the unit cell are also investigated. From this unit cell, a metal-only reflectarray that produces circular polarization from a linear polarization is designed. The reflectarray presents a simulated directivity greater than 27 dBi with an axial ratio below 1.5 dB from 32 GHz to 50 GHz (43.9% of bandwidth). A prototype is fabricated and the measured results agree well with the simulated ones. The obtained aperture efficiency is between 56% and 41% in the considered frequency band. The measured realized gain ranges from 27 dBi to 30.3 dBi where the achieved radiation efficiency is greater than 97%.

I. INTRODUCTION

R EFLECTOR antenna is one of the key radiating element for the future communications paradigms. Both passive [START_REF] Anjinappa | Base station and passive reflectors placement for urban mmWave networks[END_REF], [START_REF] Khawaja | Coverage enhancement for NLOS mmWave links using passive reflectors[END_REF] and active [START_REF] Renzo | Smart radio environments empowered by reconfigurable intelligent surfaces: how it works, state of research, and the road ahead[END_REF], [START_REF] Molero | Metamaterial-based reconfigurable intelligent surface: 3D meta-atoms controlled by graphene structures[END_REF] reflector antennas have been proposed to enhance the link budget in forthcoming wireless communications. Another application in which reflectors or reflectarrays are widely used is in space applications due to the high directivity and versatility provided by this type of antennas [START_REF] Nayeri | Reflectarray antennas: theory, designs, and applications[END_REF]. All of the above applications are intended to work in millimeter-wave frequencies to achieve either a higher bandwidth or because the desired frequency is in that range. The direct consequence is the use of metal-only structures in the antennas to obtain greater efficiency [START_REF] Chou | An all-metallic reflectarray and its element design: exploring the radiation characteristics of antennas for directional beam applications[END_REF] and avoid outgassing problems in space applications.

Metal-only reflectarrays have been reported in the literature with different designs and implementations. Following the conventional reflectarray (RA) designs formed by stacked layers of PCBs, [START_REF] Deng | A low-cost metal-only reflectarray using modified slot-type phoenix element with 360°phase coverage[END_REF]- [START_REF] Antonov | Design of wideband reflectarray antennas[END_REF] present reflectarrays formed by stacking perforated metallic sheets. Their structures only use metal avoiding dielectric substrates. In [START_REF] Cho | Metallic-rectangular-grooves based 2D reflectarray antenna excited by an open-ended parallel-plate waveguide[END_REF] and [START_REF] Wang | A 60 GHz passive repeater array with quasi-endfire radiation based on metal groove unit-cells[END_REF], advantage is taken of parallel-plate metallic waveguides to efficiently reflect the incoming wave to broadside and endfire directions, respectively. Metallic square waveguides are also been considered as RA unit cells in [START_REF] Cho | High gain metal-only reflectarray antenna composed of multiple rectangular grooves[END_REF] and its 3-D printed version in [START_REF] Wu | High-gain filtering reflectarray antenna for millimeter-wave applications[END_REF], [START_REF] Chen | 3D printed reflectarray antenna at 60 GHz[END_REF] at V-band. An alternative approach to design metal-only RA unit cells is the one proposed in [START_REF] Chou | An all-metallic reflectarray and its element design: exploring the radiation characteristics of antennas for directional beam applications[END_REF] where convex or nonresonant elements are defined. RA designs that employ this geometry for their reflective elements are presented in [START_REF] Deng | A 100-GHz metal-only reflectarray for high-gain antenna applications[END_REF]- [START_REF] Zhang | Low-RCS and wideband reflectarray antenna with high radiation efficiency[END_REF]. These works demonstrate that large gain bandwidths can be achieved with the adequate choice of the nonresonant element geometry, resulting in a great advantage regarding previous resonant RA unit cells. More complex geometries for metal-only RA unit cells have also been reported. For instance, in [START_REF] Kong | A wideband reconfigurable dual-branch helical reflectarray antenna for high-power microwave applications[END_REF], a dual-branch helix has been used to obtain a linear phase response along the frequency and preserve the incident circular polarization. Another example is found in [START_REF] Mei | A low-cost, high-efficiency and full-metal reflectarray antenna with mechanically 2-D beam-steerable capabilities for 5G applications[END_REF] where metallic cylinders etched with a rectangular groove provide a stable phase difference and thus, are good candidates to design a two-states RA.

In all the above metal-only reflectarrays, only the phase response of a single polarization can be tuned in the RA design. However, the independent control for orthogonal polarizations of an incident wave in a RA is a desired requirement to extend its functionalities. There are RA unit cells that offer a control of orthogonal polarizations as the one proposed in [START_REF] Momeni Hasan Abadi | Broadband true-timedelay circularly polarized reflectarray with linearly polarized feed[END_REF] but, most of them are based on the stacking of PCB layers that have dielectric material in their structure. Nonetheless, in the literature, it is very hard to find this independent polarization control for metal-only RA. The recent development of 3D unit cells offers new possibilities to independently control two orthogonal polarizations and thus, RA unit cells based on this geometry can be developed. The three-dimensional geometry allows a high level for controling orthogonal polarizations as can been observed in dual-band metal-only polarizer in [START_REF] Jimenez | All-metal 3-D frequency-selective surface with versatile dual-band polarization conversion[END_REF]. Based on this design procedure, some metal-only reflectarrays have been conceptually proposed [START_REF] Molero | Metamaterial-based reconfigurable intelligent surface: 3D meta-atoms controlled by graphene structures[END_REF] and implemented for a single polarization [START_REF] Velasco | Fully metallic reflectarray for the Ku-band based on a 3D architecture[END_REF]. However, the design of some of the last RA unit cells are based on resonant elements which provide narrowband performance.

In this paper, a metal-only RA with wideband performance and independent control of incident polarizations is presented. In order to achieve this wideband control of the orthogonal polarizations, the RA unit cells have a 3D geometry which enables the excitation of two orthogonal transverse electro-magnetic (TEM) modes. The work in [START_REF] Molero | Broadband 3D-printed polarizer based on metallic transverse electro-magnetic unitcells[END_REF] is also based in the excitation of TEM modes in a 3D unit cell in order to achieve broadband polarization conversion. However, such unit cell operated in transmission and its topology was not conceived to operate in reflection. In addition, the purely metallic nature of the proposed RA structure enables an easy and feasible redesign by geometric scaling for tuning in the desired frequency band. To the best of the authors' knowledge, it is the first design of a metal-only RA with wideband performance and independent control of incident orthogonal linear polarizations. The outline of this paper is the following one. Section II presents and discusses the electromagnetic (EM) performance of the proposed RA unit cell. In Section III, the design of a circular-polarized RA is done by means of the proposed RA unit cells. Section IV shows the prototype and its measurements as well as a discussion of the results. Finally, Section IV presents the conclusions from this work.

II. REFLECTARRAY UNIT CELL: DESIGN AND ANALYSIS

Fig. 1 illustrates the geometric evolution of the proposed RA unit cell from its original design (labelled as (0)) to its optimized design (labelled as (3)). RA unit cell (0) can be seen as a combination of horizontal and vertical parallel plates whose groove depths are varied independently for each polarization. It is similar to the RA unit cells introduced in [START_REF] Cho | Metallic-rectangular-grooves based 2D reflectarray antenna excited by an open-ended parallel-plate waveguide[END_REF], [START_REF] Wang | A 60 GHz passive repeater array with quasi-endfire radiation based on metal groove unit-cells[END_REF] but here for both xand y-directions. All the unit cells designs illustrated in Fig. 1 only use metal in their structure. The tuning elements, highlighted in red and green, are metallic blocks whose heights h V and h H are modified to change the phase reflection response of the vertical (V-pol) and horizontal (H-pol) polarizations, respectively. Impinging wave is vertically polarized when the electric field (E-field) is in y-direction while it is horizontally polarized when the E-field is in the x-direction. The propagation of the incident wave is considered in the z-direction and the reflected one is in the minus z-direction. In the performed EM simulations, periodic environment is applied along the xand y-directions since the local periodicity approach is widely used in the literature for analysing quasi-periodic structures such as reflectarrays. The EM software used in all the simulations of the paper is CST Studio Suite whose Frequency Solver is employed for the RA unit cell simulations while the Time Solver, for the complete RA design. The design procedure for both RA unit cell and complete RA is aimed for the frequency band from 32 GHz to 50 GHz. This frequency range corresponds to the full operating frequency band of the WR22 waveguide standard.

