Does the speed of light transmission in an optical fiber change with the refractive index of the surrounding material? I am learning about distributed fiber optic sensors where properties along the cable can be continuously determined, eg. temperature from Raman backscatter shift at a resolution of ~0.1 C at ~1 m intervals over ~ 10 km. If I understand correctly the location is determined from the return time of the laser pulse.
My question is whether this return time (or maybe the intensity) is affected by the refractive index of the material outside the fiber and if that effect can be measured?
 A: The fiber optic core's refractive index will change the speed of the transmission of the wave packet (the rate of information delivery) with the relation $\frac{1}{n}$. The cladding of the fiber will not in any way effect the speed of light transmission in the fiber. It will, however, change the intensity coming through the far end of the fiber. This is because different refractive indices of core and cladding will result in different critical angles, through which light is totally internally reflected. The equation for this is $\sin(\theta_c) = \frac{n_2}{n_1}$, so if there is a large kink in the optical fiber, or if there is a large incoming angle, or if there is a mode scrambler in the line, or for any number more reasons, the critical angle could change and more light could be refracted out from the fiber. If light is being refracted out of the fiber, it can be measured by measuring the incident light and the transmitted light, and then, by inference, the difference must be the light lost.
tl;dr intensity dropoff would occur and can be measured, there will be no speed difference.
A: The structure of the optical fiber will determine whether or not the refractive index of the outside medium can affect the transmission speed or absorption of an optical signal in the fiber.  If the fiber has no cladding, or thin enough cladding that the evanescent wave extends substantially (e.g., a few tens of nanometers) into the outside medium, then the properties of the outside medium can certainly affect the signal transmission.
A good way to measure the effect is with an interferometer.  Split a laser beam into two beams and run one beam through a length of the optical fiber being tested.  Bring the two beams back together with a beamsplitter and locate an interference fringe.  Vary the properties of the medium surrounding the fiber and track any resulting shift in the fringe position.  Any transmission speed difference will be directly proportional to the shift in fringe position.
