Fourier series expansion method for Floquet-mode analysis of photonic crystal waveguides formed by circular cylinders

This paper presents a formulation of Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. The formulation is based on the Fourier series expansion method with the help of the recursive transition-matrix algorithm (RTMA) for the scattering analyses of cylinder arrays. The Fourier series expansion method introduces an artificial periodicity in the transverse direction and the fields outside the cylinders are then expressed in the plane-wave expansions. RTMA uses also the cylindrical-wave expansions to match the tangential components of the fields. The present formulation uses the expansion bases that have symmetric properties because the periodicity cell has a structural symmetry, and reduces the computation cost.