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Waveguide power

Waveguide power

Waveguide power

(OP)
Hello,

I am not an electrical engineer, so please be patient with me.
I'm trying to simulate a waveguide with a dielectric material load. I've set a source power of 1 W. The waveguide cross section area is 84 cm^2
If I plot the electric and magnetic fields along the cross-section of the waveguide, it looks like this:


In order to calculate the power of the field (to verify that I indeed have 1 W), I multiplied the power density (which I got by multiplying the electric field by the magnetic field and dividing by 2) by the waveguide cross-section area. But I had to divide by 2 again. My question is:
Why do I have to divide by 2? Why doesn't 0.5*(E*H)*Area give me the correct power?

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