Transcript Optical Communications : Fundamentals

광통신 : Fundamentals
Chang-Hee Lee
([email protected])
Korea Advanced Institute of Science and
Technology
2003.4.11
C.-H. Lee, 03/04//11
1
Content
•
•
•
•
•
•
Fundamentals
Optical Transmitters and receiver
Optical fiber and dispersion
Wavelength Division Multiplexing
Optical amplifier
Optical Nolinearities
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2
Photophone(A.G. Bell, 1880)
Sun
200 m
Transmitter
vibrator & mirror
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Receiver
Se crystal
3
Advantages of Optical Comm.
• Low loss(0.2 dB/km)
– Coaxial cable : 1 dB/m
– Twisted-pair wire : 10 dB/km
• Wide bandwidth(~ 106 Gb/s - km)
– Coaxial cable : ~ 300 Mb/s - km
– Twisted-pair wire : ~ 3 Mb/s - km
•
•
•
•
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Abundant law material(SiO2)
Immunity to interference
Electrical isolation
Signal security
4
Insertion Loss Comparison
10000
RG141
(4 GHz)
Loss (dB)
1000
100
10
External Modulation
Fiber Optic
(DC-18 GHz)
Direct Modulation
Fiber Optic
(DC-18 GHz)
1
RG141
(18 GHz)
RG141
(1 GHz)
RG141
(100 MHz)
0.1
1(0.3)
10(3)
100(30)
1000(300)
10000(3000)
Length (ft)
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Signals in Optical Communications
• Analog signal
– Subcarrier multiplexing
• Digital signal
– Time division multiplexing
– Frequency(or wavelength) division multiplexing
– Code division multiplexing
• Digital vs. analog
– Signal power 0.1 mW, noise power 1 W
– Analog : 20 dB signal to noise ratio
– Digital : 10-22 bit error rate
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Digital Signals
• Non return to zero
1 0 1 0 1 1 0 0 1 1 1
– Small bandwidth, no clock component
• Return to zero
1 0 1 0 1 1 0 0 1 1 1
– Large signal bandwidth, clock component
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Digital Transmission Hierarchy
Voice channel bandwidth
8,000 Hz sampling rate
8 bit/sample
= 64 kbit/sec
7 x T2
Frame time : 125 sec
..
.
T4 or
DS4 MUX
274.176 Mb/s
..
.
T3 or
DS3 MUX
44.736 Mb/s
4 x T1
..
.
T2 or
DS2 MUX
24 x 64 kb/s
..
.
6 x T3
6.312 Mb/s
T1 or
DS1 MUX
North American
hierarchy
1.544 Mb/s
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Standard Transmission Rates
America
Europe
Japan
Level
Mb/s
Voice
channel
Mb/s
Voice
channel
Mb/s
Voice
channel
1
1.544
24
2.048
30
1.544
24
2
6.312
96
8.448
120
6.312
96
3
44.736
672
34.368
480
32.064
480
4
274.176
4032
139.264
1920
97.728
1440
565.148
7680
396.200
5760
5
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SDH(SONET) Hierarchy
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Level
Rate(Mb/s)
OC -1
OC - 3
OC - 9
OC - 12
OC - 18
OC - 24
OC - 36
OC - 48
OC - 96
OC - 192
OC - 768
51.84
155.52
466.56
622.08
933.12
1,244.16
1,866.24
2,488.32
4,976.64
9,953.28
39,813.12
Voice channel
672
2,016
6,048
8,064
12,096
16,128
24,192
32,256
64,512
129,024
516,096
SDH level
STM 1
STM 4
STM 16
STM 64
STM 256
10
Progress in Optical Communications
Year
Sources
~ 1980 GaAs LED
and FP LD
Wavelength Attenuation
(nm)
(dB/km)
Dispersion
Gb/s-km
800 - 900
> 5 dB/km
Miltimode
5
~ 1985
FP LD
1,300
0.4 - 0.6
Min. @1,310
100
~ 1990
DFB LD
1,300 and
1,550
0.4 - 0.6
0.2
Min. @1,310
< 1,000
Present
DFB LD
1,550
Amplifiers Min. @1,310
or Comp.
