IEC TR 61282-4:2013

Fibre optic communication system design guides - Part 4: Accommodation and utilization of non-linear effects

IEC/TR 61282-4:2013(E) which is a technical report, is intended to describe physically and analytically non-linear effects in fibre optic systems, their impact on system performance, and ways of minimizing the effects or using them to advantage. It contains some of ITU-T Recommendation G.663 with additional material. This second edition cancels and replaces the first edition, published in 2003, and constitutes a technical revision. This edition includes the following significant technical change with respect to the previous edition: clarifications on the compensation for nonlinear impairments with digital signal processing. Key words: physically and analytically non-linear effects in fibre optic systems

General Information

• Status: Published
• Publication Date: 18-Nov-2013
• ICS: 33.180.01 - Fibre optic systems in general
• Technical Committee: SC 86C - Fibre optic systems, sensing and active devices
• Current Stage: PPUB - Publication issued
• Start Date: 19-Nov-2013
• Completion Date: 15-Feb-2014

Relations

• Revises: IEC TR 61282-4:2003 - Fibre optic communication system design guides - Part 4: Accommodation and utilization of non-linear effects
• Effective Date: 05-Sep-2023

Standards Content (Sample)

IEC/TR 61282-4 ®
Edition 2.0 2013-11
TECHNICAL
REPORT
Fibre optic communication system design guides –
Part 4: Accommodation and utilization of non-linear effects

IEC/TR 61282-4:2013(E)
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IEC/TR 61282-4 ®
Edition 2.0 2013-11
TECHNICAL
REPORT
Fibre optic communication system design guides –

Part 4: Accommodation and utilization of non-linear effects

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
S
ICS 33.180.01 ISBN 978-2-8322-1174-8

– 2 – TR 61282-4 © IEC:2013(E)
CONTENTS
FOREWORD . 3
1 Scope . 5
2 Normative references . 5
3 Abbreviations and symbols . 5
3.1 Abbreviations . 5
3.2 Symbols . 6
4 General . 7
4.1 System trends leading to non-linear effects. 7
4.2 Optical amplifiers and non-linearities . 7
4.3 Background and notation . 8
4.3.1 Wavelength and frequency . 8
4.3.2 Various velocities . 8
4.3.3 Chromatic dispersion . 10
4.3.4 Fibre types . 10
4.4 General optical non-linearities . 10
5 Optical non-linearities based on scattering . 11
5.1 General description of scattering . 11
5.2 Stimulated Brillouin scattering (SBS) . 12
5.2.1 Phenomenon. 12
5.2.2 Effects . 13
5.2.3 Mitigation . 14
5.3 Stimulated Raman scattering (SRS). 14
5.3.1 Phenomenon. 14
5.3.2 Effects . 15
5.3.3 Mitigation . 15
6 Optical non-linearities based on index effects . 16
6.1 General description of induced non-linear phase . 16
6.2 Self-phase modulation (SPM) . 16
6.3 Cross-phase modulation (XPM or CPM) . 17
6.4 Modulation instability (MI) . 18
6.5 Four-wave mixing (FWM) . 19
6.5.1 Effect . 19
6.5.2 Transmission impairments . 19
6.5.3 Mitigation . 20
6.6 Compensation for non-linear impairments with digital signal processing . 20
7 Summary . 20
Bibliography . 22
Figure 1 – Power effects of stimulated Brillouin scattering for a narrow-band source . 14
Figure 2 – Schematic of a fibre Raman laser . 16
Figure 3 – SPM – Non-linear phase shift and frequency change during pulse modulation . 17
Figure 4 – MI – Spectral side-lobes 100 ps wide, 7 W peak pulse in 1 km fibre . 18
Figure 5 – FWM – Input and output photon frequencies . 19

Table 1 – Correspondence of wavelength and frequency . 9

TR 61282-4 © IEC:2013(E) – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION SYSTEM DESIGN GUIDES –

Part 4: Accommodation and utilization of non-linear effects

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC/TR 61282-4, which is a technical report, has been prepared by subcommittee 86C: Fibre
optic systems and active devices, of IEC technical committee 86: Fibre optics.
This second edition cancels and replaces the first edition, published in 2003, and constitutes a
technical revision.
This edition includes the following significant technical change with respect to the previous
edition:
– clarifications on the compensation for nonlinear impairments with digital signal processing.

