---
title: "Short note: Multimode graded index fibre"
subject: "Propagation and Antenna"
chapter: 6
key: "semester_6/propagation_and_antenna:multimode-graded-index-short-note"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/multimode-graded-index-short-note
site: BCT Engineering
---

# Short note: Multimode graded index fibre

Propagation and Antenna · Chapter 6: Optical Fibres

- Asked in: 2073 Magh, 4 marks
- Video: [Graded Index Fiber | L 19 | Optical Communication](https://www.youtube.com/watch?v=3huV7xIJdHo) — Dopamine
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/multimode-graded-index-short-note
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-6

## Question

Write a short note on multimode graded index fiber.

## Short answer

A multimode graded-index fibre has a core index that decreases parabolically from the axis to the cladding, so rays follow curved paths and arrive at nearly the same time, giving low intermodal dispersion. It has a large core (50–62.5 µm), works with cheap LEDs, and suits LANs and data centres up to a few km.

## Answer

A **multimode graded-index (GI) fibre** is a fibre whose core refractive index is highest at the axis and decreases gradually (usually parabolically) to the cladding value at the core edge, and which supports many modes.

#### Index profile

```text
n(r) = n1 √(1 − 2Δ (r/a)^α),   r < a
n(r) = n2,                     r ≥ a
```

α = 2 (parabolic) is the usual profile. Core diameter is 50 or 62.5 µm, cladding 125 µm.

#### Ray propagation

```text
 cladding ______________________________
           .-.      .-.      .-.
 core    /    \   /    \   /    \
 ----*----------------------------->
          \  /     \  /     \  /
 cladding ______________________________
```

Rays bend gradually towards the axis by continuous refraction and follow sinusoidal or helical paths. Rays far from the axis travel longer paths but through lower-index (faster) glass, so they arrive at almost the same time as the axial ray.

#### Features

- Intermodal dispersion much lower than step-index multimode (bandwidth ~0.5–2 GHz·km versus ~20–50 MHz·km).
- Larger core than single mode, so cheap LED/VCSEL sources and connectors can be used.
- Loss about 2.5 dB/km at 850 nm, 0.6–1 dB/km at 1300 nm.
- **Applications:** LANs, data centres (OM3/OM4 fibre), campus and building backbones up to a few km.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the usual index profile?
   A. Step
   B. Triangular only
   C. Uniform
   D. Parabolic (alpha = 2)
   Answer: D. Parabolic is near-optimum for equalising delays. (Key point: Profile)

2. Why do outer rays arrive almost with the axial ray?
   A. They travel longer paths but through lower-index, faster glass
   B. They take the shortest path
   C. They are absorbed
   D. They travel in the cladding
   Answer: A. Speed v = c/n(r) compensates path length. (Key point: Ray propagation)

3. How does bandwidth compare with step-index multimode?
   A. About the same
   B. About 0.5-2 GHz.km versus 20-50 MHz.km
   C. Lower
   D. Tens of GHz.km
   Answer: B. Intermodal dispersion is much reduced. (Key point: Bandwidth)

4. Where is graded-index multimode fibre used?
   A. Submarine long-haul
   B. Power transmission
   C. LANs, data centres, campus backbones
   D. Radio towers
   Answer: C. Large core allows cheap LED/VCSEL sources. (Key point: Applications)

## Related in Propagation and Antenna

- [Graded index fibre ray transmission](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Agraded-index-fiber) — Propagation and Antenna, chapter 6
- [Fibre losses; multimode vs single mode](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afiber-losses-multimode-vs-single) — Propagation and Antenna, chapter 6
- [Acceptance angle and NA of step-index fibre](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aacceptance-angle-na-step-index) — Propagation and Antenna, chapter 6, asked 2×
- [Multimode vs single mode; NA derivation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amultimode-vs-single-na-derivation) — Propagation and Antenna, chapter 6

## Related in other subjects

- [Optical fiber, NA, single vs multimode](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aoptical-fiber-na-acceptance-mode-comparison) — Engineering Physics, chapter 6