  Electromagnetic metasurface design based on far-field constraints without the
complete knowledge of the fields on both sides of the metasurface is typically
a time consuming and iterative process, which relies heavily on heuristics and
ad hoc methods. This paper proposes an end-to-end systematic and efficient
approach where the designer inputs high-level far-field constraints such as
nulls, sidelobe levels, and main beam level(s); and a 3-layer non-uniform
passive, lossless, omega-type bianisotropic electromagnetic metasurface design
to satisfy them is returned. The surface parameters to realize the far-field
criteria are found using the alternating direction method of multipliers on a
homogenized model derived from the method of moments. This model incorporates
edge effects of the finite surface and mutual coupling in the inhomogeneous
impedance sheet. Optimization through the physical unit cell space integrated
with machine learning-based surrogate models is used to realize the desired
surface parameters from physical meta-atom (or unit cell) designs. Two passive
lossless examples with different feeding systems and far-field constraints are
shown to demonstrate the effectiveness of this method.
