Weird. You'd need a three-dimensional soliton for that I guess, since the beam is unguided. Is such a thing possible? Some sort of nonnlinear self-focussing maybe. You'd think that conservation of lateral momentum would prevent a free beam and a light wave from constraining each other. Seems weird to me.
One further advantage, which I don’t yet see mentioned, is the likelihood that such a low-divergence system lends itself more readily to the Q-amplification scheme of Bae, whereby the available motive power of the beam upon the target may be multiplied manyfold by consecutive reflections from both source and target mirrors.
There are two conditions: (a)If the gain medium is not between the mirrors, then it is a laser shining on a resonator, and it is no different from a laser shining on a mirror. I don't think that is what was proposed
(b) If the gain medium is between the mirrors it is an ordinary Fabry-Perot interferometer laser cavity and of course there is a force on both mirrors. The problem is to keep them aligned to the accuracy required for resonance. To achieve this you need the kind of suspension and pointing accuracy of the LIGO experiment. There has been a short range interferometer demonstration in space that this can be done, but doing it on the scale of mirror you require for propulsion seems a very long shot to me.
The other problem is coherence time. If the propagation time around the cavity is longer than the coherence time of the laser transition, you won't be able to establish coherent oscillation. That will affect your beam quality, which you need for the collimation.
All clear on the Q-amplification idea. I imagine the relative parallel alignment of the mirrors over a path length of many AU is, as you mention, practically impossible. I believe eLISA is expected to work with a path length of 1 million Km, which is only about 0.01 AU.
Just to be clear, it was I who mentioned this idea. It's not in the actual proposal (see link here).
Next we will learn that it is possible to use the beam for braking, by reflecting it not back to the origin, but rather reflecting it forwards in the direction of travel.
Well sure. You just take the incoming beam from earth and amplify it with your on-board laser, powered by the beam from earth, and squirt it out the front at a higher intensity. Simples.
Well in theory yes, but whether a) it can be made to work within a reasonable mass budget, and b) whether the resultant braking force is large enough to be useful - are unknowns at this point. But generally there has to be some sort of braking effect because of momentum conservation.
Limbach in the latest post describes the beam tightening as akin to optical tweezers.