  The synthesis of a metasurface exhibiting a specific set of desired
scattering properties is a time-consuming and resource-demanding process, which
conventionally relies on many cycles of full-wave simulations. It requires an
experienced designer to choose the number of the metallic layers, the scatterer
shapes and dimensions, and the type and the thickness of the separating
substrates. Here, we propose a generative machine learning (ML)-based approach
to solve this one-to-many mapping and automate the inverse design of dual- and
triple-layer metasurfaces. Using this approach, it is possible to solve
multiobjective optimization problems by synthesizing thin structures composed
of potentially brand-new scatterer designs, in cases where the inter-layer
coupling between the layers is non-negligible and synthesis by traditional
methods becomes cumbersome. Various examples to provide specific magnitude and
phase responses of $x$- and $y$-polarized scattering coefficients across a
frequency range as well as mask-based responses for different metasurface
applications are presented to verify the practicality of the proposed method.
