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We propose a method derived from the simple plane wave expansion that caneasily solve the interface problem between vacuum and a semi-infinite photoniccrystal. The method is designed to find the complete set of all theeigenfunctions, propagating or evanescent, of the translation operators $\{{\bfT_R} \}$, at a fixed frequency. With these eigenfunctions and theireigenvalues, the transmitted and reflected waves can be determined. Two kindsof applications are presented for 2D photonic crystals. The first is aselection rule for determine the normal direction of the vacuum-photoniccrystal interface to achieve the highest attenuation effect at a gap frequency.The second is to calculate the transmittance and reflectance for a lightincident from vacuum to an semi-infinite photonic crystal. As an example werecalculate a system studied previously by K. Sakoda et al. and get results inagreement with theirs

Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite photonic crystal