Differential method for TM-polarized Floquet-mode analysis of photonic crystal waveguides formed by circular cylinders

The TM-polarized Floquet-modes propagating in a photonic crystal waveguides formed by circular cylinders are formulated based on the differential theory with the scattering-matrix propagation algorithm. The present formulation does not introduce the staircase approximation, which is widely used in the rigorous coupled-wave algorithm (or Fourier modal method), and follows Li´s Fourier factorization rules by using Fourier factorization with the complex polarization bases. The guided Floquet-modes are obtained by solving the dispersion equation numerically.