Optical amplifiers - Part 7: Four wave mixing effect in optical amplifiers

IEC/TR 61292-7:2011(E) applies to optical amplifiers (OAs) using active fibres and waveguides, containing rare-earth dopants, currently commercially available. It provides guidance on crosstalk caused by the four-wave mixing (FWM) effect. The object of this technical report is to provide introductory information for understanding of the crosstalk issue raised by the FWM effect.

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IEC/TR 61292-7
Edition 1.0 2011-11
TECHNICAL
REPORT
Optical amplifiers –
Part 7: Four wave mixing effect in optical amplifiers
IEC/TR 61292-7:2011(E)
---------------------- Page: 1 ----------------------
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---------------------- Page: 2 ----------------------
IEC/TR 61292-7
Edition 1.0 2011-11
TECHNICAL
REPORT
Optical amplifiers –
Part 7: Four wave mixing effect in optical amplifiers
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
ICS 33.160.10; 33.180.30 ISBN 978-2-88912-803-7
® Registered trademark of the International Electrotechnical Commission
---------------------- Page: 3 ----------------------
– 2 – TR 61292-7 © IEC:2011(E)
CONTENTS

FOREWORD ........................................................................................................................... 3

INTRODUCTION ..................................................................................................................... 5

1 Scope and object .............................................................................................................. 6

2 Normative references ....................................................................................................... 6

3 Abbreviated terms ............................................................................................................ 6

4 FWM effect in EDFAs ....................................................................................................... 7

4.1 General ................................................................................................................... 7

4.2 Introduction of the FWM effect ................................................................................. 7

4.3 FWM crosstalk enhancement in EDFA ..................................................................... 8

Annex A (informative) A technique for measurement of four wave mixing effect in OAs ....... 10

Annex B (informative) Underestimation of FWM crosstalk by reduced number of WDM

inputs ................................................................................................................................... 18

Bibliography .......................................................................................................................... 21

Figure 1 – Example of generation of FWM light ....................................................................... 8

Figure 2 – Examples of EDFA with FWM effect ....................................................................... 9

Figure A.1 – Basic measurement set-up ................................................................................ 10

Figure A.2 – Measurement flow chart .................................................................................... 14

Figure A.3 – Calculation of crosstalk ..................................................................................... 16

Figure B.1 – Total number of combinations and number of combinations without the

FWM channel that contribute to the FWM product generation for each channel number ........ 19

Figure B.2 – Total channel number dependence of the ratio of the number of the

combinations under the condition f = f over the total number of combinations ..................... 19

F r

Figure B.3 – Calculated FWM signal power when all the signal channels are input and

excluding the channel that coincides with the FWM channel ................................................. 20

Figure B.4 – Dependence of the difference between the FWM signal powers for signals

with all the channels and without the FWM channel on the total channel number for

various EDF dispersion values .............................................................................................. 20

Table A.1 – Recommended test conditions ........................................................................... 12

---------------------- Page: 4 ----------------------
TR 61292-7 © IEC:2011(E) – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
OPTICAL AMPLIFIERS –
Part 7: Four wave mixing effect in optical amplifiers
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 61292-7, which is a technical report, has been prepared by subcommittee 86C: Fibre

optic systems and active devices, of IEC technical committee 86: Fibre optics.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
86C/1029/DTR 86C/1036/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.
---------------------- Page: 5 ----------------------
– 4 – TR 61292-7 © IEC:2011(E)

This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.

A list of all parts of IEC 61292 series, under the general title Optical amplifiers, 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.
A bilingual version of this publication may be issued at a later date.
---------------------- Page: 6 ----------------------
TR 61292-7 © IEC:2011(E) – 5 –
INTRODUCTION

The four-wave mixing (FWM) effect is known as one of the major restrictions in DWDM

transmission systems. Although observation, conditions for generation, and evaluation

methods have been reported in the literature, no international standards have been published

on this subject, and manufacturers and users evaluate this phenomenon using their own

techniques.

This technical report is dedicated to the subject of four-wave mixing (FWM) effects in optical

amplifiers. It provides an overview of the FWM effect and references information on test

methods. The technology of optical amplifiers is quite new and still emerging; hence

amendments and new editions to this technical report can be expected.
---------------------- Page: 7 ----------------------
– 6 – TR 61292-7 © IEC:2011(E)
OPTICAL AMPLIFIERS –
Part 7: Four wave mixing effect in optical amplifiers
1 Scope and object

This part of IEC 61292, which is a technical report, applies to optical amplifiers (OAs) using

active fibres and waveguides, containing rare-earth dopants, currently commercially available.

