Transport Network Guide

Ch 05 — Fibre Nonlinearities and Power Optimisation

14 min read

Fibre Nonlinearities and Power Optimisation

Optical fibre is only approximately linear: above a per-channel power of a few milliwatts the silica’s refractive index begins to depend on intensity, and a family of distortion mechanisms — collectively known as fibre nonlinearities — start to corrupt the signal. This chapter explains the Kerr-effect family (SPM, XPM, FWM) and the scattering effects (SBS, SRS) one impairment at a time, treats the GN- and EGN-models that quantify accumulated nonlinear interference (NLI), and then walks the Gordon-Mollenauer launch-power optimum that every long-haul DWDM design has to solve. The chapter closes with effective-area considerations, why coherent links deliberately preserve high local dispersion, and the modern mitigation toolkit (digital backpropagation, probabilistic constellation shaping).

ConceptWhat it says
Kerr EffectThe intensity-dependent refractive index of silica. Three distinct impairments share this single underlying physics: SPM (a channel distorts itself), XPM (one channel distorts its neighbour), and FWM (two or three channels mix to generate spurious tones). Kerr is deterministic, instantaneous, and intensity-driven.
Scattering NonlinearitiesEnergy transfer to molecular vibrations. SBS scatters power backward off acoustic phonons within an extremely narrow bandwidth (~20 MHz) and clamps single-channel power to ~+7 dBm CW. SRS scatters power forward off optical phonons across a ~13 THz Stokes shift, transferring energy from short-wavelength channels to long-wavelength channels.
Nonlinear Interference (NLI)The aggregate ASE-like noise term produced by Kerr nonlinearity in a long, multi-channel chain. The GN-model treats NLI as Gaussian; the EGN-model corrects for the non-Gaussian residual on the constellation. Both let the planner predict NLI from launch power, span loss, dispersion, and channel count without solving the nonlinear Schrödinger equation.
Launch-Power OptimumThe Gordon-Mollenauer balance between two opposing curves: ASE-limited OSNR rises with launch power, NLI-limited noise rises faster than launch power. Total noise has a minimum — typically 0 to +2 dBm per channel for modern coherent systems on G.652.D — and that minimum sets every span’s per-channel target.
Effective Area (Aeff)The cross-sectional area over which the optical mode propagates. Larger Aeff dilutes intensity and reduces every Kerr nonlinearity proportionally, which is why submarine and long-haul terrestrial cables increasingly specify G.654 (Aeff ≈ 110-130 µm²) over standard G.652.D (Aeff ≈ 80 µm²).

The Two Families of Nonlinearity

graph TD
    NL["Fibre nonlinearities"] --> KERR["Kerr effect<br/>(intensity-driven)"]
    NL --> SCAT["Scattering<br/>(phonon-mediated)"]
    KERR --> SPM["SPM<br/>self-phase modulation:<br/>a channel distorts itself"]
    KERR --> XPM["XPM<br/>cross-phase modulation:<br/>neighbour channel distorts you"]
    KERR --> FWM["FWM<br/>four-wave mixing:<br/>two-three channels generate<br/>spurious tones"]
    SCAT --> SBS["SBS<br/>stimulated Brillouin scattering:<br/>backward, ~20 MHz bandwidth,<br/>clamps single-channel power"]
    SCAT --> SRS["SRS<br/>stimulated Raman scattering:<br/>forward, ~13 THz shift,<br/>tilts power across the band"]
    style NL fill:#1D9E75,stroke:#0F6E56,color:#fff
    style KERR fill:#D85A30,stroke:#993C1D,color:#fff
    style SCAT fill:#378ADD,stroke:#185FA5,color:#fff
    style SPM fill:#7F77DD,stroke:#534AB7,color:#fff
    style XPM fill:#7F77DD,stroke:#534AB7,color:#fff
    style FWM fill:#7F77DD,stroke:#534AB7,color:#fff
    style SBS fill:#BA7517,stroke:#854F0B,color:#fff
    style SRS fill:#BA7517,stroke:#854F0B,color:#fff

Two physical origins, five named impairments. Kerr nonlinearities respond instantaneously to optical intensity; scattering nonlinearities involve energy exchange with molecular vibrations.

