Engineering

Dispersion — when the pulses smear

Loss weakens a signal; noise buries it. Dispersion does something different — it spreads each light pulse out in time until neighbouring pulses overlap and the receiver can no longer tell where one bit ends and the next begins. A signal can arrive strong and clean of noise and still be unreadable because it is smeared. This is the third limit on reach, and at high bit rates it often bites first.

Mental model

A bit is a short pulse of light. Dispersion makes that pulse arrive as a wider pulse than it started — because different parts of it travel at slightly different speeds down the fiber. Send bits close together (high bit rate) and once each pulse has widened enough, it bleeds into its neighbours. The receiver sees mush instead of clean ones and zeros. That overlap is called inter-symbol interference, and it is what dispersion ultimately causes.

PULSE SPREADING along the fiber At the transmitter (0 km): crisp, well-separated pulses 1 0 1 1 0 1 ██ __ ██ ██ __ ██ each bit is a tidy block Halfway down the fiber: pulses have widened, edges soften ▓▓▒ ▒_▒ ▓▓▒ ▓▓▓ ▒_▒ ▓▓▒ still just about separable Near the dispersion limit: pulses overlap — bits blur together ▒▓▓▓▒▒▓▓▓▓▓▓▓▓▒▒▓▓▓▒ receiver can no longer tell 1 from 0 └ where did each bit begin? → errors from inter-symbol interference The signal here may be PLENTY strong and low-noise — it is simply too smeared in TIME to decode. That is a dispersion limit, not a loss or OSNR limit.

Chromatic dispersion (CD)

A laser pulse is not a single perfect colour — it contains a small spread of wavelengths (its spectral width). In glass, different wavelengths travel at slightly different speeds. So the "blue" edge of the pulse and the "red" edge arrive at slightly different times, and the pulse widens. That is chromatic dispersion. It is deterministic and predictable: it depends on the fiber type, the wavelength, the distance, and how spectrally "wide" the source is.

Fiber / condition	Dispersion coefficient D	Note
Standard SMF (G.652) at 1550 nm	≈ +17 ps/(nm·km)	The number to remember for the C-band
Standard SMF (G.652) at 1310 nm	≈ 0	G.652 is designed with its zero-dispersion point near 1310 nm
NZDSF (G.655)	Lower (a few ps/(nm·km))	Non-zero dispersion-shifted — kept small but deliberately non-zero in the C-band

The units tell the whole story. ps/(nm·km) = picoseconds of spreading, per nanometre of source spectral width, per kilometre of fiber. Multiply all three together and you get total spreading in picoseconds.

The total-CD formula

Total CD (ps/nm) = D [ps/(nm·km)] × Length [km] ...that gives the dispersion "amount" the link presents (ps/nm). The actual pulse spreading in picoseconds is then: Pulse spread (ps) = D × Length × source_spectral_width (nm) = Total CD (ps/nm) × spectral width (nm) Two things to notice: • CD ACCUMULATES with distance — every km adds D more ps/nm. • A spectrally NARROW source (fine laser) spreads less than a wide one.

Because CD accumulates linearly with distance, engineers talk about a fiber's accumulated dispersion in ps/nm at a given point, and about a transponder's CD tolerance — the maximum ps/nm it can receive before the smear causes errors. The link closes (for dispersion) when accumulated CD stays under the transponder's tolerance.

Direct-detect reach limit — a worked example

A traditional direct-detect receiver (it simply detects light on/off — no fancy processing) has a fixed CD tolerance. Illustrative figures:

A 10G direct-detect signal tolerates roughly 1000 ps/nm before it needs compensation.
On G.652 fiber at 1550 nm (D ≈ 17 ps/(nm·km)), that is a reach of about 1000 ÷ 17 ≈ 60 km (commonly quoted as ~60–80 km depending on the exact tolerance and margin).
40G direct-detect tolerates roughly 16× less accumulated CD than 10G — so its uncompensated reach is roughly 16× shorter (only a few km). Higher rates are dramatically more dispersion-sensitive.