Coming back to the RA unit cell evolution shown in Fig. 1, geometric modifications have been introduced from (0) to (3) unit cell designs. These modifications have an impact in the EM performance of the original RA unit cell. Fig. 2 shows the reflection phase response of each RA unit cell design when the parameter h V varies, keeping the value of parameter h H fixed in the sweep. Due to the desired independent phase response of each polarization, the phase response for the H-pol should not be changed. In order to clearly observe this fact, the phase difference for the H-pol is also included in Fig. 2 in which the phase response reference is the case when h H is minimum. Notice that all the RA unit cell designs presented in Fig. 1 are symmetric both for xand y-directions and thus, it is enough to analyze the variation of one of the tuning parameters, h V in our case. Figs. 2(a) and 2(b) show the EM performance for both orthogonal polarizations. It can be observed that the phase range is approximately 720 o because the length of the RA unit cell L is almost one wavelength at the center frequency. Nevertheless, the phase response along the frequency illustrated in Fig. 2(a) is quite nonlinear with an inadequate phase difference to achieve the independent control of both polarizations (see Fig. 2(b)). For RA unit cell (1), the reflection phase response and the phase variation of the orthogonal polarization are displayed in Figs. 2(c) and 2(d), respectively. With the inclusion of roundness with a radius r on the edges of the parallel plate, a higher linearity in the phase response can be achieved and also, a decrease in the variation of the phase response for the H-pol. The separation between parallel plates for this RA unit cell is also greater (s > s o ) providing a better impedance matching with free space and thus, enhancing the phase linearity along the frequency [START_REF] He | Dielectric metamaterial-based impedance-matched elements for broadband reflectarray[END_REF]. Figs. 2(e) and 2(f) display the phase behaviour of both polarizations for the RA unit cell [START_REF] Khawaja | Coverage enhancement for NLOS mmWave links using passive reflectors[END_REF]. The only geometrical modifications regarding the RA unit cell (1) is the narrowing of the separation between parallel plates (labelled as s r in Fig. 1) starting from a particular distance L o from the beginning of the unit cell design. This inclusion produces an improvement of the phase linearity along the frequency as can be observed in Fig. 2(e) and a reduction of the phase difference in the phase response of the H-pol shown in Fig. 2(f). This enhancement in the phase response is at expense of limiting the length range of the tuning parameter h V . However, it is not a problem because the tuning phase response is still beyond 360 o , required value for a suitable RA design. An additional design improvement can be done by rounding the edges of the ends of the parallelplate waveguides by r 1 and r 2 as it is illustrated in the RA unit cell (3) of Fig. 1. In this way, the linear phase response Phase difference (deg.) (h) Fig. 2. Reflection phase response with a V-pol plane wave excitation under a normal incidence when tuning length h V is modified: (a) RA unit cell (0), (c) RA unit cell [START_REF] Anjinappa | Base station and passive reflectors placement for urban mmWave networks[END_REF], (e) RA unit cell (2) and, (g) RA unit cell [START_REF] Renzo | Smart radio environments empowered by reconfigurable intelligent surfaces: how it works, state of research, and the road ahead[END_REF]. Phase difference in the orthogonal polarization (H-pol) when tuning length h V is modified: (b) RA unit cell (0), (d) RA unit cell (1), (f) RA unit cell (2) and, (h) RA unit cell [START_REF] Renzo | Smart radio environments empowered by reconfigurable intelligent surfaces: how it works, state of research, and the road ahead[END_REF].

h V = 0 mm h V = 1 mm h V = 2 mm h V = 3 mm h V = 4 mm h V = 5 mm h V = 6 mm h V = 7 mm (a)
h V = 0 mm h V = 1 mm h V = 2 mm h V = 3 mm h V = 4 mm h V = 5 mm h V = 6 mm h V = 7 mm (c)
h V = 0 mm h V = 1 mm h V = 2 mm h V = 3 mm h V = 4 mm h V = 5 mm h V = 6 mm (e)
is preserved as it is shown in Fig. 2(g) and the phase response difference in the H-pol is further enhanced by reducing the range of variation between +0.5 o and -1 o . Therefore, this RA unit cell design meets the desired requirements and it is the one selected for the RA antenna design.

The magnitude performance of the selected RA unit cell is shown in Fig. 3. It can be seen that the cross-polar component has a negligible excitation since it is below -60 dB over the considered bandwidth. The performance is similar to the unit cell presented in [START_REF] Palomares-Caballero | Metal-only reflectarray unit cell for dual-polarization control[END_REF] because of the employed 3D geometry. This fact is preserved for different values of h V and for oblique incidence situations as displayed in Fig. 3(b).

Fig. 4 shows the E-field distribution of the selected RA unit cell when it is illuminated by a V-pol plane wave. The E-field distributions have been plotted at different planes of interest (H, V 0 and V 1 ) indicated in Fig. 4(a). The vector and the magnitude distributions of the y component of the E-field are illustrated in Fig. 4(b). From this figure, it can be realized that the electric field is propagating mainly along the parallel-plate waveguide (subfigure framed in orange and blue). In contrast, in the V 1 plane, which contains the propagating path for the H-pol, the V-pol can hardly propagate with the magnitude of the E-field being close to zero as shown in the subfigures framed in green included in Fig. 4(b). This fact is due to the mode field distribution when the V-pol plane wave is impinged on the RA unit cell. Almost all the power propagates along the conductors that form the parallel plate waveguide where the tuning element is placed. On both sides of this waveguide, the E-field decays strongly in the x-direction as can be seen in the plane H of Fig. 4(b). Beyond the tuning element, the E-field distribution between RA unit cells is rapidly attenuated because the mode becomes evanescent since it becomes a TE 10 waveguide mode whose waveguide width is 2w h1 . This can be observed in the waveguide zone indicated in the planes V1 and H of Fig. 4(b). The same rationale is valid for an illumination of the RA unit cell with a H-pol plane wave. All above observations give an explanation about the remarkable isolation in the phase response tuning of the incident orthogonal polarizations.

The electric field distribution analyzed in the unit cell shows that the highest electric field intensity is located in the gap of the parallel-plate waveguide. The size of this gap determines the maximum power-handling capacity before multipactor phenomenon appears, which is of particular concern in satellite applications. Using the commercial software SPARK3D, the calculation of the multipactor power threshold is performed. At 41 GHz, the maximum power-handling capacity is 8699 W.

