1. Introduction

In 1914, Max Abraham firstly introduced orbital angular momentum(OAM) in electromagnetic waves [1]. The experimental study by Allen showed that the Laguerre-Gaussian (LG) mode carries OAM, and the OAM beam has a helical phase wave front of exp(imφ), where m is the topological charge and φ is the azimuthal angle [2]. Since then, the OAM beams have been successfully employed for widespread applications including optical imaging [3], optical tweezers [4] and optical communications [5]. Owning to their fascinating properties and wide application areas, there have been a lot attempts to generate OAM beams. Conventional optical components are based on refraction, reflection or diffraction of wave beams, in which control on the wavefront is achieved via controlling the propagation of light in bulk materials. Recently, spatial phase modulation or polarization manipulations have been employed for the control of phase and thus the generation of OAM beams. In this way phase and polarization changes are accumulated through propagation in refractive optical components such as lenses and wave plates. Generally, the major approach to achieving OAM beams are based on macroscopic bulky optical components such as spiral phase plates(SPPs) [6–8], q-plates [9], mode converters formed from cylindrical lenses [10], spatial light modulators (SLMs) [11], and specialty optical fibers [12].

Recent advances in optical metamaterials/metasurfaces made the new approaches for the manipulation in intensity, polarization and phase distribution of beams in the optical [13–21], terahertz [22,23], and microwave band [24–26]. The phase can be manipulated throughout the entire 2π range by properly arranging the structural parameters of metasurface units. Therefore, an incident wave can be converted to an OAM beam with metasurface of full range phase modulation. Various metasurfaces have been designed for manipulating beams. However, most of the metasurfaces were designed by rotating the direction of the metallic structures and controlling the spiral array arrangement to achieve phase shift [13–26], which is difficult to be fabricated in the sub-wavelength range because it is harder to control the micro electric platform precisely in the role of the biaxial motions. In addition, most work is focused on the transmission mode, and only a few work is focused on the reflection mode [26].

In this paper, we demonstrate a simple design to generate OAM beams by using metasurface with gradient reflection phase which is divided into eight regions equally instead of the spiral arrangement and each part is packed with the identical metasurface units in microwave band. Also, the reflection phase variation is determined just by the geometric parameters of the metasurfaces, which is dependent on the patch size of the metasurfaces instead of rotation of the metasurface structures. By this way, the reflection phase with full range of 2π can be realized for freely arranging metasurface with proper phase distribution to transform plane wave to OAM beams. Such structures are compact, versatile and can be readily integrated with on a printed circuit board. This work will greatly promote the study and application of OAM beams.

2. Metasurface designs

The essence of metasurface is to realize spatial variation in the optical response using separation elements arrays and varying geometric parameters, such as elements shape, size, orientation [26–28], and then optical wave fronts can be designed at will. In order to design the proposed metasurface with gradient reflective phase, we empolyed a metasurface unit, which is comprised of top metallic patch layer, metallic ground layer, and dielectric spacer in between. The top metallic patch layer and metallic ground layer are connected with metallic vias the two metallic layers. The designed structure unit is schematically depicted in Fig. 1(a) and (b), the metallic ground layer and the metallic patch layer is located varying optical axis orientations in the xy plane, and each layer has a thickness of t = 0.035mm, the dielectric layer has a thickness of h = 1.60 mm and a dielectric constant of 2.65. The dimensions of the structure are as follows: p = 10mm, d = 0.5mm, r is the size of metallic patch layer with a variation value design parameters respectively. The model of the metasurface unit cell is investigated by CST Microwave Studio. The boundary condition is set with “unit cell”, so the cells are arrayed along x and y directions. In Fig. 2, it depicted the reflection phase shifts and scattering amplitudes for eight metasurface units with different radius of metallic patch layer. The eight units cell has a linear reflection phase change range of 360° which is determined by its radius. The simulation model and result approve a good reflection phase response of the element unit. The concrete designed parameters are shown in TABLE 1 as well.

 

Fig. 1 Schematic diagram of designed metasurface unit. (a) 3D view and (b) side view. The size of the unit cell is 10mm x10mm.

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Fig. 2 The reflection phase shifts and the amplitudes, it showed that each patch layer introduces a specific phase shift determined by its radius.

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Table 1. Design parameters: the size of metallic patch layer.

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Based on the above analysis, as shown in Fig. 3(a), we designed and fabricated metasurface with gradient reflective phase which is divided into eight regions equally, which are composed of 400 metasurface elements, each region was occupied by the same kind of metasurface units as well as Table 1, and each unit has a square lattice with a period of 10mm. It is important to note that in order to obtain −180 degree reflection phase, we use a square patch layer to cover the full dielectric layer instead of the eighth types of Table 1. Eight regions are arranged in sequence around the center of the metasurface according to the phase increment, which has 2π phase shift by π/4 steps around the center. Therefore, when the plane waves normally incident to the reflective metasurface, as shown in Fig. 3(b), the reflected wave will become an OAM beam with the topological charge l = 1.

