Theoretical analysis of resonant mode splitting in a single microfiber knot-ring resonator

In this paper, we established a theoretical model and made an analysis of single knot-ring resonator by polarization transmission matrix. The theoretical analysis shows that two orthogonal polarization modes of knot-ring, which are originally resonant at the same wavelength, will be split into two resonant modes at two different wavelengths. The mode splitting owes to the twisted coupler of the knot-ring, which makes these two orthogonal polarization modes couple each other. This results can provide a novel method to implement coupled-resonator-induced transparency in a single knot-ring.