AbstractOptical prisms are made of glass and map temporal frequencies into spatial frequencies by decomposing incident white light into its constituent colors and refract them into different directions. Conventional prisms suffer from their volumetric bulky and heavy structure and their material parameters are dictated by the Lorentz reciprocity theorem. Considering various applications of prisms in wave engineering and their growing applications in the invisible spectrum and antenna applications, there is a demand for compact apparatuses that are capable of providing prism functionality in a reconfigurable manner, with a nonreciprocal/reciprocal response. Here, we propose a nonreciprocal metasurface-based prism constituted of an array of phase- and amplitude-gradient frequency-dependent spatially variant radiating super-cells. In conventional optical prisms, nonreciprocal devices and metamaterials, the spatial decomposition and nonreciprocity functions are fixed and noneditable. Here, we present a programmable metasurface integrated with amplifiers to realize controllable nonreciprocal spatial decomposition, where each frequency component of the incident polychromatic wave can be transmitted under an arbitrary and programmable angle of transmission with a desired transmission gain. Such a polychromatic metasurface prism is constituted of frequency-dependent spatially variant transistor-based phase shifters and amplifiers for the spatial decomposition of the wave components. Interesting features include three-dimensional prism functionality with programmable angles of refraction, power amplification, and directive and diverse radiation beams. Furthermore, the metasurface prism can be digitally controlled via a field- programmable gate array (FPGA), making the metasurface a suitable solution for radars, holography applications, and wireless telecommunication systems.
New coordinates for a simpler canonical derivation of the Hawking effect
