Modal Dispersion Simulator: Multimode Pulse Broadening in Optical Fiber

simulator intermediate ~10 min
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ΔT = 67.6 ns — pulse broadens from 2 ns to 67.6 ns over 1 km

A step-index fiber with n1=1.48 and n2=1.46 produces a modal delay spread of 67.6 ns over 1 km, broadening a 2 ns input pulse to 67.6 ns and limiting bandwidth to about 6.5 MHz-km.

Formula

ΔT = (L × n₁ / c) × (n₁ - n₂) / n₂
τ_out = sqrt(τ₀² + ΔT²)
BW × L ≈ 0.44 / ΔT

Many Paths, One Fiber

In a multimode optical fiber, light does not travel along a single path. Hundreds of guided modes propagate simultaneously, each bouncing off the core-cladding interface at a different angle. The axial ray travels the shortest path straight down the center, while high-order modes zigzag at steep angles, covering considerably more distance. This path-length difference is the root cause of modal dispersion.

Pulse Broadening

A sharp laser pulse launched into a multimode fiber arrives at the far end as a broadened blob. The fastest mode (axial) arrives first; the slowest mode (highest order, bouncing at the critical angle) arrives last. The delay spread between them grows linearly with fiber length. When the spread exceeds the pulse spacing, adjacent bits overlap — inter-symbol interference destroys the signal.

Bandwidth-Distance Tradeoff

Modal dispersion imposes a hard ceiling on the bandwidth-distance product. A step-index multimode fiber with a 2% index difference has a BW-L product of only about 20 MHz-km — enough for 100 Mbit/s over 200 metres, but hopeless for long-haul telecom. Graded-index fibers with parabolic profiles equalise mode velocities and push the product above 1 GHz-km.

Visualising Mode Delay

This simulation shows the input pulse shape at the launch end and the broadened output pulse at the far end. As you increase fiber length or index difference, watch how the output pulse widens and flattens. The animated ray paths inside the fiber cross-section show low-order and high-order modes racing each other — a visceral demonstration of why single-mode fiber dominates long-distance communication.

FAQ

What is modal dispersion in optical fiber?

Modal dispersion occurs in multimode fibers because different guided modes travel at different group velocities. The highest-order modes bounce at steeper angles and travel longer paths, arriving later than the axial mode. This spreads a sharp input pulse into a broader output pulse, limiting data rate.

How do you calculate modal dispersion?

For step-index fiber, the maximum modal delay spread is ΔT = (L * n1 / c) * (n1 - n2) / n2, where L is fiber length, n1 and n2 are core and cladding indices, and c is the speed of light. The output pulse width is sqrt(input_width^2 + ΔT^2).

How does graded-index fiber reduce modal dispersion?

Graded-index fiber has a parabolic refractive index profile that equalises mode group velocities. Higher-order modes travel in regions of lower index (faster speed), compensating for their longer geometric paths. This reduces modal dispersion by a factor of about delta/2 compared to step-index fiber.

What is bandwidth-distance product?

Bandwidth-distance product (MHz-km) is a fiber's figure of merit — the maximum data bandwidth multiplied by transmission distance. For step-index multimode fiber it is typically 20-50 MHz-km; graded-index reaches 200-2000 MHz-km; single-mode fiber is limited only by chromatic dispersion.

Sources

Embed

<iframe src="https://homo-deus.com/lab/fiber-optics/modal-dispersion/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub