-
OPTCOM - Dipartimento di Elettronica e Telecomunicazioni - Politecnico di Torino – Torino – Italy www.optcom.polito.it
http://www.optcom.polito.it/
-
OFC 2016 www.optcom.polito.it 2
http://www.ismb.it/
-
OFC 2016 www.optcom.polito.it 3
-
OFC 2016 www.optcom.polito.it 4
-
OFC 2016 www.optcom.polito.it 5
credit: http://www.nfafranchiseconsultants.com/alternatives-financial-performance-representations/
-
OFC 2016 www.optcom.polito.it 6
-
OFC 2016 www.optcom.polito.it 7
credit http://newsroom.unl.edu/announce/snr/2761/15222
credit: http://greenpediatrics.com/
homeopathy-what-how-and-why/
-
OFC 2016 www.optcom.polito.it 8
-
OFC 2016 www.optcom.polito.it 9
credit: http://travel-
representatives.com/
credit:
http://www.cisco.com/c/en/us/products/coll
ateral/optical-networking/ons-15200-series-
dwdm-systems/datasheet_c78-728877.html
-
OFC 2016 www.optcom.polito.it 10
credit: http://www.hillsborococ.org/
what-is-the-problem/
credit: http://fios.verizon.com/beacon/fiber-optics-vs-coaxial-cables/
-
OFC 2016 www.optcom.polito.it 11
ch
ASE
OSNRP
P
-
OFC 2016 www.optcom.polito.it 12
ch
ASE NLI
OSNRP
P P
ch
ASE
OSNRP
P
a model needs to allow to estimate PNLI efficiently and with acceptable accuracy
-
OFC 2016 www.optcom.polito.it 13
ch
ASE NLI
OSNRP
P P
OSNR
ASE ASE
B
P G df OSNR
NLI NLI
B
P G f df
-
OFC 2016 www.optcom.polito.it 14
Manakov
222
2
2
222
2
2
( , ) 8( , ) ( , ) ( , ) ( , ) ( , )
2 9
( , ) 8( , ) ( , ) ( , ) ( , ) ( , )
2 9
x
x x x y x
y
y y x y y
E z tj E z t E z t j E z t E z t E z t
z t
E z tj E z t E z t j E z t E z t E z t
z t
-
OFC 2016 www.optcom.polito.it 15
32 GBaud
400 km SMF
first-order Gaussian
(but not so higher order pdf’s)
-
OFC 2016 www.optcom.polito.it 16
Manakov
222
2
2
222
2
2
( , ) 8( , ) ( , ) ( , ) ( , ) ( , )
2 9
( , ) 8( , ) ( , ) ( , ) ( , ) ( , )
2 9
x
x x x y x
y
y y x y y
E z tj E z t E z t j E z t E z t E z t
z t
E z tj E z t E z t j E z t E z t E z t
z t
-
OFC 2016 www.optcom.polito.it 17
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
-
OFC 2016 18
- A. Splett, C. Kurtzke, K. Petermann,
ECOC ’93, vol. 2, p. 41,1993.
- H. Louchet et al., PTL, vol.15,
p. 1219, 2003.
- Jau Tang, JLT, vol.20, no.7,
p. 1095, 2002.
M. Nazarathy et al, Opt. Exp.,
vol.16, p. 15777, 2008
Xi Chen, W. Shieh, Opt. Exp.,
vol. 18, p. 19039, 2010
- P. Poggiolini et al., PTL, vol.
23, p. 742 2011
- A. Carena et al., JLT, v. 30,
p. 1524, 2012
P. Johannisson, M. Karlsson,
JLT, v. 31, p. 1273, 2013
P. Serena, A. Bononi, JLT,
v. 31, p. 3489, 2013
“GN model”
name used
here for the
first time
A. Bononi, O. Beucher, P. Serena, OE,
vol. 21, p. 32254, 2013 P. Johannisson, M. Karlsson,
JLT, v. 31, p. 1273, 2013
S. J. Savory, PTL, vol. 25,
p.961, 2013
for OFDM
-
OFC 2016 19
[1] A. Splett, C. Kurzke, and K. Petermann, “Ultimate Transmission Capacity of Amplified Optical Fiber Communication Systems Taking into Account Fiber Nonlinearities,” in Proc. ECOC 1993, vol. 2, pp. 41-44, 1993.
[2] Jau Tang, “The Channel Capacity of a Multispan DWDM System Employing Dispersive Nonlinear Optical Fibers and an Ideal Coherent Optical Receiver,” J. Lightwave Technol., vol. 20, pp. 1095-1101, 2002.
[3] H. Louchet et al., “Analytical Model for the Performance Evaluation of DWDM Transmission Systems,” IEEE Phot. Technol. Lett., vol. 15, pp. 1219-1221, Sept. 2003.
[4] Jau Tang, “A Comparison Study of the Shannon Channel Capacity of Various Nonlinear Optical Fibers,” J. Lightwave Technol., vol. 24, pp. 2070-2075, 2006.
[5] M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, Pak Cho, R. Noe, I. Shpantzer, V. Karagodsky “Phased-Array Cancellation of Nonlinear FWM in Coherent OFDM Dispersive Multi-Span Links,” Optics Express, vol. 16, pp. 15778-15810, 2008.
[6] X. Chen and W. Shieh, “Closed-Form Expressions for Nonlinear Transmission Performance of Densely Spaced Coherent Optical OFDM Systems,” Optics Express, vol. 18, pp. 19039-19054, 2010.
[7] W. Shieh and X. Chen, “Information Spectral Efficiency and Launch Power Density Limits Due to Fiber Nonlinearity for Coherent Optical OFDM Systems,” IEEE Photon. Journal, vol. 3, pp. 158-173, 2011.
[8] P. Poggiolini, A. Carena, V. Curri, G. Bosco, F. Forghieri, “Analytical Modeling of Non-Linear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett., vol. 23, pp. 742-744, 2011.
[9] Torrengo E, Cigliutti R, Bosco G, Carena A, Curri V, Poggiolini P, Nespola A, Zeolla D, Forghieri F. Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links. Opt Express 2011;19(26):B790–B798.
[9] A. Carena, V. Curri, G. Bosco, P.Poggiolini, F. Forghieri, “Modeling of the Impact of Non-Linear Propagation Effects in Uncompensated Optical Coherent Transmission Links,” J. of Lightw. Technol., vol. 30, pp. 1524-1539, May 15th 2012.
[10] P. Poggiolini “The GN Model of Non-Linear Propagation in Uncompensated Coherent Optical Systems,” J. of Lightwave Technol., vol. 30, no. 24, pp. 3857-3879, Dec. 15 2012.
[11] Johannisson P, Karlsson M. “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system.” J Lightwave Technol 2013;31(8):1273–1282.
[12] Nespola A, Straullu S, Carena A, Bosco G, Cigliutti R, Curri V, Poggiolini P, Hirano M, Yamamoto Y, Sasaki T, Bauwelinck J,Verheyen K, Forghieri F. GN-model validation over seven fiber types in uncompensated PM-16QAM Nyquist-WDM links. IEEE Photonics Technol Lett 2014;26(2):206–209.
[13] Serena P, Bononi A. “An alternative approach to the Gaussian noise model and its system implications.” J Lightwave Technol 2013;31(22):3489–3499.
[14] Poggiolini P, Bosco G, Carena A, Curri V, Jiang Y, Forghieri F. “The GN model of fiber non-linear propagation and its applications.” J Lightwave Technol 2014;32(4):694–721.
