• 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.

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

• 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

a = core radius

n_(1 )= refractive index at the core axis

$\Delta$ = relative refractive index difference

$\Delta = \frac{n_{1}^2- n_{2 }^2}{2n_{1}^2 } ≈ \frac{n_{1}- n_{2}}{n_{1}}$

$\alpha$ = profile parameter which gives the characteristics

refractive index profile of the fiber core.

• 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:

$$NA(0)= n_{1}\sqrt{2∆}$$

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