  Electromagnetic metasurfaces have attracted significant interest recently due
to their low profile and advantageous applications. Practically, many
metasurface designs start with a set of constraints for the radiated far-field,
such as main-beam direction(s) and side lobe levels, and end with a non-uniform
physical structure for the surface. This problem is quite challenging, since
the required tangential field transformations are not completely known when
only constraints are placed on the scattered fields. Hence, the required
surface properties cannot be solved for analytically. Moreover, the translation
of the desired surface properties to the physical unit cells can be
time-consuming and difficult, as it is often a one-to-many mapping in a large
solution space. Here, we divide the inverse design process into two steps: a
macroscopic and microscopic design step. In the former, we use an iterative
optimization process to find the surface properties that radiate a far-field
pattern that complies with specified constraints. This iterative process
exploits non-radiating currents to ensure a passive and lossless design. In the
microscopic step, these optimized surface properties are realized with physical
unit cells using machine learning surrogate models. The effectiveness of this
end-to-end synthesis process is demonstrated through measurement results of a
beam-splitting prototype.