[15] Serena P, Bononi A. “A time-domain extended Gaussian noise model.” J Lightwave Technol. 2015;33(7):1459–1472.
[16] V. Curri et al., “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Optics Express, v. 21., no. 3, pp. 3308-3317, Feb. 2013.
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OFC 2016 www.optcom.polito.it 20
-
OFC 2016 www.optcom.polito.it 21
2. C. R. Menyuk, ‘Pulse propagation in an elliptically birefringent Kerr medium,’ IEEE J. Quantum Electron., vol. 25, no. 12, pp. 2674-2682,
Dec. 1989.
5. S. G. Evangelides Jr., L. F.Mollenauer, J. P. Gordon, and N. S. Bergano, ‘Polarization multiplexing with solitons,’ J. Lightwave Technol.,
vol. 10, no. 1, pp. 28-35, Jan. 1992.
6. D. Marcuse, C. R. Menyuk, and P. K. A. Wai, ‘Application of the Manakov-PMD equation to studies of signal propagation in optical fibers
with randomly varying birefringence,’ J. Lightwave Technol., vol. 15, no. 9, pp. 1735-1746, Sept. 1997.
10. A. Vannucci, P. Serena, and A. Bononi, ‘The RP method: a new tool for the iterative solution of the nonlinear Schrodinger equation,’ J.
Lightwave Technol., vol. 20, no. 7, pp. 1102-1112, July 2002.
11. K.V. Peddanarappagari and M. Brandt-Pearce ‘Volterra series transfer function of single-mode fibers,’ J. of Lightwave. Technol., vol.
15, no. 12, pp. 2232-2241, Dec. 1997.
12. A. Mecozzi, C. Balslev Clausen, and M. Shtaif, ‘Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,’
IEEE Photon. Technol. Lett., vol. 12, no. 4, pp. 392-394, Apr. 2000.
13. E. E. Narimanov and P. P. Mitra, ‘The channel capacity of a fiber optics communication system: perturbation theory,’ J. Lightwave
Technol., vol. 20, no. 3, pp. 530-537, Mar. 2002.
16. M. Secondini, E. Forestieri, and C. R. Menyuk, ‘A combined regular logarithmic perturbation method for signal-noise interaction in
amplified optical systems,’ J. Lightwave Technol., vol. 27, no. 16, pp. 3358-3369, Aug. 2009.
20. J. P. Gordon and L. F. Mollenauer, ‘Phase noise in photonic communications systems using linear amplifiers,’ Opt. Lett., vol. 15, no.
23, pp. 1351-1353, 1990.
21. D. Marcuse, ‘Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion,’ J. Lightwave Technol.,
vol. 9, no. 3, pp. 356-361, Mar. 1991.
24. A. Mecozzi, ‘Limits to long haul coherent transmission set by the Kerr nonlinearity and noise of the inline amplifiers,’ J. Lightwave.
Technol., vol. 12, no. 11, pp. 1993-2000, Nov. 1994.
25. G. Bellotti, M. Varani, C. Francia, and A. Bononi, ‘Intensity distortion induced by cross-phase modulation and chromatic dispersion in
optical-fiber transmissions with dispersion compensation,’ IEEE Photon. Technol. Lett.,
vol. 10, no. 12, pp. 1745-1747, Dec. 1998.
26. A. Cartaxo, ‘Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and
dispersion compensators,’ J. Lightw. Technol., vol. 17, no. 2, pp. 178-190, Feb. 1999.
27. R. Hui, K. R. Demarest, and C. T. Allen, ‘Cross-phase modulation in multispan WDM optical fiber systems,’ J. Lightwave. Technol., vol.
17, no. 6, pp. 1018-1026, Jun. 1999.
28. A.Mecozzi, C. Balslev Clausen, andM. Shtaif, ‘System impact of intrachannel nonlinear effects in highly dispersed optical pulse
transmission,’ IEEE Phot. Technol. Lett., vol. 12, no. 12, pp. 1633-1635, Dec. 2000.
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OFC 2016 www.optcom.polito.it 22
29. P. P. Mitra and J. B. Stark, ‘Nonlinear limits to the information capacity of optical fiber communications,’ Nature, vol. 411, no.
6841, pp. 1027-1030, Jun. 2001.
33. B. Xu and M. Brandt-Pearce, ‘Comparison of FWM- and XPM-induced crosstalk using the Volterra series transfer function method,’
J. Lightwave. Technol., vol. 21, no. 1, pp. 40-53, Jan. 2003.
35. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, ‘Information capacity of optical fiber channels with zero
average dispersion,’ Phys. Rev. Lett., vol. 91, pp. 203901-1 to 203901-4, Nov. 2003.
36. A.Mecozzi, ‘Probability density functions of the nonlinear phase noise,’ Opt. Lett., vol. 29, no. 7, pp. 673-675, 2004.
38. E. Ciaramella and E. Forestieri, ‘Analytical approximation of nonlinear distortions,’ IEEE Photon. Technol. Lett., vol. 17, no. 1,
pp. 91-93, Jan. 2005.
39. S. Kumar and D. Yang, ‘Second-order theory for self-phase modulation and cross-phase modulation in optical fibers,’ J.
Lightwave Technol., vol. 23, no. 6, pp. 2073-2080, June 2005.
40. K.-P. Ho and H.-C. Wang, ‘Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in
dispersive transmission systems,’ IEEE Photon. Technol. Lett., vol. 17, no. 7, pp. 1426-1428, July 2005.
41. S. Kumar, ‘Effect of dispersion on nonlinear phase noise in optical transmission systems,’ Optics Lett., vol. 30, no. 24, pp. 3278-
3280, Dec. 2005.
42. K.-P. Ho and H.-C. Wang, ‘Effect of dispersion on nonlinear phase noise,’ Opt. Lett., vol. 31, no. 14, pp. 2109-2111, July 2006.
44. A. T. Lau, S. Rabbani, and J. M. Kahn, ‘On the statistics of intrachannel four-wave mixing in phase-modulated optical
communication systems,’ J. Lightwave Technol., vol. 26, no. 14, pp. 2128-2135, July 2008.
46. A. D. Ellis, J. Zhao, and D. Cotter, ‘Approaching the non-linear Shannon limit,’ J. Lightwave Technol., vol. 28, no. 4, pp. 423-
433, Feb. 2010.
47. A.Mecozzi, ‘A unified theory of intra-channel nonlinearity in pseudolinear phase-modulated transmission,’ IEEE Photon. J., vol. 2,
no. 5, pp. 728-735, Aug. 2010.
50. A. Bononi, P. Serena, N. Rossi, and D. Sperti, ‘Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?’
in Proc. of ECOC 2010, paper Th.10.E.1, Torino (IT), Sept. 2010.
51. J. Reis and A. Teixeira, ‘Unveiling nonlinear effects in dense coherent optical WDM systems with Volterra series,’ Optics Express,
vol. 18, no. 8, pp. 8660-8670, Apr. 2010.
-
OFC 2016 www.optcom.polito.it 23
55. L. Beygi, E. Agrell, M. Karlsson, and P. Johannisson, ‘Signal statistics in fiber-optical channels with polarization multiplexing and
self-phase modulation,’ J. Lightwave Technol., vol. 29, no. 16, pp. 2379-2386, Aug. 2011.
56. Chongjin Xie, ‘Fiber Nonlinearities in 16QAM Transmission Systems,’ in Proc. ECOC 2011, paper We.7.B.6, Geneva (CH), Sept.
2011.