A. Resonances in the unit cell

As described above, the selected RA unit cell mostly allows the wave propagation along its structure to the polarization whose E-field is perpendicular to the parallel-plate waveguide (see Fig. 4(b), subfigure framed in orange). Nevertheless, although in the regions where the E-field amplitude is very weak or even evanescent, some cavity resonances can be generated if the resonance conditions are fulfilled for a certain frequency. In Figs. 5(a) and 5(b), the plane of interest H is displayed for a unit-cell environment of two cells with different length for the tuning element and at different frequencies. It can be seen how the large part of the incident E-field tends to propagate along the area of the parallel plate waveguides. However, when the frequency increases or the tuning length h V is longer, some resonances appear in the evanescent regions, i.e., the regions enclosed with dashed line in Figs. 5(a) and 5(b). These resonances completely alter the linear phase response of the unit cell as displayed in Fig. 5(c). The reflection coefficient in phase for different tuning length values has been investigated and all the possible resonances between unit cells occur outside of the operating bandwidth. This physical insight reveals the performance limitation in frequency of the proposed RA unit cell. Nonetheless, the operating frequency band where the reflection phase produces an acceptable phase linearity is from 32 GHz to 50 GHz, this is, a 43.9% bandwidth. 6(c) correspond to oblique incidence in the E-plane while, Figs. 6(d), 6(e) and 6(f) correspond to oblique incidence in the H-plane. E-plane stands for the YZ plane (ϕ = 90 o and θ varies) and H-plane stands for the XZ plane (ϕ = 0 o and θ varies) of the axis illustrated in Fig. 1. Observing the simulated results for both planes and different oblique incidence angles, the linear phase response is maintained along the frequency range for the different tuning lengths and approximately preserving the phase difference between curves. As expected, as the value of the angle of incidence increases, the performance deteriorates especially for the high end of the frequency range where the slope of the phase curves starts to increase. This is a consequence of the frequency approach of the out-of-band resonances towards the operating bandwidth. For the sake of completeness, the phase difference for the orthogonal polarization is presented in Fig. 7 under the same oblique incidence conditions shown in Fig. 6. Notice that the independent control of the orthogonal polarization is kept and the absolute phase difference is not more than 2 o for almost all the oblique incidence cases under study. The only case that exceeds this error at the end of the frequency range is the one presented in the Fig. 7(c). A huge increase in the phase difference appears near 50 GHz. This fact is also a consequence, in this particular case of oblique incidence, of a displacement of the out-of-band resonances closer to the operating bandwidth. The behavior presented above is for a V-pol plane wave impinging on the RA unit cell. The same performance is obtained in the case of an H-pol plane wave excitation due to the symmetry exhibited by the RA unit cell design.

B. Oblique incidence performance

C. Independent beam control by incident polarization

Thanks to the wideband linear phase-response of the selected unit cell and its independent control of orthogonal polarizations, an example of RA design where the reflected beam for each linear polarization has different outgoing direction is shown in Fig. 8. A more detailed view of the RA system can be seen in Fig. 9(a) except that the directions for the V-pol and H-pol linear polarizations are (ϕ = 45 o , θ = 10 o ) and (ϕ = 105 o , θ = 20 o ), respectively. The phase maps required in each polarization to achieve the above-mentioned directions are shown in Figs. 8(c) and 8(d). Lastly, Fig. 8(e) presents the directivity achieved by the RA over the considered frequency range. We observe a similar directivity for both polarizations with the same behavior along the frequency.

III. CIRCULARLY-POLARIZED REFLECTARRAY DESIGN

Complementary to the previous subsection II.C, this section is devoted to the design and analysis of a RA that provides a circular polarization from a linear polarization. In order to generate the circularly-polarized reflected wave, the RA is rotated by 45 o regarding the feed antenna which has a linear polarization. In this manner, both orthogonal polarizations are excited in the RA structure [START_REF] Momeni Hasan Abadi | Broadband true-timedelay circularly polarized reflectarray with linearly polarized feed[END_REF]. Additionally, to improve the blockage efficiency, the feed antenna illuminates the RA with an offset angle θ i = 20 o . Fig. 9(a) illustrates the depicted RA system whose selected feed antenna is a commercial 20 dBi horn antenna (Flann WR22 Standard Gain Horn). The distance between the RA and the center of the horn antenna aperture is F [see caption of Fig. 9] and F/L RA =1.47, which ensures an amplitude taper from the center of the RA to the edges approximately equal to -10 dB at the center frequency. The reflected angle of the beam θ r radiated by the RA has been chosen to be equal to the incident angle (θ r = θ i ) and in the same radiation plane, that is, the Z ' Y ' plane in Fig. 9(a). If a direction other than the specular direction is chosen for the reflected beam, a beam squint with frequency will appear [START_REF] Targonski | Minimization of beam squint inmicrostrip reflectarrays using an offset feed[END_REF], which will be more noticeable the more different is the direction selected regarding to the specular one. The total number of RA unit cells employed in the RA design has been set to 21x21 and thus, at 32 GHz and 50 GHz, the electric size of the RA is 9λ x 9λ and 14λ x 14λ, respectively.

In order to achieve an increase in the directivity of the feed antenna and transform the linear polarization received in the RA to a circular polarization, the phase maps for the V-pol and H-pol have to be carefully calculated. Firstly, the phase map calculation of a single polarization, for instance V-pol, has been considered. The phase of the incident wave at the center of each V-pol tuning element is obtained by simulation. In Fig. 9(b), these tuning elements are highlighted for a RA zone of 3x3 unit cells. In the same figure, the decomposition of the incident E-field (E inc ) into the E-field for the V-pol (E y ) and H-pol (E x ) is also displayed. The simulated phases obtained at 41 GHz, the center frequency of the operating bandwidth. In this manner, a more accurate design in terms of phase correction in the RA is possible when compared to the phases calculated through ray tracing method [START_REF] Plaza | A simple model for analyzing transmitarray Lenses[END_REF]. Once the incident phases are obtained, the phase map of the RA is computed since the positions of RA unit cells and the direction of the reflected beam is known [START_REF] Nayeri | Reflectarray antennas: theory, designs, and applications[END_REF].

For the orthogonal polarization (H-pol), a similar procedure is done. The phases obtained from the simulation are the ones corresponding to the central zones of the tuning elements for H-pol. To produce the circular polarization, both orthogonal polarizations must have a difference phase of ±90 o . In our RA design, it is selected a phase difference equals to +90 o and in consequence, the circular polarization is LHCP. The opposite circular polarization, RCHP, can be produced if the linear polarization of the horn antenna is aligned to the x ′direction instead of the y ′ -direction (see axis in Fig. 9). The phase maps for both polarizations are displayed in Fig. 10.

It is important to say that a constant phase reference can be added to the presented phase maps without introducing any error on the theoretical design of the reflectarray [START_REF] Nayeri | Reflectarray antennas: theory, designs, and applications[END_REF]. Nevertheless, this constant phase reference should be chosen carefully because it modifies the physical structure of the RA since the lengths of the tuning elements change accordingly. This implies that the unit cells located in the central zone of the RA, which has the greatest influence due to the amplitude taper, must respect a good linearity of the phase response with frequency. For the unit cell used, the performance of the RA is specially affected at the ends of the operating bandwidth.

The phase maps presented in Fig. 10 produce satisfactory performances for the directivity and axial ratio (AR) in the considered frequency range.

