  We investigate theoretically electromagnetic plane-wave scattering by
self-complementary metasurfaces. By using Babinet's principle extended to
metasurfaces with resistive elements, we show that the frequency-independent
transmission and reflection are realized for normal incidence of a circularly
polarized plane wave onto a self-complementary metasurface, even if there is
diffraction. Next, we consider two special classes of self-complementary
metasurfaces. We show that self-complementary metasurfaces with rotational
symmetry can act as coherent perfect absorbers, and those with translational
symmetry compatible with their self-complementarity can split the incident
power equally, even for oblique incidences.
