An analytical model to investigate the resonant modes of the self-rolled-up microtube using conformal transformation.

Self rolled-up microtube is a natural device that may couple light vertically out of a planar photonic device. It is instructive to understand the optical resonant modes propagating inside the microtube waveguide. All previous models for the microtube resonant modes ignored the nonconcentric nature of its structure. Conformal transformation was used for the first time to address this issue and to obtain equivalent planar parallel-piped waveguide structure which in turn leads to an approximate analytical solution of the resonant modes of the tube. This work paves the way for accurately calculating the coupling coefficient between the microtube and a planar waveguide. The results calculated using this model matched very well with published experimental data and COMSOL simulation.