It provides guidance on crosstalk caused by the four-wave mixing (FWM) effect. The object of

this technical report is to provide introductory information for understanding of the crosstalk

issue raised by the FWM effect. This report also presents a measurement method in Annex A.

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 61290-10-4: Optical amplifiers – Test methods – Part 10-4: Multichannel parameters –

Interpolated source subtraction method using an optical spectrum analyzer
NOTE A list of informative references is given in the Bibliography.
3 Abbreviated terms
ASE amplified spontaneous emission
AWG arrayed waveguide
CW continuous wave
DFB distributed feed-back (laser diode)
DOP degree of polarization
DWDM dense wavelength division multiplexing
ECL external cavity laser (diode)
EDF erbium-doped fibre
EDFA erbium-doped fibre amplifier
FWM four-wave mixing
MUX multiplexer
OA optical amplifier
OFA optical fibre amplifier
O-MUX optical multiplexer
OSA optical spectrum analyzer
ROADM reconfigurable optical add/drop multiplexer
SPM self-phase modulation
VOA variable optical attenuator
WDM wavelength division multiplexing
WSS wavelength selective switch
XPM cross-phase modulation
---------------------- Page: 8 ----------------------
TR 61292-7 © IEC:2011(E) – 7 –
4 FWM effect in EDFAs
4.1 General
The EDFA is a crucial element to configure photonic network systems based on WDM

transmission because the EDFA compensates for loss in node devices such as ROADMs and

WSSs, and expands capacity and distance which leads to large scale networks. Therefore the

EDFA is required to amplify many channels of dense WDM signals and is also required to

produce higher power for respective channels in order to compensate for loss in node devices

and transmission fibre. These demands have recently led to adverse deterioration of WDM

signals caused by the nonlinear effect in the EDF. Previously this nonlinear effect was not

thoroughly considered because the effect on signal deterioration was small.

As for the L-band EDFA, the emission cross section at 1,58 µm is extremely small as

compared to that at 1,55 µm. As reported, the L-band amplifier requires a ten times longer

EDF length in order to realize the 20-dB to 30-dB gain needed for practical use. Thus critical

problems of signal deterioration by nonlinear effects were noted by the long fibre length

amplification in L-band [1]. The FWM effect in multi-channel amplification is usually observed

in an EDFA composed of long EDF, or in a high power EDFA. This technical report provides a

method and procedure to measure crosstalk caused by the FWM (four-wave mixing) effect in

the EDFA.
4.2 Introduction of the FWM effect

The nonlinear effects in EDF originate in the 3rd polarization of permittivity, the same as in

transmission fibre, and lead four-wave mixing (FWM), cross-phase modulation (XPM) and

self-phase modulation (SPM) [2][6]. In FWM, wavelength-multiplexed signals generate noise

on other channels. Therefore, crosstalk is imposed between the signal and the noise products

generated by FWM in DWDM transmission systems. Figure 1 is a schematic diagram
explaining the generation of FWM products.

When the signal lights of three different wavelengths are launched into EDFA, new lights

(idler) are generated by the FWM effect. The newly generated wavelengths do not correspond

with any of the above mentioned three wavelengths. When signal frequencies are f , f , and f ,

p q r
generated idler light caused by FWM is expressed as follows.
f = f
F p,q,r
(1)
= f + f − f
p q r

The generated FWM products overlap with signal wavelength, and crosstalk is imposed on the

signal.

Besides FWM idler generation by three wavelengths, FWM products are generated when two

signals with different wavelengths are launched into EDFA. This FWM effect resulting from

two signal wavelengths is called degenerate four-wave mixing.
---------------------- Page: 9 ----------------------
– 8 – TR 61292-7 © IEC:2011(E)
f f
q r
f = f + f − f
FWM
pqr p q r
f f f f f f f
ppr pqr qqr prq qqp qrp rrp
+ +
f f f
qqr rpq rqp
+ +
f f IEC 2559/11
ppq rrq
Figure 1 – Example of generation of FWM light
4.3 FWM crosstalk enhancement in EDFA

On a fundamental level, the origin of nonlinear response in the material is related to harmonic

motion of bound electrons under the influence of an applied field. As a result, the induced

polarization P from the electric dipoles is not linear in the electric field E, and is expressed in

following Formula [2].
P=χ E+χ E× E+χ E× E× E+ (2)
1 2 3

The first term represents the linear effect; the second term represents second order non-

linearity; and third term represents third order non-linearity. χ , χ , χ are first order, second

1 2 3
order, and third order susceptibility.

