This paper presents an electromagnetic inversion algorithm for the design of cascaded metasurfaces that enables the design process to begin from more practical output field specifications such as a desired power pattern or far-field performance criteria. Thus, this method combines the greater field transformation support of multiple metasurfaces with the flexibility of the electromagnetic inverse source framework. To this end, two optimization problems are formed: one associated with the interior space between two metasurfaces, and the other for the exterior space. The cost functionals corresponding to each of these two optimization problems are minimized using the nonlinear conjugate gradient algorithm with analytic expressions for the gradient operators. A total variation regularizer is incorporated into the optimization procedure to favour smooth field variations from one unit cell to the next. The numerical implementation of the developed design procedure is presented in detail along with several two-dimensional (2D) simulated examples to demonstrate the capabilities of the method.

This paper summarizes and synthetically evaluates a method proposed for metasurface design. The method takes as input a set of desired far-field (FF) performance specifications and produces an effective susceptibility distribution that, when illuminated with a known incident field, produces a FF radiation pattern exhibiting the desired specifications. To this end, electromagnetic inversion (inverse source) is used to solve for the desired tangential fields on the output side of the metasurface. A finite-difference frequency-domain solver, recently developed for simulation of metasurfaces, is used to synthetically evaluate the proposed method using a two-dimensional (2D) example. It should be noted that microscopic metasurface design (i.e., the design of the physical metasurface implementation) is beyond the scope of this paper.

This paper summarizes, extends, and synthetically evaluates a method for metasurface design which uses electromagnetic inversion. After the inversion algorithm determines a homogenized surface susceptibility model to implement a desired power pattern, the susceptibility distribution is converted to a three-layer admittance sheet topology. Lastly, full-wave commercial software is used to simulate and verify the performance of a metasurface designed and implemented using the proposed procedure.

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.