We report the fabrication and characterization of photonic structures using tapered optical nanofibers. Thanks to the extension of the evanescent electromagnetic field outside of the nanofiber two types of devices can be built: a ring interferometer and a knot resonator. We propose a general approach to predict the properties of these structures using the linear coupling theory. In addition, we describe a new source of birefringence due to the ovalization of a nanofiber under strong bending, known in mechanical engineering as the Brazier effect.