“…These excitation, reflection, and transmittance coefficients are all associated with the scattering components of an electromagnetic field. The concepts of the zero field, scattered field, and total field have been introduced in our previous work [19][20][21], i.e., the zero field is the field when there are no scatterers at all, and the scattered field is calculated by subtracting the zero field from the total field with scatterers. Since σ , R and T can be calculated recursively starting from β 1 , ρ 1 and τ 1 , the geometry optimization for N periodic indentations is reduced into that for a single one, resulting in a great reduction of the computational cost.…”