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Image from Wikipedia on Gaussian beams.

I'm trying to understand how Gaussian beams interact with matter. Maybe I have a conceptual issue, but is the beam in the image not propagating in the z direction? In that case, I want to understand what happens to the beam if it enters a new medium at say z = -2 (where z=0 at beam waist).

Specifically, I'd like to know how to calculate the new beam waist position of a Gaussian beam once it is enters (at right angles) a medium of different refraction index. Say I know width of the beam at the surface of the medium, how do I find out where the new beam waist is?

I've tried to apply the ray transfer matrix [1 0; 0 n] to the beam parameter transformation, but I don't get any new information from that. It seems reasonable to me that the new Rayleigh range would simply be multiplied by n - but why would this be the case?

Any help would be appreciated!

Thank you!

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  • $\begingroup$ I think I don't get your question. You ask about the refraction angle of a (Gaussian) light beam, which falls normal onto a flat surface. Is that right? $\endgroup$
    – NotMe
    Commented Jul 12, 2017 at 17:54
  • $\begingroup$ Hi there! I don't mean the refraction angle, but rather the position of the beam waist in the new medium. $\endgroup$
    – user6922607
    Commented Jul 13, 2017 at 18:30
  • $\begingroup$ If a beam falls orthogonal onto a surface, why should it form a focus point? This is impossible by symmetry. So I'm not sure, whether or not I understand your question. Could you please clarify it. $\endgroup$
    – NotMe
    Commented Jul 13, 2017 at 18:42
  • $\begingroup$ Hi, thanks for the comment! I've tried to edit the question to make it more clear. Does it make sense? $\endgroup$
    – user6922607
    Commented Jul 28, 2017 at 20:14
  • $\begingroup$ After editing your question, I finally understood it. You have a lens which focuses a Gaussian beam and you want to know what happens, if you put a flat object in the beam path in front of the focal point. I have never done this, but I guess your suggestion is correct: Use the transfer matrix method (ABCD-matrix) for the Gaussian beam and just put a second think lens with radius $R\to \infty$ in the beam path. The Rayleigh length should become shorter, because Snellius law effectively focuses the beam. $\endgroup$
    – NotMe
    Commented Jul 29, 2017 at 10:22

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Look at chapter 4 here, though some details of the derivation are not completely clear to me https://s3.cern.ch/inspire-prod-files-f/fd149f5c80b07118f03732f683bd7ee5

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