Polarization Effects in Microfiber Loop and Knot Resonators

We theoretically investigate the polarization effect of three-dimensional (3-D) microfiber/nanofiber (MNF) loop resonators and knot resonators. Due to the lack of circular symmetry, the coupling at the joint regions of loop resonator and knot resonator are highly polarization-dependent. Using Jones matrices to express coupling coefficients, we suggest a matrix formula to describe the propagation of arbitrary polarized incidence through the resonator. Thereby, the polarization effect of 3-D loop resonators and knot resonators can be comprehensively investigated. We find that the polarization properties of the resonance spectrum and Q -factor are strongly dependent on the parameters of the twisted region. Results obtained in this work may serve as helpful guidelines for MNF resonator design and fabrication.