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Learn more about Fiber Optic Cable:
Graded index (GI) fiber is made with a range of materials in the core which are chosen to minimize modal dispersion caused by different path lengths of different modes being transmitted down the fiber. The core index profile is curved - a parabola to be exact - with lower index glass on the outside of the core. The lower index glass transmits the higher angle light rays (called high order modes) faster than the lower index glass near the center of the core.
GI Fiber animation
The index profile of the core of multimode GI fiber is not continuous, which is hard if not impossible to manufacture, but is in steps, from hundreds of steps to thousands depending on the fiber design and manufacturing process. As a mode of light goes through each step, it is bent slightly until it is reflected back toward the core of the fiber.
To help visualize the layers in the fiber, consider a Fresnel lens, a "flat" lens made from annular rings of glass that approximate a regular lens. These lenses are used in lighthouse lights like this one:
A Fresnel lens like this one used in a lighthouse is a flat lens made of segments of a regular lens.
Index of refraction is related to the speed of light in the fiber; N=C/V, so a higher index of refraction indicates that light travels at a slower speed (V) relative to the speed of light in a vacuum (C.) Since the light is going into a lower index of refraction material in the outside of the core, it speeds up compared to the speed at the center of the core. By carefully designing and manufacturing the fiber, you can get the average speed of a higher-order mode approximately the same as the modes going straight down the fiber, reducing modal dispersion.
While the majority of graded-index fiber is all glass, there are some GI POF fibers also.