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In this paper, an interesting phenomenon is revealed in the finite difference time domain (FDTD) simulation of a Gaussian pulse propagation in a rectangular waveguide. It is found that when a Gaussian pulse is used in a rectangular waveguide, an electric field peak will occur at the cutoff frequency of the dominant mode of the waveguide even when the FDTD simulation is implemented in the absence of nonlinear material. It appears that the spectrum power at the zero frequency of the Gaussian pulse is transformed into the spectrum power at the cutoff frequency of the dominant mode. The cause is investigated, and an explanation based on the Poynting theorem is presented.