The second order susceptibility χ is responsible for such nonlinear effects as second-

harmonic generation and sum-frequency generation. However it is nonzero only for media that

lack inversion symmetry at the molecular level. Since SiO is a symmetric molecule, χ

2 2

vanishes for silica glass. As a result, optical fibres do not normally exhibit second-order

nonlinear effects.

The lowest-order nonlinear effects in optical fibres originate from the third order susceptibility

χ which is responsible for phenomena such as four-wave mixing. Hence the nonlinear effect

which leads FWM is generated by third term in Formula (2).

From Formula (2), assuming signals with angular frequencies of ω , ω , and ω , and

p q r

respective electric field E(ω ,z), E(ω ,z), E(ω ,z), we can describe propagation equation of the

p q r

electric field by FWM effect E(ω ,z) as follows [4]. Notation z represents position along the

fibre length.
2 2 2 2
∂ E(ω , z) n ∂ E(ω , z) ς ∂E(ω , z)
F F F
− −
2 2 2
∂z c ∂t c ∂t
(3)
4π ∂
= (Dχ )⋅ E(ω , z)× E(ω , z)× E (ω , z)
3 p q r
2 2
c ∂t

Here, n is the refractive index of the core, c is velocity of light, and D is degeneration factor of

FWM. The background loss of EDF is denoted by ζ.
---------------------- Page: 10 ----------------------
TR 61292-7 © IEC:2011(E) – 9 –

When we assume a boundary condition of three signals which are launched into EDF as

E(ω ,0), E(ω ,0) , E(ω ,0), considering gain distribution along the EDF length, FWM signal

p q r
power which emits at z = L is expressed as follows [5],[8].
256π ω  Dχ 
F 3
 
P(ω , L)= P(ω ,0)× P(ω ,0)× P(ω ,0)
F p q r
4 4
 
n c
eff
 
(4)
iΔΔ z
iβ z z z z L
× e e G(ω ) × G(ω ) × G(ω ) ×G(ω ) dz
p 0 q 0 r 0 F z

Here P(ω ,0), P(ω ,0), and P(ω ,0) are input power to the EDF respectively, and β represents

p q r F

propagation constant of FWM light. G(ω ), G(ω ), and G(ω ) represent gain evolution along the

p q r

EDF at the frequency of ω , ω , and ω respectively. The propagation constant difference Δβ

p q r
is given as follows [7],[8].
2πλ
∆β= D( f − f)( f − f) (5)
c p r q r

where f = ω / 2π (j = p,q,r), λ =f /c, and D is the chromatic dispersion of the EDF. Δβ

j j r r c

represents the propagation constant difference of input powers with the angular frequency of

ω , ω , and ω respectively. Δβ originates in the chromatic dispersion of EDF. Larger

p q r

dispersion leads to larger Δβ. As a result, FWM in an EDFA is enhanced with an increase of

powers of signals P(ω ,0), P(ω ,0) and P(ω ,0), and with an increase in the interaction length

p q r
of fibre as shown above in Formula (4).
Figure 2 shows FWM generation in two EDFAs which are composed of different EDF

respectively [3]. The case of conventional EDF is shown in the figure on the left, and FWM

generation with amplified signals is observed. The figure on the right shows the case of

optimized EDF to suppress FWM generation. FWM generation of optimized EDF is mitigated

as compared with conventional EDF. FWM generation is suppressed by appropriate EDF

design as shown in the figure on the right.
–10
–10
–20
–20
–30
–30
–40
–40
–50
–50

1 568 1 570 1 5721 5 721 5 76 1 578 1 580 1 582 1 5841 5 86 1 588 1 568 1 570 1 5721 5 721 5 76 1 578 1 580 1 582 1 5841 5 86 1 588

Wavelength (nm) Wavelength (nm)
IEC 2560/1 1 IEC 2561 /11
Figure 2 – Examples of EDFA with FWM effect
Output power (dBm)
Output power (dBm)
---------------------- Page: 11 ----------------------
– 10 – TR 61292-7 © IEC:2011(E)
Annex A
(informative)
A technique for measurement of
four wave mixing effect in OAs
A.1 Overview

N channels of signal which are equally spaced for frequencies (f ,f ,…, f ) are normally

1 2 N

launched into an OA which amplifies multiple WDM signals. However if amplification

characteristics with N channel input are observed, FWM light cannot be separated from signal

light since FWM light was generated on signal frequencies.

In this measurement method, a single channel at wavelength f is removed from a block of N

input channe
...

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