Kerr Nonlinearities — One at a Time

Self-Phase Modulation (SPM)

SPM is the simplest Kerr impairment: a channel modulates its own phase as a function of its own intensity. The instantaneous refractive index seen by the pulse depends on the pulse’s own envelope, so the leading edge sees a different refractive index than the peak, which sees a different index than the trailing edge. The result is a frequency chirp that broadens the pulse spectrum — and, when chromatic dispersion is present, broadens or compresses the pulse in time depending on the sign of the dispersion.

Key Insight

SPM is the only nonlinearity present even in a single-channel system. If a coherent 100G signal launched alone into a fibre still degrades at high power, SPM is the suspect.

Cross-Phase Modulation (XPM)

XPM is the inter-channel cousin of SPM: channel A’s intensity envelope modulates channel B’s phase, because both channels share the same nonlinear medium. In a DWDM system XPM is typically twice as strong as SPM per neighbour, since the cross-Kerr coefficient is 2× the self-Kerr. In dense grids (50 GHz spacing or tighter) the cumulative XPM from many neighbours dominates SPM by an order of magnitude.

Walk-off Saves You

Chromatic dispersion makes channels travel at different group velocities, so a pulse on channel A only overlaps a given pulse on channel B for a finite time before they walk away from each other. Higher local dispersion (G.652.D, 17 ps/(nm·km)) reduces XPM strength because the interaction time per pulse pair shortens — this is why coherent systems prefer high-dispersion fibre.

Four-Wave Mixing (FWM)

FWM is the parametric process: three optical frequencies f1, f2, f3 mix in the Kerr nonlinearity to generate a fourth frequency f4 = f1 + f2 - f3. The new tone falls on top of (or close to) other DWDM channels and acts as crosstalk. FWM efficiency is sharply phase-matching dependent — it peaks when channels are equally spaced in a low-dispersion fibre (e.g. legacy NZDSF / G.655 was a dispersion-shifted fibre originally optimised against XPM but cursed with strong FWM at 100 GHz spacing).

Kerr impairmentWhat it doesWorst caseMitigation
SPMPulse self-chirps, broadens spectrumSingle-channel high-power linksLower launch; CD pre/post-compensation; PCS
XPMNeighbour intensity modulates your phaseDense DWDM grids on low-dispersion fibreHigher CD (G.652.D not G.655); larger Aeff; lower launch
FWMNew tones fall onto DWDM channelsEqual channel spacing on low-CD fibreHigher CD; unequal spacing (legacy mitigation); flex-grid

Intra-channel vs Inter-channel Kerr

In modern high-symbol-rate coherent transmission (32-96 Gbaud), pulse spreading from chromatic dispersion is so large that successive symbols on the same channel overlap during propagation. Intra-channel SPM, intra-channel XPM (iXPM), and intra-channel FWM (iFWM) become the dominant effects within a channel; inter-channel XPM and FWM still act between channels. The GN-model treats both regimes uniformly as a single NLI noise contribution.

Scattering Nonlinearities

Stimulated Brillouin Scattering (SBS)

SBS is energy exchange between the optical wave and an acoustic phonon in the silica. A small fraction of the forward signal scatters off a propagating acoustic wave and reflects backward, downshifted by ~11 GHz (the Brillouin frequency for silica at 1550 nm). The interaction has an extremely narrow gain bandwidth — about 20 MHz — which is why SBS only matters for CW or narrow-linewidth signals; modulated signals with linewidth >> 20 MHz spread the power above the SBS threshold across many phonon modes and never excite any single one strongly.

