Mumbai University > Electronics and telecommunication > Sem 7 > optical communication and networks

Marks: 10

Years: MAY 2012

Determining Numerical Aperture for graded index fibers is more complex than for step index fibers, since it is a function of position across the core end face.

$\Rightarrow$ Graded Index Fiber does not have a constant refractive index in the core. Due to this property they are also called inhomogeneous core fibers.

$\Rightarrow$ It has a decreasing core index n(r) with radial distance from a maximum value of $n_1$ at the axis to a constant value $n_2$ beyond the core radius a in the cladding.

The index variation is given by

Where, r = radial distance from the fiber axis

a = core radius

$n_1 =$ refractive index at the core axis

$ Δ =$ relative refractive index difference

$Δ =\dfrac {n_1^2 - n_2 ^2}{2n_1^2} ≈ \dfrac {n_1- n_2}{n_1} $

$\alpha$ = profile parameter which gives the characteristics

Refractive index profile of the fiber core.

$\Rightarrow$ Light incident on the fiber core at position r propagates as guided mode if it is within local NA. The local NA is defined as:

Where the axial NA is defined as:

$NA(0)= n_1 \sqrt{2∆}$

Figure 1.6

$\Rightarrow $Thus, the NA of GIF decreases from NA (0) to 0 as r moves from fiber axis to core-cladding boundary.