This article presents a theoretical characterization of the regular polygonal waveguide (RPW) having n-sides. Based on the symmetrical circular symmetry of the RPW and the circular waveguide (CW), the analogy between the electromagnetic (EM) behaviors of these to waveguide (WG) is established. After a brief recall about the state of the art concerning the WG engineering and its application, we introduce a basic theory of the WG presenting a regular polygonal cross-section with n-sides. By considering, the fundamental mode TE11, we develop the main mathematical formulas summarizing the different characteristics (cut-off frequency, fc, propagating constant, k11 and S-parameters) appropriated to any RPW in function of its physical parameters (number of sides, n, diameter, D and height, h). In order to verify the validation of the developed analytical expressions, comparisons between the HFSS simulated and theoretical dispersion diagrams of regular pentagonal (n=5), hexagonal (n=6), heptagonal (n=5) metallic (copper) WG with for example, 50 mm outer diameter are presented. So, it was demonstrated that very good correlation between the theoretical predictions (fc(n), k11(n)) is found with a relative error less than 1%. As application of the present study in terms of EM wave shielding, simulation of metallic wall with hexagonal aperture is also performed. Finally, discussion about the future work is drawn in conclusion.
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