On the Use of Electromagnetic Inversion for Metasurface Design

Abstract

We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a set of performance criteria such as half power beamwidths and null directions, rather than satisfying a fully-known complex field. In addition, the inverse source formulation allows the metasurface and the region over which the desired field specifications are provided to be of arbitrary shape. Some of the main challenges in solving this inverse source problem, such as formulating and optimizing a nonlinear cost functional, are addressed. Lastly, some two-dimensional (2D) and three-dimensional (3D) simulated examples are presented to demonstrate the method, followed by a discussion of the method's current limitations.

Electromagnetic Inversion with Local Power Conservation for Metasurface Design

“…First, C 1 (x) is minimized without the LPC constraint using the conjugate gradient method as described in more detail in [12]. This provides an estimate for x that satisfies the field constraints and Love's condition prior to applying the LPC constraint.…”

“…The main limitation of the procedure presented in Section II and [12] is that the synthesized susceptibilities may require (undesirable) loss and/or gain. To overcome this limitation, we first note that a necessary condition for a passive and lossless metasurface is that the input and output fields must satisfy LPC [15], [16].…”

Full-Wave Verification of an Electromagnetic Inversion Metasurface Design Method

“…An overview of the steps involved in the inversion approach is shown in Figure 1. First, we minimize a cost functional that quantifies the difference between the desired data and simulated data due to a set of equivalent electric and magnetic currents J and M [7]. The currents found from this stage are used as the initial guess for the second optimization stage that takes the incident field into consideration and uses particle swarm optimization (PSO) to enforce local power conservation (LPC), a necessary condition for a passive and lossless metasurface [8].…”

Full-Wave Verification of an Electromagnetic Inversion Metasurface Design Method

“…Metasurfaces can facilitate the systematic control of electromagnetic fields with numerous applications reported in the past decade [1]- [5]. Recently, the electromagnetic inversion framework has been proposed as a design tool to determine a homogenized metasurface model [6], [7]. The main advantage of this framework lies in its ability to work with a variety of desired specifications given on arbitrary specification domains.…”

“…The currents found from this stage are used as the initial guess for the second optimization stage that takes the incident field into consideration and uses particle swarm optimization (PSO) to enforce local power conservation (LPC), a necessary condition for a passive and lossless metasurface [8]. The currents found in the second stage are then used to compute the transmitted fields on the output side of the metasurface, assuming Love's equivalence condition was enforced [7]. The final stage consists of computing the surface susceptibilities (χ ee , χ em , χ mm , χ me ) from the generalized sheet transition conditions (GSTCs).…”