Not an optics expert but I consult for a company that makes lasers. Afaik not currently possible. The beam divergence is only one of many limiting factors
I just recently watched a great video explaining how lithography machines push the limits of what's possible: https://www.youtube.com/watch?v=rdlZ8KYVtPU&t=1151s
Note that the best ASML machines can eke out an improvement on the order of a factor of two at best, not two thousand, which is what would be likely needed to power space probes at light-year distances.
https://en.wikipedia.org/wiki/Gaussian_beam#Beam_waist
the divergence angle is inversely proportional to your aperture diameter
https://en.wikipedia.org/wiki/Airy_disk
in theory by putting a bunch of laser emitters in solar orbit and operating them as a phased array you can make an aperture the size of the solar system. 1.22λ/d at, say, 400nm and 2 astronomical units of diameter is about 1.6 attoradians of divergence; at a radius of 4.3 light years (the distance to proxima centauri) this works out to an airy disk focal point of 66 microns. optical phased array lasers have been demonstrated https://en.wikipedia.org/wiki/Phased-array_optics but nobody knows how to make one out of satellites yet
i've only glanced at the proposal https://arxiv.org/pdf/2309.07061.pdf and they're proposing 4.1-meter-diameter 3.6-gram probes, which would allow you to use a phased array about a million times smaller, about 5 million km, 13 times the distance to the moon. i don't see where they're proposing how they propose to beam 100 gigawatts onto the probes so i don't know if this is their proposal
dispersion, by contrast, which means wavelength-dependent indices of refraction, doesn't affect lasers and doesn't happen in a vacuum; probably the person who mentioned it was using the wrong term by accident and meant divergence
If you put 100 gigawatts on a 4.1 meter diameter very thin reflector, you're going to melt it. That's 10 gigawatts/square meter. Most of the light misses the targets.
> i don't see where they're proposing how they propose to beam 100 gigawatts onto the probes so i don't know if this is their proposal
A phased array on Earth, several kilometers in scale.
> but nobody knows how to make one out of satellites yet
Probably no one ever will make a huge (solar system scale) coherent power transmission system out of satellites, because of the thinned array curse-- https://en.wikipedia.org/wiki/Thinned-array_curse
It would be cool if we made a very large scale telescope, where a sparse array is less of a problem.