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The full-wave analysis based on the singular integral equation method is developed to correctly investigate dispersion properties and field distributions inside a rectangular waveguide grating used in low-voltage traveling wave amplifiers. Simplified treatments of periodic structures with rectangular grating are widely used in the analysis of microwave electron beam devices, providing an actually good accuracy for the calculation of dispersion curves of natural modes in a wide range of grating parameters. However, they do not guarantee the correct field distributions in a close proximity to the grating just where an electron beam is usually passed to get more effective beam-wave coupling. The amplitude of the minus-first spatial harmonic, which is mostly responsible for the resonant beam-wave interaction, can be substantially larger than that predicted by the simplified analysis. In addition, the contribution of the higher spatial harmonics to the total field is shown to be significantly larger than that evaluated from the simplified treatment. Consequences of the enhanced influence of higher harmonics on beam-wave interaction are discussed.