Propagation Characteristics for Wave Fields in Periodic Configuration of Scatterers

The scattering problems for periodic array of scatterers are formulated by taking advantages of the geometrical periodicity. For planar array of scatterers, reflection and transmission coefficients are derived as integrals over a surface of the single scatterer in the reference unit cell. In order to determine the physical quantity on the surface of scatterer, the boundary integral equation is used. The fundamental solution in a form of integral with rapidly convergent integrand is adopted for the numerical analysis. The accuracy of the reflection and transmission coefficients is confirmed by the energy balance. The reflection and transmission coefficients are applied to determine the dispersion relation for the triply periodic scatterers.