– 4 – TR 61282-4 © IEC:2013(E)
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
86C/1166/DTR 86C/1189/RVC
Full information on the voting for the approval of this technical report can be found in the report
on voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 61282 series, published under the general title Fibre optic
communication system design guides, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until the
stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to
the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
TR 61282-4 © IEC:2013(E) – 5 –
FIBRE OPTIC COMMUNICATION SYSTEM DESIGN GUIDES –

Part 4: Accommodation and utilization of non-linear effects

1 Scope
This part of IEC 61282, which is a technical report, is intended to describe physically and
analytically non-linear effects in fibre optic systems, their impact on system performance, and
ways of minimizing the effects or using them to advantage. It contains some of ITU-T
Recommendation G.663 [1] with additional material. More details on applications are
considered in [2] and networks in [3].
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments)
applies.
IEC 60793-1 (all parts), Optical fibres – Part 1: Measurement methods and test procedures
IEC 60793-2 (all parts), Optical fibres – Part 2: Product specifications
IEC/TR 61292-3, Optical amplifiers – Part 3: Classification, characteristics and applications
3 Abbreviations and symbols
3.1 Abbreviations
BER bit-error ratio
DCF dispersion compensating fibre
DWDM dense wavelength division multiplexing/demultiplexing
EDFA erbium-doped fibre amplifier
FWHM full width at half-maximum
FWM four-wave mixing
FPM four-photon mixing
IL insertion loss
MI modulation instability
OA optical amplifier
OFA optical fibre amplifier
ORL optical return loss
OTDR optical time-domain reflectometer
PDC passive dispersion compensator
PDL polarization dependent loss
___________
Figures in square brackets refer to the bibliography.

– 6 – TR 61282-4 © IEC:2013(E)
PMD polarization mode dispersion
Rg regenerator
RMSW root-mean-square width
Rx receiver
SBS simulated Brillouin scattering
SLM single longitudinal mode
SMF single-mode fibre
SOA semiconductor optical amplifier
SPM self-phase modulation
SRS simulated Raman scattering
TDM time-division multiplexing
Tx transmitter
XPM (CPM) cross-phase modulation
3.2 Symbols
A (fibre) effective area in μm
eff
c speed of light in a vacuum in km/s or nm/ps
D chromatic dispersion coefficient in ps/nm-km
f signal (modulation frequency in GHz
g non-linear gain coefficient
l light intensity in μW/μm
L (fibre) effective length in km
eff
n phase (refractive) index
N group index
n linear (phase) index
n non-linear (phase) index
S (chromatic) dispersion slope in ps/nm -km
subscript Brillouin scattering
B
subscript pump signal
P
subscript Raman scattering
R
subscript Stokes signal
S
t time in ps to s
group velocity (speed) in km/s or nm/ps
v
g
v phase velocity (speed) in km/s or nm/ps
p
z distance coordinate along fibre in km
α (power) attenuation coefficient in np/km or dB/km
-1
β propagation wave number in km
-1 -1
Γ non-linearity coefficient in W or mW
λ light vacuum wavelength in nm to μm
φ optical phase
ν optical frequency in THz
ω optical circular frequency in THz

TR 61282-4 © IEC:2013(E) – 7 –
4 General
4.1 System trends leading to non-linear effects
The market demand for new advanced telecommunications services has driven the rapid
increase of system bandwidth, and, for some applications, longer system distances.
Greater bandwidth has been addressed in two ways. One way is by increasing the channel bit-
rate, accomplished with optoelectronic time-division multiplexing (TDM) and various types of
signal encoding. Another way is by increasing the number of channels, accomplished with
channel multiplexing, such as polarization division multiplexing or (more commonly) by dense
wavelength division multiplexing (DWDM). Bandwidth limitations of the optical fibre cable can
be overcome with various dispersion management techniques.
Longer distances, defined to be the optical path lengths between 3R regenerators, can be
achieved by two methods. One method is by increasing the span length, where a span is
defined to be the optical path between optical amplifiers (OAs). A longer span length may be
attained with fibre cable of lower attenuation coefficient and with fibre optic passive
components having lower loss. The span length may also be increased with increased
launched channel power from the output of the OA at the beginning of the span or with lower
allowed power at the input of the OA at the end of the span. Another method of increasing the
optical path length is to increase the number of spans. This increases the number of OAs, but
improvements can be limited by amplifier noise degradation.
There are a number of interactive trade-offs in system design. For example, increasing the bit-
rate reduces the span length by requiring higher received power or by requiring lower link
dispersion. The latter may be addressed by dispersion compensation, but this introduces
losses. Increasing the number of channels in DWDM systems also reduces span length due to
optical multiplexing and demultiplexing losses. The loss limitations of a span can be overcome
with OAs, but these introduce noise.
4.2 Optical amplifiers and non-linearities
An OA accepts a modulated signal at its input and emits an essentially identically shaped
signal at its output. However, the optical power is higher (desired), and there is some additional
noise (not desired). This technical report is concerned with the effects of higher power on the
fibre and the implications for system design. These non-linear effects are so-called because
they are not linearly proportional to launched power into the fibre or to the fibre length in either
absolute units or in dB units. They are affected primarily by characteristics of the optical signal
(power, optical spectrum, modulation, state of polarization), of the optical fibre (effective area,
effective length, gain coefficients, non-linear index, dispersion, dispersion slope, polarization
mode dispersion), and of system aspects such as distance between regenerators and the
number and spacing of channels in DWDM systems. Power levels as low as several mW can
induce non-linear effects.
One class of non-linear effects is stimulated scattering of the signal. Stimulated Brillouin
scattering limits the power transmitted through the fibre by scattering some light backwards in
the fibre. Stimulated Raman scattering mainly causes forward crosstalk in a DWDM system.
Another class of non-linear effects is phase-shifting of the signal. This leads to self-phase
modulation and modulation instability that produce distortion even on a single channel, or to
cross-phase modulation and four-wave mixing that introduce interference between channels.
These interact with chromatic dispersion to degrade or enhance system performance. Soliton
formation is another related effect.

