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In this paper, an accurate and efficient characterization of two-dimensional photonic bandgap structures with periodic defects is performed, which exploits a full-wave diffraction theory developed for one-dimensional gratings. 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 wavelength, incidence angle, geometrical and physical parameters. A comparison with other theoretical results reported in the literature is shown with a good agreement. The transmission properties of photonic crystals with periodic defects are studied, investigating the effects of the variation of geometrical and physical parameters; design efficiency maps and formulas are given; moreover, the application of the analyzed structures as filters is discussed.