What is index fiber? How you define the modes in an optical fiber? Give a relation between core diameter and numerical aperture.

Ans.:  The index profile of a single mode fiber is usually a step index type. Where the refractive index is constant throughout the core. In such a fiber the refractive index profile abruptly changes at the junction of the core and the cladding Because of this abrupt change they are called step index fibers. In the graded-index fiber, the highest index is at the centre and decreases gradually until it reaches the index number of the cladding that is near the surface. From these terms there are three types of optical fibers:  1. Multimode step-index fiber (MMSIF) 2. Multimode graded-index fiber (MMGIF) 3. Single-mode step-index fiber, (SMSIF) The multimode step-index fiber (MMSIF) has a large core diameter ranging from 100 um due to which there are many paths through which light can travel. Therefore, the light ry travelling the straight path through the centre reaches the end before the other rays, which follow a zig-zag path. The difference in the length of time it takes the various light rays to exist the fibre is called modal dispersion. A typical structure and index profile of a multimode step index fibre are shown in figure. The multimode graded index fiber is an improvement on the multimode step index fiber. Because light rays travel faster through the lower index of refraction, light at the fiber core travels more slowly than the light nearer the surface. Therefore, both light rays arrive at the exits point at almost the same time thus reducing modal dispersion. A typical graded index fiber has core diameters ranging from 50 to 85 um and a cladding diameter of 125 um. Fig. shows the typical structure and index profile of a multimode graded index fiber. Graded index fibers can be manufactured with a variety of different index grading profiles. One of the most popular profile functions is the alpha profile function. In which the index of refraction within the core is made to vary radically as where n is the core index at radial distance r from the core axis, n is the index at the core axis, is the normalized difference between the core and cladding indexes, d is the core diameter and is the grading profile index number. Graded index fibers generally will not support as many modes as the corresponding step index fibers. When a finite value of alpha is used, then the number of supported modes for a large number of modes is reduced according to the expression:  Graded index fibers are almost always used as multimode fibers and can give better performance as single mode fiber if designed carefully. The single mode step index fiber is widely used for wide band communication application have a light ray can travel in only one path making modal dispersion zero. This fiber has a very fine thin core of uniform refractive index of a higher value which is surrounded by a cladding of lower refractive index. Typical single mode step index fiber has a core diameter in the range 5 to 10 um with standard cladding diameter of 125 um. Fig. shows the typical structure and index profile of a single mode step index fiber.