Explain about the intermodal dispersion in optical fibers.

Intermodal Dispersion Δτ_im)

This dispersion arises even when light that is launched into the fiber is strictly monochromatic. This is better understood by using ray theory. Into this type of dispersion, the temporal extend of optical pulse occurs due to the different path lengths covered by the various rays which are guided by the core of an optical fiber. The rays traveling beside the axis of the fiber reach destination quicker than the rays which take an oblique path by the fiber core. All the angle of travel (which is guided by the fiber because of total internal reflection at the core-cladding interface) is a permitted mode of propagation of energy through the fiber and velocity of the energy thus transported through each mode is different and leads to intermodal dispersion. The fibers which assist many these modes of travel are therefore termed as multimode fibers. Intermodal dispersion is the main contributor to dispersion into step-index multimode fibers (SI-MM). Typical value ~ 75ns/km.nm

Propagation of electromagnetic waves by the optical fiber can be solved through applying appropriate boundary circumstances to the propagation equations specified by Maxwell's theory. That derivation gives the number of modes and field distribution of all of these modes which is guided with the fiber. For a step index fiber of core radius a, core and cladding refractive indices of n₁ and n₂ correspondingly, this theory provides the number of modes sustained into the fiber as V²/2 here V is a dimensionless quantity termed as V-number of the fiber and is specified by:

2Πa/λ (√(n₁² - n₂²)) = 2Πa/λ (N.A.)

Hence the expression for number of modes into a step-index fiber is specified by:

N ≈ V²/2 = ½ (2Πa/λ (√(n₁² - n₂²)))² = (2Π²a²/λ²)(n₁² - n₂²)