Method of calculating local dispersion in arbitrary photonic crystal waveguides

We introduce a novel method to calculate the local dispersion relation in photonic crystal waveguides, based on the finite-difference time-domain simulation and filter diagonalization method (FDM). In comparison with the spatial Fourier transform method (SFT), the highly local dispersion calculations based on FDM are considerably superior and pronounced. For the first time to our knowledge, the presented numerical technique allows comparing the dispersion in straight and bent waveguides.