Laser Cutter Power/Wavelength to Cut Paper I've been reading up on laser cutting and it seems that 808nm at around 2 watts is typical to cut paper. How would one calculate the wavelength and power required to cut an arbitrary material?
 A: Here are some of the relevant bits of physics/questions to ask:


*

*To cut a material, it needs to absorb heat faster than it can lose it.

*heat is conducted away: this is typically linear with temperature gradient

*heat can be radiated away: this is more important at higher temperatures (follows $T^4$ relationship)

*laser power may be reflected or absorbed: the right wavelength will be the one that is "mostly absorbed" and will depend on the material.

*the mechanism for "cutting" matters: is it melting, burning, or enhancing a chemical reaction (etching, oxidation)

*does the cut have to be very small (narrow)?

*does the surrounding material deform if it gets hot?

*how many meters of material do you want to cut per unit time?


Based on the above considerations it is hard to give a general "formula" for the power and wavelength. I would say that higher power means you can cut faster - which in turn means that you can make a narrower cut without heating up the surrounding material (it didn't have time to heat up). This is also a cleaner cut. As for the wavelength - typically you will use a laser that can efficiently generate a lot of power (CO2 laser can have efficiency up to 20% but a longer wavelength, around 10 µm), and that is well absorbed by the material. You also want to be able to focus it to a small spot - both to increase the power density and to make a fine cut. The longer the wavelength, the harder it is to focus something because of diffraction...
A: Aside from the "it's complicated answer," there's also the "check for prior experimental research" answer. Without digging into it very far I used one trick. I found this Wikipedia article on Laser cutting and clicked ctrl+f to search the document for 'paper' and came up with this hit: 

CO2 lasers are used for industrial cutting of many materials including
  mild steel, aluminium, stainless steel, titanium, Taskboard, paper, wax,
  plastics, wood, and fabrics.

So if I were building a paper laser cutting apparatus of some kind I'd search further to see what co2 lasers were capable of, and perhaps experiment with building one.
