Abstract
This paper reviews the past analytical and non-analytical approaches for the Surface Plasmons (SPs) effect, present a simple description to the widely adopted curvilinear coordinate method. Based on the concept of Fourier decomposition of any complicated grating profiles, a comprehensive analysis is given to the contribution of every order components to the overall behavior of the practical zero-order metal gratings. It successfully predicts the energy gap, resonant SPs modes, the red-shift behavior and the broadening effect of energy gap by higher order components. At the same time, it's found that within certain wavelength range of interest, only first several orders of components are needed to be taken into account to predict the behavior of the non-sinusoidal gratings. As an application, this analysis approach is extended to behavior of the triangular gratings. The limitation and possible generalization of this method are also discussed.