  Recently, metamaterials-inspired diffraction gratings (or metagratings) have
demonstrated unprecedented efficiency in wavefront manipulation by means of
relatively simple structures. Conventional one-dimensional (1D) gratings have a
profile modulation in one direction and a translation symmetry in the other. In
1D metagratings, the translation invariant direction is engineered at a
subwavelength scale, which allows one to accurately control polarization line
currents and, consequently, the scattering pattern. In bright contrast to
metasurfaces, metagratings cannot be described by means of surface impedances
(or local reflection and transmission coefficients). In this paper, we present
a simulation-based design approach to construct metagratings in the "unit cell
by unit cell" manner. It represents an analog of the local periodic
approximation that has been used to design space-modulated metasurfaces and
allows one to overcome the limitations of straightforward numerical
optimization and semianalytical procedures that have been used to date to
design metagratings. Electric and magnetic metagrating structures responding
to, respectively, transverse electric and transverse magnetic incident plane
waves are presented to validate the proposed design approach.
