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Plane wave scattering by an infinite array of semi-infinite thick plates

Tasinkevych Y.

Journal of Technical Physics

2007

Vol. 48, no 3-4

147-162

The problem of plane electromagnetic wave scattering by periodic system of semi-infinite thick plates of rectangular shape is solved in this paper. The case of TM-polarization is considered in this paper. The field distribution in the free space region above the plates is found in the form of series of spatial harmonics in accordance with the Floquet's theorem. In the plate region the field is found in the form of parallel-plate waveguide modes. The continuity condition for tangential components of electric and magnetic field vectors is applied in order to find unknown partial wave amplitudes. To satisfy the boundary conditions and the singular behavior of the electric field vector near the plate edges, the use is made of the known properties of certain Fourier expansion with corresponding coefficients being properly chosen Legendre functions. The final rigorous solution is given in the form of infinite series of spatial harmonics with unknown coefficients being the solution of the corresponding doubly infinite system of linear equations which can be solved only numerically.