Terahertz vortex beams are a type of optical beam with a helical optical phase structure and frequencies in the range of 0.1-10 THz. Meanwhile, they have potential applications in emerging fields such as high-resolution terahertz imaging, electron acceleration, and manipulation of quantum states. The terahertz coding phase gradient metasurface serves as an important device for modulating terahertz waves, featuring simple structure, small size, low cost, low loss, and high efficiency. By introducing phase gradients in the super-unit-cell, the coding elements are formed to enable more flexible control of electromagnetic waves by altering the coding elements and coding sequences. Currently, the generation of multibeam multi-modal terahertz vortex waves is generally achieved by adopting the coding metasurface. However, this approach requires a large number of coding metasurface units, resulting in high computational complexity and a complex design process with large dimensions. To generate multibeam multi-modal terahertz vortex waves more flexibly and simply, we propose a transmissive coding phase gradient metasurface. By utilizing Fourier convolution operations and the phase superposition principle, the generation of multibeam multi-modal terahertz vortex waves is realized. This technology holds potential application significance in fields such as wireless communication and high-resolution imaging.

First, we design the transmission metasurface units based on the Pancharatnam-Berry (PB) geometric phase principle. Next, the designed metasurface units are employed to form the 6×6 super-unit-cell, in which phase gradients are introduced to create coding elements. Then, three coding phase gradient metasurfaces are designed to produce double beams and generate single beams of l=-1 and l=-2 vortex waves. Additionally, Fourier convolution of the double beams coding sequences is performed with the vortex wave coding sequences of different modalities, with the coding phase gradient metasurface for generating single-mode double beams vortex waves acquired. The phase distribution of the coding phase gradient metasurface which generates double vortex beams with l=-2 is matrix inversion and then combined with the phase distribution of the coding phase gradient metasurface which generates double vortex beams with l=-1 using the phase superposition principle, thus preventing the overlapping of spiral waves generating different modes. By arranging the coding elements, this process leads to the coding phase gradient metasurface capable of generating multibeam multi-modal terahertz vortex beams.

When 2.0 THz x- and y-polarized waves are vertically incident on the metasurface units (Fig. 1), the amplitudes of the co-polarized transmission for both polarizations are approximately 0.9, and their co-polarized transmission phase differences are close to 180°, which meets the requirements of the PB geometric phase principle (Fig. 2). Then, phase gradients are introduced in the super-unit-cell and 2-bit coding elements are designed (Fig. 4). Based on the Fourier convolution operation (Fig. 9) and phase superposition principle, the coding phase gradient metasurface is designed (Fig. 12). The far-field scattering of the coding phase gradient metasurface is simulated by CST Microwave Studio. The results show that under the vertical incidence of 2.0 THz linear polarization (LP) waves, it is possible to simultaneously generate two vortex beams of l=-1, two vortex beams of l=-2, two vortex beams of l=+1, and two vortex beams of l=+2 [Fig. 13(a)]. Additionally, these eight vortex waves do not overlap and do not interfere with each other. The elevation angle θ and azimuth angle φ of each beam can also be obtained [Figs. 13(b) and (c)]. In the x-direction, there are two vortex beams of l=-1 with an azimuth angle of 270° and elevation angles of 58° and 78° respectively. In the +y direction, there are two vortex beams of l=+2 with azimuth angles of 25.5° and 333.5° and an elevation angle of 65°. In the +x direction, there are two vortex beams of l=+1 with an azimuth angle of 90° and elevation angles of 55° and 80° respectively. In the -y direction, there are two vortex beams of l=-2 with azimuth angles of 153° and 207° and an elevation angle of 46°.

We propose a coding phase gradient metasurface working at a frequency of 2.0 THz based on the PB geometric phase principle, Fourier convolution operation, and phase superposition principle. Under the vertical incident of the LP wave, a newly coding phase gradient metasurface can generate eight vortex waves in total, with mode orders of l=±1 and l=±2 respectively. Compared to the reported metasurfaces for generating multibeam multi-modal terahertz vortex waves, this metasurface features small dimensions, relatively simple principles, few unit elements, easy material acquisition, and the ability to design different modes of vortex waves. This enables more flexible and diverse control of terahertz beam steering. Finally, potential applications are presented in wireless communication, radar, high-resolution imaging, energy transfer, and stealth technology.