Structure of modes with greater than unity azimuthal number in twisted anisotropic optical fibers

We solved the vector wave equation to obtain modes with azimuthal number 2 of weakly guiding twisted anisotropic optical fiber. We considered the mutual action of linear anisotropy of the fiber material, twisted mechanical stress, and spin-orbital interaction. We established that modes with azimuthal number 2 are represented by linearly or circularly polarized optical vortices depending on the interplay between anisotropy of the material and the twisting/ spin-orbit-interaction effect. We established analytical expressions for the corresponding propagation constants at arbitrary fiber parameters, such as a linear anisotropy, twisting, and spin-orbital-interaction. We demonstrated the orbital birefringence and optical Zeeman effect for high-order modes with azimuthal number 2 in twisted anisotropic fibers.