Optical fibers and fiber transmission
At 10 Gb/s, a multimode fiber has power to spare for 2 km, but dispersion cuts the link at 300 m. On a single-mode fiber, the same transmitter reaches tens of kilometers.
01Light through a thread of glass
An optical fiber is a dielectric waveguide that works at frequencies of about 200 THz. It has a silica glass core surrounded by a cladding of slightly lower refractive index, and the light is trapped in the core. Compared with a copper cable it has three decisive advantages: it loses 0.2 dB per kilometer instead of tens of dB, it supports terahertz bandwidths, and it is not affected by electromagnetic interference or by ground potential differences between its ends.
That is why almost all of the world's data traffic travels over fiber: the submarine cables between continents, the backbones between cities, the connection of cellular base stations and, more and more, the last stretch to every home.
02Total internal reflection and numerical aperture
A ray that travels along the core and reaches the cladding at an angle greater than the critical angle is entirely reflected, without loss, as seen in geometric optics. This limits the angle at which light can enter through the face of the fiber and be guided:
A large aperture makes it easier to couple the light from a cheap source but, as will be seen shortly, it allows more distinct paths inside the fiber.
03Multimode and single-mode
As in a metal waveguide, only certain field configurations propagate in the fiber, the modes. How many fit is given by the normalized frequency, which combines the core radius \( a \), the aperture and the wavelength:
| Fiber | Core / cladding | Aperture | Use |
|---|---|---|---|
| Multimode OM3 / OM4 | 50 / 125 µm | 0.2 | Data centers and building networks, up to hundreds of meters |
| Single-mode G.652 | 8.2 / 125 µm | Around 0.12 | Backbones, FTTH access, links of tens of kilometers |
| Single-mode G.657 | Similar to the G.652 | Higher | Indoor installations, tolerates tight bends |
With an 8.2 µm core and NA = 0.12, V is 2.36 at 1310 nm: the fiber is single-mode above about 1285 nm, its cutoff wavelength. The 50 µm multimode fiber at 850 nm has V ≈ 37 and hundreds of modes.
04Attenuation and windows
Light is lost through absorption by the glass and its impurities, and above all through Rayleigh scattering: microscopic fluctuations in the density of the glass deflect the light with an intensity proportional to \( 1/\lambda^4 \). Between 850 and 1550 nm this loss drops by a factor of 11. Toward the far infrared the absorption of the silica itself grows, and between the two lies the minimum, near 1550 nm.
| Window | Typical loss | Source and fiber |
|---|---|---|
| 850 nm | About 3 dB/km | Low-cost VCSEL on multimode |
| 1310 nm | About 0.35 dB/km | Laser on single-mode; almost zero chromatic dispersion |
| 1550 nm | About 0.2 dB/km | DFB laser on single-mode; amplified with erbium-doped fiber |
To the loss of the fiber are added that of each fusion splice (about 0.1 dB) and that of each connector (up to 0.5 dB), and bends that are too tight, which let light escape from the core.
05Dispersion: the pulse broadens
A light pulse arrives wider than it left, and if it broadens too much it overlaps the next one. There are two main causes:
- Modal dispersion, in multimode fibers: each mode travels a different path and arrives at a different moment. In a step-index fiber with \( n_1 - n_2 = 0.02 \), the difference is about 67 ns per kilometer. Modern multimode fibers are graded-index: the index drops toward the edge of the core, the modes that travel along the outside go faster and the difference shrinks by orders of magnitude. It is specified with the bandwidth–distance product: 2000 MHz·km in an OM3 at 850 nm.
- Chromatic dispersion, in all of them: the velocity depends on the wavelength, and no source emits just one.
At 10 Gb/s each bit lasts 100 ps, so chromatic dispersion limits long links at 1550 nm. A 10 Gb/s transmitter without compensation tolerates an accumulated dispersion \( D \cdot L \) of the order of 1000 ps/nm, about 60 km of G.652. Beyond that, compensating fibers or coherent receivers that correct it by digital processing are used.
06Emitters, receivers and the link budget
The source is an LED, a VCSEL or a semiconductor laser, and the receiver, a PIN or avalanche photodiode, as seen in optoelectronics. The design of a link starts with a power budget in decibels, just like the one for power in lines: all the losses are subtracted from the transmitter power, and what arrives has to exceed the receiver sensitivity with a margin, typically 3 dB, for aging and future repairs.
The optical power in dBm along the link: two 0.5 dB connectors, a splice every 2 km (the length of a reel) and the slope of the fiber attenuation. The receiver is a PIN with the typical sensitivity for the chosen speed. The values are typical catalog values.
07Where it appears in electronics
| System | How it uses fiber |
|---|---|
| Fiber to the home (GPON) | One single-mode fiber per house, with passive optical splitters; downstream at 1490 nm and upstream at 1310 nm |
| Data center | Pluggable transceivers with VCSELs on multimode for the short runs |
| Submarine cable | Single-mode at 1550 nm with erbium amplifiers every 50 to 100 km and tens of wavelengths per fiber |
| Cellular base station | Fiber between the baseband unit and the radio on the tower |
| Electrical substation | Total galvanic isolation between equipment at very different ground potentials |
Installation, connectors and field measurements are covered in optical fiber, in the technician program.
08In the lab
Illuminate a multimode fiber with a red laser, project the output cone onto a screen and measure its diameter at a known distance. Calculate the half-angle and the numerical aperture.
With a source and an optical power meter, measure the loss of a reel of fiber, of a connector and of a splice. Build the budget of a link and compare it with the end-to-end measurement.
Wind a single-mode fiber around mandrels of decreasing diameter and measure the increase in loss at 1310 and at 1550 nm. Explain why 1550 nm is more sensitive.
09Common mistakes
- Mixing multimode and single-mode. A single-mode transceiver on a multimode fiber, or the reverse, loses tens of dB or suffers modal dispersion.
- Looking at the tip of a connected fiber. Radiation at 1310 and 1550 nm is invisible and can damage the retina.
- Forgetting dispersion in the budget. At 10 Gb/s over multimode, the power would be enough for kilometers but modal dispersion limits it to a few hundred meters.
- Dirty connectors. A dust particle on an 8 µm core adds decibels; they are cleaned and inspected before every connection.
10Self-assessment
What is the numerical aperture of a fiber with \( n_1 = 1.48 \) and \( n_2 = 1.46 \)?
\( \sqrt{1.48^2 - 1.46^2} \approx 0.24 \), with an acceptance half-angle of 14°.
Is a fiber with an 8.2 µm core and NA = 0.12 single-mode at 1310 nm?
Yes: \( V = 2\pi \cdot 4.1 \cdot 0.12 / 1.31 \approx 2.36 < 2.405 \).
How much arrives from a 0 dBm transmitter through 40 km of fiber at 0.25 dB/km with 1 dB of connectors?
\( 0 - 10 - 1 = -11 \) dBm.
Why do 10 Gb/s links over multimode reach only about 300 m?
Because of modal dispersion: with 2000 MHz·km and about 6.7 GHz of required bandwidth, the maximum distance is 0.3 km, much less than the power would allow.
11Further reading
- Gerd Keiser. Optical Fiber Communications. 5th ed., McGraw-Hill, 2015. The most widely used course text: fibers, sources, detectors and link design with power and rise-time budgets.
- Govind P. Agrawal. Fiber-Optic Communication Systems. 5th ed., Wiley, 2021. The rigorous treatment of dispersion, optical amplifiers and coherent systems.
- John M. Senior. Optical Fiber Communications: Principles and Practice. 3rd ed., Pearson, 2009. Very complete on the physics of the fiber and on components, with many numerical examples.