57. Chongjin Xie, ‘Impact of nonlinear and polarization effects on coherent systems,’ in Proc. ECOC 2011, paper We.8.B.1, Geneva
(CH), Sept. 2011.
62. A. Bononi, P. Serena, N. Rossi, E. Grellier, and F. Vacondio, ‘Modeling nonlinearity in coherent transmissions with dominant
intrachannel-four-wavemixing,’ Optics Express, vol. 20, pp. 7777-7791, 26 March 2012.
65. L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, ‘A discrete-time model for uncompensated single-channel
fiber-optical links,’ IEEE Trans. on Communic., vol. 60, no. 11, pp. 3440-3450, Nov. 2012.
67. M. Secondini and E. Forestieri, ‘Analytical fiber-optic channel model in the presence of cross-phase modulations,’ IEEE Photon.
Technol. Lett., vol. 24, no. 22, pp. 2016-2019, Nov. 15th 2012.
68. Olivier Rival and Kinda Mheidly ‘Accumulation rate of inter and intrachannel nonlinear distortions in uncompensated 100G PDM-
QPSK systems,’ in Proc. OFC 2013, Los Angeles (CA), paper JW2A.52, Mar. 2013.
90. F. Vacondio, C. Simonneau, L. Lorcy, J.C.Antona, A. Bononi and S. Bigo, ‘Experimental characterization of Gaussian-distributed
nonlinear distortions,’ in Proc. of ECOC 2011, Geneva, paper We.7.B.1, Sept. 2011.
91. F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona and S. Bigo, ‘On nonlinear distortions of highly
dispersive optical coherent systems,’ Optics Express, Vol. 20, No. 2, pp. 1022-1032, Jan. 2012.
92. O. V. Sinkin, J.-X. Cai, D. G. Foursa, H. Zhang, A. N. Pilipetskii, G. Mohs, and Neal S. Bergano, ‘Scaling of nonlinear impairments
in dispersion uncompensated long-haul transmission,’ in Proc. of OFC 2012, Los Angeles
(US), paper OTu1A.2, Mar. 2012.
113. M. A. Sorokina, S. K. Turitsyn, ‘Regeneration limit of classical Shannon capacity,’ Nature Communications, 5:3861, DOI:
10.1038/ncomms4861, www.nature.com/naturecommunications.
-
OFC 2016 www.optcom.polito.it 24
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 25
transmission spectrum
f
WDM ( )G f
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 26
the “link function”:
it is the “FWM efficiency”
of the whole link
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 27
it contains
the full description of the link
span by span, amplifier by amplifier
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 28
for identical spans with lumped amplification:
2
1 22
22 4
1 2
2
2
2 2
1 2
2
21
2
2
22
eff 1
2sin 2
sin
1
1 2 2
s s f f f fL
s s
j L
s
N f f L
f f f f
f fe e
j f f f LfL
-
OFC 2016 www.optcom.polito.it 29
eff
1 exp 2
2
sLL
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 30
for identical spans with lumped amplification:
2
1 22
22 4
1 2
2
2
2 2
1 2
2
21
2
2
22
eff 1
2sin 2
sin
1
1 2 2
s s f f f fL
s s
j L
s
N f f L
f f f f
f fe e
j f f f LfL
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 31
for identical spans with lumped amplification:
2
1 22
22 4
1 2
2
2
2 2
1 2
2
21
2
2
22
eff 1
2sin 2
sin
1
1 2 2
s s f f f fL
s s
j L
s
N f f L
f f f f
f fe e
j f f f LfL
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 32
for identical spans with lumped amplification:
2
1 22
22 4
1 2
2
2
2 2
1 2
2
21
2
2
22
eff 1
2sin 2
sin
1
1 2 2
s s f f f fL
s s
j L
s
N f f L
f f f f
f fe e
j f f f LfL
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 33
for identical spans with lumped amplification:
2
1 22
22 4
1 2
2
2
2 2
1 2
2
21
2
2
22
eff 1
2sin 2
sin
1
1 2 2
s s f f f fL
s s
j L
s
N f f L
f f f f
f fe e
j f f f LfL
-
OFC 2016 www.optcom.polito.it 34
2 2
2
2 2
1
2
2
1 2
sin 2
sin 2
s s
s
s
f f
f
N f f L
f f LfN
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 35
for identical spans with lumped amplification:
1
2
22
22 4
2
2 1 2
2
ef
2
f 1
1
1 2
s sL j L f f f fe e
j ff f fL
1 2
1 2
2 2
2
2 2
2
sin 2
sin 2
s s
s
N f f Lf f
f ff f L
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 36
for identical spans with lumped amplification:
1
2
22
22 4
2
2 1 2
2
ef
2
f 1
1
1 2
s sL j L f f f fe e
j ff f fL
sN
-
OFC 2016
2
2 1 2
22 4
2
2 1 2
1 2 1NLI WDM WDM WDM
2
eff 1
2
2
1 2
1
1 2
( )16
( ) ( ) ( )27
d ds s f f fL j L f
s
e e
j f f ff
G f f
L
N G f G f G f f
f f
www.optcom.polito.it 37
integral can be easily dealt with
numerically in a matter of seconds
-
OFC 2016 www.optcom.polito.it 38
credit: http://travel-
representatives.com/
credit:
http://www.cisco.com/c/en/us/products/coll
ateral/optical-networking/ons-15200-series-
dwdm-systems/datasheet_c78-728877.html
http://www.computerhowtoguide.com/2011/11/google-adsense-alternatives-that-work.html
-
OFC 2016 www.optcom.polito.it 39
credit: http://www.dtvisiontech.com/2015_12_01_archive.html
-
OFC 2016 www.optcom.polito.it 40
submarine
terrestrial
long-haul
terrestrial
medium-short
haul
-
OFC 2016 www.optcom.polito.it 41
3BER 4 10
raised-cosine spectra
roll-off 0.05
EDFA NF 5 dB
ASE added at the RX
-
OFC 2016 www.optcom.polito.it 42
red: SMF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 43
PM-QPSK PM-8QAM
PM-16QAM
PM-64QAM
PM-32QAM
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
33.6 GHz 50 GHz red: SMF
-
OFC 2016 www.optcom.polito.it 44
PM-QPSK PM-8QAM
PM-16QAM
PM-64QAM
PM-32QAM
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
33.6 GHz 50 GHz
red: SMF
-
OFC 2016 www.optcom.polito.it 45
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
red: SMF
blue: PSCF
red: SMF
-
OFC 2016 www.optcom.polito.it 46
blue: PSCF
red: SMF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 47
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 48
dispersion
D
ps/(nm km)
loss
dB/km
non-linearity
1/(W km)
PSCF 20.1 0.17 0.8
SMF 16.7 0.2 1.3
NZDSF
(E-LEAF)
3.8 0.22 1.5
-
OFC 2016 www.optcom.polito.it 49
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 50
blue: PSCF
red: SMF
green: NZDSF
MARKERS: simulations
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 51
5% error bar
blue: PSCF
red: SMF
green: NZDSF 33.6 GHz
50 GHz 37.5 GHz
MARKERS: simulations
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 52
32 GBaud
15 channels
60 km spans
LINES: incoherent GN model
PM-16QAM
PM-32QAM
PM-64QAM
blue: PSCF
red: SMF
green: NZDSF
-
OFC 2016 www.optcom.polito.it 53
32 GBaud
15 channels
60 km spans
LINES: incoherent GN model
blue: PSCF
red: SMF
green: NZDSF
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 54
MARKERS: simulations blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
LINES: incoherent GN model
-
OFC 2016 www.optcom.polito.it 55
credit:
https://www.koozai.com/blog/analytics/pre
dictive-analytics-and-digital-campaigns/
-
OFC 2016 www.optcom.polito.it 56
2
2 1 2
22 4
2
2 1 2
1 2 1NLI WDM WDM WDM
2
eff 1
2
2
1 2
1
1 2
( )16
( ) ( ) ( )27
d ds s f f fL j L f
s
e e
j f f ff
G f f
L
N G f G f G f f
f f
if span loss is greater than 10-12 dB
this term can be neglected
-
OFC 2016 www.optcom.polito.it 57
2
22
2
2
eff
1 2
24 2
NLI WDM WDM W M1 2
1
D2 1
21 4
16( ) ( ) ( )
27(
d d
) s
f
L
f f f
N G f G f G f f
f f
G f f
it can be integrated analytically ! (with some approximations)
-
OFC 2016 www.optcom.polito.it 58
2 3 22 2eff ch
2 ch2
2
2
NLI as16
27inh
2
sR
fs
L PP N R N
R
Other versions address non-uniform spans and all-different channels: P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, F. Forghieri, ‘The GN model of fiber non-linear
propagation and its applications,’ J. of Lightw.Technol., vol. 32, no. 4, pp. 694-721, Feb. 2014.
