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So I conclude as following:(please point out if I’m wrong )
At each z point the Power in path= (power in the waveguide)/(power in the all transverse mesh)
At each z point the Relative Power= (power in the all transverse mesh at z )/(power of input field )

I’m still confused about Power overlap integral.
1.What dose the numerator and denominator mean in the formula of picture “POI.png”?
2.If the reference field is the input field, what’s the difference between Power overlap integral and Relative Power?
3.What does people usually use for with the results of Power overlap integral?