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In this paper, an accurate and efficient characterization of a two-dimensional (2-D) electromagnetic band-gap (EBG) structures is performed, which exploits a full-wave diffraction theory developed for one-dimensional diffraction gratings. EBG materials constituted by 2-D arrays of dielectric rods with arbitrary shape and lattice configuration are analyzed, and the transmission and reflection efficiencies are determined. The high convergence rate of the proposed technique is demonstrated. Results are presented for both TE and TM polarizations, showing the efficiencies as a function of frequency and physical parameters. Comparisons with other theoretical results reported in the literature are shown with a very good agreement, and the authors' theory is also favorably compared with available experimental data. Useful design contour plots are reported by which a very immediate and accurate visualization of the band-gap configurations can be obtained, and design formulas are also included. Finally, the behavioral differences when a periodical defect is present are also highlighted.