Optical fibre in depth: loss, dispersion and wavelengths

Lesson 2 introduced fibre as a glass core and cladding that guide light, and compared multimode and single-mode grades by reach. A designer who must choose fibre types for a twenty-year plant, explain why a link fails, or decide whether a new transceiver will work over existing cabling needs to look deeper: at where loss comes from, how pulses spread, why particular wavelengths are used, how bends and reflections affect modern high-speed optics, and how several signals can share one fibre. This lesson covers those physical foundations.

Light in glass

Light travels more slowly in glass than in a vacuum, by the factor of the refractive index, about 1.47 for the silica used in fibre. That sets the propagation delay of every fibre link: about 4.9 µs per kilometre, or 4.9 ns per metre. In a data centre this is small compared with switch and software delays, but between data centres, and in large AI training clusters where thousands of processors wait on each other, it adds up.

The core has a slightly higher refractive index than the cladding, typically by about 0.3% to 1%, and light striking the boundary at a shallow enough angle is totally reflected. The range of angles the fibre accepts is described by its numerical aperture (NA): about 0.2 for 50 µm multimode fibre and about 0.12 to 0.14 for single-mode. A larger NA collects light more easily from cheap sources but supports more modes.

Where loss comes from

The attenuation of a fibre has several causes:

• Rayleigh scattering: tiny variations in the density of the glass, frozen in when it was drawn, scatter light in all directions. Scattering is proportional to \(1/\lambda^{4}\), so it falls rapidly at longer wavelengths. It is the dominant loss in modern fibre.
• Absorption: by the glass itself at long wavelengths (infrared absorption, rising beyond about 1,600 nm), and by impurities. Hydroxyl (OH) ions from water once caused a large "water peak" at 1,383 nm; low-water-peak fibre (ITU-T G.652.D) has almost eliminated it, opening the whole range from 1,260 nm to 1,625 nm for use.
• Bending: when the fibre bends too tightly, some light escapes the core. Macrobends are visible bends below the minimum bend radius; microbends are tiny distortions from pressure, such as a fibre crushed by a cable tie or squeezed in a cold, shrinking jacket.
• Connectors and splices: the largest losses in a short data centre link, from misalignment of cores, gaps, angles and contamination (Lesson 6).

# Rayleigh scattering scales as 1 / wavelength**4.
# Scale a measured 0.33 dB/km at 1310 nm to other wavelengths.
ref_nm, ref_loss = 1310, 0.33
for nm in (850, 1310, 1550):
    loss = ref_loss * (ref_nm / nm) ** 4
    print(f"{nm:5d} nm  scattering loss about {loss:.2f} dB/km")

# Chromatic dispersion: pulse spread = D * spectral width * length
def spread_ps(D, width_nm, km):
    return D * width_nm * km

for band, D in (("O-band 1310 nm", 0.5), ("C-band 1550 nm", 17.0)):
    t = spread_ps(D, 0.1, 10)
    print(f"{band}: spread over 10 km = {t:.1f} ps")

symbol_ps = 1e12 / 53.125e9   # 106.25 Gb/s PAM4 lane = 53.125 GBd
print(f"Symbol period at 53.125 GBd = {symbol_ps:.1f} ps")

  850 nm  scattering loss about 1.86 dB/km
 1310 nm  scattering loss about 0.33 dB/km
 1550 nm  scattering loss about 0.17 dB/km
O-band 1310 nm: spread over 10 km = 0.5 ps
C-band 1550 nm: spread over 10 km = 17.0 ps
Symbol period at 53.125 GBd = 18.8 ps

The result explains the wavelengths used. Multimode fibre works at 850 nm, where cheap vertical-cavity surface-emitting lasers (VCSELs) are available, accepting about 2 to 3 dB/km because data centre links are short. Single-mode links use the O-band near 1,310 nm, where loss is about 0.3 to 0.4 dB/km and, crucially, chromatic dispersion is nearly zero; long-haul links use the C-band near 1,550 nm, where loss is lowest and optical amplifiers work.

Dispersion

Dispersion spreads each pulse in time, so that at high symbol rates neighbouring symbols blur together. There are three kinds:

• Modal dispersion, in multimode fibre only: different modes travel different path lengths. Graded-index fibre compensates by making the outer parts of the core faster. The result is expressed as effective modal bandwidth (EMB), a bandwidth-length product: OM3 is specified at 2,000 MHz·km at 850 nm, OM4 at 4,700 MHz·km, and OM5 at 4,700 MHz·km at 850 nm and 2,470 MHz·km at 953 nm, so that it supports several wavelengths.
• Chromatic dispersion, in all fibre: different wavelengths travel at slightly different speeds, and every real laser emits a small range of wavelengths. It is measured by the dispersion coefficient \(D\) in ps/(nm·km). Standard single-mode fibre has \(D \approx 0\) near 1,310 nm and about 17 ps/(nm·km) at 1,550 nm.
• Polarization mode dispersion (PMD): the two polarizations of light travel at slightly different speeds in imperfect fibre. It matters on long, high-speed links, rarely within a building.