10,000
DFB LD
WDM
1,550
Amplifiers
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“
100,000
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Digital Optical Transmission
- Baseband transmission
- Recovery of input data without error
- Requires Nyquist channel(no intersymbol interference)
Transmitters/
MUX
Data
in
Optical
fiber
Optical
amplifier
Optical
amplifier
Optical
fiber
Optical
amplifier
Optical
amplifier
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Data
out
DMUX/
Receivers
12
Eye Diagram
Periodic superposition of data
Level “1”
Eye closure
Decision
threshold
Level “0”
Eye closure
Decision time
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Timing jitter
13
Optical Transmitters
DFB LD
Driver IC module
Driver IC
Fiber
Bandwidth
Impedance
matching
Data
Data
Bandwidth
Impedance
matching
Temperature
control
Chirping
Extinction ratio
Output power
Automatic
power control
An optical transmitter with a modulator
integrated DFB LD has
the same configuration.
Direct modulation
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Output
Output
DFB LD
module
Chirping
Extinction ratio
Output power
Temperature and
power control
Automatic
bias control
SBS suppression
External modulation
SBS : stimulated brillouin scattering
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Semiconductor Injection Laser
E2
E2
hn12
E2
hn12
hn12
E1
E1
Absorption
(in phase)
E1
Spontaneous emission
hn12
Stimulated emission
Current injection
Cleaved facet
Optical and carrier
confinement
Lasing spot
0.1 ~ 0.2 m
250 ~ 500 m
~ 100 m
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Output to be
coupled into a fiber
15
Light output (mW)
Modulation of Injection Laser
2
P1
1
P0
0
20
40
Time
Current (mA)
lb
lb+lm
Extinction ratio r = P1/P0
Time
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Effects of Temperature/Aging
Light output (mW)
P1'
P1
For constant average power
- decreases extinction ratio
Pave
P0
Po'
lb
l +l
' b m
lb
lb'  lm'
For fixed bias
- decrease average power
- decreases extinction ratio
- a large amount of chirp
Current (mA)
Control circuits for temperature, average power,
and extinction ratio are required
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Bias & Modulation Current Control
Vcc
LD
MONITOR PD
Ibias
DATA
APC
PEAK
DETECTOR
VBB
Im
CONTROL
CIRCUIT
GRD
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- Low speed transmitter
Temperature, bias & modulation current control
- High speed transmitter
Temperature and bias current control
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External Modulator
Output
V1
Ground
DFB LD
module
V2
Electro-optic material
- Phase shift  (V1-V2)
- Transfer function
= Eo * Cos[ p (V1-V2)/2Vp]
* Exp[ i p (V1+V2)/2Vp]
- Chirp parameter = (V2+V1) / (V2 - V1)
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1.0
0.8
0.6
0.4
0.2
0.0
1.0
2.0
3.0
(V1-V2)/Vp
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Integrated EA Modulator
DFB laser
Popt
Linear model
P
C1 ~P0 e-(V/V0)a
Optical output
Pmax
0
P0/e
Modulator
SI-InP
burying layer
AR coat
Active
layer
Absorption
layer
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C2
0
V
V0
Pmin
V
b
Input signal
20
Comparison of Modulation Methods
Modulator
Chirping Voltage* BW Loss
parameter
[GHz] [dB]
Laser diode - a < 3
1.5
29
LiNbO3
-1 <a < 1
5-8
110
>5
Electro-a >2
2
42 ~ 10
absorption
MI-DFB
-a >2
2
20
DFB-MZ
-1 <a < 1
5
55
* Modulation voltage for 10 dB extinction ratio
** Chirping in EA modulator and MI-DFB depend on
operating wavelength
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Guiding of Light
Total internal reflection
Optical fiber
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Types of fiber
n2 n1
Single mode
Step index
125m cladding
8~12m core
125~400m cladding
Multimode
Step index
50~200m core
125~640m cladding
Multimode
Graded index
