An improved finite-difference frequency-domain method based on Taylor series expansion, local coordinate transformation, and boundary condition matching is developed for analyzing the band diagrams of 2-D photonic crystals. This newly proposed scheme can deal with piecewise homogeneous structures with curved dielectric interfaces. It also shows much better performance in modeling structures of highly index contrast ratio. We have verified this improved scheme with frequently-used plane-wave expansion method through the calculation of the band diagrams of a 2-D photonic crystal with square lattice. We also compare the scheme with the staircase approximation. We further improve the convergence behavior by adopting high-order terms. The result of this adopting is also demonstrated.
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