In one line
In a step-index fibre the core has one uniform refractive index that drops suddenly at the cladding, while in a graded-index fibre the core index is highest at the centre and decreases gradually towards the cladding.
Explained simply
Picture runners on a track where the outer lanes are faster. A runner on a longer, outer path can still finish with the inner runner because the outer lanes are quicker. In a graded-index fibre, rays that travel farther from the axis move through lower-index glass where light is faster, so all rays arrive nearly together.
How it works
- Step index: \(n = n_1\) throughout the core, \(n = n_2\) in the cladding. Rays travel in straight zig-zag lines by TIR. Steeper rays take a longer path and arrive later, causing intermodal dispersion.
- Graded index: \(n(r)\) decreases smoothly from \(n_1\) at the axis to \(n_2\) at the core edge, usually parabolically. Rays bend gradually (refraction, not sharp reflection) and follow curved, sine-like paths.
- Off-axis rays travel longer paths but mostly in lower-index (faster) regions, so their travel time nearly equals the axial ray's. Intermodal dispersion is greatly reduced.
| Feature | Step index | Graded index |
|---|---|---|
| Core index | Uniform | Decreases from axis outward |
| Ray path | Zig-zag (straight segments) | Smooth curved (helical/sinusoidal) |
| Guiding | TIR at boundary | Continuous refraction |
| Dispersion | Higher (multimode) | Lower |
| Modes (approx.) | \(V^2/2\) | \(V^2/4\) |
| Cost | Cheaper | Costlier to make |
Key formula
Graded profile: \(n(r) = n_1\sqrt{1 - 2\Delta\left(\frac{r}{a}\right)^2}\) for \(r < a\), and \(n = n_2\) for \(r \ge a\). \(r\) is distance from the axis, \(a\) the core radius, \(\Delta = (n_1 - n_2)/n_1\).
Quick example
For \(V = 31.4\), a step-index multimode fibre carries about \(V^2/2 \approx 493\) modes, while a graded-index fibre with the same V carries about \(V^2/4 \approx 246\). Graded-index multimode fibre is used in building and campus networks because it gives higher bandwidth than step-index multimode.
Common mistakes
- Drawing zig-zag straight rays in a graded-index fibre; they should be smooth curves.
- Saying graded-index fibres guide light purely by TIR at the boundary.
- Making the index increase towards the edge in graded fibre; it decreases.
How MU asks it
Asked as "Explain step-index and graded-index fibres with refractive index profiles" (5 marks). For full marks draw both index profiles (n versus r), show ray paths in each, and give a comparison table.