P. Johannisson and M. Karlsson, “Perturbation analysis of nonlinear propagation in a strongly dispersive optical communication system,” J. Lightw. Technol., vol. 31, no. 8, pp. 1273–1282, Apr. 15, 2013.
P. Poggiolini “The GN Model of Non-Linear Propagation in Uncompensated Coherent Optical Systems,”
J. of Lightwave Technol., vol. 30, no. 24, pp. 3857-3879, Dec. 15 2012.
-
OFC 2016 www.optcom.polito.it 59
5% error bar
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
with numerical integration
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 60
5% error bar
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
closed-form formula
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 61
MARKERS: simulations blue: PSCF red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
LINES: incoherent GN model
with numerical integration
-
OFC 2016 www.optcom.polito.it 62
blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
LINES: incoherent GN model
closed-form formula
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 63
2 3 22 2eff ch
2 ch2
2
2
NLI as16
27inh
2
sR
fs
L PP N R N
R
-
OFC 2016 www.optcom.polito.it 64
credit: http://travel-
representatives.com/
credit:
http://www.cisco.com/c/en/us/products/coll
ateral/optical-networking/ons-15200-series-
dwdm-systems/datasheet_c78-728877.html
-
OFC 2016 www.optcom.polito.it 65
lines: GN model; markers: experiment
-
OFC 2016 www.optcom.polito.it 66
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 67
http://www.improfestuk.co.uk/2014/problem-solved.html https://www.flickr.com/photos/wingedwolf/5471047557
credit: http://www.improfestuk.co.uk/2014/problem-
solved.html
http://www.improfestuk.co.uk/2014/problem-solved.htmlhttp://www.improfestuk.co.uk/2014/problem-solved.htmlhttp://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjRyfXMwqLLAhVDvRQKHV2DD8kQjRwIBw&url=http://www.improfestuk.co.uk/2014/problem-solved.html&bvm=bv.115339255,d.bGQ&psig=AFQjCNE6wMoGO6x_p9sw7gWhAeyR_H3jTA&ust=1457025754562557http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjRyfXMwqLLAhVDvRQKHV2DD8kQjRwIBw&url=http://www.improfestuk.co.uk/2014/problem-solved.html&bvm=bv.115339255,d.bGQ&psig=AFQjCNE6wMoGO6x_p9sw7gWhAeyR_H3jTA&ust=1457025754562557http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjRyfXMwqLLAhVDvRQKHV2DD8kQjRwIBw&url=http://www.improfestuk.co.uk/2014/problem-solved.html&bvm=bv.115339255,d.bGQ&psig=AFQjCNE6wMoGO6x_p9sw7gWhAeyR_H3jTA&ust=1457025754562557
-
OFC 2016 www.optcom.polito.it 68
credit: http://www.improfestuk.co.uk/2014/problem-
solved.html
credit: https://www.flickr.com/
photos/wingedwolf/5471047557
http://www.improfestuk.co.uk/2014/problem-solved.htmlhttp://www.improfestuk.co.uk/2014/problem-solved.htmlhttp://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjRyfXMwqLLAhVDvRQKHV2DD8kQjRwIBw&url=http://www.improfestuk.co.uk/2014/problem-solved.html&bvm=bv.115339255,d.bGQ&psig=AFQjCNE6wMoGO6x_p9sw7gWhAeyR_H3jTA&ust=1457025754562557http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjRyfXMwqLLAhVDvRQKHV2DD8kQjRwIBw&url=http://www.improfestuk.co.uk/2014/problem-solved.html&bvm=bv.115339255,d.bGQ&psig=AFQjCNE6wMoGO6x_p9sw7gWhAeyR_H3jTA&ust=1457025754562557http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjRyfXMwqLLAhVDvRQKHV2DD8kQjRwIBw&url=http://www.improfestuk.co.uk/2014/problem-solved.html&bvm=bv.115339255,d.bGQ&psig=AFQjCNE6wMoGO6x_p9sw7gWhAeyR_H3jTA&ust=1457025754562557
-
OFC 2016 www.optcom.polito.it 69
-
OFC 2016
NLI WDM W1 2 1 2
2
11 2
DM WDM
2
16( ) (( ) ) ( )
27
d d, ,
G f G f G f f
f
f
f f f
G f
f
www.optcom.polito.it 70
for identical spans with lumped amplification:
1
2
22
22 4
2
2 1 2
2
ef
2
f 1
1
1 2
s sL j L f f f fe e
j ff f fL
sN
1 2
1 2
2 2
2
2 2
2
sin 2
sin 2
s s
s
N f f Lf f
f ff f L
1 2
1 2
2 2
2
2 2
2
sin 2
sin 2
s s
s
N f f Lf f
f ff f L
-
OFC 2016 www.optcom.polito.it 71
5% error bar
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: incoherent GN model
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 72
5% error bar
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: GN model
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 73
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 74
max,dB NLI,dB
1
3L P
-
OFC 2016 www.optcom.polito.it 75
spanNLI nP
3
NLI NLI chP P P
-
OFC 2016 www.optcom.polito.it 76
1 2 5 10 20 50 20
25
30
35
40
45
50
number of spans
Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, ‘Impact of the transmitted signal initial dispersion transient on the
accuracy of the GN-model of non-linear propagation,’ Proc. of ECOC 2013, paper Th.1.D.4, London (UK), Sept. 2013.
2
NLI
1/W , dB
P
PM-QPSK, 32 GBaud
9 channels, 33.6 GHz
SMF, 100km spans
simulation
GN model
incoherent GN
-
OFC 2016 www.optcom.polito.it 77
1 2 5 10 20 50 20
25
30
35
40
45
50
number of spans
Carena, G. Bosco, V. Curri, P. Poggiolini, and F. Forghieri, ‘Impact of the transmitted signal initial dispersion transient on the
accuracy of the GN-model of non-linear propagation,’ Proc. of ECOC 2013, paper Th.1.D.4, London (UK), Sept. 2013.
