  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.
