Can a fibre be doped??
As far as I know, yes.
Polyethylene can be doped with iodine to create a conductive plastic. But the iodine tends to escape from it, making the change quite temporary.10w
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Yes; in fact, it usually is. In addition to the amplifier application linked above, doping is a common method for adjusting the refractive index of the glass used, so as to have a gradient of index from the core of the fiber to the outer layers, which makes the fiber have its guiding property. You could use entirely different glasses with different refractive index, but more often it's one kind of glass with doping materials used to tweak that value up or down a bit.10w
Doping is a universal concept appliable to any material.10w