# Does the beam quality factor M2 really ruin long range laser warfare in space?

After doing a lot of reading on space warfare on Atomic Rockets, ToughSF and other websites, I was almost sold on laser dominance. Sure, a continuous wave laser could be countered by cooling the hull and hinders itself with the plasma it creates from penetrating deeply, but pulsed lasers circumvent these issues neatly.

However, then I came across Children Of A Dead Earth, which is a physics simulation of space combat. Kerbol Space Programm, except that Jebediah Kerbin doesn't try to get himself killed anymore, instead he kills others with high yield rail-guns. In CoadE lasers are only viable at really short distances because apparently the beam quality factor, M2 is horrible for high powered lasers.

M2 is the beam quality factor, which can be considered a multiplier of the beam waist. So, an M2 of 5 means the beam waist is 5 times that of a diffraction-limited beam. In terms of area, this means the beam is 25 (52) times the area of a diffraction-limited beam, or 25 times as weak. As you can see, having an M2 even in the high single digits will yield beams a far cry from “perfect” diffraction-limited beams. In practice, it is not the pumping efficiency, nor the power supply, nor diffraction, which ultimately limits lasers. It is the beam quality factor. In the end, M2 ends up being the number one limit on laser damage in combat. In small lasers, M2 close to 1 is easily achieved without issue, but in high power lasers, M2 can easily reach into the millions if not accounted for. This is because generally, M2 scales linearly with laser power. Each optical component of a laser affects the M2. In particular, using a deformable mirror to focus a laser at arbitrarily long ranges (such as from 1 km to 100 km) is measured at reducing M2 to between 1.5 to 3. Problematic, but not exactly debilitating. But the main issue is Thermal Lensing (Note that this is different from Thermal Blooming, which only occurs outside the laser in the presence of an atmosphere). The heating of a laser gain medium generates a thermal lens that defocuses the beam, ultimately widening the beam waist, preventing the beam from focusing properly. Also note that thermal lensing actually occurs in every single optical component of the laser, though it is strongest in the lasing medium. Thermal lensing increases M2 roughly linearly with input power. This means if you have 1 kW laser with an M2 of 1.5 (which is reasonable), this means dumping 1 MW into that same laser will yield an M2 of about 1500.

Other sources only discuss the diffrection limit, meaning a perfect laser and then they call it a day. M2 actually seems to mean that a more powerful laser will perform worse than a less powerful one.

M2 can apparently be fought by cooling the laser (which means even more radiators) or making it physically bigger (more mass). None of these solutions are great.

Does this really ruin the long-range death-ray, continuous wave or pulsed beam?

• I have never played CoaDE, but I have read the game boards for ideas. Apparently, although lasers were intended as short ranged weapons and point defenses, they are considered extremely dominant in the current meta, with laserstars (ships that sacrifice everything to mount the biggest possible spinal laser) being considered most effective, simply because of their massive range. Sure, the beam loses energy quickly, but if you use a big enough laser, it will kill enemies with railguns before they have any chance of hitting you. Oct 18, 2019 at 21:40

CoaDE was made with a lot of pretty pessimistic assumptions about laser technology. That's resulted in an interesting space combat simulation. The assumptions they've made aren't wrong, per se, but in order for them to be present in your fictional future too, you have to assume that laser technology has barely progressed from the present day.

Now, I Am Not A Laser Scientist But...

$$\mathrm{M^2}$$ scales linearly with power due to thermal effects within a single laser. As you crank that laser up, even with a fixed and high efficiency, some proportion of the power it is developing will turn to heat, and the heat will affect that laser in some way. More power, more heat, more bad. Pretty clear cut.

However.

This is only a problem if your laser cannon is driven by a single massive laser. There are two obvious solutions to this.

1. Use a whole bunch of low-$$\mathrm{M^2}$$, low-power lasers and combine their beams.
2. Use a laser that's not subject to these kinds of thermal effects, such as a Free Electron Laser.

I'm not going to go into option 2 here, but be aware that it is a potentially practical solution to this problem.

CoaDE only has incoherent beam combining, and the creator sensibly observes that it isn't very useful, making option 1 basically uninteresting within the game. That's not the case in the real world, though.

The current state of the art laser "weapons" use fibre lasers. The maximum power of an individual fibre laser is limited in various ways, and one of these is that you want to keep the power down to stop these troublesome thermal effects you've mentioned. For military use, you clearly need All The Power. This was solved by firing a whole load of fibre lasers into the same optics, chucking out one single high power beam. Early designs used incoherent beam combining and had terrible beam quality (lots of interfering out-of-phase beams do that). News designs use spectral beam combining. This uses multiple frequencies of lasers, which introduces its own problems (it requires more complex optics, for example) but has significantly improved beam quality whilst increasing power. There's another option which performs coherent beam combining on multiple beams of the same frequency. This is quite difficult, and the technique is not used in industrial or military settings, yet.

In the future, having a bunch of phase-locked lasers which can be cleanly combined into a single high-power, high-quality beam is clearly the way to go. Phase correcting optics or other techniques could be used to synchronise them. The individual emitters might be diode or fibre lasers or something else that forms a super-futuristic high power optical phased array, but none of this is science fiction. This stuff is very much an area of active research, and it will come in due course. Only when we do is it worth taking the scare quotes off laser "weapons".

• THANK you. I've been hearing this "you can't use lasers because diffraction" all over the place and found it a bit... whiffy... but didn't understand the physics enough to challenge the idea. Now I understand where the flawed assumption is. Oct 18, 2019 at 14:11
• Thanks. So these fancy low arrays will still not produce a perfect diffrection limited laser, meaning we will still have a non-1 M2. Can I calculate this array as one single big laser? Would assuming an M2 between 3 and 20 for such a design be reasonable? Oct 18, 2019 at 14:29
• @TheDyingOfLight I don't know if you can realistically get perfectly diffraction-limited laser beams without an optical phased array, but if you can, a bunch of emitters that are all in phase would be able to do it just fine. You can indeed treat the array as one big laser. I have no idea what an $\mathrm{M^2}$ would be, as I'm not a laser scientist, so your guess is as good as, and probably better than mine ;-) Oct 18, 2019 at 14:43
• Don't the lasers used for laser fusion do something equivalent to coherent combining? They're all triggered by a cascade from a single trigger pulse, so as long as the optical paths are coherent, the beams are... Oct 18, 2019 at 18:18
• @ZeissIkon there's more magic you can do with ultrashort pulses, I believe. Maybe I could mention that, but it seems a bit out of scope, as I think its a tricky technique to weaponise (quite low efficiency, for a start). Oct 18, 2019 at 18:34