If you look at CO2 lasers, at 40W ($350 on eBay) you can cut plywood, at 150W ($5000 on eBay) you can cut metal. Both of those are 1040 nm.

The 450 nm modules you can get up to 5W ($100 on eBay), but those can hardly cut anything, they're more like engravers.

CO2 lasers are typically at 10.6 microns. They can cut metal but you need at least 100W and RF pumping. Metal-cutting lasers are more commonly fiber lasers with wavelengths of ~1050nm.

That's just straight up energy transfer. Doesn't matter exactly what wavelength you use provided you dump enough energy in, and this one is so inefficient it doesn't make sense.

“ is it more affective in cutting / etching these materials with a lower optical output power.”

Probably because it’s more likely to be absorbed.

On the other hand, absorption can’t be > 100%. So a longer wavelength laser an cut just as well for the same power as long as the mtls absorbs all the photons