**1. Introduction**

The orbital angular momentum of electromagnetic waves has been explored in recent years for its potential applications in wireless communications [1–3] and imaging [4,5]. EM wave carrying orbital angular momentum has a helical wavefront and an amplitude singularity in the propagating direction. The helical wavefront can be expressed by the term *exp*(*il*Φ), where Φ is the azimuthal angle and *l* is the topological charge. The topological charge corresponds to the OAM mode and, theoretically, the OAM mode is vast.

The OAM in EM waves is typically generated using techniques like spiral phase plates [6,7], spiral reflectors [8], antennas [9–11], dieletric resonators [12], computer-induced holograms [13], transformation electromegnetics [14] and metasurfaces [15,16]. The common idea in these techniques is to introduce the desired phase distribution on the radiation aperture. The spiral phase plate method gives the incident wave different phase retardation according to the term *exp*(*il*Φ) by modulating the length of the wave path in corresponding areas. The antenna array approach usually use a circular antenna array to excite array elements with the same amplitude but different phases.

Compared to these methods, metasurfaces for generation of beams carrying OAM have advantages including low profile and simple EM wave control, i.e., the magnitude/phase/polarization of the EM waves can be manipulated simply by changing the shape, geometry, size, orientation and arrangemen<sup>t</sup> of the structures [17]. Reflective metasurfaces were used to generate single and double mode vortex beams in mircrowave [18–21] and terahertz regimes [22]. An active transparent metasurface was proposed for generating EM beams carrying OAM in the microwave frequency range [23]. However, these designs only focus on the OAM controlling of microwaves leaving the

polarization state of the transmitted wave the same as that of the incidence. Simultaneously control the polarization and OAM of EM waves can enhance the performances of OAM beams in applications like radar imaging. Recently, metasurfaces using Geometric-Phase were applied for simultaneous OAM and spin angular momentum control [24–26]. These techniques impart a new degree of freedom to EM wave control and pave a way for future applications.

In this paper, multi-layered metasurfaces generating OAM beams with efficient linear polarization conversion were proposed. The patches on the outer sides of the designed metasurface receive and re-radiate the incident wave, respectively. The cross-polarized transmission is higher than −1 dB around 5.15 GHz with an extremely low co-polarized transmission below −35 dB. The transmission phase can be fully controlled by the length of the stripline in the middle layer. By arranging the metasurface unit cells according to desired phase distributions, the proposed metasurfaces can generate EM beams carrying different modes of OAM. This design method was demonstrated by both simulation and measurement.

This paper is organized as follows: Section 2 presents the design of the unit cells and the metasurfaces. In this section, detailed geometries of the unit cell are introduced, the characteristics of the unit cell are shown and the metasurface designs are presented. Section 3 presents the simulated and measured results of the metasurfaces, which verify the designs and show OAM generation with polarization conversion. In Section 4, the conclusions are drawn and the originality of this work is presented.

#### **2. Design of The Metasurface**

A flowchart illustrating the main goal and the adopted methodology of this study is presented in Figure 1. The unit cell pattern of the proposed multi-layered laminated metasurface is depicted in Figure 2, where the gray parts represent the substrate Rogers 4350 B with *r* = 3.48 and tan*δ* = 0.0037. The yellow parts represent the metal structures with a thickness of 0.035 mm. The top and bottom layers of the metasurface are circular patches which can couple or decouple the incident wave with a cross-polarization conversion. The middle layer of the metasurface is a stripline structure and is separated from the top and bottom layers by the first and second ground layers, respectively. Two vias connect the two ends of the stripline to the top and bottom layers, respectively. The geometric dimensions are *p* = 17.92 mm, *R* = 16.64 mm, *r* = 0.8 mm, *w* = 1.2 mm, *fx* = *fy* = 3 mm, *h*1 = 1.524 mm and *h*2 = 0.254 mm. The length of the stripline *S* varies from 1.66 mm to 8.49 mm to achieve a 360◦ transmission phase control.

**Figure 1.** Flowchart illustrating the main goal and the adopted methodology of this paper.

**Figure 2.** Geometry of the unit cell: (**a**) Top layer. (**b**) First ground layer. (**c**) Middle layer. (**d**) Second ground layer. (**e**) Bottom layer. (**f**) Side view.

The unit cell design takes its inspiration from the patch antenna. The top/bottom layer couples the y-polarized/x-polarized incident wave into the guided mode in the stripline structure and then, the bottom/top layer decouples the guided wave into the x-polarized/y-polarized free space propagation. It is by selecting the positions of the vias in orthogonal direction (e.g., in *x* and *y* directions), that the polarization of the transmitted wave is converted.