ParameterValue
Brillouin frequency shift~11 GHz at 1550 nm
Brillouin gain bandwidth~20 MHz (silica)
SBS threshold (single-channel CW)~+7 dBm into 20-25 km of G.652.D
Practical relevance for coherent DWDMNegligible (modulation linewidth >> 20 MHz)
Practical relevance for single-line-width pumpsCritical (Raman pumps are intentionally line-broadened)

Warning

Raman pump lasers — being narrow-linewidth and high-power — would trigger SBS catastrophically if not deliberately broadened to several GHz of linewidth via direct phase modulation or multi-laser combining. Vendor pump modules ship with this broadening built in.

Stimulated Raman Scattering (SRS)

SRS exchanges energy with an optical phonon rather than an acoustic phonon, producing a much larger frequency shift (~13 THz, ~100 nm at 1550 nm) and a much broader gain spectrum (~40 nm). In Ch03 we exploited SRS deliberately as an amplifier; here it is the uncontrolled cousin. In a fully loaded C+L DWDM signal, SRS transfers power forward from short-wavelength channels to long-wavelength channels — typically 3-4 dB per 80 km span across the C+L window — producing the SRS power tilt that the C+L compensation chain (pre-tilt + EDFA gain offset + DGE) is designed to fight.

Note

SBS and SRS share the “stimulated scattering” family but operate on completely different timescales and bandwidths. SBS is narrowband, backward, and an upper bound on per-channel CW power. SRS is broadband, forward, and a tilt across the loaded spectrum. Drafts that conflate the two are wrong.

Nonlinear Phase Noise and Dispersion

In direct-detect systems a phase rotation caused by Kerr nonlinearity is harmless (the receiver only sees intensity). In coherent systems, phase is the data — Kerr-induced phase noise lands directly on the constellation and rotates QAM symbols toward decision-region boundaries. Two interactions with dispersion matter:

  1. Walk-off averages XPM. Higher local dispersion reduces XPM-induced phase noise per neighbour.
  2. Pulse overlap (intra-channel Kerr) is enabled by dispersion. The same dispersion that helps inter-channel XPM hurts intra-channel SPM/iXPM/iFWM at high symbol rates.

The net is a flat-bottomed optimum: too little dispersion → strong XPM; too much dispersion → strong intra-channel Kerr. G.652.D at 17 ps/(nm·km) sits comfortably in the favourable region for 32-96 Gbaud coherent.

The GN- and EGN-Models — Predicting NLI

For a long DWDM chain the per-channel nonlinear interference power can be approximated, in the Gaussian-Noise (GN) model of Poggiolini and colleagues, as

P_NLI = η · P_ch^3

where η depends on fibre attenuation, dispersion, effective area, channel spacing, channel count, and span count. NLI scales as the cube of per-channel power, which is the fundamental reason a launch-power optimum exists. The Enhanced GN (EGN) model adds modulation-format-dependent corrections — Gaussian symbols (which PCS approximates) generate slightly more NLI than uniform-QAM symbols, but the difference is offset by their better OSNR sensitivity.

Key Insight

The cubic scaling of P_NLI is the single most important fact in long-haul nonlinearity engineering. A 1 dB increase in launch power produces a 3 dB increase in NLI noise but only a 1 dB increase in OSNR — the cost-benefit ratio inverts at the optimum.

The GN-model reduces nonlinearity engineering to an analytic exercise: given fibre and span parameters, η is a number; the Gordon-Mollenauer optimum is then found by setting dN_total / dP_ch = 0 over the sum of ASE and NLI noise. Modern planning tools (Ciena MCP, Nokia WaveSuite, GNPy as the open-source reference) embed an EGN-model evaluator and return optimal launch power per span automatically.

Worked Example — Launch-Power Optimum on a 10 × 100 km G.652.D Chain

Consider a representative long-haul chain: 10 spans of 100 km G.652.D fibre at 0.20 dB/km, EDFAs with NF = 5 dB matching span loss, 96 channels at 50 GHz spacing in C-band, modulation DP-16QAM at 32 Gbaud (400G class). Per-stage OSNR follows the standard formula; total noise is the sum of ASE and NLI.

