Full-Vector Finite-Element Beam Propagation Method for Helicoidal Waveguides and Its Application to Twisted Photonic Crystal Fibers

A full-vector beam propagation method based on a finite-element scheme for a helicoidal system is developed. The permittivity and permeability tensors of a straight waveguide are replaced with equivalent ones for a helicoidal system, obtained by transformation optics. A cylindrical, perfectly matched layer is implemented for the absorbing boundary condition. To treat wide-angle beam propagation, a second-order differentiation term with respect to the propagation direction is directly discretized without using a conventional Padé approximation. The transmission spectra of twisted photonic crystal fibers are thoroughly investigated, and it is found that the diameters of the air holes greatly affect the spectra. The calculated results are in good agreement with the recently reported measured results, showing the validity and usefulness of the method developed here.