  Optical high-finesse cavities are a well-known mean to enhance light-matter
interactions. Despite large progress in the realization of strongly coupled
light-matter systems, the controlled positioning of single solid emitters in
cavity modes remains a challenge. We pursue the idea to use nanofibers with
sub-wavelength diameter as a substrate for such emitters. This paper addresses
the question how strongly optical nanofibers influence the cavity modes. We
analyze the influence of the fiber position for various fiber diameters on the
finesse of the cavity and on the shape of the modes.
