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 America
(000.4430) General : Numerical approximation and analysis
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics
Linfang Shen and Sailing He, "Analysis for the convergence problem of the plane-wave expansion method for photonic crystals," J. Opt. Soc. Am. A 19, 1021-1024 (2002)