2
NLI
1/W , dB
P
PM-QPSK, 32 GBaud
9 channels, 33.6 GHz
SMF, 100km spans
simulation
GN model
incoherent GN
-
OFC 2016 www.optcom.polito.it 78
-
OFC 2016 www.optcom.polito.it 79
-
OFC 2016 www.optcom.polito.it 80
-
OFC 2016 81
P. Poggiolini, G. Bosco, A. Carena,
V. Curri, Y. Jiang, F. Forghieri, JLT,
vol. 33, p. 459, 2015.
A. Carena, G. Bosco, V. Curri, Y.
Jiang, P. Poggiolini, F. Forghieri,
OE, vol. 22, pp.16335, June 2014.
P. Serena, A. Bononi, JLT, vol. 33,
p. 1459, 2015
P. Serena,
JLT, vol. 34, p. 1476, 2016
R. Dar, M. Feder, A. Mecozzi, M.
Shtaif, JLT, vol. 34, p. 593, 2016
R. Dar, M. Feder, A. Mecozzi, M.
Shtaif, JLT, vol. 33, p. 1044, 2015
R. Dar, M. Feder, A. Mecozzi, and
M. Shtaif, OE, vol.21, pp.25685,
Nov. 2013.
R. Dar, M. Feder, A. Mecozzi, M.
Shtaif, OE, vol. 22, p. 14199, 2014
-
OFC 2016 www.optcom.polito.it 82
EGNNLIG f GN
NLIG f corr
NLIG f
-
OFC 2016 www.optcom.polito.it 83
EGNNLIG f GN
NLIG f corr
NLIG f
-
OFC 2016 www.optcom.polito.it 84
EGNNLIG f GN
NLIG f corr
NLIG f
-
OFC 2016 www.optcom.polito.it 85
credit: http://www.dtvisiontech.com/2015_12_01_archive.html
-
OFC 2016 www.optcom.polito.it 86
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: EGN model
-
OFC 2016 www.optcom.polito.it 87
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: EGN model
PM-QPSK
PM-8QAM
PM-16QAM
PM-32QAM
PM-64QAM
-
OFC 2016 www.optcom.polito.it 88
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
MARKERS: simulations
32 GBaud
15 channels
100 km spans
LINES: EGN model
-
OFC 2016 www.optcom.polito.it 89
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
5% error bar
32 GBaud
15 channels
100 km spans
LINES: EGN model
MARKERS: simulations
-
OFC 2016 www.optcom.polito.it 90
32 GBaud
15 channels
60 km spans
LINES: EGN model
PM-16QAM
PM-32QAM
PM-64QAM
blue: PSCF
red: SMF
green: NZDSF
-
OFC 2016 www.optcom.polito.it 91
MARKERS: simulations blue: PSCF red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
LINES: EGN model
-
OFC 2016 www.optcom.polito.it 92
spanNLI nP
-
OFC 2016 www.optcom.polito.it 93
1 2 5 10 20 50 20
25
30
35
40
45
50
number of spans
Carena A, Bosco G, Curri V, Jiang Y, Poggiolini P, Forghieri F. ‘EGN model of non-linear fiber propagation,’ Optics Express, vol. 22,
no. 13, pp.16335–16362, June 2014.
2
NLI
1/W , dB
P
PM-QPSK, 32 GBaud
9 channels, 33.6 GHz
SMF, 100km spans
simulation
GN model
EGN model
-
OFC 2016 www.optcom.polito.it 94
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 95
f
f
WDMB
f
Constraint: identical total throughput
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 96
a constant value while dividing BWDM into more channels
means same maximum reach
3
NLI NLI chP P P
3
NLI NLI chG G G
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 97
f
f
WDMB
f
Constraint: identical total throughput
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 98
1 10 100 1000 8
10
12
14
16
18
20
GN
simulations
inc GN
BWDM = 500 GHz, PM-QPSK, 100 km spans, spacing 1.05 x (symb. rate)
number of channels in 500 GHz
2
(THz/W) dB
NLIG
201 channels
2.4 GBaud
15 channels
32 GBaud
5 channels
96 GBaud
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 99
1 10 100 1000 8
10
12
14
16
18
20
GN
SPM+XPM
no FWM
EGN
2
(THz/W) dB
NLIG
number of channels in 500 GHz
201 channels
2.4 GBaud
15 channels
32 GBaud
5 channels
96 GBaud simulations
BWDM = 500 GHz, PM-QPSK, 100 km spans, spacing 1.05 x (symb. rate)
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 100
1 10 100 1000 12
14
16
18
20
22
24
6.8 GBaud
32 GBaud
96 GBaud
GN
SPM+XPM
no FWM
EGN
simulations
BWDM = 500 GHz, PM-QPSK, 100 km spans, spacing 1.05 x (symb. rate)
number of channels in 500 GHz
2
(THz/W) dB
NLIG
-
OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 101
1 10 100 1000 12
14
16
18
20
22
24
6.8 GBaud
32 GBaud
96 GBaud
GN
SPM+XPM
no FWM
EGN
simulations
BWDM = 500 GHz, PM-QPSK, 100 km spans, spacing 1.05 x (symb. rate)
number of channels in 500 GHz
2
(THz/W) dB
NLIG
P.Poggiolini, A.Nespola, Y.Jiang, G.Bosco, A.Carena, L.Bertignono,
S.M. Bilal, S. Abrate, and F. Forghieri, “Analytical and Experimental
Results on System Maximum Reach Increase Through Symbol Rate
Optimization, JLT, v. 34, n. 8, pp. 1872-1885, Apr 2016.
A. Nespola, Y. Jiang, L. Bertignono, G. Bosco, A. Carena, S.M. Bilal,
F. Forghieri, P. Poggiolini “Effectiveness of Digital Back-Propagation
and Symbol-Rate Optimization in Coherent WDM Optical Systems”,
OFC 2016 Thursday, paper Th3D.2
-
OFC 2016 www.optcom.polito.it 102
[1] W. Shieh andY. Tang, “Ultrahigh-speed signal transmission over nonlinear
and dispersive fiber optic channel: The multicarrier advantage,” IEEE
Photon. J., vol. 2, no. 3, pp. 276–283, Jun. 2010.
[2] C. Behrens, R. I. Killey, S. J. Savory, Ming Chen, and P. Bayvel,
“Nonlinear
transmission performance of higher-order modulation formats,” IEEE
Photon. Technol. Lett., vol. 23, no. 6, pp. 377–379, Mar. 2011.
[3] L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of
coherent optical communications systems,” Opt. Exp., vol. 19, no. 9,
pp. 8079–8084, Apr. 2011.
[4] Q. Zhuge, B. Chˆatelain, and D. V. Plant, “Comparison of intra-channel
nonlinearity tolerance between reduced-guard-interval CO-OFDM systems
and Nyquist single carrier systems,” presented at the Optical Fiber
Communication Conf. , Los Angeles, CA, USA, Mar. 2012, paper
OTh1B.3.
[5] A. Bononi, N. Rossi, and P. Serena, “Performance dependence on channel
baud-rate of coherent single-carrier WDM systems,” presented at the Eur.
Conf. Optical Communication, London, U.K., Sep. 2013, paper Th.1.D.5.
[6] N. Rossi, P. Serena, and A. Bononi, “Symbol-rate dependence of
dominant
nonlinearity and reach in coherent WDM links,” J. Lightw. Technol.,
vol. 33, no. 14, pp. 3132–3143, Jul. 2015.
[7] M. Qiu, Q. Zhuge, X. Xu, M. Chagnon, M. Morsy-Osman, and D. V. Plant,
‘Subcarrier multiplexing using DACs for fiber nonlinearity mitigation
in coherent optical communication systems,” presented at the Optical
Fiber Communication Conf. , San Francisco, CA, USA, Mar. 2014, paper
Tu3J.2.
