If we know the center electric amplitude E0 of a Gaussian beam as shown in the equation below. We can calculate the beam power according to the equation shown here.
The power can be calculated by integrating the Poynting over a incident surface.
I =<S> = 1/2 (E x H)
I =<S> = 1/2 (E x H)
Then the final power is:
The beam intensity at center of the beam is
So the relation between the power and center beam intensity of a Gaussian beam is: