Cascaded Metasurface Design Using Electromagnetic Inversion With Gradient-Based Optimization

This article 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 (FF) 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 (CG) algorithm with analytic expressions for the gradient operators. The numerical implementation of the developed design procedure is presented in detail, including a total variation (TV) regularizer that is incorporated into the optimization procedure to favor smooth field variations from one unit cell to the next. The capabilities of the method are demonstrated by converting the produced surface susceptibilities into three-layer admittance sheet models, which are simulated in several 2-D examples.