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The purpose of this paper is to analyze far and near field emitted field patterns through more exact calculation of the modes formed in finite periodic dielectric gratings.

For the mode calculation, equations are newly defined by applying vertical boundary condition on the assumption that transverse electric modes are generated in the structure. After finding modes, near field patterns are calculated using the wave number and coefficient of the mode.

Additionally, the results from these calculations are compared with that of the rigorous-coupled method. Finally, far field patterns are derived by applying fast Fourier transform to near field patterns and also compared with the results of rigorous-coupled method.

For convenience of coordinate, we use rectangular coordinate, though the shape of radome is a hemisphere.

In this paper, the authors derive more exact near field patterns without the assumption of infiniteness so that these results can be used practically for a making real frequency-selective structure.

Conventional periodic finite dielectric gratings analysis has been done using Floquet–Bloch wave theory, coupled-mode, rigorous-coupled method which is based on the assumption of infiniteness of the structure.