Hey Dirk,



This is an old discussion that has gone on as long as we've had this feature. The problem is that M^2 defines how much larger the beam size is compared to the embedded beam. Whether that size increase is due to the Rayleigh range changing, or the beam divergence changing is not stated explicitly. You can scale both of them by M, one of them by M^2, or one by any number and the other by its reciprocal times M2. 



What we do in the code is defined in the documentation:







In other words, we scale the beam size and divergence angle by M. We chose that because beam size and divergence angles are the most commonly measured parameters, but it is inherently ambiguous as to what is 'really' changing.

Hi Dirk, 



Allow me to jump in here for Mark. I just did a little digging on this, and I believe that the paper you'll want to take a look at is "How to (Maybe) Measure Laser Beam Quality," from OSA's 1997 Annual Meeting. The section of interest should be "The 'embedded gaussian' picture." I couldn't find anything nearly as explicit in Siegman's Lasers.  



Siegman does identify some "Practical Problems with M^2" in the above paper, so I'd be interested to hear your additional thoughts on your comments about the Rayleigh range and M^2 above. Did you mean "independency" here?



Cheers,

Nick