Design of Beamforming, Transparent Metasurfaces Using Integral Equations

TL;DR

This paper introduces an integral equation-based method for designing transmissive metasurfaces that achieve perfect transmission and wavefront transformation, validated through simulations and comparisons with existing approximations.

Contribution

The paper presents a novel integral equation approach for designing metasurfaces with improved accuracy over local periodicity approximations.

Findings

Integral equation method yields better collimation.

Designs successfully transform wavefront amplitude and phase.

Validated designs with finite element simulations.

Abstract

An accurate method for designing transmissive metasurfaces is presented that provides perfect transmission while transforming the amplitude and phase of the wavefront. The designed metasurfaces consist of three spatially-varying, electric impedance sheets separated by two dielectric substrates. The design method uses integral equations to account for interactions within and between the impedance sheets, allowing for accurate design. In this paper, a comparison between the integral equation method and the local periodicity approximation is presented. The comparison includes one design example for a transmitted field of uniform phase and amplitude. The design using integral equations provides better collimation. Two other examples involving an amplitude tapered transmitted field are reported to show the versatility of the proposed design technique. In all the examples, the metasurface is $7.35\lambda_0$ wide, the focal length is $4\lambda_0$, and has an overall thickness of $0.1355 \lambda_0 $ at the operating frequency of 5GHz. The designs are verified using a commercial finite element electromagnetic solver.