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For calculating the mean power at a specific cross section of a waveguide, one can calculate the mean value of the temporal function of Poynting Vector, P(t), where P(t) is the ExHy-EyHx. Note that I am not talking about phasors or a sinusoidal state. If I integrate over the waveguide cross section and take the mean value over time, I simply obtain the power output. I notice that the P(t) is oscillating with double the frequency of the frequency of each field, and that's normal. If I take the fourier transform of P(t), I will notice a Peak at the double frequency. How can I relate this to power/frequency term if I want a gaussian modulated time function instead of a plain sine? Can I divide with 2 to obtain the "correct" frequency? Of course this is required to calculate the reflection coefficient of a structure as Pout/Pin as a function of frequency, but this double frequency somewhat confuses me