Looking into the manual I did not find any information what Zemax exactly calculates if M2>1.
Best regards
Dirk
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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.
Hello Mark,
thanks for your answer.
Can you tell me on which page this is decribed in Siegman's famous book "Lasers"? Or can you tell me the name of the Siegman paper to which you relate?
From my point of view an undependency between rayleigh range and M2 does not make sense if you have aberrated (M²>1) TEM00 laser beams. Also the ISO norm which describes how to measure M² of TEM00 laser beams uses the formula where zR ~ 1/M².
Regards
Dirk
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
@Mark.Nicholson
Hello Mark,
I read your article about M2 definition in zemax, which I think is very good. 1. I try to deduce the relationship between M2 and the waist size and the waist. I multiply the formula of the waist size by M, and the result is basically the same as the result of the Paraxial Gaussian Beam Data in ZEMAX. Is my formula correct? 2. Another question, waist (in physical optics propagation) = waist size or waist (Paraxial Gaussian Beam data)? I don't really understand the difference between waist size and waist.