[8] F. Yaman et al., “First quasi-single-mode transmission over transoceanic
distance using few-mode fibers,” presented at the Optical Fiber
Communication Conf. , Los Angeles, CA, USA, Mar. 2015, paper Th5C.7.
[9] H. Nakashima et al., “Experimental investigation of nonlinear tolerance
of subcarrier multiplexed signals with spectrum optimization,” presented
at the Eur. Conf. Optical Communication, Valencia, Spain, Sep. 2015,
paper Mo.3.6.4.
[10] J. Fickers, A. Ghazisaeidi, M. Salsi, G. Charlet, P. Emplit, and
F. Horlinet, “Multicarrier offset-QAM for long-haul coherent optical
communications,” J. Ligthw. Technol., vol. 32, no. 4, pp. 4671–4678,
Dec. 2014.
[11] P. Poggiolini, A. Carena, Y. Jiang, G. Bosco, and F. Forghieri, “On the
ultimate potential of symbol-rate optimization for increasing system
maximumreach,”
presented at theEur.Conf.Optical Communication,Valencia,
Spain, Sep. 2015, paper We.4.6.2.
[12] A. Nespola, L. Bertignono, G. Bosco, A. Carena, Y. Jiang, S. M. Bilal,
P. Poggiolini, S. Abrate, and F. Forghieri, “Experimental demonstration of
fiber nonlinearity mitigation in a WDM multi-subcarrier coherent optical
system,” presented at the Eur. Conf. Optical Communication, Valencia,
Spain, Sep. 2015, paper Mo.3.6.3.
[13] A. Carbo, J. Renaudier, R. Rios-Mller, P. Tran, and G. Charlet,
“Experimental analysis of non linear tolerance dependency of multicarrier
modulations versus bandwidth efficiency,” presented at the Eur. Conf.
Optical Communication, Valencia, Spain, Sep. 2015, paper Th.2.6.6.
-
OFC 2016 www.optcom.polito.it 103
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 104
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 105
credit: https://www.dreamhost.com/blog/2009/05/13/broken-browsers-part-one/
-
OFC 2016 www.optcom.polito.it 106
EGN GN corrNLI NLI NLIG f G f G f
4 3
corr corr corr corr corr
NLI SPM X1-XPM X M
2 1
i i
i i
G f G f G f G f G f
2
1 2 1
GN
NLI WD 2 1 2 1M WDM WD 2M
16( ) ( ) ( ) ( ) d d( ) , ,
27G fG f f fG f G f f f f f f
FWM XPM SPM SPM
-
OFC 2016 www.optcom.polito.it 107
SPM SPM
SPM
corr 3( ) ( ) ( )m m m m mG f P f f
SPM
/2 /2 /2
2
1 2 2
/2 /2 /2
2
1 2 2 1 2 1 2
1 2 1 2
/2 /2 /2
2
1 2 2
/2 /2 /2
80( )
81
( ) ( ) ( ) ( ) ( )
, , , ,
16
81
m m m m m m
m m m m m m
m m m m m m
m m m m m m
f B f B f B
m m
f B f B f B
m m m m m
f B f B f B
m
f B f B f B
f R df df df
s f s f s f s f f f s f f f
f f f f f f
R df df df
2
1 2 1 2 1 2 2 2
1 2 1 2 2 2
( ) ( ) ( ) ( ) ( )
, , , ,
m m m m ms f f f s f s f s f f f s f
f f f f f f f f
SPM
/2 /2 /2 /2
1 2 1 2
/2 /2 /2 /2
1 2 1 2 1 2 1 2
1 2 1 2
16( )
81
( ) ( ) ( ) ( ) ( ) ( )
, , , ,
m m m m m m m m
m m m m m m m m
f B f B f B f B
m m
f B f B f B f B
m m m m m m
f R df df df df
s f s f s f f f s f s f s f f f
f f f f f f
is the Fourier transform
of the pulse used by the n-th channel, and: ch
2
WDM
1
N
n n n n
n
G f P R s f f
ns f
-
OFC 2016 www.optcom.polito.it 108
ch
X1-XPM
corr 2 X1-XPM
1
N
m n n n
nn m
G f P P f
X1-XPM
/2 /2 /2
'
1 2 2
/2 /2 /2
2' '
1 2 2 1 2 1 2
'
1 2 1 2
80
81
, , , ,
m m n n n n
m m n n n n
f B f B f B
n
m n
f B f B f B
m n n n n
f R R df df df
s f s f s f s f f f s f f f
f f f f f f
-
OFC 2016 www.optcom.polito.it 109
X2
1corr 2
X2
1
mn
m m n
n mn m
G f P P f
X2
/2 /2 /2
'
1 2 2
/2 /2 /2
2' '
1 2 2 1 2 1 2
'
1 2 1 2
80
81
, , , ,
n n m m m m
n n m m m m
f B f B f B
n
m n
f B f B f B
n m m m m
f R R df df df
s f s f s f s f f f s f f f
f f f f f f
corr
X3 X3
12
1
mn
m m n
n mn m
G f P P f
X3
/2 /2 /2
'
1 2 2
/2 /2 /2
2' '
1 2 1 2 2 1 2 2
' '
1 2 1 2 2 2
16
81
, , , ,
m m m m m m
m m m m m m
f B f B f B
n
m n
f B f B f B
n m m m m
f R R df df df
s f f f s f s f s f s f f f
f f f f f f f f
corr
X4 X4 X4
13
1
mn n
n n n
n mn m
G f P f f
X4
/2 /2 /2
2 '
1 2 2
/2 /2 /2
2' '
1 2 2 1 2 1 2
'
1 2 1 2
/2 /2 /2
2 '
1 2 2
/2 /2 /2
2
1 2
80
81
, , , ,
16
81
n n n n n n
n n n n n n
n n n n n n
n n n n n n
f B f B f B
n
n
f B f B f B
n n n n n
f B f B f B
n
f B f B f B
n n
f R df df df
s f s f s f s f f f s f f f
f f f f f f
R df df df
s f f f s f
' '
1 2 1 2 2 2
' '
1 2 1 2 2 2, , , ,
n n ns f s f f f s f
f f f f f f f f
X4
/2 /2 /2 /2
' '
1 2 1 2
/2 /2 /2 /2
' ' ' '
1 2 1 2 1 2 1 2
' '
1 2 1 2
16
81
, , , ,
n n n n n n n n
n n n n n n n n
f B f B f B f B
n
n
f B f B f B f B
n n n n n n
f R df df df df
s f s f s f f f s f s f s f f f
f f f f f f
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OFC 2016 www.optcom.polito.it 110
max
corr
M1 M1
min
12
1
min max ch
min max
when 1, 2, ;
when 1, 1, 2.
lml
n l l
n m l ln m
G f P P f
n m l n l N
n m l l n
M1
/2 /2 /2
'
1 2 2
/2 /2 /2
2' '
1 2 2 1 2 1 2
'
1 2 1 2
80
81
, , , ,
n n l l l l
n n l l l l
f B f B f B
l
n l
f B f B f B
n l l l l
f R R df df df
s f s f s f s f f f s f f f
f f f f f f
max
corr
M2 M2
min
12
1
min max
min max ch
when 1, 1, 1;
when 1, 1, .
lml
n l l
n m l ln m
G f P P f
n m l l n
n m l n l N
M2
/2 /2 /2
'
1 2 2
/2 /2 /2
2' '
1 2 2 1 2 1 2
'
1 2 1 2
80
81
, , , ,
n n l l l l
n n l l l l
f B f B f B
l
n l
f B f B f B
n l l l l
f R R df df df
s f s f s f s f f f s f f f
f f f f f f
chcorr
M3 M3
2
1, 1
when is odd, 5 2;
when is even, 2 2, 2 3.
