I have the following statement which I don't know how to explain:
Suppose I have 2 identical monochromatic waves (same intensity and phase) shooting into the same receiver. If each wave's intensity is I, based on energy conservation I would expect the 2 waves together will bring a total intensity of 2I. For example if each wave carries 100mW power, I'm expecting a 200mW total power on the receiver side.
However the summation using phasor gives a different result: if we consider that intensity is proportional to the square of wave's amplitude, the square root of 100 gives 10 for the amplitude of 1 wave (for simplicity I use 10 as amplitude which included the constants), adding the other wave of the same phase which gives 20 as amplitude of the new beam, then square it to get intensity which is 400mW instead of 200 in the above example.
If we keep going by summing 4 50mW waves with the same convention, we get (4 x sqrt(50))^2 = 800mW ... which the logic is obviously not correct.
My ultimate goal is to sum up power of beams with different intensities and phases. Phasor addition works great if I have amplitude and phase, but when I try to use intensity to get wave's amplitude I got the above dilemma. Could someone point out where my logic go wrong, and please explain the way to do power summation with intensity and phase known for each wave? Thanks!