  In recent times, three-dimensional (3D) metamaterials have undergone a
revolution driven mainly by the popularization of 3D-printing techniques, which
has enabled the implementation of modern microwave and photonic devices with
advanced functionalities. However, the analysis of 3D metamaterials is complex
and computationally costly in comparison to their 1D and 2D counterparts due to
the intricate geometries involved. In this paper, we present a fully-analytical
framework based on Floquet-Bloch modal expansions of the electromagnetic fields
and integral-equation methods for the analysis of 3D metamaterials and
metagratings. Concretely, we focus on 3D configurations formed by periodic
arrangements of rectangular waveguides with longitudinal slot insertions. The
analytical framework is computationally efficient compared to full-wave
solutions and also works under oblique incidence conditions. Furthermore, it
comes associated with an equivalent circuit that allows to gain physical
insight into the scattering and diffraction phenomena. The analytical
equivalent circuit is tested against full-wave simulations in commercial
software CST. Simulation results show that the proposed 3D structures provide
independent polarization control of the two orthogonal polarizations states.
This key property is of potential interest for the production of full-metal
polarizers, such as the one illustrated.
