Electromagnetic metasurface design based on farfield 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 farfield constraints such as nulls, sidelobe levels, and main beam level(s); and a 3-layer nonuniform 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 inhomogenous 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.

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