### Comparison of Step Index and Graded Index Fibres

Comparison of Step Index Fibres and Graded Index Fibres(GRIN)→

S.No. Step Index Fibre Graded Index Fibre
1. In a step-index fibre, the refractive index of the core a constant value. In graded-index fibre, the refractive index in the core decreases continuously in a nearly parabolic manner from a maximum value at the centre of the core to a constant value at the core-cladding interface.
2. For a step-index fibre, the variation of refractive index is mathematically expressed as,
$\begin{cases} & \mu(r)=\mu_{1} \qquad 0 < r < a \quad for (core)\\ & \mu(r)=\mu_{2} \qquad r >a \quad for(Cladding)\\ \end{cases} \\ Where \: \mu_{1} > \mu{2}$
Parabolic refractive index variation in GRIN fibre is mathematically expressed as,
$\begin{cases} & \mu^{2}(r)=\mu^{2}_{1} \left[ 1- \left(\frac{r}{\alpha} \right)^{2} \right] \qquad 0 < r < a \quad for (core) \\ & \mu(r)=\mu^{2}_{2} \qquad \qquad \qquad \qquad r > a \quad for (Cladding) \end{cases}$
3. In the step-index fibre, the propagating light rays reflect abruptly from the Core cladding boundary. In graded-index fibre, the propagating light rays bend smoothly as they approach the cladding.
4. for given fibre diameter, the numerical aperture of step-index fibre is large. For the same fibre diameter, the numerical aperture of graded-index fibre is small.
5. In the step-index fibre, there may be some irregularities at the interface between the core and cladding. In the graded-index fibre, there are no such irregularities at the interface between core and cladding.
6. The step-index fibre has higher attenuation. The graded-index fibre has lower attenuation.
7. For a step-index fibre of a given physical size, with a loss of power of the order of $12 \frac{dB}{km}$, the numerical aperture is of the order of $0.2$ to $0.35$. For a graded-index fibre of the same physical size, with an attenuation between $5$ to $10 \frac{dB}{km}$, the numerical aperture tends to run between $0.16$ and $0.2$
8. In step index fibre, the time interval at the output end or pulse dispersion is expressed as,
$\Delta \tau = \frac{\mu_{1} l}{c} \left ( \frac{\mu_{1}}{\mu_{2}} - 1 \right)=\frac{\mu_{1} l}{c} \Delta$
Where $l$ → The length of the fibre.
In a graded index fibre, the time interval at the output end or pulse dispersion is expressed as,
$\Delta \tau = \frac{\mu_{2} l}{2c} \left ( \frac{\mu_{1} - \mu_{2}} {\mu_{2}} \right)^{2}=\frac{\mu_{2} l}{2c} \Delta^{2}$
Where $l$ → The length of the fibre.
9. Pulse dispersion in multimode step-index fibre is large. Pulse dispersion in a graded-index fibre is small.
10. A good quality step-index fibre may have a bandwidth of $50 MHz km$ The equivalent graded-index fibre can have $200$, $400$, or $600 MHz km$ bandwidth.