Electromagnetic scattering by periodic system of parallel-plate waveguides with thick walls

Electromagnetic wave scattering by a periodic array of semi-infinite thick-walled parallel plate waveguides is studied in this paper. The scattered field in the free space above the waveguides is sought in the form of a series of spatial harmonics in accordance with the Floquetpsilas theorem, whereas in the waveguide regions it is sought in the form of parallel plate waveguide modes. To satisfy the boundary and edge conditions by field components in the free space above the array the use is made of certain Fourier expansion with corresponding coefficients being properly chosen Legendre functions. As a result, the amplitudes of spatial harmonics are given in the form of infinite series of Legendre functions with unknown coefficients being the solution of certain doubly infinite system of linear equations. The exact solution to the one can not be obtained, however, and numerical calculations are required to find the unknown expansion coefficients approximately.