Based on the computed phase maps, the physical implementation of these phase responses in the RA has been carried out by a lookup table that relates the lengths of the tuning element with their reflection phase values. This lookup table has been created with the simulated reflection phase shift values at 41 GHz and their corresponding tuning lengths. Due to the similarity of the phase response of the RA unit cell in normal In Fig. 12(a), the provided directivity and AR by the RA are presented. Additionally, the maximum directivity that the reflectarray can produce is also included. The achieved directivity ranges from 27.25 dBi to 30.3 dBi with an AR below 1.5 dB for the entire frequency range. To calculate the different efficiencies that impact the aperture efficiency of the RA, the analysis presented in [START_REF] Yu | Aperture efficiency analysis of reflectarray antennas[END_REF] has been used. The coefficients q and q e of the cosine models of the feed antenna and RA unit cell radiation patterns have been obtained by simulation. Since a large frequency range is considered, these coefficients vary with frequency and consequently, the amplitude taper in the plane of the reflectarray also changes with frequency. The range of values for q is from 9.5 to 20 while q e goes from 0.5 to 0.85. The illumination efficiency (η i ) and spillover efficiency (η s ) over the frequency are presented in Fig. 12(b). In addition to these two efficiencies, the aperture efficiency (η a ) resulting from the product of η i and η s and, the aperture efficiency obtained in simulation (η s,sim ), which is calculated by the difference between the maximum achievable directivity and the produced directivity, are shown [see Fig. 12(a)]. We can observe that η a is between 68% and 77% while η a,sim is not greater than 58%. This difference is due to additional efficiency factors considered in the fullwave simulation, which decrease η a . Thanks to the metal-only structure of the RA, the material losses, in this case metal, are very low and a simulated radiation efficiency is above 97% in the frequency range. Thanks to the metal-only structure of the RA, the material losses, in this case metal, are very low and a simulated radiation efficiency is above 97% in the frequency range.

Other efficiency factors such as blockage efficiency or return loss efficiency are negligible in our RA design. This is because the feed antenna illuminates the RA at oblique incidence and the reflection coefficient of the horn antenna is around -25 dB in the considered frequency range. Another relevant efficiency factor is the phase efficiency that takes into account the deviation from the desired phase distribution at RA aperture. Error phase maps have been calculated to observe the phase deviation produced at different frequencies. The calculation of these errors has been carried out by the difference between the desired phase distribution in the RA aperture and the one extracted, in the plane of the aperture, with CST Studio Suite. It is important to point out that for a correct calculation of the phase distribution in this aperture, the effect of the incident wave in simulation must be removed and only the wave reflected by the RA must be considered. The error phase maps for V-pol and H-pol at different frequencies are shown in Fig. 13 and Fig. 14, respectively. Phase errors located in the central area of RA are the ones that degrade performance the most, since this is the area that receives most of the illumination from the feed antenna. The cause of these phase errors is due to the perturbation of the unit cell phase response by the non-periodic environment, the modification of the oblique incidence angle across the RA and the non-perfect phase behavior of the unit cell in frequency. Nevertheless, in general, we do not find very large phase errors along the frequency for the two polarizations in the proposed RA design.

In addition, it can be observed how the phase errors are greater at the higher frequencies of the operating band. This results in a reduction of the phase efficiency. Additionally, it is relevant to note that there is some loss in the polarization efficiency due to the excitation of the cross-polar component in certain areas of the RA. This produces an undesired radiation around the specular direction. These efficiency factors decrease the η a . By taking into account the phase responses at different frequencies in the RA design process combined with an optimization algorithm, an improved aperture efficiency could be achieved. Nevertheless, this would lead to a higher computational cost in the design process. Table I summarizes the sources of losses that are present in the proposed RA design over the considered frequency band.

IV. FABRICATION, MEASUREMENTS AND DISCUSSION

In order to experimentally verify the design process presented in the previous sections, the RA has been fabricated and characterized in the anechoic chamber of University of Granada. A photo of the prototype is shown in Fig. 15(a). Thanks to the geometry of the proposed unit cell, it can be easily manufactured in 3D printing allowing a low cost and low weight prototype. Indeed, the manufacturing process followed for the prototype is based on stereolithography (SLA) 3D printing and a subsequent silver metallization. The printer used was the Form 3 from Formlabs with the high temp resin that allows a high precision printing with a thickness layer of 25 µm. The 3D printer achieves a XY resolution of 25 µm and the laser spot size is 85 µm. In relation to the tolerances, for feature size lower than 4 mm, the standard deviation is 30 µm. These properties in the 3D printing process produce a reliable manufacturing of the proposed reflectarray design.

Regarding the metallization process, it was carried out by JetMetal [START_REF] Metal | Metallization principle[END_REF], a company that offers a silver coating in plastic pieces by means of spray metallization. The silver coating has a thickness of 2.5 µm which is approximately 7 times the skin depth for the minimum operating frequency. According to [START_REF] Feuray | Evaluation of metal coating techniques up to 66 GHz and their application to additively manufactured bandpass filters[END_REF], the average roughness produced in this metallization process is 2 µm which reduces the conductivity achieved by the silver. This decrease in the conductivity is almost negligible since it maintains the conductivity around 3•10 7 S/m. In Fig. 15(b), the implementation of the RA system is displayed. Some supports have been printed with the same 3-D printer to align the feeding horn with the center of the RA and the main beam direction of the RA with the receiving horn antenna of the measurement setup. The comparison between simulated and measured radiation patterns in the E-and Hplanes for the LHCP and RHCP are presented in Fig. 16. We can observe a remarkable agreement for both the coand cross-polarization at different frequencies. The half power beam width (HPBW) at 35 GHz, 41 GHz and 47 GHz are approximately 7 o , 6 o , 5 o , respectively. In the HPBW, the maximum levels of cross-polar component, both simulated and measured, are -24.8 dB sim.

35GHz , -27.5 dB meas. 35GHz , -20.8 dB sim. 41GHz , -24.1 dB meas.

41GHz , -18.7 dB sim. 47GHz and -16.3 dB meas. 47GHz . It can be noted that the cross-polar component increases with frequency. In order to complete the assessment of the proposed RA and to report more information about its radiation pattern performance, Figs. 17 and 18 show the measured 3-D LHCP and RHCP at different frequencies. In Fig. 17, we can observe the narrowing of the main beam as the frequency increases and, the appearance of side lobe levels at ϕ = 45 o or 135 o . Nevertheless, the maximum side lobe level is not greater than -20 dB. On the other hand, in Fig. 18, it is more clearly seen how the RHCP level increases with frequency and around the main beam zone. At 50 GHz, the highest level of cross-polar is achieved and it is -12.3 dB. in the literature. In this work, a wider 3-dB gain bandwidth with similar peak aperture efficiency is obtained compared to the other works. However, we can highlight that it is the first metallic RA that allows the control of both incident linear polarizations in addition to produce a large 3-dB AR bandwidth (43.9%). Recent work in [START_REF] Zhu | Additively manufactured metalonly millimeter-wave dual circularly polarized reflectarray antenna with independent control of polarizations[END_REF] also achieves the independent control but for orthogonal circular polarizations. Its operating bandwidth is below millimeter frequencies with a lower peak aperture efficiency and 3-dB gain bandwidth regarding the proposed RA.

For the sake of completeness, Table III shows a comparison with the state-of-the-art works about fully-dielectric RAs in millimeter-wave frequencies. To make a fair comparison, the included works either produce circular polarization or independently control the incident linear polarizations. It can be seen that although the other works can achieve similar 3-dB gain and AR bandwidths, the aperture efficiency is lower than the one obtained with the proposed RA. This is because it is difficult to find dielectrics with lower losses than metal in this frequency range and thus, metal-only RAs achieve higher radiation efficiency. Particular attention should be paid to the work in [START_REF] Cheng | Dual circularly polarized 3D printed broadband dielectric reflectarray with a linearly polarized feed[END_REF]. In that work, a unit cell design that controls the phase of both orthogonal incident polarizations by modifying the length of dielectric cuboids has been proposed. Nevertheless, the unit cell design relies on dielectrics, unlike the RA unit cell proposed in this work, which only uses metal in its structure. One of the consequences of using only metallic structures is the strong boundary conditions they impose, which in our design allow a negligible phase variation of the orthogonal polarization (lower than 1 o ). In contrast, the dielectric RA unit cell presented in [START_REF] Cheng | Dual circularly polarized 3D printed broadband dielectric reflectarray with a linearly polarized feed[END_REF] shows high phase variation for the polarization that is not intended to be modified. Additionally, our RA design mitigates the shadowing effect that appears in [START_REF] Cheng | Dual circularly polarized 3D printed broadband dielectric reflectarray with a linearly polarized feed[END_REF] and [START_REF] Nayeri | 3D printed dielectric reflectarrays: lowcost high-gain antennas at sub-millimeter waves[END_REF] since all the RA unit cells have the same length (L in Fig. 1). A high aperture efficiency is also obtained in this work with wider 3-dB gain bandwidth. Finally, it is noteworthy to say that thanks to the performance offered by the proposed RA unit cell, the 3-dB AR bandwidth is extended but in the presented results we have only considered the standard frequency band supported by WR22 waveguide. * If the value is not given explicitly, it is calculated from the reflection losses of the RA unit cell.