WHY HIGHER RATES DIE FASTER (direct-detect, illustrative) Rate CD tolerance Uncompensated reach on G.652 (D=17) 10G ~1000 ps/nm ~1000/17 ≈ 60 km (quoted ~60–80 km) 40G ~16x LESS ~16x shorter → only a few km ...tolerance drops roughly with the SQUARE of the bit rate, so quadrupling the rate (10G→40G) cuts CD tolerance ~16x. Worked check at 10G, 80 km G.652: accumulated CD = 17 ps/(nm·km) × 80 km = 1360 ps/nm 1360 ps/nm > ~1000 ps/nm tolerance → OVER the limit → this 80 km 10G span needs dispersion compensation (or coherent).

Compensating CD — DCF/DCM vs coherent

There are two eras of answer to chromatic dispersion.

Old way — DCF / DCM in the glass

A Dispersion Compensating Module (DCM), built from a spool of Dispersion Compensating Fiber (DCF) with the opposite sign of dispersion, is spliced into the line to cancel the accumulated CD. Physical, per-span, tuned to a design distance. It also adds loss (so it eats loss budget) and adds latency, and it only fixes CD — not PMD.

Modern way — coherent DSP in silicon

A coherent receiver captures the full optical field and a DSP chip electronically reverses the dispersion after detection — no compensating fiber at all. It handles enormous accumulated CD (and PMD too) in software, tuned automatically. This is why new builds have no DCMs: the compensation moved from glass into a chip.

Key idea — why coherent killed the DCM

For decades every long span carried a physical DCM to undo chromatic dispersion, at the cost of extra loss, latency, and per-distance engineering. A coherent transponder's DSP undoes CD (and PMD) electronically, adapting automatically to whatever the fiber presents. So modern coherent line systems simply omit the DCMs — dispersion is no longer a thing you fight in the glass; it is a thing the DSP cleans up in silicon. If you see a design with no dispersion compensation and lots of accumulated CD, that is not a mistake — it is coherent.

Polarization-mode dispersion (PMD)

CD is not the only way pulses spread. Light travels in two polarization states at once, and if the fiber's core is not perfectly round (from manufacturing, bends, or stress), those two polarizations travel at slightly different speeds. The gap between them is the Differential Group Delay (DGD), and its accumulation over distance is Polarization-Mode Dispersion (PMD).

Property	Chromatic dispersion (CD)	Polarization-mode dispersion (PMD)
Cause	Different wavelengths travel at different speeds	Two polarizations travel at different speeds (non-round core)
Units	ps/(nm·km) → accumulates as ps/nm	ps/√km → accumulates as ps of DGD
Behaviour	Deterministic, stable, predictable	Statistical — varies with time, temperature, vibration
Scales with distance as	Linear (× km)	Square-root (× √km)
Fixable by DCF?	Yes (DCM undoes it)	No — DCF cannot fix PMD
Fixable by coherent DSP?	Yes	Yes — the DSP tracks and compensates it

Two things make PMD tricky. First, it grows only as the square root of distance (ps/√km), so it is small on short links and matters mostly on long ones. Second, it is statistical — the DGD wanders over time with temperature and mechanical stress, so a link can be fine one hour and marginal the next. PMD starts to matter at 10G and above, and especially on older fiber that was manufactured before tight PMD specs. It sets a PMD-limited reach that no dispersion-compensating fiber can extend — only coherent DSP (or lower rates) helps.

Common mistake — old fiber, high rate

Lighting a decades-old dark-fiber route at 10G/40G direct-detect and being surprised by intermittent errors that come and go with the weather. That is the classic signature of PMD on aged fiber: statistical, time-varying, and not fixable by adding a DCM or an amplifier. On suspect old fiber, either measure PMD before committing to a rate, or plan for coherent optics whose DSP tracks the wandering DGD.

