Download - EEC239A 15 Notes 03 NonlinearFibers
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EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Chapter II Propagation of Signals in Optical Fiber (cont’d)
Fiber Nonlinearities
(Chapter 2.4 and Section 5.8 and Appendix E.2 of text)
Notes_3_2EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Fiber Nonlinearities
• Optical Fibers are Far ‘Better’ than Copper Wires but Not Ideal; in addition to dispersion, there are nonlinearities
• Many Nonlinear Mechanisms
Self Phase Modulation
Cross Phase Modulation
Four-Wave Mixing
Stimulated Raman Scattering
Stimulated Brillouin Scattering
NonlinearIndex Effect
StimulatedProcess
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Notes_3_3EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
SELF PHASE MODULATION
• The material index , and the group velocity is Intensity Dependent!!
t'/
t/Propagation
13d)-(5 ~ where ,y Equvilentl 200
0 InnInInc
Notes_3_4EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Pictorial-Self Phase Modulation
Propagation direction
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Notes_3_5EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
CROSS-PHASE MODULATION (XPM)
• Essentially the same mechanism (optical Kerr effect) as SPM causes XPM, and SPM is a special case of XPM
1
2
• Presence of 2 pulse affects the propagation or the phase of 1 pulse• Occurs only when they overlap in time
Notes_3_6EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Pictorial-Cross Phase Modulation
s
due to reduced interaction length
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Notes_3_7EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Pictorial-Stimulated Processes (SBS)
• Lightwave (photon) and Acousticwave (phonon) interaction causes SBS, SRS, etc.
optical wave in
acoustic wave
optical wave trans
SBS (doppler shifted)
Notes_3_8EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Pictorial-Stimulated Processes (SRS)
• Lightwave (photon) and Acousticwave (phonon) interaction causes SBS, SRS, etc.
optical wave in
acoustic wave
optical wave transp p
s
s
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Notes_3_9EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Fiber Nonlinearities-2
• All Nonlinear Optical Mechanisms, by definition are ‘optical power dependent’. Typically, they are due to ‘third order nonlinearity’ whose magnitudes are often depicted by (3) and the nonlinear polarization is PNL ~ 0 (3) E3
• This nonlinear polarization is responsible for the nonlinear optical effects and will scale nonlinearly with Intensity.
• For a given power, Large effective area ( Aeff) fiber provides lower intensity and lower nonlinear optical effects
• Nonlinear optical effects will be dominant before absorption reduces the power level, hence effective length of interacting region Leff~1/bs
Notes_3_10EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Effective Length
Effective Length
P
Leff
P
L L
Equivalent for nonlinear effects
For long lengths /1 L
eff eL
/1L
kmLkmdB eff 20,/22.0
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Notes_3_11EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Effective Area
Effective Area
I
I
r r 2/1/effA
Equivalent for nonlinear effects
,
,2
2
rIrdrd
rIrdrdAeff
Typical value 250 m
Notes_3_12EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Linear and Nonlinear Optics-1
Polarization in linear world was:
In the real world(including nonlinearity)
Again,
,~
,~,~ 1
0 rErrPL
,~
,~
,~
,~,~
0 rPrPrErrP NLLT
,~
,~,~ 1
0 rErrPL
,~
,~
,~
:,~,~
,~
:,~,~ 3
02
0 rErErErrErErrPNL
Optical fiber has no Because it is centrosymmetric
,~ 2 r
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Notes_3_13EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Linear and Nonlinear Optics-2
• See appendix F:
These are frequency domain responses.in the time domain (for linear):
t
L trEttrtrP ''10 ,,,
t t t
NL dtdtdttrEtrEtrEttttttrtrP 3213213213
0 ,,,,,,,
Notes_3_14EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Linear and Nonlinear Optics-4
• For isotropic and time independent
trEtrPNL ,, 330
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Notes_3_15EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
SELF PHASE MODULATION-1
• The material index , and the group velocity is Intensity Dependent!!
• n= n0 + n2 I
t/
Propagation
t'/
low-high-low index
SPM induces chirp! (effectively negative chirp parameter or >0)
Notes_3_16EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
SELF PHASE MODULATION-2
• Instead of linear case
‘Optical Kerr Effect’ gives
anc
12500
or
bc
1251 100
aEC
1354
31 2310
0 or
bEnC
1354
31 23
20
0 or approximately
cEn
nC
1358
3 2300
Equivalently, 13d-5 ~ , 20
0 InnInwhereInC o
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Notes_3_17EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
SELF PHASE MODULATION-3
• Nonlinear Length is defined as:
• Consider initially unchirped Gaussian pulse with envelope:
P0 is the peak power of the pulse
• If the link length is comparable to or greater than the LNL then the pulse acquires a distance-dependent chirp.