V. CONCLUSIONS

A metal-only RA design that allows the phase control of impinging orthogonal polarizations is presented in this paper. Based on a unit cell with 3-D geometry, an independent phase tuning in a wide frequency range is achieved. In each unit cell, the modification of the reflected phase is implemented by the variation of the lengths of some metallic blocks in the propagating path of the wave inside the RA unit cell. The simulated results reveal a fairly linear reflected phase response along the frequency with high level of independent phase tuning in both orthogonal polarizations. In addition, this performance is maintained up to an angle of approximately 30 o in oblique incidence. Thanks to this performance provided by the RA unit cell, a circularly-polarized RA antenna is designed. The RA is rotated by 45 o regarding the linearlypolarized feed antenna to excite both polarizations in the unit cells that compose the RA. A prototype is fabricated and the measured results agree with the ones obtained in simulation. The presented RA antenna, which operates from 32 GHz to 50 GHz, produces a 3-dB gain bandwidth of 40.96% with a 2-dB AR bandwidth of 43.9%. Besides, the measured AR performs well in azimuth and elevation angles keeping the minimum values for AR around main beam direction. Finally, the measured realized gain has good agreement with the simulated one providing a radiation efficiency greater than 97% with a peak aperture efficiency of 55.4%.

Fig. 1 .

 1 Fig. 1. Design evolution of the proposed RA unit cell. The dimensions are: p = 4, wo = 2.54, L = 7.6, so = 1.46, w = 2.1, s = 1.92, r = 0.64, sr = 0.72, Lo = 1.52, r 1 = 0.64, r 2 = 0.4, w h1 = 1.6 and, w h2 = 0.24. All dimensions are in mm.

Fig. 3 .

 3 Fig. 3. Co-polarized and cross-polarized reflection in magnitude of the RA unit cell (3) in: (a) normal incidence and, (b) oblique incidence (ϕ = 90 o and θ = 20 o ).

Fig. 4 .Fig. 5 .

 45 Fig. 4. (a) 3-D view of the proposed reflectarray unit cells and some of the planes of interest. (b) E-field distribution in the planes of interest when a Vpol plane wave impinges the unit cell under normal incidence. The subfigures on the left are vector plots while the subfigures on the right are magnitude plots

Fig. 6 .

 6 Fig. 6. Reflection phase response of the proposed reflectarray unit cell under oblique incidence when h V varies. Oblique incidence in the E-plane (ϕ = 90 o ) where: (a) θ = 10 o , (b) θ = 20 o and, (c) θ = 30 o . Oblique incidence in the H-plane (ϕ = 0 o ) where: (d) θ = 10 o , (f) θ = 20 o and, (g) θ = 30 o . The excitation is a V-pol plane wave.

Fig. 6

 6 Fig. 6 presents the reflection phase behavior of the selected RA unit cell under oblique incidence. Figs. 6(a), 6(b) and

Fig. 7 .

 7 Fig. 7. Phase difference in the orthogonal polarization of the proposed reflectarray unit cell under oblique incidence when h V varies. Oblique incidence in the E-plane (ϕ = 90 o ) where: (a) θ = 10 o , (b) θ = 20 o and, (c) θ = 30 o . Oblique incidence in the H-plane (ϕ = 0 o ) where: (d) θ = 10 o , (f) θ = 20 o and, (g) θ = 30 o . The excitation is a V-pol plane wave.

Fig. 8 .

 8 Fig. 8. Simulated 3-D radiation pattern at 41 GHz of a reflectarray based on the proposed RA unit cell: directivity (a) for V-pol and, (b) for H-pol. Their reflected beam directions are (ϕ = 45 o , θ = 10 o ) and (ϕ = 105 o , θ = 20 o ), respectively. The phase maps required for (c) V-pol and, (d) for H-pol. (e) Simulated directivity along the frequency for both incident linear polarizations.

Fig. 9 .

 9 Fig. 9. (a) 3D view of the reflectarray system. (b) Front view of the proposed reflectarray design. The dimensions are: F = 123.2 mm, L RA = 84 mm, and θ i = θr = 20 o .

Fig. 10 .

 10 Fig. 10. Phase maps in reflectarray at 41 GHz: (a) for V-pol and, (b) for H-pol.

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Simulated results of the normalized radiation patterns of the reflectarray along the operating bandwidth: (a) for the E-plane and, (b) for the H-plane. The solid and dashed lines correspond to LHCP and RHCP, respectively.

Fig. 13 .

 13 Fig. 13. Error phase maps for V-pol at different frequencies: (a) 32 GHz, (b) 35 GHz, (c) 38 GHz, (d) 41 GHz, (e) 44 GHz, (f) 47 GHz and, (g) 50 GHz.

Fig. 14 .

 14 Fig. 14. Error phase maps for H-pol at different frequencies: (a) 32 GHz, (b) 35 GHz, (c) 38 GHz, (d) 41 GHz, (e) 44 GHz, (f) 47 GHz and, (g) 50 GHz.

  This article has been accepted for publication in IEEE Transactions on Antennas and Propagation. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TAP.2023.3240583

Fig. 15 .

 15 Fig. 15. (a) Prototype of the RA design. (b) Setup to measure the RA.

Fig. 19

 19 illustrates the measured AR for different frequencies in the considered bandwidth. A 3-D acquisition has been carried out to observe how the AR behaves for different azimuth and elevation angles up to θ = 20 o . From this figure,

Fig. 16 .Fig. 17 .Fig. 18 .Fig. 19 .

 16171819 Fig. 16. Simulated and measured results of the normalized radiation patterns of the reflectarray along the operating bandwidth. For the E-plane: (a) at 35 GHz, (b) at 41 GHz and, (c) at 47 GHz. For the H-plane: (d) at 35 GHz, (e) at 41 GHz and, (f) at 47 GHz.

Fig. 20 .

 20 Fig. 20. Simulated and measured realized gain and AR at the main beam direction. The solid and dashed lines correspond to simulated and measured results, respectively.

