  Surface waves supported by structured metallic surfaces, i.e. metasurfaces,
have drawn wide attention recently. They are promising for various applications
ranging from integrated photonic circuits to imaging and bio-sensing in various
frequency regimes. In this work, we show that surface states with diverse
polarization configurations can be supported by a metasurface consisting of a
single layer of bianisotropic metamaterial elements. The structure possesses
D2d symmetry, which includes mirror symmetry in the xz and yz plane, and C2
rotational symmetry along y = +-x axis. Due to this unique symmetry, the
metasuface supports both transverse electric (TE) and transverse magnetic (TM)
waves along kx and ky directions, while a purely longitudinal mode and an
elliptically polarized transverse electromagnetic (TEM) mode along ky = +-kx
directions. The versatility of the surface modes on the metasurface may lead to
new surface wave phenomena and device applications.