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50~600m core
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Optical Receiver
PIN
APD
Noise
Group delay
Preamplifier
Bandwidth
Dynamic range
Phase margin
Ambiguity level
AGC
amplifier
Decision
circuit
Data
Optical signal
Gain
control
Clock
regeneration
Clock
Linear channel(Analog)
Digital
Narrow band
Low speed
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Clock
extraction
Jitter
Jitter transfer
AGC : automatic gain control
PIN : pin diode, APD : avalanche photodiode
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Input optical power
Receiver Sensitivity & Dynamic Range
Dynamic range
Transimpedance
Preamplfier
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High impedance
Load or feedback resistance
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Clock Recovery Circuit
0
B/2
B f
0
B/2
Pre-filter
* High pass
filter
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B f
0
B/2
B
Non-linear
processor
* Squarer
* Differentiate & rectify
* Exclusive-OR
* Delay & multiply
f
0
B
f
Narrow
band filter
* Phase-locked-loop(PLL)
* Surface acoustic wave(SAW) filter
* Dielectric resonator
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Decision Circuit
Signal
AMP
Signal
D
D
D
Q
FLIPFLOP
CLOCK
Q
Data
Data
Recovered clock
T(360)
 Threshold ambiguity
- Minimum input signal amplitude
- Required for a given error rate
 Clock phase margin (CPM)
Maximum deviation of the clock edge from the center of
the signal eye pattern for desired error rate
(Typically specified in degrees, 360 being the ideal value)
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CPM
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SDH/SONET Requirements
Transmitter
Bit
Wave
rate Reach length P min P max
(Mb/s)
(m) (dBm) (dBm)
-23
-14
1.3
SR
OC-1
-8
51.8
IR 1.3,1.5 -15
-5
0
LR 1.3,1.5
-15
-8
1.3
SR
OC-3
-8
155
IR 1.3,1.5 -15
-5
0
LR 1.3,1.5
-15
-8
1.3
SR
OC-12
-8
622
IR 1.3,1.5 -15
-3
2
LR 1.3,1.5
-10
-3
1.3
SR
OC-48 2,488
-5
0
IR 1.3,1.5
-5
0
LR 1.3,1.5
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Receiver
Sens Overload
Technology
(dBm) (dBm)
Option
-31
-14
PIN-Bipolar or CMOS
-28
-8
PIN-Bipolar or CMOS
-34
-10
PIN-Bipolar or CMOS
-23
-8
PIN-Bipolar or CMOS
-28
-8
PIN-Bipolar or CMOS
-34
-10
PIN-GaAs FET
-23
-8
PIN-Bipolar
-28
-8
PINFET or Ge APD- Bipolar
-28
-8
PINFET or Ge APD- Bipolar
-18
-3
PIN-GaAs FET
-18
0
PIN-GaAs FET
-26
-10
InGaAs APD-FET or Bipolar
Note : Receiver sensitivity & overload specified at 10-10 BER
at end-of-life with worst case transmitter
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System impairments
• Chromatic dispersion
• Polarization effects
– PMD, PDL, PHB
• Noise accumulation (Optical SNR)
• Spectral dependence of gain and self filtering
• Fiber nonlinearities
– SBS, SRS
– SPM, XPM, FWM, MI
• Crosstalks
• Optical surge generation
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Modes in Optical Fiber
n2
n1
n2
Propagation constant
a
b
n1 > n2
b(w) = bo  b1 Dw
ko n1
 b2 Dw2/2 Dispersion
Guided mode
ko n2
Radiation mode
wo Optical frequency
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a
w
 b3 Dw3/6 Higher order
dispersion
 ..
bn = dn b / dwn | w = wo
Dw = w - wo
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Material Dispersion of Silica
1.45
30
1.44
1.43
Group index
1.2 1.3 1.4 1.5 1.6 1.7
1.465
Wavelength [m]
1.464
1.463
Dispersion[ps/nm/km]
Index
1.46
Anomalous dispersion
20
10
1.2 1.3 1.4 1.5 1.6 1.7
-10
Wavelength [m]
1.462
-20
1.461
Normal dispersion
1.2 1.3 1.4 1.5 1.6 1.7
Wavelength [m]
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Waveguide Dispersion
Index of refraction
n1
n1 > n2
Waveguide
n2
Radius
Mode profiles
w1
w3 > w2 > w1
w2
Effective index
n3 > n2 > n1
w3
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Dispersion in Optical Fiber
D[ps/km.nm]
D = 2p c b2 / l2
+40
