Representation of the scattering coefficient of a large scale periodic structure by a small sample

In this paper, the relations of the scattering coefficients of the periodic structures with different dimensions are analyzed in detail. A criterion for representing the scattering coefficients of a large scale periodic structure by a small sample is given for the first time. At first, a theoretical analysis proves that the representation is feasible. Then, a Boundary Meshless Model (BMM) for calculating the scattering coefficient is derived. The scattering coefficients of small periodic structures representing different local parts of large scale one are calculated using BMM. The results and their analysis show preliminarily that only the small periodic structure which has the same number of periods as and at least the half dimension of the large one is representative. Applying this conclusion, we believe, can not only hugely improve the computational efficiency but also can make possible the fast estimation in engineering and improvement of the measurement of scattering coefficient.