Dispersion and polarization conversion of whispering gallery modes in arbitrary cross-section nanowires

We investigate theoretically the optical properties of Nano-Wires (NWs) with cross sections having either discrete or cylindrical symmetry. The material forming the wire is birefringent, showing a different dielectric response in the plane and along the axis of the wire, which is typically the case for wires made of wurtzite materials, such as ZnO or GaN. We look for solutions of Maxwell`s equations having the proper symmetry. The dispersions and the linewidths versus angle of incident light for the modes having high momentum in the cross-section plane, so called whispering gallery modes, are calculated. We put a special emphasis on the case of hexagonal cross sections. The energy positions of the modes for a set of azimuthal quantum numbers are shown. We demonstrate the dependence of the energy splitting between TE and TM modes versus birefringence. The polarization conversion from TE to TM with increase of the axial wave vectoris discussed for both cylindrical and discrete symmetry.