Single-mode fibre types and bend-insensitive fibre

ITU-T recommendations define single-mode fibre types:

• G.652.D: standard low-water-peak single-mode fibre, the default for data centres and most networks.
• G.657.A1 and A2: bend-insensitive fibres, compatible with G.652.D but with much lower bend loss. A trench of lower refractive index around the core holds light in at tight bends: G.657.A1 tolerates a 10 mm bend radius and A2 7.5 mm.
• G.654: low-loss, large-effective-area fibre for submarine and long-haul links.
• G.655 and G.656: non-zero dispersion-shifted fibres for dense wavelength-division multiplexing over long distances.

Bend-insensitive fibre is now normal for data centre cabling, both single-mode (G.657.A1 or A2) and bend-insensitive multimode. It tolerates tight routing in cassettes, cable managers and congested trays. It does not remove the need to follow cable bend radius limits, which protect the cable's structure as well as the light; the cable's minimum bend radius during installation is typically 20 times its outer diameter, and 10 times after installation.

Cable constructions also matter. Data centre trunk cables increasingly use 200 µm coated fibres in place of 250 µm, and rollable ribbon, in which fibres are bonded intermittently so the ribbon can be rolled into a compact bundle for high fibre counts yet spread flat for fast mass fusion splicing. A 3,456-fibre cable that once needed a 40 mm diameter can now fit in about 30 mm.

Reflections and connector polish

Every connection reflects a little light back toward the transmitter. The strength of the reflection is the reflectance (in dB, negative; more negative is better), or equivalently the return loss (the same magnitude, positive). Reflections matter because they can disturb the laser, and because two reflections in a link create a weak delayed copy of the signal at the receiver, which acts as noise.

• Physical contact (PC) and ultra physical contact (UPC) connectors have a domed end face polished flat to the fibre, with reflectance of about −40 to −50 dB.
• Angled physical contact (APC) connectors are polished at 8°, so reflected light is directed out of the core into the cladding, giving reflectance of −60 dB or better. They are colour-coded green.

Multi-level signalling such as PAM4, used at 50 Gb/s per lane and above, has less margin than the older two-level NRZ signalling, so it is more sensitive to reflections. Single-mode parallel optics such as 400GBASE-DR4 and 800G DR8 therefore specify a limit on the number and reflectance of connections, and many designers now use MPO-APC connectors for single-mode trunks. APC and UPC connectors must never be mated with each other: the angled and flat faces leave an air gap that causes high loss and can damage both.

Using more than one wavelength

A fibre can carry several signals at once on different wavelengths, combined and separated by optical filters. This is wavelength-division multiplexing (WDM), and in the data centre it lets one fibre pair carry several lanes, reducing fibre counts:

• Coarse WDM (CWDM): wavelengths 20 nm apart, such as 1,271, 1,291, 1,311 and 1,331 nm. 100G CWDM4 and 400GBASE-FR4 use four CWDM wavelengths on one duplex single-mode pair for 2 km.
• LAN-WDM: four wavelengths about 4.5 nm apart near 1,310 nm, used in LR4 optics for 10 km.
• Shortwave WDM and bidirectional (BiDi) optics on multimode fibre: two to four wavelengths between about 850 nm and 940 nm. 400GBASE-SR4.2 sends two wavelengths in opposite directions on each fibre of an 8-fibre MPO, reaching 70 m on OM3, 100 m on OM4 and 150 m on OM5. OM5 was designed for these applications.
• Dense WDM (DWDM): wavelengths about 0.4 or 0.8 nm apart near 1,550 nm, with optical amplifiers, for data centre interconnect between buildings and long-haul links (Lesson 11).

The design choice is between parallel fibres (one lane per fibre, MPO connectors, cheaper optics, many fibres) and WDM (several lanes per fibre, duplex LC connectors, more expensive optics, fewer fibres). Lesson 5 compares the transceivers that use each.

Latency and hollow-core fibre

Because light in silica travels at about two-thirds of its speed in a vacuum, each kilometre adds about 4.9 µs. Hollow-core fibre guides light through an air-filled core surrounded by microstructured glass, so light travels at nearly its vacuum speed, about 3.3 µs per kilometre, roughly 30% less delay, with very low nonlinearity and dispersion. Hollow-core fibre is being deployed by some operators between data centres in a region, where the lower latency allows sites to be further apart while behaving like one large facility. It needs special splicing and connectors and is not yet a general-purpose replacement for standard fibre.