It seems to me like that kind of concentrated power would be capable of vaporizing any small particles (or even turning them into plasma briefly) in the way.
Maybe, but they say that it's focused in the center of the chamber because that's where you want ignition to start. In that case, you might not have that high flux at the entry aperture (you might not want this for other material reasons, too). In any case, I don't think you want to start combustion at the edge because that's the least efficient place to do it.
Maybe the beam is wide enough before it is focused so that the soot wouldn't block enough of it to be a problem before the soot is blown out of the chamber.
No. But I only intended to address the point that if the beam is focused in the center then it would take more than a speck of soot to block the wider, lower flux, defocused beam where it enters the cylinder.
Carbon has a very high melting point, never mind boiling point. If you would heat it up that much you would melt the optical port.
However, you can simply heat the carbon (all that energy has to go somewhere). Once it's hot enough it can burn in the chamber - and it would probably be hot enough to ignite the fuel as well.
That said, I don't think soot is that common anyway. Normally you run lean which prevents soot. It does need to be able to self clean, but occasional poor efficiency from soot should not be common enough to hurt.
