Generalized finite-difference time-domain method utilizing auxiliary differential equations for the full-vectorial analysis of photonic crystal fibers

We present the generalized finite-difference time-domain full-vectorial method by reformulating the time-dependent Maxwell's curl equations with electric flux density and magnetic field intensity, with auxiliary differential equations using complex-conjugate pole-residue pairs. The model is generic and robust to treat general frequency-dependent material and nonlinear material. The Sellmeier equation is implicitly incorporated as a special case of the general formulation to account for material dispersion of fused silica. The results are in good agreement with the results from the multipole method. Kerr nonlinearity is also incorporated in the model and demonstrated. Nonlinear solutions are provided for a one ring photonic crystal fiber as an example.