Nl
n l l
nn m m
G f P P f
n l n
n l n n
M3
/2 /2 /2
'
1 2 2
/2 /2 /2
2' '
1 2 1 2 2 1 2 2
' '
1 2 1 2 2 2
16
81
, , , ,
l l l l l l
l l l l l l
f B f B f B
l
n l
f B f B f B
n l l l l
f R R df df df
s f f f s f s f s f s f f f
f f f f f f f f
-
OFC 2016 www.optcom.polito.it 111
4
2
E2
E
a
a
6 4
2 2
E E9 12
E E
a a
a a
corr
NLI0 0G
EGN GNNLI NLIG f G f
-
OFC 2016 www.optcom.polito.it 112
-
OFC 2016 www.optcom.polito.it 113
EGN GN corrNLI NLI NLIG f G f G f
-
OFC 2016 www.optcom.polito.it 114
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OFC 2016 www.optcom.polito.it 115
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 116
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OFC 2016 www.optcom.polito.it 117
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OFC 2016 www.optcom.polito.it 118
NLIP
-
OFC 2016 www.optcom.polito.it 119
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OFC 2016 www.optcom.polito.it 120
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OFC 2016 www.optcom.polito.it 121
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OFC 2016 www.optcom.polito.it 122
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations
5% error bar
MARKERS: simulations
32 GBaud
15 channels
100 km spans
LINES: EGN model
-
OFC 2016 123
no ASE, at max-reach
-
OFC 2016 124
no ASE, at max-reach
-
OFC 2016 www.optcom.polito.it 125
MARKERS: simulations blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
32 GBaud
15 channels
60 km spans
LINES: EGN model
case study
-
OFC 2016 www.optcom.polito.it 126
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OFC 2016 www.optcom.polito.it 127
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OFC 2016 www.optcom.polito.it 128
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OFC 2016 www.optcom.polito.it 129
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OFC 2016 www.optcom.polito.it 130
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OFC 2016 www.optcom.polito.it 131
Carsten Schmidt-Langhorst, Robert Elschner, Felix Frey, Robert
Emmerich, Colja Schubert, “Experimental Analysis of Nonlinear
Interference Noise in Heterogeneous Flex-Grid WDM Transmission”,
ECOC 2015, paper Tu.1.4.3, Sept. 2015.
̂
̂
-
OFC 2016 www.optcom.polito.it 132
̂
-
OFC 2016 www.optcom.polito.it 133
norm
alized a
uto
covari
ance
time (symbols)
‘delta’
correlated
component
‘long’ correlated component
̂
autocovariance
-
OFC 2016 www.optcom.polito.it 134
̂
-
OFC 2016 www.optcom.polito.it 135
norm
alized a
uto
covari
ance
time (symbols)
autocovariance
‘delta’
correlated
component
‘delta’
correlated
component
̂
̂
-
OFC 2016 www.optcom.polito.it 136
-
OFC 2016 www.optcom.polito.it 137
-
OFC 2016 www.optcom.polito.it 138
norm
alized a
uto
covari
ance
time (symbols)
̂
autocovariance
-
OFC 2016 www.optcom.polito.it 139
norm
alized a
uto
covari
ance
time (symbols)
‘delta’
correlated
component
̂
autocovariance
CPÊ
‘delta’
correlated
component
-
OFC 2016 www.optcom.polito.it 140
norm
alized a
uto
covari
ance
time (symbols)
‘delta’
correlated
component
autocovariance
‘delta’
correlated
component
̂
̂
-
OFC 2016 www.optcom.polito.it 141
̂
̂
with CPE
-
OFC 2016 www.optcom.polito.it 142
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OFC 2016 www.optcom.polito.it 143
MARKERS: simulations no CPE blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
32 GBaud
15 channels
60 km spans
LINES: EGN model
case study
-
OFC 2016 www.optcom.polito.it 144
MARKERS: simulations no CPE blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
32 GBaud
15 channels
60 km spans
LINES: EGN model
-
OFC 2016 www.optcom.polito.it 145
blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
LINES: EGN model
MARKERS: simulations with CPE
+ 8%
-
OFC 2016 www.optcom.polito.it 146
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
LINES: EGN model
MARKERS: simulations no CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 147
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
MARKERS: simulations with CPE
5% error bar
32 GBaud
15 channels
100 km spans
LINES: EGN model
-
OFC 2016 www.optcom.polito.it 148
-
OFC 2016 www.optcom.polito.it 149
55 km spans
10250 km
150 2 PSCF
Jin-Xing Cai, Yu Sun, Hongbin Zhang, Hussam G. Batshon, Matt
Vincent Mazurczyk, Oleg V. Sinkin, Dmitri G. Foursa, and Alexei
Pilipetskii, “49.3 Tb/s Transmission Over 9100 km Using C+L
EDFA and 54 Tb/s Transmission Over 9150 km Using Hybrid-
Raman EDFA,” v. 33, n. 13, pp. 2724-2734, July 2015
-
OFC 2016 www.optcom.polito.it 150
Likely, many systems already do it with their CPEs.
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 151
credit: http://www.nfafranchiseconsultants.com/alternatives-financial-performance-representations/
-
OFC 2016 www.optcom.polito.it 152
-
OFC 2016 www.optcom.polito.it 153
-
OFC 2016 www.optcom.polito.it 154
markers: simulations no CPE blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
-
OFC 2016 www.optcom.polito.it 155
blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
markers: simulations with CPE
-
OFC 2016 www.optcom.polito.it 156
blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model for PM-QPSK
markers: simulations with CPE
-
OFC 2016 www.optcom.polito.it 157
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations no CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 158
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations with CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 159
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model for PM-QPSK
markers: simulations WITH CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 160
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model for PM-QPSK
markers: simulations WITH CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 161
2
NLI
1/W
dB
P
NO CPE CPE
number of spans number of spans
PSCF
100 km
Spans
See circles
prev. slide
-
OFC 2016 www.optcom.polito.it 162
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 163
total WDM signal
Stokes vector channel Stokes vector
precession
-
OFC 2016 www.optcom.polito.it 164
-
OFC 2016 www.optcom.polito.it 165
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 166
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OFC 2016 www.optcom.polito.it 167
-
OFC 2016 www.optcom.polito.it 168
with Raman
without Raman
-
OFC 2016 www.optcom.polito.it 169
32 GBaud
15 channels
100 km spans
noise figure 5 dB
EGN model
5% error bar
blue: PSCF
red: SMF
green: NZDSF
-
OFC 2016 www.optcom.polito.it 170
32 GBaud
15 channels
100 km spans
noise figure 5 dB
EGN model
5% error bar
blue: PSCF
red: SMF
green: NZDSF
-
OFC 2016 www.optcom.polito.it 171
-
OFC 2016 www.optcom.polito.it 172
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 173
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OFC 2016 www.optcom.polito.it 174
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OFC 2016 www.optcom.polito.it 175
-
OFC 2016 www.optcom.polito.it 176
targetOSNR 9 dB
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 177
-
OFC 2016 www.optcom.polito.it 178
ch
ASE NLI
OSNRP
P P
ch NLI
ASE NLI
OSNRP P
P P
this simple correction
is quite effective (for
the center channel)
H. Louchet et al., “Analytical Model for the
Performance Evaluation of DWDM Transmission
Systems,” IEEE Phot. Technol. Lett., vol. 15, pp.
