--- title: "Graded index fibre ray transmission" subject: "Propagation and Antenna" chapter: 6 key: "semester_6/propagation_and_antenna:graded-index-fiber" source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/graded-index-fiber site: BCT Engineering --- # Graded index fibre ray transmission Propagation and Antenna · Chapter 6: Optical Fibres - Asked in: 2076 Baisakh, 3+5 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/graded-index-fiber - Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-6 ## Question What are the various features of graded index fiber? Explain the refractive index profile and ray transmission in a multimode graded index fiber. ## Short answer Graded-index fibre has a core index peaking at the axis and decreasing nearly parabolically (α≈2). Rays follow sinusoidal paths, with outer rays travelling faster in lower-index regions, equalising transit times and greatly reducing intermodal dispersion (bandwidth ~0.5-2 GHz·km). Local NA is maximum on axis and zero at the core edge. ## Answer #### Features of graded-index fibre - The core refractive index is **not uniform**: it is highest at the axis and decreases gradually to the cladding value n2 at the core boundary. - Usually multimode, with core diameter 50 or 62.5 µm and cladding 125 µm; NA about 0.2–0.3. - Rays follow **curved, sinusoidal paths** instead of zig-zags. - **Much lower intermodal dispersion** than step-index multimode fibre, so bandwidth is about 100 times higher (~0.5–2 GHz·km). - Accepts LED or VCSEL sources and is easier to couple than single-mode fibre. - More costly to make than step-index multimode fibre. #### Refractive index profile ```text n(r) = n1 · √( 1 − 2Δ (r/a)^α ) for r < a (core) n(r) = n1 · √( 1 − 2Δ ) = n2 for r ≥ a (cladding) Δ = (n1² − n2²) / (2n1²) ≈ (n1 − n2)/n1 ``` where *a* is the core radius and α is the profile parameter: α = 1 triangular, **α = 2 parabolic** (the usual choice, near optimum), α → ∞ step index. ```text n ^ n1 | .--. | / \ parabolic core | / \ n2 |--' '--- cladding +-----+---+---+----> r -a 0 a ``` #### Ray transmission in multimode graded-index fibre ```text cladding ________________________________ .-. .-. .-. core / \ / \ / \ outer ray axis ---*-----------------------------> axial ray \ / \ / \ / cladding ________________________________ ``` - A ray entering at an angle moves into regions of **lower index**. By Snell's law it bends continuously away from the normal, until it turns back towards the axis. It never reaches the cladding in the ideal case; the turning is gradual refraction rather than a single sharp reflection. - So rays travel in **sinusoidal (meridional) or helical (skew) paths** that repeatedly cross the axis. - The axial ray takes the shortest path but in the highest-index (slowest) glass. Oblique rays take longer paths but spend most of their time in lower-index (faster) glass, since velocity v = c/n(r). - With a near-parabolic profile, the extra path length is almost exactly compensated by the higher speed, so all modes arrive at about the same time. Intermodal pulse spreading falls from about L·n1Δ/c (step index) to about L·n1Δ²/(8c) (parabolic), giving much larger bandwidth. - The local numerical aperture NA(r) = √(n(r)² − n2²) is maximum at the axis and zero at the core edge, so the fibre collects less light than a step-index fibre of the same n1 and n2. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In a graded-index fibre, where is the core refractive index highest? A. At the core-cladding boundary B. Uniform across the core C. Only in the cladding D. At the axis, decreasing to n2 at the core boundary Answer: D. The index is maximum on the axis and falls gradually to the cladding value. (Key point: Index profile) 2. Which value of the profile parameter alpha gives the usual parabolic profile? A. alpha = 2 B. alpha = 1 C. alpha = 0 D. alpha tending to infinity Answer: A. alpha = 1 is triangular, alpha = 2 parabolic, and alpha -> infinity is step index. (Key point: Profile parameter) 3. How do rays travel in a graded-index fibre? A. In sharp zig-zags by TIR at the boundary B. Along curved sinusoidal or helical paths by continuous refraction C. Only along the axis D. Straight into the cladding Answer: B. A ray bends gradually away from the normal as it enters lower-index regions and turns back to the axis. (Key point: Ray path) 4. Why is intermodal dispersion much lower than in step-index fibre? A. Only one mode is carried B. The axial ray is faster than all others C. The extra path of oblique rays is compensated by their higher speed in lower-index glass D. The cladding is thicker Answer: C. Pulse spreading drops from about L n1 Delta/c to L n1 Delta^2/(8c) for a parabolic profile. (Key point: Dispersion reduction) ## Related in Propagation and Antenna - [Short note: Multimode graded index fibre](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amultimode-graded-index-short-note) — 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 - [Refractive index, critical frequency and MUF](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Arefractive-index-fc-muf) — Propagation and Antenna, chapter 4 - [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× ## 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 - [Newton's rings, refractive index of liquid](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-rings-liquid-refractive-index) — Engineering Physics, chapter 4, asked 2× - [Refractive index of liquid film by interference](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acoherent-sources-film-refractive-index-method) — Engineering Physics, chapter 4 - [Optical fiber vs satellite transmission](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aoptical-fiber-vs-satellite) — Data Communication, chapter 4