Re: "The detached sail will accelerate but the probe will decelerate"
"The idea is only to detach one part of the sail. The laser will still hit that part and accelerate it further. But the laser is being reflected from the detached part and hits the probes remaining sail from the front, which decelerates the probe. But this would be a highly complicated stunt given the differences and the communication latency of 12 years. You could just pre-program the procedure and fire the laser at the right time (six years earlier) in the hope that everything is where is should be. And this simple calculation doesn't even include relativity, which will already play a big role at 0.2c,"
I get the idea. I just think it's stupid. First, the laser hitting the detached sail will push it forwards and the probe backwards (assuming it works), so the sail will need some sort of power of its own to continually readjust the focus of the reflection. Second, we'll worry about how narrowly focused the laser beam needs to be to hit a single object (and not the probe's sail) from six light years away, sent six years ago based on where you think the probe will be. Then, as you say, the fact that you've already pushed the probe to 0.2c makes slowing it down harder as it's now heavier.
This is why I suggest chucking the whole sail and everything else you don't immediately need out the front, or equivalently just firing the whole recording equipment out the back of the probe when you get there would decelerate it more. If it's going at 0.2c, I reckon that will get it down to about 0.19999c, maybe a bit more. Which is still better than the sail detachment idea.
Also, suppose you can accelerate a 1kg probe to 0.2c in six months of laser shining. I reckon that the power requirement is 0.2^2c^2/2/180/24/3600 (0.2^2c^2/2 is the kinetic energy of the probe), which means the laser needs to be about 1GW in power, after heat loss from the atmosphere. And that ignores relativistic effects: both special and general. (The special effect is the mass of the craft getting heavier, so we need to add that into the calculation. The general effect is the loss of power due to gravity on the laser itself, as it will still have to leave the Earth's gravity well. You can build a space-based laser, but on order to harvest 1GW from the sun, well, it's going to have to be big. Something like 3-4sq km.) Chinny reckon.