Per-channel launchOSNR_ASE (dB)NLI noise (dB-equiv)Total noise (dB)Net SNR (dB)Notes
-1 dBm24.031.023.223.2ASE-limited; reach-limited
0 dBm25.028.023.523.5Approaching optimum
+1 dBm26.025.023.523.5Optimum (G-M point)
+2 dBm27.022.021.821.8NLI-limited
+3 dBm28.019.018.918.9NLI dominates; constellation broken
+5 dBm30.013.013.013.0Catastrophic — well into NLI brick wall

Two things to read from the table:

  1. The optimum is flat around +1 dBm — within ±1 dB of optimum, total SNR varies by only ~0.3 dB. Field deployments rarely tune to better than ±0.5 dB.
  2. Past the optimum, every extra 1 dB of launch costs ~3 dB of total SNR (NLI cubic), so erring high is far worse than erring low. The operational rule is: when in doubt, drop launch power 0.5-1 dB below the calculated optimum.

Rule of Thumb

On modern G.652.D coherent links, the per-channel launch optimum sits between 0 and +2 dBm. On large-Aeff G.654 cables it moves up to +2 to +4 dBm (more “headroom” before NLI kicks in). On legacy G.655 NZDSF it drops to ~-1 to 0 dBm (small Aeff, low dispersion → strong XPM and FWM).

Effective Area Aeff Across Fibre Types

xychart-beta
    title "Effective area (Aeff) by fibre type — bigger is better for nonlinearity"
    x-axis ["G.655 NZDSF", "G.652.D", "G.654.B", "G.654.E"]
    y-axis "Aeff (µm²)" 60 --> 140
    bar "Aeff" [70, 80, 110, 130]
Fibre typeTypical AeffDispersion at 1550 nmLoss at 1550 nmNLI relative to G.652.D
G.655 NZDSF~70 µm²~4 ps/(nm·km)0.21 dB/km+1 to +2 dB worse
G.652.D~80 µm²~17 ps/(nm·km)0.20 dB/kmReference (0 dB)
G.654.B~110 µm²~20 ps/(nm·km)0.18 dB/km-1.5 dB better
G.654.E~130 µm²~22 ps/(nm·km)0.16 dB/km-2.5 dB better

NLI scales inversely with Aeff (intensity = power / area), so a 50% larger Aeff cuts NLI by ~1.8 dB. Combined with G.654’s lower attenuation (~0.16-0.18 dB/km vs 0.20 dB/km), modern submarine and ultra-long-haul terrestrial systems gain 3-4 dB of total system margin over G.652.D — enough for one extra modulation step or several hundred extra kilometres of reach.

Warning

G.655 NZDSF was the long-haul workhorse from ~1996 to ~2008, designed to suppress XPM in 10G EDFA-based DWDM systems by reducing dispersion. In coherent systems the design choice has reversed: low dispersion now hurts (strong XPM, strong FWM at equal spacing), and digital CD compensation has eliminated the original motivation for shifted-dispersion fibres. New builds default to G.652.D or G.654.

In direct-detect 10G systems, dispersion-compensating modules (DCMs) — long spools of fibre with opposite dispersion sign, often DCF — were inserted at every amplifier site to keep the cumulative CD near zero. DCMs add ~6-8 dB of insertion loss per site and have small Aeff that increases Kerr nonlinearity locally.

Coherent systems delete the DCM entirely. Chromatic dispersion is compensated digitally in the receiver DSP (frequency-domain filter; see 06-coherent-dsp-internals), so local dispersion can stay high all the way through the link. This produces three benefits at once:

  1. Strong walk-off averages XPM across many bit slots → less inter-channel Kerr noise.
  2. No DCMs → no extra insertion loss → more OSNR margin.
  3. No DCMs → no high-NLI dispersion-compensating fibre → no localised hotspots.

