> Do we actually have a method of propulsion apart from rocket fuel?
There are several alternatives (solar sails, tethers, nuclear), but the engineering details are yet to be worked out, and all of them still ultimately depend on the same principles as rockets: something has to go in the opposite direction for the vehicle to accelerate.
The idea on solar sails is that they don't need to send something in the opposite direction, they steal momentum (vectored in the travel direction) from the gases and/or photon radiation emitted from the Sun.
There are several alternatives (solar sails, tethers, nuclear), but the engineering details are yet to be worked out, and all of them still ultimately depend on the same principles as rockets: something has to go in the opposite direction for the vehicle to accelerate.