Laser beam width distribution

Question

I have questions about laser beam width. Beam divergence aside, does a laser beam has constant beam width? Are there any (micro)fluctuations in the width? Furthermore, is there a distribution for photon number in terms of beam width? I mean something like dividing the beam for N segments, and what is the probability of finding n photons in the first, second, etc segments. Plus, if I think that photons are constantly bouncing left and right, up and down in the beam due to scattering, am I thinking wrong? I'm new to this topic, I'm not even sure my questions make sense, so any help or source would be greatly appreciated.

Answer 1

If we use the generalization of a standard Gaussian beam as a quantum field, then you would expect a measurement to find a photon at a space-time point to be proportional to the square probability amplitude. That is, measurements will be noisy when you do them away from the beam core since you get few photons, but averaged together you get a probability density that looks just like a normal illustration of a classical beam. If you measure different segments of the beam you will get Poisson-distributed numbers of photons, but since the photon rate is huge this will average together into pretty tightly a peaked normal distribution. There could be uncertainty about phase and even mode of the beam making a mixture that blurs things a bit.

Does this mean photons bounce back and forth? Not really. I think the best way of thinking about it is that your measurement queries the wavefunction "is there a photon here?" and it responds by giving you one or not (and changing itself). The photons are not in any well-defined place in this case.