What physical mechanism causes the smearing. I've searched breaking indexes, but found nothing.The maximum frequency of the light pulses that aren't smeared in such a way that one cannot retrieve the original light pulses any more basically.
Of course this is dependent on the construction of the light guide (it is all about breaking indexes), length and used light color (wavelength).
Then you need to have a driver than can switch a LED, VCSEL, FP or other type of laser on and off in a quick enough and a detector that is fast enough (followed by an amplifier with enough bandwidth)
The only thing I can think of would be different path lengths through the fibre - eg some light reflecting multiple times at smaller angles along the lenght/sides of the fibre, and others going straight or fewer reflections at wider angles.
Though at the speed of light I'm struggling to believe this can be significant compared with the pulse time.