A modified implementation of the plane-wave expansion for calculation of photonic crystals band structures is introduced in order to circumvent the slow convergence stemming from field discontinuities. By using an adequate form of the Fourier transform of the dielectric constant, a fast convergence rate is achieved for any photonic crystal pattern. This result, which generalizes previous convergence studies, is exemplified in the important case of photonic crystal with circular holes. We further consider more sophisticated structures, such as elliptical hole-shapes as well as supercell calculations for waveguides. We also address calculations of ultraflat photonic bands.

• Received 12 April 2005

DOI:https://doi.org/10.1103/PhysRevB.73.075107