Fiber attenuation

Fiber attenuation is the rate at which guided light loses power as it travels along an optical fiber, expressed in decibels per kilometre. Because the loss is exponential in length, a single dB/km figure describes any length: standard single-mode silica fiber has about 0.33 dB/km at 1310 nm and about 0.2 dB/km at 1550 nm, near the absolute minimum of silica, so a 15 km span at 1550 nm halves the power. Graded-index multimode fiber has roughly 2.5–3.5 dB/km at 850 nm, and polymer fiber on the order of 150 dB/km in the visible.

Definition

If $P_\mathrm{in}$ enters a fiber of length $L$ (in km) and $P_\mathrm{out}$ leaves it, the attenuation coefficient in dB/km is

$$\alpha_\mathrm{dB} = \frac{10}{L}\log_{10}\frac{P_\mathrm{in}}{P_\mathrm{out}}.$$

The same loss written as a natural exponential, $P(z) = P_\mathrm{in}e^{-\alpha z}$, has $\alpha$ in nepers per kilometre (km⁻¹), with $\alpha_\mathrm{dB} = 4.343\,\alpha$. At 0.2 dB/km, $\alpha$ = 0.046 km⁻¹ and the $1/e$ length is 21.7 km. Working in decibels makes a link calculation a sum: 80 km at 0.2 dB/km is 16 dB, to which connector and splice losses are added in the link budget.

Loss mechanisms in silica

• Rayleigh scattering. Frozen-in density and composition fluctuations, far smaller than the wavelength, scatter light with a $\lambda^{-4}$ dependence. Written as $A/\lambda^4$ with $A$ about 0.9 dB·µm⁴/km for germanium-doped cores, it contributes about 0.16 dB/km at 1550 nm, 0.31 dB/km at 1310 nm and 1.7 dB/km at 850 nm. It is the dominant term across the telecom windows and is treated in Rayleigh scattering.
• Infrared absorption. Vibrational absorption of the Si–O bond rises steeply beyond about 1.6 µm and closes the low-loss window on the long-wavelength side.
• Ultraviolet absorption. Electronic absorption tails fall off quickly and matter little above 1 µm.
• Impurity absorption. Hydroxyl (OH) groups produce an overtone peak at 1383 nm. Older fibers showed roughly 0.5–2 dB/km there; low-water-peak fibers reduce it to near the Rayleigh background, which opens the E-band for coarse WDM.
• Waveguide and bending losses. Macroscopic bends and microscopic deformations from cabling radiate power out of the core; see bend loss and microbend loss. These are added by installation, and single-mode fiber is more bend sensitive at 1550 nm than at 1310 nm because its mode is wider.

Pure-silica-core fibers, which avoid germanium doping and its extra scattering, have reported losses of about 0.14–0.15 dB/km at 1550 nm. Hollow-core fiber removes most of the glass from the light path and is covered separately.

Measurement

Three methods are standard, with full procedures in How to Measure Fiber Attenuation and Bend Loss. The cutback method measures transmitted power through a long length, then cuts the fiber back to a few metres near the launch without disturbing the input coupling and measures again; the difference removes the launch loss. As a worked example, 0.500 mW measured after 2 m and 0.402 mW after 5.002 km give

$$\alpha_\mathrm{dB} = \frac{10}{5.0}\log_{10}\frac{0.500}{0.402} = 0.19\ \mathrm{dB/km}.$$

Insertion-loss measurement with a stable source and an optical power meter is non-destructive and is used for installed links, where it measures the whole span including connectors. Optical time-domain reflectometry infers the loss from the slope of Rayleigh backscatter along the fiber, which also locates splices, bends and breaks; splice and segment-boundary losses need a bidirectional average because backscatter efficiency varies between fibers.

Historical milestones

In 1966 Kao and Hockham argued that glass fiber could serve for communication if its loss fell below about 20 dB/km. Corning reported fiber below that threshold in 1970, at about 17 dB/km near 633 nm, which passes 2% of the light through 1 km. By 1979 Miya and colleagues had reached 0.2 dB/km at 1.55 µm, close to today's standard values.

Pitfalls

Launch conditions matter for multimode fiber: an overfilled launch excites lossy high-order modes and exaggerates short-length loss, so measurements use a mode scrambler or controlled launch. Short single-mode samples near cutoff can carry a leaky second mode. Power meter linearity and connector repeatability often limit accuracy more than the fiber itself, since 0.1 dB of connector variation is already half a kilometre of fiber at 1550 nm.

Common questions

What is the attenuation of optical fiber in dB/km?

For standard single-mode telecom fiber, about 0.33 dB/km at 1310 nm and 0.2 dB/km at 1550 nm; cable specifications often allow somewhat more, around 0.35–0.4 and 0.22–0.3 dB/km. Graded-index multimode fiber is about 2.5–3.5 dB/km at 850 nm and 0.5–1 dB/km at 1300 nm.

Why is attenuation lowest near 1550 nm?

Rayleigh scattering falls as $\lambda^{-4}$, so it is 11 times weaker at 1550 nm than at 850 nm, while infrared absorption rises steeply beyond about 1.6 µm. The sum of the two has its minimum between 1.55 and 1.6 µm.

What is the difference between attenuation and dispersion?

Attenuation reduces the power of the signal; dispersion spreads its pulses in time without removing energy. Attenuation limits how weak the signal becomes at the receiver, and dispersion limits how fast it can be modulated over a given distance.

References: Saleh & Teich, Fundamentals of Photonics 3rd ed. 2019, Ch. 10; G. P. Agrawal, Fiber-Optic Communication Systems 4th ed. 2010, Ch. 2; K. C. Kao & G. A. Hockham, Proc. IEE 113, 1151 (1966); T. Miya et al., Electron. Lett. 15, 106 (1979).