– 8 – TR 61282-4 © IEC:2013(E)
4.3 Background and notation
4.3.1 Wavelength and frequency
These simple concepts are essential in discussing advanced optical transmission systems.
One can interchangeably talk about the vacuum wavelength λ in nm and optical frequency ν in
THz (10 Hz or 1 000 GHz). The optical frequency is not to be confused with the signal
modulation frequency f or the signal bit-rate B. By using the speed of light in a vacuum c, one
can change between wavelength and frequency through the fundamental relation:
λ(nm)×ν (THz) = c(nm/ps)
(1)
where  c ≈ 299,792,458 nm/ps
The fundamental mode of a single-mode fibre has a phase (refractive) index n, which is
dimensionless, with a value around 1,46 in silica fibre. It decreases as the wavelength of light
increases and details depend upon the refractive index profile of the fibre and the characteristic
λ
of the fundamental mode. The wavelength of light in a fibre decreases to and the speed of
n
c
the light decreases to , but the light's frequency v does not change.
n
Examples of the wavelength/frequency correspondence from Equation (1) are shown in the two
left columns of Table 1 for several significant wavelengths of interest. Note that as the (vacuum)
wavelength increases, the frequency decreases.
For DWDM systems it is important to be able to relate wavelength and frequency in terms of
differences. These differences describe channel widths and separations. From Equation (1),
two wavelengths separated by Δλ may be related to the frequency separation Δν by
Δλ Δν
= − (2)
λ ν
The fractional changes in wavelength and frequency are the same, though of opposite sign
(important in later discussions of chirp). This can also be written as
Δλ λ c
− = = (3)
Δν c
ν
and examples of the correspondence in wavelength and frequency spreads are shown in the
two right columns of Table 1. For a communications engineer, dealing in frequency, which is
related to information content, is more natural than dealing with wavelength. Note that a
constant frequency spread has a larger wavelength spread at longer wavelengths.
2π
It is sometimes convenient to use the notation β(ω) = n(ω) for the propagation wave
λ
number in the material. It depends upon the circular frequency ω = 2πν, so Equation (1) is
ω n(ω) = cβ(ω ) (4)
4.3.2 Various velocities
It is important to distinguish between two types of velocities in optical fibre. The phase of an
iφ
optical wave, as written in e , is

TR 61282-4 © IEC:2013(E) – 9 –
 nz 
φ = β z − ω t = 2π  −ν t  (5)
λ
 
where
z is the distance along the fibre;
t is the time.
dz
For a point of constant phase along the optical wave, dφ = 0 = βdz – ωdt, so is the phase
dt
velocity (actually “speed”) given by
ω c
v = = (6)
p
β (ω) n(ν )
Table 1 – Correspondence of wavelength and frequency
Wavelength Frequency 1 nm spread 100 GHz spread
nm THz GHz nm
1 260,000
(nominal lower limit due to cut-off) 237,931 188,8 0,530
1 310,000
(nominal zero dispersion for category B1 fibre) 228,849 174,7 0,572
1 395,000
(nominal water peak) 214,905 154,1 0,649
1 550,000
(nominal zero dispersion for category B2 fibre) 193,414 124,8 0,801
1 552,524
(ITU grid reference) 193,100 124,4 0,804
1 625,000
(nominal upper limit due to attenuation) 184,448 113,5 0,881

Although the optical subcarrier travels at the phase velocity, this is not the primary interest of a
communications engineer. The subcarrier is modulated to produce an analogue or digital signal.
The more slowly varying signal envelope and its associated energy travel at the group velocity.
−1
 dβ  c
v = = (7)
 
g
dω N
 
is the group velocity. Here
d n d n
N = n − λ = n + υ (8)
dλ dυ
is the group index. (For silica fibre in the wavelength regions of interest, this is slightly larger
than the phase index because the wavelength derivative is positive.) These “group” quantities
describe the speed at which energy and information (such as pulses) travel down the fibre.
Also, this index is the appropriate one for the pulses generated by an optical time-domain
reflectometer (OTDR). The group index can easily be measured as the time delay of a pulse or
the phase shift of an RF modulation, both for a known physical length of fibre.

