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.

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.

Relatively common on motorcycles too (well, not exactly unheard of: my '86 Honda XLV750 has it, as do various recent Ducatis and BMWs.)

I had an eye operation using a YAG laser. Whatever is not transparent gets heated up and destroyed fast. The blacker the better.