No matter what lens is put in the beam path of a Gaussian beam, it will always go through a waist of non-zero width.
Why not just a point? I know the maths, I'm wondering whether there is any physics that prevents it.
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While I concur that you may use the uncertainty principle to understand this, it isn't necessary. If you have a classical EM field that's governed by the nice wave equation derived from Maxwell's equations, then you can compute a diffraction integral that tells you that you must have a finite waist, even if the far-field divergence is very large.
Why not just a point?
Uncertanty principle I guess. In a point focus, the momentum would be defined with a finite $\Delta p < \infty$ (either I guess you can relate it to the lens numerical aperture in a purely geometrical picture where all rays wave-vectors coincide in the focus, or you take $\Delta p=0$ if you consider that the waist of a gaussian beam has a plane front). In any case, because $\Delta p \Delta x \ge$ constant, problems arise with a finite $\Delta p$ ,as the position would be perfectly defined ($\Delta x=0$).