i don't know what are the instruments you have. the mode dispersion measurement is the easiest way.
for step index
mode dispersion = (L n1 Δ )/c
for graded index fiber
mode dispersion = ((L n1 Δ² )/8c
where L=length of the fiber
n1=refractive index of the core
Δ= (n1-n2)/n1
c=speed of light
the change in measurement of mode dispersion gives nature of the fiber.