Once it got to where it was going, how did it 'slow down' ?
The same lasers can be used to decelerate the spacesship as well.
Forwards separable sail concept used for deceleration, from his paper Roundtrip Interstellar Travel Using Laser-Pushed Lightsails, Journal of Spacecraft and Rockets 21 (1984), pp. 187-195. The paralens in the image is a huge Fresnel lens made of concentric rings of lightweight, transparent material, with free space between the rings and spars to hold the vast structure together, all of this located between the orbits of Saturn and Uranus.
So granted, this concept requires that we have the capability of constructing a thousand mile wide structure in deep space.
But that's just a minor engineering issue. The math works, it seems. :-)