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.