Single-mode, multi-mode, etc. All fibers. Let's use my LASER marker at work as an example. Divergence in that fiber happens AFTER two things happen - first the photons need to leave the fiber,then they have to cross-over their 'hip' (where the collimated beam is tightest) THEN they diverge.

That's how fiber LASER markers work. I'm the operator of them where I work (I do everything outside of SMT - x-rays, LASER marking, high-voltage testing, etc.) Every LASER coming out of that fiber hits focal point about 2 feet past the fiber, where it begins to diverge.

Do not trust a LASER coming out of a fiber to be unfocused or not have enough power density to blind you. Period.