Electromagnetic design optimization: Application to a patch antenna reflection loss on a textured material ('metamaterial') substrate

As electromagnetic analysis and prediction codes have improved dramatically over the past decade, design using these tools becomes an obvious next step to improve antenna or other RF device performance. Both shape and material can be varied to improve antenna characteristics, such as reflection loss and gain. Typical implementations involve a choice of applicable electromagnetic prediction codes (e.g., moment method, finite element method, etc.) nested within a nonlinear optimization construct. Currently, a popular approach to electromagnetic optimization entails use of non-linear and multi-modal optimization methods such as genetic algorithms and simulated annealing. These are known to require thousands of points to achieve a globally optimal solution, even for design spaces that are parametrically small. Generality of design is lost because one is often forced to seek from amongst an endless array of parametric models for shape and material to converge to a solution in a reasonable time.; This work demonstrates that a non-parametric solution to a difficult electromagnetic optimization problem is possible by analyzing the eigendecomposition of a unique form of a Finite Element Boundary Integral (FE-BI) system solution. This new expansion of the FE-BI matrix system provides a broadband approximant that is orders of magnitude faster than the baseline FE-BI prediction code. More importantly, the identified functional form of the eigenvalues allows for the optimal adjustment of the electromagnetic system.; The design goal of this work is to increase the effective bandwidth of a patch antenna by texturing (via contrasting materials) the supporting substrate. The aforementioned eigenvalue adjustments are used to derive the required substrate material texture. This forms a "metamaterial" antenna design approach, as discussed in numerous publications. This new approach is a dramatic leap forward from traditional metamaterial design approaches in that no parametric assumptions or engineering judgments for texturing are required to perform an optimization. Optimized designs with only a few iterative updates are therefore possible. This work demonstrates that antenna reflection loss can be optimized over a wide bandwidth using straightforward engineering principles.