The structure of circular polarization singularity lines ($C$-lines) of the electromagnetic field and Möbius optical ribbons near a subwavelength silicon nanoparticle of toroidal shape is analyzed for a plane monochromatic uniformly elliptically polarized wave incident in two cases: with its wave vector parallel to the torus axis and lying in the plane of the torus' generating circle. Depending on the parameters of the incident wave, between two and six closed $C$-lines are observed near the nanoparticle. Patterns of changes in their size and shape, as well as the fraction of points of topological types lemon, star, and monstar on each $C$-line, are analyzed. The twist coefficient of Möbius optical ribbons constructed around points of different topological types on the $C$-lines is investigated for the case in which the center of the polarization ellipse moves along a small-radius circle centered at a $C$-line point, the plane of which coincides with the plane of the degenerate ellipse (circle) of polarization at that point.

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• Near-field optics
• Polarization vortices