Optical design: BPP beam parameter product M^2 and beam expander

[newshurik]

We work on optical simulation where we use not ideal beam expander.
Not ideal means that for beam expander designed for single mode (M^2=1), the output beam has M^2 >1 (M^2 = M squared)

In our system we want to use beam expander with multimode laser beam.
The beam expander is not ideal (for example M^2 after beam expander is 5 instead of 1).
What will be M^2 of the output beam if the M^2 of the input beam is 30: 30+5 OR 30*5 ?

Of course M^2 is not well defined parameter, what is important to us is to understand the phenomena in this case.

I hope I am in right place :-)
Thanks!

 

[UltrafastPED]

M^2 is a property of the beam, not of the optical elements.

Are your beams Gaussian, or something else?

You can find basic details here: http://www.rp-photonics.com/m2_factor.html
and more general: http://www.rp-photonics.com/beam_quality.html

Melles-Griot has some has some Gaussian formulas which include M^2:
http://mccombe.physics.buffalo.edu/lab-manuals/MG-GaussianBeams.pdf

Look for "M2 AND THE LENS EQUATION"

 

[newshurik]

In real world real lenses (and also optical systems) increase M^2 parameter of the laser beam.
We know how beam expander affect on Gaussian TEM00 (single mode or M^2=1) beam. We want to predict how same beam expander will work with multimode (high M^2) laser beam.