Multimode Step-Index Optical Fibre — Modal Dispersion

WJEC A-Level Physics · Interactive ray paths, time delay & output pulse broadening

Ray Propagation in Fibre Cross-Section

Axial ray (shortest path)
Intermediate rays
Off-axis ray (TIR, longest path)
Core (n₁)
Cladding (n₂)
Schematic only — bounce density depends on n₁, n₂ but not on L (a real 100 m fibre would have ~10⁶ bounces). All quantitative effects of L appear in the calculations and pulse panels.

Input vs Output Pulse

Showing a continuous train of 1s (binary pattern 11111111…) — the worst case for pulse overlap. The bit period T is the time from the start of one pulse to the start of the next. The input pulse width (how long each pulse is ON) is set independently by the transmitter; the gap inside each bit slot is "off-time" for that bit, not a 0.
INPUT
(sharp)
OUTPUT
(broadened)
Pulse broadening Δt sets the maximum bit-rate of the fibre.

Fibre Parameters

Calculations

sin θc = n₂ / n₁

Physics Notes

Modal dispersion arises because rays at different angles travel different path lengths through the fibre.

All rays travel at the same speed v = c/n₁ inside the core, but the axial ray goes straight down the axis, while the zig-zag ray at the critical angle moves only at speed v·sin θc along the axis (the component of v parallel to the fibre).

The time difference Δt limits the fibre's bandwidth — pulses arriving closer together than Δt overlap and become unreadable.