Anomalous dispersion : blue travel fast
+20
Material dispersion
NDSF
DSF
0.0
-20
Waveguide dispersion
-40
Normal dispersion : red travel fast
1100
1200
1300
1400
1500
1600
1700
Wavelength[nm]
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Distance @ 1 dB penalty[km]
Effects of Fiber Dispersion
100000
Loss limit
0.1ps/nm.km
3 ps/nm.km
17 ps/nm.km
10000
1000
100
Loss limit
10
1
1
10
100
Bit rate[Gb/s]
Fiber loss : 0.3 dB/km, Transmitter output : -3dBm, Sensitivity : -26 dBm at 2.5Gb/s, Slope : -1.5dB/bit rate
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Dispersion Compensation I
Anomalous dispersion
Fiber output
Transmission
fiber
time
Normal dispersion
Dispersion
compensator
Dispersion compensator
output
time
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Dispersion Compensation II
• Passive methods
– Dispersion shifted fiber(DSF)
– Compensation fiber(DCF, two-mode fiber)
– Fiber grating or interferometers
– Spectral filter
• Active methods
– Prechirping
– Spectral inversion(MSSI)
– Nonlinear transmission
– Soliton transmission
• Electrical methods
– Duobinary signal, transversal filter
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Polarization Mode Dispersion I
Birefringence Mechanisms
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Polarization Mode Dispersion II
• Group delay difference between two orthogonal
propagation modes
• Origin of PMD
– loss of degeneracy by distortion of fiber core,
– Inhomogeneous stress and temperature distribution
• PMD shows statistical behavior
• ITU-T recommendation
– PMD should be less than 0.1 times the bit period
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Polarization Mode Dispersion III
Y
Z
PMD(Dt)
Length
PMD(Dt)
Highly coupled
PMD(Dt)
Probability
Uncoupled
Probability
X
PMD(Dt)
Length
Maximum PMD < 0.1 x bit period
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Wavelength Division Multiplexing
n channels
fiber
l demux
+40
3rd window
(1550nm)
15 THz
(120nm)
+20
NDSF
1.5
0.0
1.0
-20
0.5
-40
A<0.2dB/km
A<0.35dB/km
Attenuation[dB/km]
Dispersion[ps/km.nm]
l mux
0.0
1200
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1300
1400
1500
Wavelength[nm]
1600
1700
40
WDM Economic Advantage
TDM based system
1
SONET
Terminal
Regen
Regen
Regen
Regen
SONET
Terminal
Regen
Regen
SONET
Terminal
40 km
16
SONET
Terminal
Regen
Regen
WDM based system
1
SONET
Terminal
16 SONET
Terminal
W
D
M
~30 dB, 120 km SAVES FIBER
REGENERATORS
REGEN SITES
W
Amp
D
M
SONET
Terminal
SONET
Terminal
Decreases cost of bandwidth and simplifies the network
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Transmission Capacity Evolution
TDM
WDM
Capacity (Gb/s)
10000
1000
Installed
Research
10x / 2.5 yrs
100
10
10x / 6 yrs
1
Source : NTT + Paper
0.1
1980
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1985
1990
Year
1995
2000
2005
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WDM Sources
• Discrete sources ;
– static & dynamic spectral stability
• Active filter tunable sources
– fiber laser, tunable semiconductor laser
– Broadband sources & filter
• Geometrical selection design
• Array technologies
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WDM Receiver Options
• Fiber Fabry-Perot filter
• Active tunable filter
– Acousto-optic, semiconductor
•
•
•
•
Multilayer interference filter
Fiber grating filter
Planner Si/SiO2 waveguide Mux/Demux
Integrated InP-based technologies
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Arrayed Waveguide Grating
Input/output waveguide
Input/output waveguide
Dx
Lf
Slab Waveguide

d
Slab Waveguide
Arrayed-waveguide
Waveplate
Arrayed-waveguide
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MUX/DMUX with AWG
Multiplexing
l1
l2
l3
l4
l5
l1,l2,l3,l4, l5
l1,l2,l3,l4, l5
Demultiplexing
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l1
l2
l3
l4
l5
46
Why Optical Amplifiers?
