Electromagnetic metasurfaces are electrically thin structures with small inclusions that allow for electromagnetic wave manipulation beyond the capabilities of conventional thin materials. Using the often desired passivity and losslessness attributes, single metasurfaces fail to provide certain electromagnetic wave transformations. To handle this, cascaded metasurface systems, consisting of two separated metasurfaces, are considered to overcome the power conservation limitations created by these attributes.

This thesis focuses on the design optimization and validation of electromagnetic cascaded metasurfaces with internal sources, with an exploration of many different use cases. It starts with an overview of the conceptual framework that guides the entire process with a methodology overview. It covers the topic of metasurfaces in general, starting from a qualitative introduction to metamaterials, their historical context, and evolution, before advancing to a quantitative examination that includes the mathematical formulations and theoretical underpinnings. This part of the thesis establishes a foundation for metasurfaces in general before transitioning into the core of the thesis.

The core of the thesis casts the design variables, originally formulated in an earlier work, in the forms of matrices and vectors, and then optimizes a design cost functional through the nonlinear conjugate gradient (CG) scheme. This CG scheme is also adapted to a more affordable system where one of the metasurfaces is replaced by a simple metallic sheet. The optimization scheme is considered in both complex and real domains to show the equivalency of optimization in both domains.

The results chapter presents an analysis of various setups and simulations for cascaded metasurfaces with an internal source for beam shaping and matching scenarios. This draws comparisons between the nonlinear CG method and previously implemented gradient descent approaches. It explores different user-defined specifications, showcasing the practicality and effectiveness of analytical techniques, antenna array approaches, and far-field masks. This is then followed by an investigation of the impact of other considerations such as reconfigurability, metallic traces and matching two different dielectric media. Finally, the thesis outlines potential future work, including the exploration of three-dimensional beam shaping and reconfigurability as the next steps in metasurface design.