It's a much lower number than I expected, probably because in sci fi it's never a signalling laser, it's always a launch laser and that's a whole 'nuther animal. FUN FACT - disturbing portions of the historical record thinks Sirius was red. There are two real ways to resolve this: (1) presume that the historical record, as evidenced time and time again, is faulty (2) presume that the Sirians were pointing a launch/signalling laser at us for a few hundred years back in antiquity. (2) is a lot more fun and could be the impetus for a pretty fun sci fi conspiracy tale, or so I've heard. Or, if you're Larry Niven and Jerry Pournelle, you take the idea and throw it in the distant future at a completely different part of the galaxy so that your social commentary doesn't have to include people. 100MW is chump change. I've worked with powerplants that big. You can buy them on Alibaba. Which leads me to believe that divergence is more important than we're accounting for but I'm too lazy to do more than throw some numbers at an online calculator and watch it choke on the light years.
Do remember that we're discussing a case of illuminating Earth (and only Earth) with some dispersionless, cylinder-like, 100% efficient laser beam with perfect accuracy. Even then, with those idealisations, power scales with the square of the radius of the thing we want to illuminate. Accuracy is also fun: in our case, it's like pinpointing something roughly the size of a credit card on the surface of our Moon, but without the joys of 4.3 years worth of one-way delay or tracking a moving object. Also, I didn't say that divergence isn't significant. Just that it likely won't involve higher maths to find an approximation, which is semi-true. Had to do a double integral over a disk to get from intensity [W/m²] to power [W]. Here's how we can calculate the power delivered by a Gaussian beam, and it's ripe for plugging numbers in. I took the formulae and symbols from the article. There's also a calculation of how narrow the beam would have to be at its narrowest point, which turned out to be essentially zero (which I, perhaps mistakingly, interpreted as equivalent to a point source). Pinging am_Unition for peer review and help in moving it forward. It's not pretty, though. My initial intensity assumption goes asymptotically to infinity the narrower the beam, so there's possibly a problem/fuckup. I absolutely encourage everyone to play around with the numbers. Maybe it could work for other wavelengths?