Warning

Drafts inserting DCMs into coherent designs are wrong. DCMs disappeared from coherent line systems around 2012 and have never returned. The only modern role for any dispersion-shaping module is in specialty short-reach or analogue-RoF systems unrelated to mainstream DWDM.

Mitigation Toolkit

Beyond launch-power optimisation and fibre-type selection, three mitigations apply to operational systems:

Digital Backpropagation (DBP)

DBP simulates the inverse nonlinear Schrödinger equation in the receiver DSP, undoing SPM (and partially XPM) by applying the conjugate phase rotation. DBP delivers 1-3 dB of NLI margin in long-haul subsea systems where every dB matters, but is computationally expensive (multiple steps per span) and is therefore reserved for premium platforms.

Probabilistic Constellation Shaping (PCS)

PCS shapes the symbol-occurrence probability toward a Maxwell-Boltzmann distribution rather than the uniform distribution of standard QAM. The result is a Gaussian-like signal that approaches the Shannon capacity by ~1 dB and — relevant here — has slightly more graceful behaviour at the NLI-dominated edge of the launch-power curve. PCS also makes the modulation rate-adaptive: a single transponder can dial bits-per-symbol continuously between, e.g., DP-QPSK and DP-64QAM. Full treatment in 06-coherent-dsp-internals.

Per-Channel Power Control

Modern ROADM nodes integrate per-channel VOAs in the WSS that adjust each wavelength’s power to the network management system’s calculated optimum, span by span. This catches residual SRS tilt and per-channel imbalance that static EDFA gain settings cannot.

Summary

Fibre nonlinearity sets the upper bound on per-channel power in every modern long-haul DWDM design. The GN/EGN-models make NLI a calculable noise term that scales as the cube of launch power; the Gordon-Mollenauer optimum is the minimum of (ASE noise) + (NLI noise) and sits between 0 and +2 dBm per channel on G.652.D. Larger Aeff (G.654) and higher local dispersion (which kills DCMs) are the two structural choices that buy the most margin. Operational mitigation is layered: per-channel power control catches residual tilt, PCS shapes the constellation, and DBP cleans up SPM in premium deployments.

See Also

References

Standards (ITU-T)

  1. ITU-T G.652 — Characteristics of a single-mode optical fibre and cable (11/2016). https://www.itu.int/rec/T-REC-G.652
  2. ITU-T G.654 — Characteristics of cut-off shifted single-mode optical fibre and cable (03/2020). https://www.itu.int/rec/T-REC-G.654
  3. ITU-T G.655 — Characteristics of non-zero dispersion-shifted single-mode optical fibre and cable (11/2009). https://www.itu.int/rec/T-REC-G.655
  4. ITU-T G.650.2 — Definitions and test methods for statistical and non-linear related attributes of single-mode fibre and cable (07/2015). https://www.itu.int/rec/T-REC-G.650.2
  5. ITU-T G.663 — Application related aspects of optical amplifier devices and subsystems. https://www.itu.int/rec/T-REC-G.663

Books

  1. G. P. Agrawal, Nonlinear Fiber Optics, 6th ed., Academic Press, 2019.
  2. G. P. Agrawal, Fiber-Optic Communication Systems, 5th ed., Wiley, 2021.
  3. I. P. Kaminow, T. Li, A. E. Willner (Eds.), Optical Fiber Telecommunications VI-A & VI-B, Academic Press, 2013.

Papers

  1. P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30, 3857 (2012).
  2. A. Carena et al., “EGN model of non-linear fiber propagation,” Opt. Express 22, 16335 (2014).
  3. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15, 1351 (1990).
  4. A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, et al., “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photon. 9, 429 (2017).
  5. J. Cho et al., “Probabilistic Constellation Shaping for Optical Fiber Communications,” J. Lightwave Technol. 37, 1590 (2019).
  6. GNPy — open-source GN-model reference implementation, Telecom Infra Project (TIP) OOPT-PSE working group. https://github.com/Telecominfraproject/oopt-gnpy

Graph View

Backlinks