Generation of Mathieu beam using a single layer transmissive metasurface

Mathieu beams is an important diffraction-free beam. In this letter, we proposed a transmissive metasurface to generate Mathieu beams in microfields. An ultrathin transmissive element with single layer is designed. It consists of two metallic I-shaped structures on both sides of the substrate. By rotating the top layered I-shaped resonator, amplitude adjustment from 0 to 1 with 1 -bit phase shift can be achieved when y-polarized incident wave is converted into x-polarized one. A metasurface prototype is designed and fabricated to generate the required Mathieu beam. Both simulation and measurement show that Mathieu beam can be effectively generated and diffraction free feature can be observed in the distance range of 0 36 ? (where ? is the wavelength at operating frequency). Compared with traditional devices to generate Mathieu beams, using metasurface reduces the complexity and cost. Our proposed method and metasurface can provide reference for complex field control in 3-dimensional space and may facilitate the uses of Mathieu beams for practical applications.