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.

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This thesis presents the theory and development of a framework for the design of electromagnetic metasurfaces. These metasurfaces can be used to systematically transform an incident electromagnetic field into a different transmitted field, providing new levels of control not typically possible with conventional materials. Although a metasurface is made up of subwavelength scattering elements, it can be macroscopically represented as a homogenized model using effective surface susceptibilities. These tensorial surface susceptibilities define the relationship between the tangential electric and magnetic fields on either side of the metasurface through a set of generalized boundary conditions known as the generalized sheet transition conditions.

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