Fine structure of polarization and optical Möbius strips topology of laser light in planar metamaterial

It is shown that upon propagation of a plane linearly polarized harmonic wave normally incident on a planar nonlinear metamaterial whose basic cell consists of two rectangular silver plates with characteristic dimensions of hundreds of nanometers, there exists in the local field a circular polarization singularity line (C-line) containing two regions where their segments come to each other to such small distance that it may appear as a self-intersection in the numerical experiment. We found that optical ribbons constructed around the ordinary points of these lines have the topology of Möbius ribbons, and the ribbons constructed in the possible self-intersection region of C-lines and spanning its two segments are orientable surfaces.