TABLE I SOURCE

 I OF LOSSES (IN DECIBELS) IN THE REFLECTARRAY ANTENNA

			SYSTEM
	RA unit cell	Feed antenna	Spillover Illumination	Phase error
	0.01 -0.07 0.04 -0.15 0.36 -1.42	0.22 -0.75	0.94 -2.73

  Table II presents the main features of comparison between the proposed RA design and those reported

	32 34 36 38 40 42 44 46 48 50
	Frequency (GHz)

TABLE II COMPARISON

 II BETWEEN THE PROPOSED RA AND REPORTED METAL-ONLY RAS

	Ref.	Center freq. (GHz)	3-dB Gain bandwidth	Peak aperture efficiency	Dual-pol control	3-dB AR bandwidth
	[8]	60	10%	35%	No	26.5%
	[10]	60	16.67%	60.3%	No	n. a.
	[12]	75	9.2%	30.2%	No	n. a.
	[15]	100	22.2%	50.1%	No	n. a.
	[16]	94	19.8%	44.8%	No	n. a.
	[17]	12.3	9.75% *	50%	No	n. a.
	[18]	38	10.5%	n. a.	No	n. a.
	[20]	9.3	24.2% *	50.6%	No	25%
	[21]	27	22.2%	n. a.	No	n. a.
	[34] †	27	18.2%	38%	Yes	18.2%
	This work	41	40.96%	55.4%	Yes	43.9%

* 1-dB gain bandwidth. † Independent control of circular polarizations.

TABLE III COMPARISON

 III BETWEEN THE PROPOSED RAS AND REPORTED FULLY-DIELECTRIC RA AT MILLIMETER-WAVES

	Ref.	Center freq. (GHz)	3-dB Gain bandwidth	Peak aperture efficiency	Radiation efficiency *	3-dB AR bandwidth
	[35]	33	30%	34%	88.5%	42.7%
	[37]	31	37.5%	32.5%	63% -89%	43.2%
	[38]	35	28.57%	16.4%	88.5%	n. a.
	[39]	30	17.24%	16.5%	20% -50%	19.3%
	This work	41	40.96%	55.4%	97% -99%	43.9%

This article has been accepted for publication in IEEE Transactions on Antennas and Propagation. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TAP.2023.3240583

ACKNOWLEDGMENT

The authors would like to thank Carmelo García-García for his help in the measurements and the spanish company Carlos Valero S.L. for its help and expertise in the metallization process.

This work was supported in part by the Spanish Government under Project PID2020-112545RB-C54, Project RTI2018-102002-A-I00, Project TED2021-129938B-I00 and Project TED2021-131699B-I00; in part by the "Junta de Andalucía" under Project A-TIC-608-UGR20, Project PYC20-RE-012-UGR, and Project P18.RT.4830; and in part by the Predoctoral Grant FPU18/01965.

Ángel Palomares-Caballero received the B.Sc. and M.Sc. degrees in telecommunication engineering from the University of Granada (UGR), Granada, Spain, in 2016 and 2018, respectively, where he is currently pursuing the Ph.D. degree through the National Pre-Doctoral Fellowship. Since 2017, he has been with the Signal Theory, Telematics and Communications Department, University of Granada. His current research interests include millimeter-wave antennas and phase shifters, gap-waveguide technology, and structures with higher symmetries.


Yee Hui

Robin Chang
email: robincyh@uitm.edu.my

Keat Junke Jiang

Hoe Yeoh

Zuntu Yusuf

Abdullahi

Yen Heng

Khong

Hua Moi

Tuh

Kiew Fui

Yit Lian Liew

Liew

Keat Hoe Yeoh
email: keathoe.yeoh@gmail.com

Yusuf Zuntu Abdullahi

Yen Khong

Hua Tuh

Yit Lian Liew

Achieving type-II SnSSe/as van der waals heterostructure with satisfactory oxygen tolerance for optoelectronic and photovoltaic applications

Keywords: 2D heterostructure, Electronic structure, Optical absorption, Type-II band edge, Power conversion efficiency

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Lately, the energy demand has climbed sharply because of the rapid digitalization evolution for fulfilling global population lifestyle and ongoing industrial revolution. Due to the worsening energy overdraft and catalyzed environmental deterioration, development of durable and efficient photovoltaics is set to become a key element in the shift to renewable energy. The obligatory call for clean and renewable resources has prompted the need to explore durable and highly efficient photovoltaic materials. A preferred photovoltaic is typically characterized by high carrier mobility, environmental stability and wide energy range optical absorption. The groundbreaking discovery of graphene in its atomically thin form in 2004 marked the beginning of the age of 2D materials. However, the zero-bandgap semiconductor's small bandgap limited its usefulness. This has led researchers to focus on 2D materials that already possess semiconducting characteristics. Numerous studies have been conducted on 2D materials such as h-BN [START_REF] Yu | Polymer composites based on hexagonal boron nitride and their application in thermally conductive composites[END_REF][START_REF] Ren | 2D Boron Nitride Heterostructures: Recent Advances and Future Challenges[END_REF], transition metal dichalcogenides (TMDC) [START_REF] Chang | Stretchable AgX (X = Se, Te) for Efficient Thermoelectrics and Photovoltaics[END_REF][START_REF] Chang | High mechanical strength and broad optical absorption in underexplored group IV nitride chalcogenides[END_REF][START_REF] Wang | Constructing a new 2D Janus black phosphorus/SMoSe heterostructure for spontaneous wide-spectral-responsive photocatalytic overall water splitting[END_REF], g-C3N4 [START_REF] Cao | Polymeric photocatalysts based on graphitic carbon nitride[END_REF] and MXene [START_REF] Bhat | Prospects challenges and stability of 2D MXenes for clean energy conversion and storage applications[END_REF], owing to their intriguing electrical properties and controllable optical characteristics.

Additionally, they can be synthesised into a wide range of nanomaterials with various potential gap and band position ranges to meet the potential requirements of a variety of photocatalytic reactions.

Van der Waals (vdW) heterostructures, which are constructed vertically utilising two or more distinct two-dimensional materials through weak vdW interactions, have recently gained popularity as a platform for the development of 2D materials. Very intriguingly, by carefully choosing the constituent materials, the band structure of the vdW heterostructures may form type-II band alignments in which photogenerated electron-hole pairs are successfully separated into two distinct layers, greatly slowing down the electron-hole recombination process and increasing the efficiency of solar cells. Hence, an attractive option for resolving the major energy and environmental problems that we are presently facing is the development of J o u r n a l P r e -p r o o f materials with dual functions that can simultaneously meet both of these needs. The synthesis of heterostructure consisting of monolayer Janus transition metal dichalcogenide is made possible by the effective fabrication of Janus MoSSe and WSSe monolayers. The primary prepping techniques used in the synthesis include chemical vapour deposition (CVD), exfoliation and layer assembly, solution processing, and hydrothermal [START_REF] Azadmanjiri | Graphene-Supported 2D transition metal dichalcogenide van der waals heterostructures[END_REF][START_REF] Lin | Low Energy Implantation into Transition-Metal Dichalcogenide Monolayers to Form Janus Structures[END_REF][START_REF] Lu | Janus monolayers of transition metal dichalcogenides[END_REF][START_REF] Zhang | Janus Monolayer Transition-Metal Dichalcogenides[END_REF]. Materials made of monolayer SnX2 (X = S, Se) have also been created [START_REF] Zhou | Ultrathin SnSe2 Flakes Grown by Chemical Vapor Deposition for High-Performance Photodetectors[END_REF][START_REF] Zhou | Large-Size Growth of Ultrathin SnS2 Nanosheets and High Performance for Phototransistors[END_REF]. The Janus SnSSe monolayer might then be created by selenizing a SnS2 monolayer or sulfurizing a SnSe2 monolayer through the CVD process, following a similar technique to that used to create MoSSe. Since most of the identified Janus monolayers are also mechanically flexible in nature, deposition of a single layer indirect band gap material with exceptional carrier mobility, such as arsenene (As), onto the Janus monolayers may lead to improved performance and commerciality than their separate components, which have relatively larger band gaps. It was reported by Chang et al and Zhao et al [START_REF] Chang | Constructing trifunctional MoTe2/As van der Waals heterostructures for versatile energy applications[END_REF][START_REF] Zhao | Van der Waals heterostructures of Janus XSeTe (X = Mo, W) and arsenene monolayers: A first principles study[END_REF] that a series of solar cells may be constructed using 2D TMDC/As heterojunctions. In particular, MoTe2/As [START_REF] Chang | Constructing trifunctional MoTe2/As van der Waals heterostructures for versatile energy applications[END_REF] can reach PCE of 30.0 %.