2
2
,0
eU
022 Pn
AL e
NL
Notes_3_18EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
SELF PHASE MODULATION-4
• Read through Appendix E.2, and use equation E.18 which shows that the SPM induced phase change is:
• Then the instantaneous frequency and the chirp factor are:
2
e
L
L
NL
2
0
212
2
2
2
eL
L
eL
L
NLspm
NL
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Notes_3_19EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
SELF PHASE MODULATION-5
• For L > Le , replace L with Le
• For = 0.22 dB/km, Le =20 km
Notes_3_20EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
1
2
CROSS-PHASE MODULATION (XPM)-1
• Essentially the same mechanism causes XPM, and SPM is a special case of XPM
• Presence of 2 pulse affects the propagation or the phase of 1 pulse
t/
t/
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Notes_3_21EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
CROSS-PHASE MODULATION (XPM)-2
• XPM Occurs only when pulses overlap in time– Propagation constant seen by 1 pulse in presence of 2 pulse is
cEEEn
nc
bEEEn
nc
aEEEc
14528
3
elyapproximator ,14524
31
or ,14524
31
212
130
0
212
10
0
212
1310
0
Notes_3_22EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
NONLINEAR WAVE EQUATIONSPM induced Chirp-1
• The text book Appendix covers nonliear Schrodinger Equation which we will skip here and use the result
• Nonlinear Length defines as the following compares the length of fiber to the possible nonlinear impairments
• SPM induces chirp, and the pulse width after propagating a distance L is given as
pulse theofpower peak a is P and 8
3 where
1552
023
0
En
n
Pn
AL eff
NL
17-5 33
4121
2
2
2
2
0 DNL
eff
DNL
effL
L
L
L
L
L
L
L
L
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Notes_3_23EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
NONLINEAR WAVE EQUATIONSPM induced Chirp-2
Which includes Dispersion (LD), Loss (Leff), and SPM(LNL)induced Chirp
see Fig 5.31 of text
1mW
10 mW
100 mWL1
0t
tL
Notes_3_24EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
FOUR WAVE MIXING-1
• INTERMIXING GENERATES NEW FREQUENCY TERMS
before
after
• In general, it is a mixing between three waves generating a fourth wave at a new frequency
ztEE
EP
iii
NL
cos where
23
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Notes_3_25EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
FOUR WAVE MIXING-2
• The power Pijk of the mixing term is related through
where Pi, Pj, Pk, are power level of each component and dijk is a degeneracy factor. ijk is a phasematching term given as
17-5 8
2
23
effkjieffeff
ijkijkijkijk LPPP
cnA
dP
19-5
where18-5exp1
2/sinexp41
i
2
22
22
2
ijkkj
abs
abs
abs
absijk
L
LL
Notes_3_26EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
FOUR WAVE MIXING-3
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Notes_3_27EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin ScatteringStimulated Raman Scattering
Simulated scattering gain
Wcm
Wcm
ePP
raman
Brillouin
APLinout
/105.3
/10212
9
/
Notes_3_28EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-1
Stimulated Brillouin Scattering
•Lowest threshold nonlinearly-Without amplifiers-With N amplifiers
mWPth 12NPP th
Nth /1
But
•Backward interaction
-Isolators can eliminate the effect-Bidirectional transmission impossible
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Notes_3_29EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-2
From reference
Brillouin
laserL
effth v
v
e
AP
1
21
modulation external 1Gb/s with
case canonicalour for 12mW
area) core(smaller sholdslower thre have fibers shifted Dispersion
55.1@20
mMHzvBrillouin
Notes_3_30EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-3• From textbook (similar definition): SBS threshold becomes
• gB : Brillouin Gain coefficient, ~ 4 E –11 m/W
• b: Normalized propagation constant of the wavegude (between 0 and 1)
• f: Brillouin bandwidth ~ 20 MHz• Pth= 1.3 mW for b=1, Aeff=50 m2, Leff= 20 km, fsource <<20
Mhz
• Pth= 14.4 mW for b=1, Aeff=50 m2, Leff= 20 km fsource =200 Mhz
B
source
effB
effth f
f
Lg
bAP 1
21
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Notes_3_31EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-3
Notes_3_32EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-4
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Notes_3_33EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-5
Notes_3_34EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin Scattering-6
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Notes_3_35EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Raman Scattering-1
Notes_3_36EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Raman Scattering-2
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Notes_3_37EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Raman Scattering-3
Opticalfrequency
Opticalfrequency
See 5.8.3 of text
Notes_3_38EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Raman Scattering-4
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Notes_3_39EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Raman Scattering-5
Notes_3_40EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Stimulated Brillouin ScatteringStimulated Raman Scattering
• SBS -- Backward Light Propagation if narrow linewidth
• SRS -- Power transfer from short to long wavelength
• Solitons– Nonlinearity balances Dispersion to achieve eigen mode at a given power level– Since Kerr coefficient (n2) is positive in most materials including fibers Solitons can be seen
in positive dispersion fiber– analogy to Dark solitons and Spatial Solitons
Dispersion
Nonlinearity
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Notes_3_41EEC 239A Optical Communication Systems and NetworkingProf. S. J. B. Yoo, UC Davis Copyright©
Solitons
• Solitons– Nonlinear Schrodinger Equation– Nonlinearity balances Dispersion to achieve eigen
mode at a given power level– Since Kerr coefficient (n2) is positive in most
materials including fibers Solitons can be seen in positive dispersion fiber
– analogy to Dark solitons and Spatial Solitons
Dispersion
Nonlinearity