 

Fig. 3 (a) Schematic diagram of designed metasurface array structure which is composed of eight regions, each region occupied by the same type of metasurface units. (b) Configuration of OAM beams generating by metasurface with gradient reflective phase.

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As shown in Fig. 3(a), considering the coordinate system of metasurface array with gradient reflective phase, the reradiated electric field from the metasurface reflective array in an arbitrary direction was expressed as Eq. (1) [26,30]:

where is the feed source pattern function, is the reflective metasurface element pattern function, is the position vector of source, is the position vector of the mnth element, is the desired main beam pointing direction of the reflective metasurface, is the propagation constant in vacuum, and ${\phi }_{mn}^{}$is the phase shift of the mnth reflective metasurface element respectively. From Eq. (1), we see that the OAM beams can be generated by the linear phase shift based on the reflective metasurface phase array design. As a result, we proposed that metasurface with gradient reflective phase can generate OAM beams after the reflection of the incident wave, which functions like a reflective array and transforms an incoming phase front into a desired outputting phase front.

3. Simulations and measurements

For the convenience of the simulation and the experiment verification, we demonstrated generation of OAM beams in 10GHz. Considering that the metal layer and metallic patch layer are perfect electric conductor(PEC), we have performed full-wave simulations using CST Microwave Studio Software to solve reflection spectra and band structures of metasurface [31]. In the simulation, the plane waves vertically incident on the top metallic patch layer, propagating along the –z direction, which are circularly polarized along the orientation of the metallic patch layer. As schematically shown in Fig. 4(a) and 4(b), we simulated the intensity and phase properties at a transverse xy-plane of z = 40 mm based on the reflective metasurface with gradient phase. The figures show that the center intensity is a dark core and a total 2π phase change around the center. From Fig. 4(a), the intensity distribution is not completely symmetric with respect to the center of the vortex, we divided the metasurface into eight parts for the simplification in design, thus the reflective phase of the setup is not changing continuously which made the incomplete symmetric distribution of intensity.

 

Fig. 4 The map with OAM topological charge l = 1 at a near-field transverse plane of z = 40mm: (a) and (b) The intensity and the near field spiral phase properties of the proposed structure of CST simulation. (c) and (d) Intensity distribution and phase pattern of the reflection spectra measured result.

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For experiment verification, we manufactured metasurface with gradient reflective phase sample of 200mm × 200mm square area on a printed circuit board with the same structural parameters as the simulation model. Such structures are compact, versatile and can be readily integrated with a printed circuit board. The measurements were performed in an anechoic chamber. The measurement setup is based on an Agilent Network Analyzer 8722ES and the scanning station. The plane waves (10GHz) were vertically incidented on the top metallic patch layer of the sample from standard horn antenna, propagating along the –z direction, and the sample and the probe was placed parallel to the xy plane. A program is developed to control the probe scanning a square area of 200mm × 200mm grids by 1mm steps at a transverse xy plane of z = 40 mm using scanning station. The reflection parameters of each sample point in this environment can be measured and recorded by using the vector network analyzer, and we can use the reference signal to calculate the real reflection electric field intensity of the sample. As a result, both electric field intensity and phase of the electromagnetic waves with OAM can be measured precisely, and then the intensity distribution and phase patterns are plotted using a Matlab code and origin. Both intensity distribution and phase pattern of the reflection spectra through the sample on near-field xy plane of z = 40 mm are shown in Fig. 4(c) and 4(d). The experimental intensity distribution shows that has a doughnut with central singularity, and phase pattern of the reflection spectra shows a total 2π phase change around the center of the metasurface as expected. The spiral phase shows clearly the OAM beams generated by this metasurface with gradient reflective phase. The measured result of the reflection spectra is in agreement with the simulated performed one. And the conversion efficiency is about 80%, which is calculated by taking the ratio of the energy of the OAM beams to the total energy of the incident wave. To obtain mode purity, we used the phase gradient method [32], which explicitly utilizes the helical phase structure and estimates the OAM mode by measuring the phase gradient, the measured result obtained a good pure mode of l = 1. Our simulation and experiments show that the reflective metasurface can be used to effectively generate OAM beams in the microwave domain. If we precisely design structures and sizes on a metasurface to achieve more 2π phase modulation, we can obtain higher order OAM mode.

4. Conclusion

We have demonstrated the generation of OAM beam with topological charge of l = 1 by using of a reflective metasurface with gradient phase distribution. The proposed metasurface is of high efficiency due to the intrinsic high-reflection of high-impedance surface, and the high impedance structure is a very simple one with very few changes of the geometric parameters in order to control reflection phase. The measured field mapping confirmed the reflected beam from our metasurface design is OAM beam with central singularity. This work will greatly promote the study and application of OAM in microwave band. We can put the OAM experimental verification result into the application of microwave communications, which will be a signicant leap forward for communications. A pivotal step toward the implementation of novel microwave concepts, applications and protocols.