Wiki / Fibers / Optical fiber

Optical fiber

Guides light along a drawn path between connectorized ends, with configurable acceptance, propagation loss, group delay, and an output cone at each end.

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In the real world

An optical fiber guides light along its own length instead of across open space. A cylindrical core of slightly higher refractive index is surrounded by a cladding of slightly lower index, and light that strikes the boundary at a shallow enough angle is totally internally reflected back into the core. Repeated indefinitely, that confinement carries a beam around bends and over distances that no free-space path could survive, which is why fiber underpins both global telecommunications and a great deal of everyday optics on the bench.

Two numbers govern how light gets in. The numerical aperture is set by the two indices and defines a cone of acceptance: light arriving within that half-angle couples into the guided mode, and light outside it does not. The core diameter then decides how many spatial modes the fiber supports — a large multimode core carries many, while a single-mode core of a few micrometres carries exactly one and therefore preserves a clean wavefront.

NA=ncore2−nclad2\mathrm{NA} = \sqrt{n_{\text{core}}^{2} - n_{\text{clad}}^{2}}
Numerical aperture from the index step — it sets both the acceptance cone on the way in and the divergence cone on the way out.
θmax⁡=arcsin⁡(NAn0)\theta_{\max} = \arcsin\left(\frac{\mathrm{NA}}{n_0}\right)
Half-angle of the acceptance cone in a medium of index n₀ — in air, simply arcsin(NA).
P(L)=P0 10−αL/10P(L) = P_0 \, 10^{-\alpha L / 10}
Attenuation along a fiber of length L for a loss coefficient α in dB per unit length.
t=ngLct = \frac{n_g L}{c}
Transit time through the fiber — the group index n_g, not the phase index, sets the delay a pulse or an interferometer actually sees.

What emerges at the far end is not the beam that went in. A fiber scrambles the spatial information it carries, so a multimode fiber illuminated with coherent light produces speckle rather than an image; the output simply diverges into a cone set by the fiber's NA. Light is attenuated along the way, by absorption and by scattering, at a rate conventionally quoted in decibels per kilometre — around 0.2 dB/km for silica telecom fiber at 1550 nm, which is the wavelength band the material is most transparent to and the reason that band dominates long-haul communication.

Fiber also delays light. The group index of silica is close to 1.47, so a pulse travels at roughly two-thirds of its vacuum speed and a fiber path is optically much longer than its physical length — a distinction that matters enormously in interferometry, where the optical path difference is what sets the fringes.

A separate and very active line of work turns the fiber's scrambling into something useful. Because the mixing is deterministic, it can be measured and inverted: a wavefront shaped correctly at the input emerges from a multimode fiber as a diffraction-limited focus at a chosen point in the output plane, and scanning that focus turns a hair-thin fiber into a microscope objective. These lensless endoscopes image deep inside tissue through a probe no wider than the fiber itself.

In OpticalSetup

A fiber is drawn rather than placed: pick the tool, click waypoints along the route you want, and double-click to finish. The result is a path, not a component, so it curves smoothly through its waypoints and can be reshaped afterwards by dragging the round handles. Everything optical about it lives on that path.

The connectors drawn at each end are the terminated patch cable you would pick up off a bench. For the same component without them — a cleaved or spliced fiber, as used in custom laboratory assemblies — draw a bare fiber instead; it behaves identically and differs only in how it renders and in the width of the end face a beam has to hit.

A new fiber starts as diagram only. Its ends block whatever light reaches them, and nothing comes out — which is the honest depiction of an unconnected cable lying on a table. Tick Beam propagates to make it an optical path, and the inspector then exposes the properties that make it one.

Getting light in

Coupling is a real test, not an assumption. A ray reaching an end face couples in only if it arrives within the acceptance cone — the Input NA, 0.22 by default — measured against that end's own axis. A beam that arrives too steeply is simply not accepted, exactly as it would not be on a bench. An objective aimed at a fiber end couples into it the same way, which is how the lensless-endoscope setups in the community gallery are built.