• Increase transmission distance
– by increasing optical power coupled to
transmission fiber(power booster)
– by compensating optical fiber losses(in-line
amplifier, remote pump amplifier)
– by improving receiver sensitivity(optical
preamplifier)
• WDM signal and soliton transmission
• Realization of transparent optical network
WDM : wavelength division multiplexing
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Optical Amplifiers
• Function : Amplification of optical signal without
conversion to electrical signal
• Ingredients : Pump energy, amplification medium
Pumping of energy
Optical input
Optical output
amplification
medium
- Doped-fiber(rare-earth)
- Fiber(nonlinear)
- Semiconductor
3R repeater output
3R : Regeneration, Reshaping, Retiming
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48
EDFA(Er-doped fiber amplifier)
Spectral gain
Energy level diagram
4I
980 nm
1480 nm
15201570 nm4
11/2
13/2
I 15/2
Inversion
30
Gain [dB]
4I
0.84
0.55
0.47
0.36
20
10
0
1501
1551
1561
Wavelength length[nm]
Erbium-doped Fiber
PIN
Wavelength
selective coupler
(~ 1550 nm)
(~ 1550 nm)
Laser-diode
pump
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P OUT
Conventional
repeater with
O/E and E/O
conversion
3R repeater
49
Amplifier Operation Points
Gain [dB]
40
Booster
amplifier
35
30
preamplifier
25
60 mW
45 mW
30 mW
in-line
amplifier
20
15
10
-10
-5
0
5
10
15
Output power[dBm]
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50
Improvement of System Gain
Booster
amplifier
Preamplifier
Improvement
in gain(dB)
Improvement Key
in length(km) technology
10 - 15
40 - 60
High efficiency
5 - 10 (APD)
10 - 15 (PIN)
15 - 30
20 - 40
40- 60
60 - 120
Low noise
In-line
amplifier
Remote pump 5 - 15
amplifier
30 - 60
Low noise
Supervisory
High pumping
power
Fiber loss : 0.25 dB/km
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51
Optical Fibers and Amplifiers
Fiber amplifier
Semiconductor amp.
Doped fiber amp.
2nd window
(1310nm)
15 THz
(85nm)
+40
+20
EDFA
2.0
3rd window
(1550nm)
15 THz
(120nm)
NDSF
1.5
DSF
0.0
1.0
NZDSF
-20
0.5
A<0.2dB/km
-40
A<0.35dB/km
DCF
Attenuation[dB/km]
Dispersion[ps/km.nm]
Optical
Amplifiers
PDFA
0.0
1100
1200
1300
1400
1500
1600
1700
Wavelength[nm]
NDSF : non-dispersion shifted fiber, DSF : dispersion shifted fiber, DCF : dispersion compensating fiber
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Cascading of Amplifiers
OA
OTX
1
Gain [dB]
...
OA
2
OA
m
OA
ORX
m+1
30
20
lo
10
0
1501
1551
1561
m
Pase |mth =  2hvnspj Bos G
j=1
Wavelength length[nm]
• Designed gain is equal to span loss at lo
• Accumulation of ASE : linear sum
• Accumulation of gain difference :
logarithmic sum : requires gain flattening
• Increase of nonlinear effect
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53
Spectra of concatenated amplifiers
0
Res : 0.2 nm
Power (dBm)
-10
10 EDFAs
-20
-30
5 EDFAs
-40
1 EDFA
-50
-60
1520
1530
1540
1550
1560
1570
Wavelength (nm)
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54
Issues of Amplifier Design
• Optimization
– maximum efficiency
– minimum noise figure
– maximum gain
– maximum gain flatness/gain peak
wavelength
•
•
•
•
Dynamic range, operation wavelength
Gain equalization
Control circuit
Monitoring of amplifier performance
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Output power[mW]
Required Optical Power
Pout = 2hv nsp SNR Bo [eal - 1]L / l
L = 1000 km
nsp = 1.5
Bo = 0.1 nm
SNR = 100
a = 0.22 dB/km
10
1.0
0.1
1
2
5
10
20
50
100
200
Amplifier spacing[km]
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Optical Nonlinearities
• Stimulated scattering(Phonon-Photon int.)
– SBS, SRS
– Phase matching is not required
• Electronic nonlinearities( n = no + n2 I)
– SPM, XPM, FWM
– FWM requires phase matching
• Suppression of fiber nonlinearities
– FWM by dispersion management
– SBS by linewidth broadening
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57
Self-phase Modulation
• Intensity modulation of the signal modulates
its own phase
• This phase modulation broadens the signal
spectrum
Leff d I
Dn = n 2
l dt
n2 : nonlinear index
Leff : effect length
I : Intensity
• Excess bandwidth leads to more pulse
broadening due to dispersion
• Dispersion compensation and
• Prechirping modifies SPM effects
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Intensity
SPM Induced Chirping
Chirping
Time
C.-H. Lee, 03/04//11
Time
• Phase modulation due to Intensity
dependent refractive index
• Linear positive chirping in center of pulse
• Chirped pulse can be compressed
in anomalous dispersion region.
