A real physical light source can never have zero size as the source here (aside from discretization issues) does. As a result, you can't get an arbitrarily narrow beam from it. There's a quantity called "etendue" that measures a sort of combination of spatial and angular spread-out-ness, and no combination of optical elements can decrease it except by absorbing some of the light.
I think this can work:
On one side place a parabolic reflector to direct the light in one direction.
On the other side place a circular reflector to direct the light back to the source. And place a tiny hole in this half circle to let the light out.
Quick drawing: http://zenphoton.com/#AAQAAkACAAEgWwAzALEBEwC0AO4A/wAAtADxAL...