The simulated distributions of the electric field component perpendicular to the unit cell (i.e., E*z*) on top and bottom layers are shown in Figure 3a,b, respectively. The incidences excite a y-polarized dipolar mode on the top layer, where the guided mode travels through the stripline structure to the bottom layer and excite a x-polarized dipolar mode, therefore converting the polarization of the transmitted waves. In addition, the guided mode experiences different phase delay when the length of the stripline varies. Also, the energy loss in the stripline structure is small and consistent regardless of its lengths. Therefore, the transmission phase can be controlled by the length of the stripline, which allows different phase distributions for different OAM beam-generating, while the transmission loss is small and stable. Notably, due to only the top and bottom layers resonate, this design has potentials to obtain low insert loss.

**Figure 3.** The simulated distributions of the electric field component perpendicular to the unit cell (i.e., E*z*): (**a**) Top layer. (**b**) Bottom layer.

The unit cell models were simulated by the commercial software CST Microwave Studio (Version 2016, Computer Simulation Technology GmbH, Darmstadt, Germany) using periodic boundary in *x* and *y* directions. The simulated transmission amplitudes and phases are shown in Figure 4a,b, respectively. The transmission phase data at 4.8–5.5 GHz are given because, at other frequency ranges, the curves are confused and not of main concern in this paper. For a *y*-polarized incidence propagating along −*z* direction, the transmitted wave is *x*-polarized and the cross-polarized transmission amplitudes with different *S* are higher than −0.5 dB at 5.14 GHz, and from 4.9 GHz to 5.4 GHz, the transmittances are higher than −3 dB which indicates a 50% power efficiency, as shown in Figure 4a. The co-polarized transmittances are below −35 dB from 4.9 GHz to 5.4 GHz, indicating an extremely high polarization conversion efficiency, compared with [27,28]. At 5.14 GHz, the co-polarized transmittance is below −38.2 dB. Eight stripline lengths were selected with a transmission phase step of 45◦ to cover a 360◦ phase difference, as shown in Figure 4b. The selected stripline lengths are 1.656 mm, 2.62 mm, 3.62 mm, 4.58 mm, 5.57 mm, 6.54 mm, 7.53 mm and 8.49 mm.

**Figure 4.** The simulated transmittance of the unit cell with different stripline lengths *S* (as in Figure 2c): (**a**) Amplitude. (**b**) Phase.

The helical wavefront of vortex beams can be expressed by the term *exp*(*il*Φ), where Φ is the azimuthal angle and *l* is the topological charge. Therefore, EM beams carrying OAM with an order of *l* experiences an azimuthal phase change of | *l* | × 360◦. The sign of the OAM order *l* defines the helicity of the vortex beam phase distribution. To generate vortex beam-carrying OAM of orders ±1 and ±2, two transmission phase distributions at 5.14 GHz with phase steps of 45◦ and 90◦, respectively were designed and shown in Figure 5a,b, which depict the desired transmission phase with regard to different positions on metasurfaces. For wave propagating along −*z* and *z* directions, these two designs have opposite helicities and generate EM beams carrying OAM with orders of 1/2 and −1/−2, respectively.

**Figure 5.** The front view of the transmission phase distribution schemes at 5.14 GHz for generating beams carrying OAM of different orders: (**a**) *l* = +1. (**b**) *l* = +2.

The two finite full structure models containing 16 × 16 unit cells are shown in Figure 6. The discretization of the metsurface is done according to the transmission phase distributions in Figure 5. The target frequency of the metasurfaces is at 5.14 GHz. It is worth pointing out that the potential applications for radar imaging can be in X/C/S band and the metasurface design can be easily tuned to other frequencies as well. The models were built up and simulated by CST Microwave studio with a Gaussian beam as excitation with a minimum beam radius of 100 mm on the metasurface. The average simulation time in a server with 256 GB memory and Intel Xeon E5 CPU is about 6 h. About 30 GB memory is used. Gaussian beam, compared with plane wave, reduces the slight amount of diffractions of the EM waves at the margins, while the phase profile of the transmitted beams are the same. Also, the margins of the metasurfaces have metal sheet in ground layers to further avoid diffractions. The used unit cells for realizing the desired transmission phase distribution designs in Figure 5a,b with phase steps of 45◦ and 90◦ respectively are selected from Figure 4b. Eight kinds of unit cell with stripline lengths of 1.656 mm, 2.62 mm, 3.62 mm, 4.58 mm, 5.57 mm, 6.54 mm, 7.53 mm and 8.49 mm are selected for Figure 5a while four kinds of unit cell with stripline lengths of 1.656 mm, 3.62 mm, 5.57 mm and 7.53 mm are selected for Figure 5b.

**Figure 6.** The simulation model of the proposed metasurface: (**a**) Front view. (**b**) Back view.
