Coupling-reducing k-points for photonic crystal fibre calculations

When describing localized electromagnetic modes in dielectric waveguides by the planewave method, a supercell geometry must necessarily be adopted. We demonstrate in the present work that the convergence of the calculations with respect to supercell size depends strongly on the choice of the transverse Bloch wave vector, k.

We describe a method to derive k-points that minimize the coupling between repeated images of the guided modes in real space. Calculations have been done for a quadratic and a triangular photonic crystal fiber structure. With the new coupling reducing (CR) k-points, the convergence of the eigenfrequencies for both the fundamental and second order modes with respect to supercell size is considerably improved.

The general approach outlined may also be applied in the case of three-dimensional photonic crystal structures.