  Metasurfaces, the two-dimensional counterpart of metamaterials, have caught
great attention thanks to their powerful capabilities on manipulation of
electromagnetic waves. Recent times have seen the emergence of a variety of
metasurfaces exhibiting not only countless functionalities, but also a
reconfigurable response. Additionally, digital or coding metasurfaces have
revolutionized the field by describing the device as a matrix of discrete
building block states, thus drawing clear parallelisms with information theory
and opening new ways to model, compose, and (re)program advanced metasurfaces.
This paper joins the reconfigurable and digital approaches, and presents a
metasurface that leverages the tunability of graphene to perform beam steering
at terahertz frequencies. A comprehensive design methodology is presented
encompassing technological, unit cell design, digital metamaterial synthesis,
and programmability aspects. By setting up and dynamically adjusting a phase
gradient along the metasurface plane, the resulting device achieves beam
steering at all practical directions. The proposed design is studied through
analytical models and validated numerically, showing beam widths and steering
errors well below 10 degrees and 5% in most cases. Finally, design guidelines
are extracted through a scalability analysis involving the metasurface size and
number of unit cell states.
