Details for implementation of a Boundary Meshless Model (BMM) and a Meshless Plane Wave Decomposition Model (MPWD) calculating scattering coefficients of periodic structures with arbitrary shaped profiels are provided. BMM based on Mommertz's determination is applicable for finite samples. In contrast, numerical calculation is performed in a groove of one period in MPWD, which is applicable for samples with infinite surfaces. Random-incidence scattering coefficients of a sine-shaped sample and corresponding infinite sample are calculated using BMM and MPWD. Comparisons with measurements demonstrate that both models have good accuracy. Directional distributions of directional scattering coefficients are similar. At last, performances of the two models are discussed.

Periodic gratings with different shapes are designed to study spectral reflectivity in normal direction using finite-difference time-domain method.It shows that very low reflectivity in wavelengths can be found with proper grating structures and even zero-reflectance can be found.Influences of depth and slot width of triangle gratings on reflectance are investigated.Parameters for a triangle grating with very low reflectivity in wave bands of 2.75-3.23 μm and 3.84-4.88 μm are found.