Core 0 µmNA 0Accept. angle 0°V 0 (0)Loss 0 dBWorst margin 0 dBFPS 0

Drag to orbit, wheel or pinch to zoom. White line: one light ray bouncing inside the glass core by total internal reflection (sideways drawing exaggerated ×4). The three coloured pulse trains are separate wavelengths sharing one fibre (false colours: real telecom light is infrared); after the connector each goes to its own receiver. Pulses spread out as they travel and fade as the glass absorbs and scatters light.

Optical Fibre Link: Total Internal Reflection, Modal Dispersion, Attenuation and WDM Power Budget

Light is trapped in a glass core by total internal reflection. Three wavelengths share one fibre; each loses power to the glass, its pulses smear out, and the receiver at the far end needs enough clean light. Will the link work?

Fibre

Wavelengths (three WDM channels)

Transmitter, receiver and hardware

Launched ray

Per channel

Live readouts

Attenuation of silica glass against wavelength

Rayleigh scattering falls as 1/λ⁴, the OH absorption peak sits near 1383 nm and the glass itself absorbs beyond about 1600 nm. The deepest valley is near 1550 nm.

Bits in and bits out (selected channel)

Dashed: what was sent. Solid: what arrives after modal and chromatic broadening (Gaussian impulse response). When the pulses overlap, the receiver can no longer tell the bits apart.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. View buttons jump to the whole link, the inside of the core, the connector and a top view.
Fibre: core diameter, glass index, the index step between core and cladding, the profile (step or graded) and the length. Small core and small index step give a single-mode fibre.
Wavelengths: choose any three between 800 and 1650 nm; the colours in the picture are only labels for channel 1, 2, 3.
Launched ray: the angle at which the light enters the end face. Above the acceptance angle the ray escapes into the cladding.
Presets are textbook-style situations, not product data sheets. Virtual bench: real laser light can damage eyes.

The science

Total internal reflection. A ray hitting the core wall at an angle (from the normal) above the critical angle θ_c = asin(n₂/n₁) is reflected completely. A ray entering the end face from air at angle θ is guided if sin θ ≤ NA = √(n₁² − n₂²); the acceptance angle is θ_a = asin NA.

Modes. The normalised frequency is V = 2π a NA / λ (a = core radius). Below V = 2.405 only one mode is guided (single-mode fibre); for many modes the count is about V²/2 for a step profile and V²/4 for a graded one.

Modal dispersion. Steep rays take a longer path. The extreme delay difference over length L is (L n₁/c)(n₁/n₂ − 1) for a step-index fibre, but only (L n₁/c) Δ²/8 for a parabolic graded profile, because rays that wander farther from the axis travel through lower-index, faster glass. A single-mode fibre has none.

Chromatic dispersion. Different wavelengths travel at different speeds: Δt = |D| L Δλ with D(λ) = (S₀/4)(λ − λ₀⁴/λ³), λ₀ = 1312 nm, S₀ = 0.092 ps/(nm² km). D is zero near 1310 nm and about 17 ps/(nm km) at 1550 nm.

Attenuation and budget. Loss in dB adds: α(λ) L plus about 0.5 dB per connector and 0.1 dB per splice. The receiver margin is P_tx − losses − (sensitivity + dispersion penalty). The dispersion penalty used is −5 log₁₀[1 − (4 σ B)²] (σ = rms broadening, B = bit rate), and the link fails when 4σB reaches 1. Sensitivity is −28 dBm at 1 Gb/s and worsens by 10 log₁₀ of the bit rate.

Simplifications. Meridional rays only (no skew rays, no mode coupling, no bend or microbend loss, no polarisation mode dispersion, no nonlinear effects, no amplifier or noise model). The attenuation curve is a smooth model of silica fibre, not a data-sheet curve. The same D(λ) formula is used for multimode glass; it is only an approximation near 850 nm. Colours in the picture are artistic. Models built with Blender, scene by Three.js.