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An accurate formulation to the problem of electromagnetic scattering by the multielements periodic grating of circular cylinders and dielectric slab is presented. The dielectric cylinders are assumed ...to have different radii and geometrical locations per unit cell and the dielectric slab is located apart from the periodic grating. Applying the boundary conditions and using the additional theorem for the cylindrical functions and the projection method, an infinite system of linear equations for the unknown coefficients of the multipole spectra is obtained. This system of equations is solved by the reduction method and the analytical expressions for both transmission and reflection coefficients are derived by using the relationship between the diffracted spectra and the multipole spectra. The numerical examples demonstrate the multiple scattering effects between the cylindrical elements of the grating and the slab boundaries on the frequency response in the transmission coefficient. It is shown that the frequency response could be controllable by properly adjusting the geometrical parameters of the dielectric slab.show more
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