Scattering of ${\rm H}$ -polarized Wave by a Periodic Array of Thick-Walled Parallel Plate Waveguides

A study is made of electromagnetic wave scattering by a periodic array of semi-infinite thick-walled parallel plate waveguides. The scattered field in the free-space region above the waveguides is sought in the form of a series of spatial harmonics in accordance with Floquet´s theorem, whereas in the waveguide regions it is sought in the form of parallel plate waveguide modes. To satisfy the boundary and edge conditions in the free-space region, Fourier series expansion with corresponding coefficients being properly chosen Legendre functions is used. As a result, the amplitudes of spatial harmonics are given in the form of an infinite series of Legendre functions with unknown coefficients being the solution of certain doubly infinite system of linear equations. The exact solution of this system cannot be constructed and numerical calculations were performed to find the expansion coefficients approximately.