59
SPM and Dispersion Compensation
• without SPM
SMF
DCF
Fiber input
DCF output
Fiber output
time
time
• Dispersion induces negative chirp
• Exact compensation of chromatic dispersion
• with SPM
SMF
DCF
Fiber input
DCF output
Fiber output
time
C.-H. Lee, 03/04//11
time
• SPM induces positive chirp decreases
dispersion induced chirp.
• DCF output has a residual positive chirp.
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Modulation Instability
• Break of a CW or a pulse into a modulated
structure spontaneously or seeded by ASE.
• Observed in anomalous dispersion regime
8p 2cn 2P o
m ax =  2
, g m ax = 4 pP o / lAeff
l AeffD
• Critical in high power directly modulated
system
• Low power, normal dispersion, external
modulator, dispersion management
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61
Eye Closure Penalty
Eye Closure Ratio (dB)
5
4
3
D (ps/nm/km)
: +1.0
: +0.5
: 0
: -0.5
: -1.0
10 Gb/s, DM
400 km
2
1
0
0
C.-H. Lee, 03/04//11
10
5
15
Fiber Input Power PF (dBm)
20
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Cross Phase Modulation
• Broadening of spectral width due to cross phase
modulation
• Induces interference in closely spaced channel
systems
• Induces timing jitters
• Minimized by increasing channel spacing
– Walk-off decreases XPM effects
– Dl > 2/(D Leff Bit rate)
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63
XPM Induced Chirping
Signal
Intensity
Interference pulse
Intensity
Intensity
Time
Blue shift
Time
Red shift
Time
• Walk off decreases XPM effects
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64
Effects of XPM
JLT’94
2.5 Gb/s
360 km
120 km amplifier spacing
D = 16 ps/nm/km
Power : 5 mW/channel
0.2 nm
1.6 nm
C.-H. Lee, 03/04//11
15 dBm/channel
65
Four-wave Mixing
Beating between two signals modulates
a signals phase at the difference frequency
Into fiber
w1
w
w2
n = no + n2 [ E12 + E22+ 2E1E2 cos(w1-w2)t]
Out of fiber
2w1-w2
w1
w2
2w2-w1
w
Phase matching is required for high generation efficiency
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66
Phase Matching Efficiency
Channel spacing[nm]
Efficiency[dB]
0.5
1
1.5
2
2.5
3
-10
-20
D = 0 ps/nm.km
-30
-40
D = 2 ps/nm.km
-50
D = 17 ps/nm.km
-60
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67
FWM Efficiency
(Pin = 3dBm/channel)
Dispersion-Shifted Fiber(25km)
Nonzero-Dispersion Fiber(50km)
D = 2 ps/kmnm
10dB/div
10dB/div
D=0
lo
Wavelength(1nm/div)
C.-H. Lee, 03/04//11
Wavelength(1nm/div)
68
Suppression of FWM
• Minimization of effects
– decrease power
– increase channel spacing
• Limited by EDFA gain bandwidth
– unequal spacing
• the power depletion is not compensated
– dispersion management
• G.655 fiber
• +/- dispersion
• spectral inversion
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69
Stimulated Raman Scattering
• Power transfer from shorter wavelength
channel to longer wavelength channel
• Deterministic penalty due to walk-off
• 0.5 dB penalty threshold(w/o compensation)
Ptol Dl Leff  40 m W .nm .M m
Dl :totalchannel spacing
• System capacity : ~ 106 Gb/s . km
• Minimization techniques
– Low power
– Spectral inversion
– Raman compensation
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70
RAMAN GAIN (x10-13 m/W)
Raman Gain Spectrum
1.2
lp=1m
1.0
0.8
0.6
0.4
0.2
0
0
6
12
18
24
30
36
42
FREQUENCY SHIFT (THz)
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71
Raman Induced Distortion
Raman gain
w
Good approx.
for f < 13 THz
Successive energy transfer to low frequency channels
w
w
Input spectrum
C.-H. Lee, 03/04//11
Output spectrum
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Summary of Nonlinear Effects
• System capacity is limited by optical
nonlinearities
– Ultimate capacity : ASE & Raman
– Real system : SPM & XPM
• Dispersion management suppresses
nonlinear effects
– FWM, XPM, Raman
• Nonlinearity limits dispersion compensation
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73