Non-linear effects: SPM, XPM, FWM, Brillouin and Raman

Attenuation and dispersion are linear: doubling the power doubles the output and nothing else changes. Above a few milliwatts per channel in a 9 µm core, glass stops being linear — the refractive index starts to depend on intensity and the light starts to scatter off acoustic and molecular vibrations it excites itself. In a single 10G span this is invisible; in an amplified DWDM system with 80 channels over 1 000 km it sets the maximum launch power and therefore the reach. This page explains the five effects, when each matters, how they are quantified and how systems are designed around them.

Why fibre is non-linear at all

Quantity	Value in G.652	Meaning
Kerr coefficient n₂	≈ 2.6 × 10⁻²⁰ m²/W	index rises with intensity: n = n₀ + n₂·I
Effective area A_eff	≈ 80 µm² (G.652), 110–150 µm² (G.654.E)	intensity = power ÷ area — a small core concentrates light
Non-linear coefficient γ = 2πn₂/(λ·A_eff)	≈ 1.3 W⁻¹km⁻¹ (G.652 at 1550), ≈ 0.7 (G.654.E)	phase shift per watt per kilometre
Effective length L_eff = (1 − e^(−αL))/α	≈ 20 km for a long span at 0.2 dB/km	the effects accumulate mostly in the first tens of kilometres after each amplifier
Typical launch power per channel	0 … +3 dBm (1–2 mW) DWDM; up to +10 dBm single channel	non-linear phase φ_NL = γ·P·L_eff ≈ 0.03–0.3 rad per span

The Kerr effects

Effect	Mechanism	Symptom	Worst when
Self-phase modulation (SPM)	a pulse's own intensity changes its phase → chirp → spectral broadening; interacts with chromatic dispersion	eye closure, pulse distortion; in coherent systems a non-linear phase noise floor	high power, many spans, low dispersion
Cross-phase modulation (XPM)	neighbouring channels' intensity modulates a channel's phase	timing jitter and phase noise from other channels	dense spacing (50 GHz), low local dispersion, many channels
Four-wave mixing (FWM)	three frequencies generate a fourth at f₁ + f₂ − f₃; mixing products land on other channels	crosstalk that grows with power³	D ≈ 0 (G.653 fibre), equal channel spacing, high power

Local dispersion helps: it walks pulses of different channels past each other so XPM/FWM average out — the reason G.655 (small non-zero D) replaced G.653 for DWDM, and G.652 (D = 17) with dispersion compensation or coherent DSP is now preferred (Fibre types).

The scattering effects

Effect	Mechanism	Threshold	Symptom	Where
Stimulated Brillouin scattering (SBS)	light generates an acoustic wave that reflects it backwards, shifted by ≈ 11 GHz	≈ +6 … +10 dBm for a narrow-linewidth CW source in long SMF (lower for narrower lines)	forward power saturates, strong backward light, noise	CW lasers: 1550 nm analog video overlay (+17 dBm) and Raman pumps; mitigated by linewidth broadening / dithering (most transmitters do this)
Stimulated Raman scattering (SRS)	photons lose energy to molecular vibrations (Stokes shift ≈ 13 THz ≈ 100 nm)	total power above ≈ +20 … +25 dBm across a wide band	power tilt: short-wavelength channels pump long-wavelength ones — C-band feeds L-band	wide-band DWDM (C+L); managed by pre-emphasis and gain-tilt control; used deliberately in Raman amplifiers (Amplification & OSNR)

Where non-linearity matters — and where it does not

System	Non-linear penalty	Design response
Single 10G LR/ER span, −8 … +4 dBm	none	ignore
PON downstream +3 … +7 dBm, 20 km	none (SBS margin fine)	ignore; video overlay at +17 dBm uses SBS suppression
10G DWDM, 40 ch, 8 × 80 km with EDFAs	XPM/FWM on G.655, SPM everywhere	launch −2 … +1 dBm/ch, dispersion map, unequal spacing on DSF
100G/400G coherent DWDM, 80+ ch, 1 000+ km	non-linear phase noise limits OSNR gain from power	optimum launch ≈ 0 … +2 dBm/ch on G.652, +3 … +5 on G.654.E; GN-model planning
400ZR pluggable, single span ≤ 120 km	small	launch −10 … 0 dBm; loss-limited
Submarine 10 000 km	dominant	G.654 large-A_eff fibre, low launch, many repeaters, C+L
Raman-amplified spans	pumps at +27 … +30 dBm	connector cleanliness and safety critical (Safety & handling)

Rule: non-linear effects appear when power per channel × number of spans gets large; one span at moderate power never shows them.

Quantifying: the OSNR vs power trade-off

OSNR improves 1 dB for every 1 dB of launch power (linear regime).
Non-linear interference (NLI) noise grows with power³ — as +3 dB of noise per +1 dB of launch.
The sum has an optimum: the non-linear threshold where linear ASE noise equals NLI; systems are planned 1–2 dB below it. The Gaussian-noise (GN) model estimates NLI from γ, D, span length, channel count and spacing; planning tools do this per route.
Coherent DSP can partially undo SPM (digital back-propagation) but not XPM/FWM from other channels.

Mitigation summary

Method	Targets	Used in
Keep launch power near optimum (0 … +3 dBm/ch)	all Kerr effects	every DWDM design
Non-zero local dispersion (G.652 / G.655 instead of G.653)	FWM, XPM	fibre choice
Dispersion management (DCM map)	SPM/XPM interaction	10G DWDM
Large-effective-area fibre (G.654.E)	all (lower γ)	new long haul
Unequal channel spacing	FWM	DSF legacy routes
Linewidth dithering	SBS	CW analog, pumps
Gain tilt compensation, pre-emphasis	SRS	wide-band DWDM
Coherent DSP with NLC	SPM	400G+ long haul
Distributed Raman amplification	(uses SRS) lowers launch power needed	ultra-long spans

In CodingBox

Non-linear effects live in the line system, not in the module memory — but the module's declared Tx power and, for tunable DWDM modules, the channel plan are the inputs a planner needs. CodingBox shows the Tx power range and wavelength/channel fields so the per-channel launch budget starts from real numbers (Check transceiver, Tunable transceivers).