Electromagnetic Inversion with Local Power Conservation for Metasurface Design

Abstract

<pre>A method based on electromagnetic inversion is extended to facilitate the design of passive, lossless, and reciprocal metasurfaces. More specifically, the inversion step is modified to ensure that the field transformation satisfies local power conservation, using available knowledge of the incident field. This paper formulates a novel cost functional to apply this additional constraint, and describes the optimization procedure used to find a solution that satisfies both the user-defined field specifications and local power conservation. Lastly, the method is demonstrated with a two-dimensional (2D) example.</pre>

Metasurface Design Using Electromagnetic Inversion

“…Since this method is based on solving an electromagnetic inverse source problem, we have referred to this approach as an electromagnetic inversion algorithm for metasurface design. Subsequently, in [102], we modified this inversion method by augmenting its associated cost functional to enforce local power conservation (LPC) [31,30] which ensures the resulting metasurfaces can be implemented using passive, lossless, and reciprocal elements.…”

“…As will be discussed, these fields need to satisfy LPC for each individual metasurface to ensure that they can be fabricated using passive and lossless elements. It is worth noting that while in [102] we used a stochastic method (particle swarm) to enforce LPC in the inversion process, in this work we use gradient-based optimization for improved convergence and computational efficiency. Furthermore, we introduce regularization into the optimization process based on the L 2 -norm total variation (TV) regularizer commonly used for the inverse problem associated with microwave imaging [113,114].…”

“…The time-average real power density of the output field can be written in terms of the equivalent currents as [102] p (5.22) the total output power will be equal to the total input power, i.e., sum(p out ) = sum(p in ), thus satisfying TPC. Finally, having found α, J 2,R , J 2,I , M 2,R , and M 2,I , we can now use (5.1) to determine the required output tangential fields E + t2 and H + t2 on Σ + 2 .…”

“…In order to ensure that the metasurfaces are passive, lossless, and reciprocal, we follow the procedure in [102] which stipulates that χ yy ee and χ zz mm are purely real (R) while χ yz em and χ zy me are purely imaginary (I). This restriction allows (5.33) to be solved analytically on each metasurface, with a unique solution for each unit cell.…”

“…In the second optimization step we use w 1 = 25, w 2 = 25, and w TV = 5 × 10 −11 , and a step length of 1. Additionally, we attempt to design a single metasurface using the procedure in [102] to produce a satisfactory FF pattern from the same incident field. The real part (absolute value) of the total magnetic field in the simulation domains for the single metasurface and the cascaded metasurface system are shown in Figures 5.10(a) and (b), respectively.…”