Determining beam intensity
In the article "Any color you like," which appeared in the April issue of Industrial Laser Solutions, the author states that a beam with an M2 value of two will give a focus spot diameter of two times that of a beam with an M2 value of one.
I believe that the correct change in spot diameter for a beam with an M2 value of two in comparison to a beam with an M2 value of one is actually increased by a factor of M or, as in the above stated case, by a factor of the square root of two, thus resulting in a change in intensity by a factor of two. In this case, the intensity for the beam with an M2 value of two actually has intensity equal to one-half that value for the beam with an M2 value of one.
Larry Marshall responds
The mm-mrad product of any beam is a constant depending only on M2 and wavelength. If you put two beams of the same wavelength through the same optical system, then they have the same diameter and divergence, so the ratio of their beam waists w'/w = M2. So a beam with M2 of 2 has twice the focal spot size and 1/4 the intensity, precisely as stated in the article.