What the fiber does to the light

Three saved properties act along the drawn length. Loss, in dB/m (0.2 by default), attenuates the light over the path's true geometric length. The group index (1.468 by default, fused silica) multiplies that length into optical path, so a fiber arm in an interferometer contributes the delay it really would, and a pulse arrives when it should rather than when a free-space path of the same drawn length would deliver it.

Wavelength, spectrum, polarization state, and pulse envelope all survive the journey, as does any group-delay dispersion the light picked up before it coupled in. Speckle does not: light emerges from the far end as a clean cone or focus rather than as the grain a real multimode fiber would impose.

Getting light out

Each end carries its own independent output specification, so the two ends can behave differently and coupling works in both directions — light entering end A leaves from B under B's spec, and vice versa. Two styles are available:

  • Diverging — the ordinary case. Light leaves the tip as a cone of half-angle arcsin(NA), using that end's output NA (0.12 by default), which is what a real fiber tip does.
  • Focused — light leaves as a converging fan of a chosen output diameter that comes to a focus a chosen distance ahead. This is not what a plain cleaved fiber does; it is there for lensless endoscopes and for the lensed and GRIN-terminated fibers that deliver a focus directly from the fiber tip. It is what lets you sketch a fiber probe that images a sample without drawing an objective in front of it.
Simplified vs. reality

The fiber is modelled as a guided path with an acceptance cone, a loss, and a delay — not as a waveguide. Nothing here computes modes, so single-mode and multimode fibers are not distinguished, and the mode scrambling that dominates a real multimode output is absent: the output is a clean cone or focus, never speckle. Bend loss is not modelled either, so a tightly drawn path costs no more than a straight one, and the loss figure is applied uniformly rather than varying with wavelength. Nine rays are launched from the output end, which sets how finely the emerging cone is sampled.

The fiber's own chromatic dispersion is a single signed β₂, entered in ps²/km at a reference wavelength and applied, as a constant across the band, as a lumped GDD of β₂ × length: 1 ps²/km is 1 fs²/mm, so 36 ps²/km over 1 m adds 36 000 fs². It adds to whatever dispersion the pulse already carries, and a compressor of the opposite sign takes it back out. Physical length sets the length used for delay, loss and dispersion together, so a coil of many metres can be drawn as a short cable; left at 0 the drawn length is used, as in sketches from before these controls existed, and β₂ at 0 adds no dispersion. A broad band gains the endpoint delay spread that one β₂ implies, the same approximation the pulse compressor uses. Duration readouts downstream follow the pulse's authored phase, and read unavailable where that phase is unknown.

One β₂ is all there is: no third- or higher-order dispersion, no wavelength dependence of β₂ across a broad band, no modal or polarisation-mode dispersion, and no nonlinear propagation — self-phase modulation, soliton dynamics and wavelength conversion in the fiber itself are not simulated, except in the opt-in hollow-core model below.

Fiber model → Hollow core · argon turns the fiber into a gas-filled capillary: its β₂ and group index come from the argon pressure and the core diameter, and a bounded split-step calculation adds Kerr self-phase modulation for one intact, transform-limited Gaussian pulse train, so the spectrum broadens and a compressor downstream can shorten the pulse. The cable's panel says which of four states it is in: a computed envelope; Kerr off, which is linear propagation within the β₂ model; a linear-only approximation, when the pulse is outside the solver's bounds or not one it can take — the light then continues with argon's linear dispersion and every readout downstream, spectrum and power included, is labelled as such; or no argon data, outside 468–2059 nm, where the light continues geometrically and no argon dispersion is claimed. With no coupled pulse energy the capillary stays dark. Its loss is computed by default as the ideal smooth fused-silica capillary's (Marcatili–Schmeltzer, 0.615 dB/m for 250 µm at 800 nm, scaling as λ²/a³), with an optional extra distributed loss, or typed as a manual total. The model has no ionization, higher modes, wall resonances, Raman response or self-steepening; its effective area is the Gaussian π(0.64a)², which makes γ about 16 % larger than the exact capillary mode would.

Related components

Further reading