When dispersion — not loss or OSNR — is the limiter

Three different walls can end a link, and they demand different fixes. Diagnose which one you have hit before reaching for hardware:

Limiter	Symptom	Signature	Fix
Loss (power)	Received power below Rx sensitivity	Low Rx power reading; short or lossy link	Add gain / amplifier, clean connectors, reduce span loss
OSNR (noise)	Errors despite adequate power	Many amplified spans; pre-FEC BER creeps up with distance	Regenerator, Raman, stronger FEC, fewer spans
Dispersion (CD)	Errors on a high-rate, longish span even with good power & OSNR	High bit rate + long G.652 span, no compensation	DCM/DCF, or (modern) coherent DSP
Dispersion (PMD)	Intermittent errors that vary with time/temperature	Old fiber, 10G+, errors come and go	Coherent DSP, or lower rate; DCF will NOT help

Diagnostic order

Check power first (is Rx power in spec?). If power is fine but errors persist, check whether the span is amplified enough to be OSNR-limited. If power and OSNR are both healthy on a high-rate link, suspect chromatic dispersion. And if the errors are intermittent and weather-following on old fiber, suspect PMD. Each points to a different remedy — and dispersion problems are the ones an amplifier can never solve.

Field checklist — assessing dispersion

Identify the fiber type (G.652 vs G.655) and the operating band — it sets the CD coefficient.
Compute accumulated CD = D × length and compare it to the transponder's CD tolerance.
Remember higher bit rates tolerate far less CD — quadrupling the rate cuts tolerance ~16×.
Decide the compensation strategy: DCM/DCF (legacy) or coherent DSP (modern, no DCM).
If using a DCM, account for the extra loss and latency it adds to the budget.
On old fiber at 10G+, measure or estimate PMD — it is statistical and DCF cannot fix it.
When erroring, isolate whether the wall is loss, OSNR, CD, or PMD before adding hardware.

Common mistakes

Treating dispersion like loss

Assuming an amplifier or cleaner connectors will fix smeared pulses. Dispersion is a timing problem, not a power one — more power just gives you a stronger smear. Compensate the dispersion (DCM or coherent), don't amplify it.

Using DCF against PMD

DCF cancels chromatic dispersion only. It does nothing for PMD, which is a polarization effect. If old-fiber errors are statistical/time-varying, DCF is the wrong tool — you need coherent DSP or a lower rate.

Ignoring rate sensitivity

Reusing a distance limit from a 10G design when upgrading to 40G/100G direct-detect. CD tolerance falls sharply with rate; the old reach no longer applies.

Forgetting DCM adds loss

Dropping a DCM into a link to fix CD and then finding the loss budget no longer closes. Compensation fiber is real fiber — it attenuates. Budget for it.

1. A 10G direct-detect link over 80 km of G.652 is erroring even though power and OSNR are fine. What is the likely limiter and the fix?

Chromatic dispersion. Accumulated CD ≈ 17 × 80 = 1360 ps/nm, over the ~1000 ps/nm direct-detect tolerance. Fix with a DCM/DCF or move to a coherent transponder whose DSP undoes CD.

2. What is the CD coefficient of standard SMF (G.652) at 1550 nm, and roughly what is it at 1310 nm?

About +17 ps/(nm·km) at 1550 nm; approximately zero at 1310 nm (G.652's zero-dispersion wavelength sits near 1310 nm).

3. A route on old fiber shows errors that appear and disappear with temperature at 10G. DCF didn't help. Why, and what will?

This is PMD — statistical, time-varying differential group delay, common on old fiber at 10G+. DCF only cancels chromatic dispersion, not PMD. The fix is a coherent transponder (its DSP tracks the wandering DGD) or a lower bit rate.

4. Why do modern coherent line systems have no DCMs?

Because the coherent receiver's DSP compensates chromatic dispersion (and PMD) electronically, adapting automatically. The compensation moved from physical fiber (DCM) into silicon, so the DCMs are simply omitted.

5. Roughly how does CD tolerance change going from 10G to 40G direct-detect, and what does that do to reach?

CD tolerance drops roughly with the square of the bit rate, so 10G→40G (4× rate) means about 16× less tolerance — and therefore about 16× shorter uncompensated reach.

Try it: chromatic-dispersion calculator

Multiply D by distance to see accumulated CD, then compare it to the rate's tolerance. Switch to a coherent optic and watch the CD limit disappear — the DSP undoes it.