Speed of light in fiber

The speed of light in vacuum is fixed by definition at $c$ = 299,792,458 m/s, which is 3.336 µs per kilometre. In any material light is slower, and in an optical fiber the speed that matters for a signal, a pulse or a timing measurement is the group velocity, $v_g = c/n_g$, where $n_g$ is the group index of the guided mode. It is slightly larger than the ordinary refractive index of the silica, because the index also changes with wavelength.

Typical values

For standard single-mode fiber of the SMF-28 type, Corning specifies an effective group index of 1.4676 at 1310 nm and 1.4682 at 1550 nm. Light therefore travels at about 204,200 km/s, 68% of its vacuum speed, and the one-way delay is 4.90 µs per kilometre at either wavelength. A 10 km data-centre interconnect adds 49 µs of one-way latency; a 6,000 km transoceanic route adds 29.4 ms before any equipment delay, and the round trip doubles both. The phase velocity, $c/n$, is slightly higher: about 207,600 km/s with $n \approx 1.444$, the index of pure silica at 1550 nm (the doped core and the guided mode are slightly higher). It carries no information.

Hollow-core fiber guides light in air, where the group index is within a few parts in ten thousand of 1, so the delay falls to about 3.34 µs/km. The saving of about 1.56 µs/km, 32% of the time in solid fiber, is the reason hollow-core links are deployed for latency-sensitive routes such as those between financial exchanges and between data centres.

Where it matters

Latency budgets for trading networks, 5G fronthaul and distributed data centres count fiber delay per kilometre. Reflectometers such as the OTDR convert round-trip time into distance using the group index, so a wrong index setting gives a proportionally wrong fiber length. Pulse timing in fiber sensors, delay lines and time-transfer links depends on it, and so does the temperature sensitivity of delay, which in standard fiber is a few tens of picoseconds per kilometre per kelvin, the reason precision timing links are compensated. Signals at different wavelengths travel at slightly different speeds because of chromatic dispersion: 17 ps/(nm·km) near 1550 nm in standard fiber.

Measurement

The group index of a fiber is measured by timing a pulse through a known length, or by measuring the length independently and reading the delay from an OTDR, whose group-index setting is adjusted until the two agree. For a precise value, a modulated signal's phase delay through the fiber is measured with a network analyzer as the modulation frequency or wavelength is stepped.

References: Corning SMF-28 Ultra optical fiber product information (effective group index); BIPM, The International System of Units (SI brochure), 9th ed. (2019).