To the best of our knowledge, the electronic and optical properties and related device applications of heterostructures consisting of monolayers SnSSe and As have not been studied thus far. In this study, the vdW heterostructure SnSSe/As has been proposed and built. Effects of biaxial strain and interlayer coupling towards band gap modulation of the heterostructure was also studied. Current findings show that the type-II band aligned SnSSe/As displays several interesting electronic characteristics, namely improved light absorption compared to its separate monolayer components and photoelectric power conversion efficiency (PCE) reaching 32%, which can be further enhanced under small tensile strain. Its more negative binding energy than that of bilayer graphene (-27.08 meV atom

Computational methods

In current work, first-principles calculations based on density functional theory (DFT) were carried out by means of Vienna Ab initio Simulation Package (VASP) [START_REF] Kresse | Efficient Iterative Schemes for Ab initio Total-energy Calculations Using a Plane-wave Basis Set[END_REF][START_REF] Kresse | Efficiency of Ab-initio Total Energy Calculations for Metals and Semiconductors Using a Plane-wave Basis Set[END_REF], under the projector augmented wave (PAW) method with the exchange and correlation functional relations described by Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF]. During alternate structural relaxation between permissible ion position and volume (performed till within a single ionic step for both), the plane-wave cutoff, total energy convergence criterion, ionic force convergence and k-points grid were set to 450 eV, 10 -5 eV, 10 -3 eV Å -1 and 6 × 6 × 1, respectively. Allowing the volume to change would ensure the inclusion of positional selectivity. As (3d 10 4s 2 4p 3 ), Sn (4d 10 5s 2 5p 2 ), S (3s 2 3p 4 ) and Se (4s 2 4p 4 ) electron configurations were considered.

Adjacent layer spacing and electronic properties are significantly impacted by vdW forces.

Hence, the long-range effect of vdW force was corrected using DFT-D3 approach of Grimme dispersion [START_REF] Grimme | A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[END_REF]. 30 Å vacuum was applied along the vertical direction to prevent interaction J o u r n a l P r e -p r o o f between recurring images. For 2D materials, there are only two periodic directions, along x and y. Since the VASP package solves the Kohn-Sham equation within conventional 3D periodic boundary conditions, it is obligatory to add sufficient artificial vacuum space along the z-direction. For thermal stability check, ab initio molecular dynamics (AIMD) simulations were performed at 300 K up to 15 ps total simulation time using the Nose-Hoover thermostat [START_REF] Nosé | A Unified Formulation of The Constant Temperature Molecular Dynamics Methods[END_REF]. To circumvent the underestimation of band gap by the use of PBE functional, the band gap magnitude of SnSSe/As and its constituent monolayers was recalculated using HSE06 [START_REF] Heyd | Efficient hybrid density functional calculations in solids: Assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional[END_REF] functional. The increment was added as scissor shift for optical calculations.

Results and discussion

Geometric stability and electronic properties

Before assembling the SnSSe/As heterostructure, atomic structures of the monolayers were first studied. The optimized lattice constant for SnSSe and As are 3.80 and 3.61 Å, respectively,

showing close values with earlier reports [START_REF] Zhang | Atomically thin arsenene and antimonene: semimetal-semiconductor and indirect-direct band-gap transitions[END_REF][START_REF] Chang | Integrated SnSSe bulk and monolayer as industrial waste heat thermoelectric materials[END_REF]. Their primitive cell is indicated by the hexagonal lattice class. Referring to Figure 1, the SnSSe/As heterostructure was then constructed by vertically stacking the structurally optimized monolayer As on monolayer SnSSe, forming a relaxed vdW heterostructure with lattice constant and interlayer distance of 3.69 and 3.09 Å, respectively. The lattice mismatch (δ), calculated using 𝛿 =

2(𝑎 1 -𝑎 2 ) (𝑎 1 + 𝑎 2 ) ⁄
, where 𝑎 1 and 𝑎 2 are the lattice constants of monolayers, is 5.1 %. This measurement is less than the critical limit of 8% while recent findings show that MoS2/graphite and MoS2/h-BN are experimentally achievable [START_REF] Liao | UItra-low friction and edge-pinning effect in large-lattice-mismatch van der Waals heterostructures[END_REF] despite having lattice mismatch exceeding 24%. To ensure the stability of the designed stacking, the interfacial binding energy (Eb) was evaluated to be -26.95 meV Å -2 based on:

𝐸 b = 𝐸 SnSSe/As -(𝐸 𝐒𝐧𝐒𝐒𝐞 + 𝐸 As ) A (1)
J o u r n a l P r e -p r o o f optical branches are contributed by the lightest S atom. As seen, there is no apparent feature of negative frequencies in the distribution, thus confirming the dynamical stability in the heterostructure.

(a) (b) (c) (d) (e) (f)

Optoelectronic properties

Quantitative assessment on the competence to transfer carriers in specific direction is crucial for evaluating the optoelectronics performance of heterostructures. Due to the close proximity between acoustic phonon wavelength and electron coherence length, the use of deformation theory [START_REF] Bardeen | Deformation Potentials and Mobilities in Non-Polar Crystals[END_REF] for calculating intrinsic carrier mobility (μ) of inorganic materials is reasonable, as shown below.

𝜇(2D) = 𝑒𝐶 2D ℏ 3 𝑘 𝐵 𝑇𝑚 * 𝑚𝐸 𝐷 2 (2)
in which e, C2D, ℏ, kB, T, m*, m and ED signify the electron charge magnitude, direction bound elastic constant, reduced Planck constant, Boltzmann constant, surrounding temperature, average effective mass, effective mass in the direction of x or y and deformation potential constant (see Supplementary file S1), correspondingly.

Table 1 Calculated direction dependent effective mass m (mo), ED (eV), C2D (N m -1 ) and μ (cm 2 V -1 s -1 ) for holes and electrons in the direction of x and y at 300 K. Relaxation time (τ) was estimated via 𝜏 = 𝜇𝑚 𝑒 ⁄ . Exciton binding energy 𝐸 𝑏 𝑒𝑥 (eV) was calculated via 𝐸 𝑏 𝑒𝑥 = 13.56(μ ε 0 2 ⁄ ) where μ = (𝑚 e -1 + 𝑚 h -1 ) -1 and ε 0 denotes the reduced effective mass and static dielectric constant, respectively. Table 1 shows the calculated μ of SnSSe/As heterostructure at 300 K. The obtained μ for holes in the heterostructure is quite high, which is attributed to the insensitivity of the VBM J o u r n a l P r e -p r o o f for strain, despite having effective mass larger than electrons. These measurements nevertheless are greater than or comparable to that of monolayer MoS2 (200.52 cm 2 V -1 s -1 )

[33], WS2 (542.29 cm 2 V -1 s -1 ) [START_REF] Kumar | C2N/WS2 van der Waals type-II heterostructure as a promising water splitting photocatalyst[END_REF], BlueP (590 cm 2 V -1 s -1 ) [START_REF] Xiao | Electronic Structures and Carrier Mobilities of Blue Phosphorus Nanoribbons and Nanotubes: A First-Principles Study[END_REF] and GaSe (866 cm 2 V -1 s -1 ) [START_REF] Cui | Two-dimensional fewlayer group-III metal monochalcogenides as effective photocatalysts for overall water splitting in the visible range[END_REF]. In addition to the appropriate band gap, applicable band edge alignments and effective segregation of photogenerated carriers, the potential of materials as solar cell and water splitting photocatalyst is also depending on their optical absorption spectra α(ω), assessable via:

