(Spoilers for the new movie.)
In Dune: Part One, lasguns (laser weaponry) are seen several times. The rifles used by the Fremen in the prologue exhibit multi-terawatt firepower, and the one used by the Harkonnens to attack Idaho's 'thopter cut buildings apart with ease. I will focus, however, on the one used by the Sardaukar to cut open the door in the ecological testing station. It melts through the door quickly and also vaporizes some rock on the other side.
The door appears to be about one to maybe two inches (~2.5-5 cm) thick.
Minimum value
Door thickness = 2.5 cm
Door composition = Aluminum
Beam thickness = 0.2 cm
The area that requires melting is approximately 0.1 cm^3. That's 0.00027 kg, which I will very conservatively assume is the total amount melted every second.
According to this source, the energy required to melt aluminum is 396 kJ/kg.
(0.00027)(396) = 0.10692 kJ (about a hundred joules)
Therefore, the absolute minimum output is about 100 watts. I repeat: This is not an upper limit, but a lower limit so conservative as to be almost absurd.
More realistic (but still conservative) value
Door thickness = 5 cm (this may be a little high, on second thought; calc for thinner door below)
Door composition = Iron
Length of cut every second = 20 cm
The area that requires melting is approximately 300 cm^3. That's 2.3619 kg.
Energy to melt iron is 1.28 MJ/kg.
(2.3619)(1.28) = 3.023232 MJ
Therefore, the output is about 3 megawatts. (With a one-inch [2.5 cm] door, this figure would be ~1.512 megawatts.) Note that both these are still conservative, as the door was probably made of "plasteel" or some other advanced materiel, and anyway this amount of energy would just barely melt it. Also, the volume that was melted may have been slightly larger. These factors could potentially put the figure in the gigawatts.
Was it on full power?
Since they wanted to get through the door as fast as possible, probably. Then again, perhaps not—maybe a higher setting has the risk of bringing the station down on them. However, I think we should assume it was at 100%.
The implications
This incident, and the appearance of handheld terawatt lasguns earlier in the film, demonstrates pretty conclusively that the Imperium and other Dune organizations have nuclear-reactor-level power generation... in small arms! The most powerful nuclear reactor in the world has an output of 7,965 megawatts, which means that they have some source of power that outputs around that much power and that fits inside a rifle-sized emitter!
Also, the laser system must be incredibly efficient, since an energy wastage of even 10% (90% efficiency) would mean that the lasgun is leaking kilowatts of power. Modern gas lasers struggle to reach 20% efficiency, so Duniverse laser tech is much better than ours. Even if the lasgun is 99.9% efficient, then the gun itself will still emit heat at a rate similar to a smallish space heater—and this is disregarding the far greater energy dump radiating from whatever the laser is cutting.
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