The convergence feature of two types of plane-wave expansion methods commonly used for photonic crystals is analyzed. It is shown that the reason for the slow convergence of these plane-wave expansion methods is not the slow convergence of the Fourier series for the permittivity profile of the photonic crystal but the inappropriate formulation of the eigenproblem. A new formulation of the eigenproblem is presented to improve the convergence in the one-dimensional case.
© 2002 Optical Society of AmericaPDF Article
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