Does a laser beam converge and diverge without lens? In the case of $TEM_{00}$ mode laser produces gaussian beam. I read in wikipedia that it converges till some point called 'beam waist'and then it diverges to infinity.
If there is a lens placed along the beam, then it converges to the focal point of lens and then it diverges. Here the beam can't converge to a single point but has a non-zero width.


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*Is it because of the Hesienberg uncertainty principle that $\Delta x$ becomes zero which further implies $\Delta p$ tends to infinity?
And the momentum can't be infinite, so it doesn't get focus to a single point. Am I right?

*I read that it happens even without a lens. How does focusing of beam happen without lens?
 A: On point 1, you are correct.  The uncertainty principle leads to the finite spot size when focusing a laser beam and the spread of the beam thereafter.  In general, in order to produce a smaller spot, you need to focus the beam in at a high angle (short focal length lens), meaning a larger spread in transverse momentum of the photons.  The same thing can be said for imaging optics.  In order for a microscope to look at a small object, you need a short focal length microscope objective that can collect light at a high angular spread.
As for point 2, "focusing" of a laser beam without a lens can happen due to some non-linear effects if you are at very-high intensities in some type of medium (air or otherwise), but that is a different subject all together.  However, spreading of a laser beam is an inherent property of the beam due to the uncertainty relationship as well.  Because the laser has a finite spot size, it must also have a spread in the transverse momentum.  This means that as the laser propagates, the beam will in general expand.  The far-field angular divergence (full angle of the "cone" of the beam) is given by (for $TEM_{0,0}$):
$\theta = \frac{2\lambda_0}{\pi n w_0}$
where $\lambda_0$ is the wavelength, $n$ is the index of refraction and $w_0$ is the waist size of the beam.  You can see here that the divergence angle is inversely proportional to the waist size of the beam, $w_0$.  For larger beams, there is less divergence.
