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. |

## Comparison of Step Index and Graded Index Fibres

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