A Passive Intelligent Metasurface: A Network Model

Abstract

Intelligent metasurfaces enable advanced wave manipulation, including negative refraction, focusing, beam splitting and beam steering, with significant potential for practical applications. However, conventional approaches often rely on active metamaterials with gain, or demand computationally intensive solutions of inverse problems to find the optimal configuration. In this work, we use the scattering framework of quantum graph theory to derive an exact, analytic expression for configuration of a passive metasurface that produces a prescribed reflected wave field. The metasurface terminates a periodic lattice of waveguides and consists of an array of channels, each a tube of length $\ell_m$ ending in a vertex whose scattering parameter $λ_m$ sets how much of the wave is lost to the wall. For any prescribed incident and reflected field, the exact lengths and scattering parameters follow channel by channel, in closed form, from the ratio of the wave amplitudes returning to and leaving the lattice, and the metasurface is passive whenever this ratio does not exceed unity in modulus. We demonstrate the construction for both a one-dimensional and a two-dimensional metasurface. The one-dimensional metasurface terminates a two-dimensional lattice and steers, splits or perfectly absorbs Gaussian beams. The two-dimensional metasurface terminates a three-dimensional lattice and generates a prescribed image in a plane inside the lattice. In each case, we obtain the exact boundary properties that produce the effect.