α(ω) = √2ω [√ε 1 2 (ω) + ε 2 2 (ω) -ε 1 (ω)] 1 2
(3)

where ε 1 (ω) and ε 2 (ω) represent the real and imaginary components of dielectric function, while ω is the light frequency. The latter is computable via sum over a sufficiently large number of empty states. ε 1 (ω) can then be realized from ε 2 (ω) through Kramer-Kronig formulation. Given that visible light occupies 45% of the whole solar spectrum range, the capacity to absorb a significant portion of visible light is crucial. Interestingly, under biaxial strain, expressed as J o u r n a l P r e -p r o o f

[(𝑙 -𝑙 0 ) 𝑙 0 ⁄ ] × 100% where l and l 0 are the lattice constants before and after strained, it can be seen in Figure 4(b) that the curve profile is smooth and total energy of unstrained form is the lowest, inferring absence of phase transition and hence good stability. The positive and negative label exemplifies the tensile and compressive strains, correspondingly. Band gap variation under different biaxial strains is highlighted in Figure 4(a). Overall, tensile strain causes the studied structure to undergo a consistent red shift whereas blue shift is noted for compressive strain till -4%, before switching to red shift under stronger compression. The former shifts the CBM downward greatly and the VBM downward marginally, leading to narrower bandgap, reducing from HSE06 corrected bad gap of 1.30 to 1.15 eV and 1.03 eV at 2% and 4% tensile strength, respectively, becoming much closer to the Shockley-Queisser (SQ) limit. In comparison to separated SnSSe and As layers, where the average α(ω) is below 0.5 × 10 5 cm -1 [START_REF] Sun | Exceptional Optical Absorption of Buckled Arsenene Covering a Broad Spectral Range by Molecular Doping[END_REF][START_REF] Alam | Optoelectronics properties of Janus SnSSe monolayer for solar cells applications[END_REF], the SnSSe/As heterostructure presents a considerable red shift of light absorption edge, a steeper increase and substantially enhanced absorption intensity reaching 10 5 cm -1 order in the visible and near infrared domains, as shown in Figure 5(a). Furthermore, the measured α(ω) of 10 4 -10 5 cm -1 is comparable to several conventional photovoltaics such as c-Si, Ge, GaAs, InP [START_REF] Massiot | Progress and prospects for ultrathin solar cells[END_REF] and Rb-based compounds [START_REF] Mahmood | Tunning of band gap of double perovskites halides Rb2CuSbX6 (X = Cl, Br, I) for solar cells and energy harvesting[END_REF][START_REF] Nawaz | Theoretical investigations of optoelectronic and transport properties of Rb2YInX6 (X = Cl, Br, I) double perovskite materials for solar cell applications[END_REF][START_REF] Haq | Ab-initio study of opto-electronic and thermoelectric properties of direct bandgap double perovskites Rb2XGaBr6 (X = Na, K)[END_REF], strengthening its credibility as potential high performance photovoltaic. Formation of SnSSe/As heterostructure creates more energy bands and raises the hybridization-based joint density of states near the VBM, which significantly increases the interband transition probability of electrons from As p states in the valence band to Sn s and Se p states of the conduction band.

To delve into the ability of SnSSe/As in harvesting solar energy, the spectroscopic limited maximum efficiency (SLME) has been evaluated. This model [START_REF] Yu | Identification of Potential Photovoltaic Absorbers Based on First-Principles Spectroscopic Screening of Materials[END_REF][START_REF] Chang | Improved Thermoelectric-Photovoltaic Performance of Ag2Se Originating from a Halogenation-Induced Wider Band Gap and Low Crystal Symmetry[END_REF] provides a quantifiable selection metric to screen photovoltaic efficiencies of materials through the integration of their band gap energies, absorption spectra and non-radiative recombination losses relating to typical in a lower SLME due to larger band gap shift from the 1.1 eV SQ limit but attaining higher SLME ~ 15% at 0.1 μm thickness. On a side note, materials with high α(ω) may also be applied as absorber shield. For instance, a YAG laser of wavelength 1064 nm is employed in various significant applications, including the cutting of materials [START_REF] Sharma | Experimental analysis of Nd-YAG laser cutting of sheet materials -A review[END_REF] and the delivery of medications [START_REF] Sklar | Laser assisted drug delivery: A review of an evolving technology[END_REF]. However, a previous study found that exposure to picosecond Nd:YAG laser pulses could harm the eyes [START_REF] Ham | Ocular Hazard from Picosecond Pulses of Nd: YAG Laser Radiation[END_REF]. In order for laser technology to be widely used, it is crucial that people are protected from harmful laser irradiation. The quest for materials that can shield people from harmful incident laser beams are therefore crucial. As pointed out in Figure 5(a), although pure arsenene can be utilized as a shielding material, SnSSe heterostructure owing to the higher α(ω) over broader spectral range provides better defense against laser beams in the ultraviolet, visible and near infrared ranges, making it a promising shield against any source of undesired laser radiation as a result. This observation is also supported by Figure 5(d), in which the SLME for SnSSe/As is almost twice that of As at saturation level.

Impact of O adatoms on photovoltaic performance

In actual application, when exposed to surrounding air, electrical performance and durability of photovoltaic will be impacted by the contamination of active layer by O atoms.

Following studies were performed on the basis that the adsorption of O atoms with the studied heterostructure is ascribed to surface adsorption, thus only interact with the top surface layer.

- 1 )Figure 1

 11 Figure 1 The (a) side and (b) top viewpoints of SnSSe/As vdW heterostructure. Grey, yellow, green and pink represents the Sn, S, Se and As atoms, respectively.

Figure 2

 2 Figure 2 The (a) calculated band structure, (b) projected density of states (PDOS) at PBE level, (c) electrostatic potential in z-direction, (d) plane-averaged charge density difference, (e) band edge alignment for SnSSe/As heterostructure and (f) its total energy profile as a function of the ab initio molecular dynamic (AIMD) simulation step at 300 K.

Figure 3

 3 Figure 3 Calculated phonon dispersion spectra along high-symmetry points and phonon DOS for SnSSe/As heterostructure.

Figure 3

 3 Figure3shows the calculated full phonon dispersion curves along high symmetry points

Figure 4

 4 Figure 4 (a) Band gap of SnSSe/As heterostructure at PBE level and (b) strain energy under various biaxial strains.

J o u rFigure 5

 5 Figure 5 Absorption coefficients α(ω) for SnSSe/As (a) in the absence of biaxial strain, (b) under 2% tensile strain and (c) under 4% tensile strain, calculated by DFT+BSE with scissor approach. (d, e and f) are their respective SLME (see Supporting Information S2 for calculation details), as the function of film thickness ranging from 0.1 to 100 μm.

J o u rFigure 6 Figure 7

 67 Figure 6 Projected band structure plot for (a) OSnSSe/As and (b) SnSSe/AsO heterostructures, at PBE level. Grey lines are contributions from O adatoms (indicated by red circle) based on 2 × 2 supercell. (c) Absorption coefficients α(ω) and (d) thickness dependence of SLME for O atom adsorbed on SnSSe surface of the heterostructure, labelled as OSnSSe/As.

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  n a l P r e -p r o o f

Declaration of competing interest

The authors declare that they have no known competing financial or personal interests.

Declaration of Interest Statement

The authors declare that they have no known competing financial or personal interests.

J o u r n a l P r e -p r o o f