1219-1221, Sept. 2003.
P. Poggiolini, A. Carena, Y. Jiang, G. Bosco, V.
Curri, and F. Forghieri, ‘Impact of low-OSNR
operation on the performance of advanced
coherent optical transmission systems,’ in Proc. of
ECOC 2014, Cannes (FR), Sept. 2014. Available with
corrections on www.arXiv.org, paper
arXiv:1407.2223.
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OFC 2016 www.optcom.polito.it 179
targetOSNR 9 dB
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 180
credit: http://www.examiner.com/article/where-are-we-going-an-exercise-
irresponsible-speculation
-
OFC 2016 www.optcom.polito.it 181
-
OFC 2016 www.optcom.polito.it 182
terrestrial
medium-short
haul
-
OFC 2016 www.optcom.polito.it 183
terrestrial
short
haul
-
OFC 2016 www.optcom.polito.it 184
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OFC 2016 www.optcom.polito.it 185
-
OFC 2016 www.optcom.polito.it 186
credit: http://www.messagehouse.org/increasing-the-
takeaway-ability-of-your-presentations/
-
OFC 2016 www.optcom.polito.it 187
credit: http://www.nfafranchiseconsultants.com/alternatives-financial-performance-representations/
-
OFC 2016 www.optcom.polito.it 188
downloadable at www.optcom.polito.it
-
More slides on
Asymptotic formulas
-
OFC 2016 www.optcom.polito.it 190
EGN GN corrNLI NLI NLIG f G f G f
-
OFC 2016 www.optcom.polito.it 191
-
OFC 2016 www.optcom.polito.it 192
1 2 5 10 20 50 20
25
30
35
40
45
50
PM-QPSK, 15 channels, 32 Gbaud, 33.6 GHz spacing,
roll-off 0.05, SMF, 100 km spans, (SPM removed)
simulation
EGN
asympt. EGN
correction
GN
number of spans
2
NLI
1 / W , dB
P
-
OFC 2016 www.optcom.polito.it 193
NLI
2 2
ef
3cor fr ch
2
ch
2
1HN
2
80
81 ss
L N fN
R f R
PG
L
22 s sR L N
1
1HN
K
k
Kk
note:
-
OFC 2016 www.optcom.polito.it 194
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations
5% error bar
-
OFC 2016 www.optcom.polito.it 195
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model asymptotic app.
markers: simulations
5% error bar
-
OFC 2016 www.optcom.polito.it 196
markers: simulations blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
-
OFC 2016 www.optcom.polito.it 197
markers: simulations blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model asymptotic app.
-
OFC 2016 www.optcom.polito.it 198
ch
ch
2opt2 2 3 eff
ch ch
ch
1 /2
2 2 221 1
2
ch
2
ch ch
corrNLI
1
1
801 / 2 1
81
21
1
2 21
2
sinint 2 1 sinint2 2
p
s s
s s s
NN
s s
n n ss
s
s ss
n
RL fR P N HN N
L f R R
n f
nN Rf
N n R
L n f
n R n RN
n f n f
G
ch 2 opt 2 span span 2p s sN n L R f R L N
-
OFC 2016 199
BWDM = 2.4 THz, PM-QPSK, 100 km spans, spacing 1.05 x (symb. rate)
2.4 GBaud
1000 channels
16 GBaud
150 channels
32 GBaud
75 channels
number of channels in 2500 GHz
2
(THz/W) dB
NLIG
-
OFC 2016 www.optcom.polito.it 200
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
More slides on
phase noise:
non-circularity test
on the «case study»:
PSCF 60 km span
PM16QAM
-
OFC 2016 www.optcom.polito.it 202
̂
̂
“non-circularity”:
2
ˆ
2
ˆdB
-
OFC 2016 www.optcom.polito.it 203
̂
̂
2
ˆ
2
ˆdB
0
-
OFC 2016 www.optcom.polito.it 204
distance (km)
no CPE
* with CPE
non-c
ircula
rity
2
ˆ
2
ˆdB
-
OFC 2016 www.optcom.polito.it 205
non-c
ircula
rity
distance (km)
2
ˆ
2
ˆdB
no CPE
* with CPE
-
More details on non-
linear polarization
noise
-
OFC 2016 www.optcom.polito.it 207
total WDM signal
Stokes vector channel Stokes vector
precession
-
OFC 2016 www.optcom.polito.it 208
-
OFC 2016 www.optcom.polito.it 209
PolN
cos sin
sin cos
j j
j j
e e
e e
U
ˆ ˆ
ˆ ˆ
ˆ
ˆ
x x
y y
j
y
j
x
j
j
e
e s
s
s
es s
s e
-
OFC 2016 www.optcom.polito.it 210
2
2
1
1
ˆ
ˆ
ˆ ˆ
ˆ ˆ
j
j
x x
y y
j
y
j
x
s s
s e e
e s e
ss
PolN-induced
phase noise
crosstalk
between the
two constellations if the Rx CPE works independently
on the two polarizations, it already
removes long-correlated PolN, too.
In our simulations this was the case.
requires an “ad hoc” algorithm to
estimate and remove its
long-correlated (LC) part
-
OFC 2016 www.optcom.polito.it 211
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations no CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 212
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations with CPE
5% error bar
-
OFC 2016 www.optcom.polito.it 213
blue: PSCF
red: SMF
green: NZDSF
32 GBaud
15 channels
100 km spans
EGN model
markers: simulations with CPE-XpolE
5% error bar
-
OFC 2016 www.optcom.polito.it 214
markers: simulations no CPE blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
-
OFC 2016 www.optcom.polito.it 215
blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
markers: simulations with CPE
-
OFC 2016 www.optcom.polito.it 216
blue: PSCF
red: SMF
green: NZDSF
5% error bar
32 GBaud
15 channels
60 km spans
EGN model
markers: simulations with CPE and XPolE
-
OFC 2016 www.optcom.polito.it 217
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OFC 2016 www.optcom.polito.it 218
http://www.messagehouse.org/increasing-the-takeaway-ability-of-
your-presentations/
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
More details on in-
line ASE
-
OFC 2016 www.optcom.polito.it 220
-
OFC 2016 www.optcom.polito.it 221
-
OFC 2016 www.optcom.polito.it 222
32 GBaud
15 channels
100 km spans
noise figure 5 dB
EGN model
5% error bar
blue: PSCF
red: SMF
green: NZDSF
-
OFC 2016 www.optcom.polito.it 223
32 GBaud
15 channels
100 km spans
noise figure 5 dB
EGN model
5% error bar
blue: PSCF
red: SMF
green: NZDSF
-
OFC 2016 www.optcom.polito.it 224
-
OFC 2016 www.optcom.polito.it 225
targetOSNR 9 dB
credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/
-
On the meaning of
the EGN model
correction formula
contributions
-
OFC 2016 227
9 channels
rectangular spectra
quasi-Nyquist-WDM
f = 0
GNNLIG f
f1
f2
-
OFC 2016 228
f1
f2
S
(SCI)
MCI M1
MCI M2
MCI M3
MCI M0
XCI X2
XCI X3
XCI X4
XCI X1
the correction
exists in
all colored islands
corrNLIG f
GNNLIG f