Notice removed Reward existing answer by Emilio Pisanty
    Bounty Ended with The Photon's answer chosen by Emilio Pisanty
    Notice added Reward existing answer by Emilio Pisanty
    Bounty Started worth 200 reputation by Emilio Pisanty
    Tweeted twitter.com/StackPhysics/status/775715672575844352
    Question Protected by Qmechanic
2 edited tags
| link
1
source | link

How well can a laser be focused over interstellar range?

I try to read up on diffraction limiting and gaussian beams, but it always gives a result saying it’s characterized by an angle which is the edges of a cross section of a cone. Which says nothing on the physical limits of how I choose that angle. It just describes (once far away from the narrowest point) the shape of a cone: width is proportional to distance from the narrowest spot.

So what’s to prevent you from describing a laser that's arbitrarily tight, at some arbitrary distance, and learning that the required angle is very close to 0?

What, in principle, prevents this from happening?

In Robert L. Forward’s “hard science fiction” novel he based the lightsail description on actual research but did not go into detail in the novel. As a plot point, the senders had to enlarge the size of a focusing device (probably a zone plate) to send the beam for breaking, so the larger sending aperture was necessary for a longer distance. Now they didn’t finish in time due to funding but saved the mission by doubling the light frequency instead. So that sounds like a diffraction effect.

I suppose the relationships of what is possible is simply scaled by wavelength, and once you divide that out there is some relationship between the possible size of the emitter, size of the target, and separation between them? Why does making the emitter larger allow the target to be smaller?

To use some concrete numbers, suppose the target is a lightsail 1 light year away, and it is 1 Mm in diameter. The wavelength in Forward’s story was green light, and if higher frequency allows better focus than the best beam would be the highest frequency that doesn’t start causing issues by breaking bonds in the atoms reflecting it, so just past visible where UV begins. What size emitter (final focusing device) would be needed?