– 10 – TR 61282-4 © IEC:2013(E)
4.3.3 Chromatic dispersion
The chromatic dispersion coefficient is defined as the wavelength variation of the group delay
per unit fibre length:
−1
2 2
dv
1 d N λ d n 2πc d β
g
D(λ) = = = − − (9)
2 2 2
dλ c dλ
c dλ λ dω
The dispersion-slope coefficient is the derivative
2 3
d β   d β
d D 4πc 2πc
 
S(λ) = = + (10)
 
3 2 2 3
dλ
λ dω  λ  dω
4.3.4 Fibre types
The various types of category B single-mode fibre according to the IEC 60793-1 series and the
IEC 60793-2 series have nominally similar attenuation coefficients. They differ primarily in their
dispersion coefficients and mode-field diameters (or effective areas, as applied to non-linear
effects). In the 1 550 nm region, category B1 (dispersion-non-shifted) fibre has a positive
dispersion coefficient that averages at about 17 ps/nm-km. Category B2 (dispersion-shifted)
fibre has a zero dispersion point in this region, whereas category B4 (non-zero-dispersion) fibre
has a small positive or negative dispersion in this region. The dispersion slope of these fibres
may be important for DWDM applications. The effective area of category B1 fibre is generally
larger than for the other two types.
4.4 General optical non-linearities
These effects have been studied since the 1970s in fibres and were induced in the laboratory
by injecting the light from high-power lasers into the fibre. Now they are of practical importance
to communications engineers since such powers are found in systems at the output of OAs,
both optical fibre amplifiers (OFAs) and semiconductor optical amplifiers (SOAs).
Consider two lightwaves of the same polarization co-propagating along the fibre. The electric
of one wave is affected by the “pump” optical power of the other wave. After an
field E E
incremental length dL of propagation, the first wave grows approximately as
 
 
1 γ 2
E (z +d z,d t) = E (z,t)exp i(β d z − ωd t)+ −α + E (L) d z (11)
 
1 1  2 
2 A
 eff 
 
Compared to the phase of Equation (5), attenuation and gain are included. The second signal
E loses power by being converted to another wavelength and by attenuation. Here
• α is the attenuation coefficient in Np/km appropriate to the exponential notation. Relating
this to log notation, 1 Np is about 4 343 dB.
• A is the effective area of the fibre cross-section over which the integrated non-linear
eff
interaction takes place. It can be slightly different (usually larger) than the area calculated
using the mode-field diameter (MFD) [4] because the field intensities are weighted
differently in the two calculations. The effective area ranges from above 85 μm for IEC
2 2
category B1 fibre, to about 60 μm for category B2 fibre, to below 25 μm for dispersion
compensating fibre (DCF). Smaller effective areas generally lead to larger non-linear
effects.
TR 61282-4 © IEC:2013(E) – 11 –
−αL
1− e
• L = is the effective length of fibre over which the integrated non-linear
eff
α
interaction takes place. It equals the fibre length only for short fibre lengths over which no
significant attenuation has taken place, but is less than the full fibre length because of the
reduced non-linear power levels with distance. For long lengths this approaches , which
α
is approximately 12,4 km at 1 310 nm (for 0,35 dB/km) and 19,7 km at 1 550 nm (for
0,22 dB/km). These are the maximum distances over which non-linear effects occur;
beyond these, the power levels causing them are low and have diminishing effect.
• γ is the non-linear coefficient. If it is real and positive, it corresponds to a gain, or to a loss
if it is negative, and it is due to scattering of photons with phonons (mechanical vibrations in
the silica), producing heat. If it is imaginary, it is effectively a change in the phase index,
the Kerr effect. Both are discussed in some detail below.
With these measurement results of optical fibres/cables, fibre optic communication systems
are designed not to be impaired by non-linear effects. Measurement of nonlinearity of installed
cabling is generally not necessary for fibre optic communication systems.
5 Optical non-linearities based on scattering
5.1 General description of scattering
In modern low-loss silica fibre, the spectral attenuation coefficient is “linear” in the sense of
dB/km. Intrinsic absorption occurs mainly in the ultraviolet region below 500 nm, and in the
infrared region above 1 650 nm. The only significant “impurity” absorption that may exist in
some fibres is due to some “water” content that results in an absorp
...