Fig. 1. Schematics of the PA-PSO algorithm. (a) and (b) Working principle of the metalens antenna. (c) and (d) Comparison between the traditional PSO and PA-PSO algorithm. The red and blue stars represent optimal and sub-optimal designs, respectively. The red dots and dashed arrows represent the positions and velocities of the particles, respectively. (c) The working principle of the PSO algorithm where the swarm of particles is guided by the radiation intensity. (d) The PA-PSO algorithm guides the swarm of particles based on the extrema condition of the radiation intensity, which shows the correct directions of the maximum radiation intensity. This approach guides the swarm of particles more efficiently, which reduces not only the computation time but also the likelihood of finding sub-optimal designs.

Fig. 2. Architecture and performance of the PA-PSO algorithm. (a) Difference between PSO and PA-PSO algorithms. The yellow background in the image represents the optimization process of the PSO algorithm. During this optimization process, the phase changes between the rings are coupled, requiring more iteration time. The blue background indicates that after introducing physics, the optimization between the rings is decoupled, and they do not influence each other. As a result, the number of optimization iterations naturally decreases. (b) Variation of the relative electric field intensity with respect to the times of iteration for PA-PSO and PSO algorithms. The purple line shows the calculation errors. The four hexagons from bottom to top represent phase distributions at different stages: initial phase distribution, PSO algorithm iteration 650 times, PSO algorithm iteration 1500 times, and PSO algorithm iteration 4100 times (PA-PSO algorithm iteration 650 times). (c) Comparison of FOVs and F/D for planar lens antennas. The colors of the points indicate the fluctuation of gains when scanning within the field of view range.

Fig. 3. Design and Characteristics of the metalens antenna. (a) Design parameters of the unit structure of the metalens antenna. (b) Transmission spectrum of the unit cells. (c) Phase spectra of unit cells when the unit cell is rotated with respect to the fast axis of the left circularized incident light.

Fig. 4. Device fabrication and experimental setup. (a) Schematic of the experimental setup for near-field measurement. (b) The fixture and metasurface lens antenna used in the test. The bottom of the fixture holds the feed source antenna and includes insertable holes to alter the position of the feed source. The distance from the feed source to the metasurface lens is 2.2 cm. (c) A enlarged view of the metamaterial lens. (d) Photograph of the experimental setup. The experimental setup consists of probes, assembled feed source antenna, metasurface lens, and a vector network analyzer connecting the probes and feed source antenna.

Fig. 5. Gain profiles of the metalens antenna when the feed is placed on the focal plane with different displacements x. Comparison between the experimental results (blue lines) and simulation results (red lines) when the feed source position is (a) at x = 0, showing a maximum gain of 21.7 dBi, which corresponds to an angle of 0°; (b) at x = 15 mm, showing a maximum gain is 21.2 dBi, which corresponds to an angle of 24°; (c) at x = 30 mm, showing a maximum gain is 18.3 dBi, which corresponds to an angle of 55°. (d) The relationship between the maximum gain angles and the corresponding gains obtained from testing the feed source at different positions.