Dispersion and bandwidth

Attenuation makes a pulse weaker; dispersion makes it wider. Different parts of the light — different modes, different wavelengths, different polarizations — travel at slightly different speeds and arrive at slightly different times, so a sharp "1" smears into its neighbours. At low rates and short distances this is invisible; at 10 Gb/s over 80 km or at 25 Gb/s over 100 m of multi-mode it is the limit. This page explains the three kinds of dispersion, the bandwidth–distance product of multi-mode fibre, how to estimate a dispersion-limited reach, and how modules and systems compensate.

Three kinds of dispersion

Kind	Cause	Where it dominates	Typical size
Modal (intermodal)	different modes take different paths	multi-mode fibre	ns/km in step-index; ~0.1–0.5 ns/km graded-index; described as bandwidth in MHz·km
Chromatic	the glass's index depends on wavelength (material) and the guide geometry adds its own (waveguide); a source has non-zero spectral width	single-mode at 1550 nm; long links at 10G+	17 ps/(nm·km) at 1550 on G.652; ≈ 0 at 1310
Polarization-mode (PMD)	the two polarization states travel at slightly different speeds due to fibre asymmetry	40G+ NRZ over long fibre; old fibre	0.05–0.5 ps/√km

Multi-mode fibre is rated by effective modal bandwidth (EMB) in MHz·km: the frequency at which the fibre's response has fallen 3 dB, times the length. Bandwidth divides by length:

Grade	EMB at 850 nm	Bandwidth over 100 m	Bandwidth over 300 m
OM1	200 MHz·km	2 GHz	0.67 GHz
OM2	500	5 GHz	1.7 GHz
OM3	2 000	20 GHz	6.7 GHz
OM4	4 700	47 GHz	15.7 GHz

A rule of thumb: a link needs bandwidth ≈ 0.7 × bit rate for NRZ. 10 Gb/s wants ~7 GHz → OM3 to ~285 m (standard says 300 m); 25 Gb/s wants ~17.5 GHz → OM4 to ~270 m in theory, but the receiver's dispersion tolerance and VCSEL spectral width bring the standard to 100 m. Hence the reach table:

Rate per lane	OM3	OM4	Limit
1 Gb/s	550–1 000 m	550–1 100 m	attenuation as much as bandwidth
10 Gb/s	300 m	400 m	modal bandwidth
25 Gb/s NRZ	70 m	100 m	modal + chromatic (VCSEL spectral width)
50 Gb/s PAM4	70 m	100 m	same, plus PAM4 SNR penalty
100 Gb/s PAM4 (802.3db)	—	50–100 m	with DSP equalisation

Full table: Reach tables. The launch condition (encircled flux) is standardised so these figures hold with real VCSELs.

Chromatic dispersion on single-mode fibre

The dispersion coefficient D (ps per nm of source width per km) crosses zero near 1 310 nm in standard G.652 fibre and is ≈ +17 ps/(nm·km) at 1 550 nm. Pulse spreading:

Δt = D × Δλ × L

Source	Spectral width Δλ	D at λ	L	Δt	Bit period (10G ≈ 100 ps)
DFB laser at 1310 nm	0.1 nm (or 1 nm −20 dB)	≈ 0–3 ps/(nm·km)	10 km	< 10 ps	fine
DFB at 1550 nm, 10G, DML	0.2 nm (chirp widens it)	17	80 km	270 ps	too much — needs EML (low chirp) or DCM
EML at 1550 nm, 10G	~0.1 nm effective	17	80 km	~140 ps → tolerable with penalty	10GBASE-ZR
Fabry-Pérot laser at 1310	3–5 nm	3	2 km	20–30 ps	fine at 1G, marginal at 10G
LED at 1300 (legacy)	50–100 nm	3	2 km	300–600 ps	100 Mb/s only
VCSEL 850 nm on OM4	0.5 nm RMS	~ −100 ps/(nm·km) at 850	0.1 km	5 ps	chromatic matters at 25G+

Dispersion tolerance appears in datasheets as ps/nm (e.g. 800 ps/nm for a 40 km ER module = 17 × 40 × ~1.2 nm): the link's D × L must stay below it (Reading a datasheet).

Dispersion-limited reach (NRZ, uncompensated)

Rate	1310 nm on G.652	1550 nm on G.652	Note
2.5 Gb/s	> 100 km	~600–1 000 km	attenuation limits first
10 Gb/s	~40–60 km (source-limited)	~60–80 km (EML), ~10–20 km (DML)	why 10G ER/ZR use EML
25 Gb/s	10 km (25GBASE-LR)	~10–15 km	25GBASE-ER at 1550 needs careful design
40 Gb/s serial	~4 km	~4 km	reason 40G/100G went to 4 × 10G/25G WDM
100 Gb/s single λ PAM4 (DR/FR/LR1)	2–10 km at 1310	—	1310 nm chosen for ≈ 0 dispersion; DSP handles the rest

Rule of thumb: reach scales with 1/(bit rate)² for a fixed source width — doubling the rate cuts dispersion-limited distance by four.

Compensation and mitigation

Method	Where	How
Choose 1310 nm	DR/FR/LR at 100G+	zero-dispersion window; pays 0.35 dB/km instead of 0.2
Low-chirp source (EML, external modulator)	10G ER/ZR, DWDM 10G	narrower effective spectrum (Lasers)
Dispersion compensation module (DCM)	10G DWDM spans	spool of negative-dispersion fibre or fibre Bragg grating cancels D × L
Dispersion-shifted / NZ-DSF fibre (G.653/G.655)	legacy long-haul plant	zero or small D at 1550
Electronic dispersion compensation	10GBASE-LRM (EDC in host), PAM4 DSP (FFE/DFE/MLSE)	equaliser undoes the smear digitally (DSP)
Coherent detection + DSP	100G–800G ZR/ZR+	dispersion compensated entirely in the digital domain, thousands of ps/nm (Coherent)
FEC	25G+	corrects the errors dispersion causes rather than preventing them (FEC & AN)

Polarization-mode dispersion

Fibre is never perfectly round; the two polarization axes see slightly different indices and the pulse splits by a differential group delay that grows with the square root of length (random mode coupling). Modern fibre: ≤ 0.1 ps/√km → 1 ps over 100 km, harmless up to 40 Gb/s NRZ. Old (pre-1995) fibre: 0.5–2 ps/√km, a problem at 10G over 100 km+ and a reason coherent DSP tracks polarization continuously.

How dispersion shows up

Observation	Meaning
Rx power well above sensitivity, yet errors or no link	dispersion (or reflections) — power is not the problem (Rx power & budget)
Link works at 1G, fails at 10G on the same fibre	modal bandwidth (MMF) or DML chirp at 1550 (SMF)
10 km LR module fine, 40 km ER fine, ZR marginal	chromatic dispersion accumulating
FEC corrected errors high, uncorrectable rare	eye closure from dispersion partially corrected (VDM & FEC metrics)
Reach shortfall on OM3 with a "300 m" module	encircled-flux non-compliance or OM3 mislabelled OM2

In CodingBox

Dispersion tolerance is not stored in the EEPROM, but the fields that predict it are: wavelength (1310 vs 1550), laser type from the compliance codes (SR VCSEL, LR DFB, ER EML), and the OM3/OM4/SMF length fields the vendor rated the module for. CodingBox shows them so a "why does this 1550 nm module not do 80 km" question has data behind it (Check transceiver).

The other limit at high launch power — self- and cross-phase modulation, four-wave mixing, Brillouin and Raman scattering, and why dispersion actually helps against some of them: Non-linear effects.