Discuss in detail about pulse broadening in graded index waveguide ?

Intermodal dispersion within multimode fibers is minimized along with the use of graded index fibers, therefore multimode graded index fibres displays substantial bandwidth improvement over multimode step index fibers. Let we consider the index profile of graded index fiber as:

n(r) = n1[1-2?(r/a)2] ; r < a (core)
= n1[1-2?] =n2 ; r ≥ a (cladding)

This is a parabolic profile. The refractive index is such in which the local group velocity is inversely proportional to the local refractive index. Therefore there is an equalization of transmission time of the axial ray that travels exclusively within the high refractive index region at the core axis and at the slowest speed. Therefore there is a decreased delay difference among the fastest and slowest modes for this graded index fiber. The delay difference is given through:

∂ Tg = {Ln1?2}/{2c}

Therefore more rigorous analysis using electromagnetic mode theory given an absolute temporal width at the fiber output as:

∂ Tg = {Ln1?2}/{8c}

The variation of intermodal pulse broadening along with features index profile is displays below:

The curve displays a sharp minimum at a features refractive index profile slightly less than 2 (α = 1.98). This corresponds to the optimum value of α within order to minimize intermodal dispersion. Moreover the extreme sensitivity of the intermodal pulse broadening to slight many in α from this optimum value is evident.

The major factor for dispersion in graded index fiber is Intramodal dispersion mechanisms like as material dispersion and waveguide dispersion. The material dispersion is due to spectral width of the optical source and waveguide dispersion is because of change in group velocity of the optical source. A pulse broadening of around 0.08 and 1 ns/km is given along with injection laser and LED correspondingly.