But what is the nuts and bolts of how it is done? What do you capture the light with? How are you propelled? Are we talking solar panels or sails or some other technology?
You first emit the photon towards the black hole, momentum gain. Absorbing the photon on the return would be a two-fer, and reflecting a three-fer.
You emit photon 1. It has momentum m. It comes back blueshifted, so you get momentum km, with k > 1. You reflect that back, and you get momentum k^2m...
It's not that simple, because as you start to move away, you redshift the photons you reflect. And the alignment issues are going to be pretty severe. And if you get too much compound interest, the photons may be blue-shifted enough to kill you or damage your ship. Still, the idea is pretty slick.