Semi-analytical calculation of resonant modes in axially asymmetric microtube resonators

Optical modes in axially asymmetric microtube resonators made by dielectric materials are calculated by means of a semi-analytical approach. The Helmholtz equation for the microtube resonators can be separately solved by decomposing the mode field profile into two parts, i.e., cross-section plane and axial direction. Effective refractive index theory is used to link between the above two parts. Analytic axial fields can be approximated by Airy functions while conventional whispering-gallery mode fields written in term of Bessel functions are characteristics of the field in the cross-section plane. The validity of the semi-analytical formulation is confirmed by comparing with finite element simulations.