  Characteristic modes of arbitrary two-dimensional periodic systems are
analyzed using scattering parameter data. This approach bypasses the need for
periodic integral equations and allows for characteristic modes to be computed
from generic simulation or measurement data. Example calculations demonstrate
the efficacy of the method through comparison against a periodic method of
moments formulation for a simple, single-layer conducting unit cell. The effect
of vertical structure and electrical size on the number of modes is studied and
its discrete nature is verified with example calculations. % Additional
examples verify the binary impact of vertical structure on the number of
radiating characteristic modes. A multiband polarization-selective surface and
a beamsteering metasurface are presented as additional examples.
