OPTCOM - Dipartimento di Elettronica e Telecomunicazioni - Politecnico di Torino – Torino – Italy www.optcom.polito.it

OFC 2016 www.optcom.polito.it 2

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.

OFC 2016 www.optcom.polito.it 20

OFC 2016 www.optcom.polito.it 21

Non-exhaustive list of prominent non-linearity modeling papers (using other approaches than the GN model)

1. C. R. Menyuk, ‘Pulse propagation in an elliptically birefringent Kerr medium,’ IEEE J. Quantum Electron., vol. 25, no. 12, pp. 2674-2682,

Dec. 1989.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

OFC 2016 www.optcom.polito.it 22

OFC 2016 www.optcom.polito.it 23

22. 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.

23. S. Kumar, ‘Effect of dispersion on nonlinear phase noise in optical transmission systems,’ Optics Lett., vol. 30, no. 24, pp. 3278-

3280, Dec. 2005.

24. 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. 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.

30. 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.

31. Chongjin Xie, ‘Fiber Nonlinearities in 16QAM Transmission Systems,’ in Proc. ECOC 2011, paper We.7.B.6, Geneva (CH), Sept.

2011.

32. Chongjin Xie, ‘Impact of nonlinear and polarization effects on coherent systems,’ in Proc. ECOC 2011, paper We.8.B.1, Geneva

(CH), Sept. 2011.

OFC 2016 www.optcom.polito.it 24

33. A. Mecozzi and R. J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems”, vol. 30, no. 12, pp. 2011—2024,

June 2012.

34. 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.

35. 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.

36. 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.

37. 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.

38. 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.

39. 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.

40. 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.

41. 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 25

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

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 27

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 28

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 29

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 30

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 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

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 34

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 35

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 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

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 37

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 38

integral can be easily dealt with

numerically in a matter of seconds

OFC 2016 www.optcom.polito.it 39

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 40

credit: http://www.dtvisiontech.com/2015_12_01_archive.html

OFC 2016 www.optcom.polito.it 41

submarine

terrestrial

long-haul

terrestrial

medium-short

haul

OFC 2016 www.optcom.polito.it 42

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 43

red: SMF

32 GBaud

15 channels

100 km spans

LINES: incoherent GN model

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

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 46

32 GBaud

15 channels

100 km spans

LINES: incoherent GN model

red: SMF

blue: PSCF

red: SMF

OFC 2016 www.optcom.polito.it 47

blue: PSCF

red: SMF

32 GBaud

15 channels

100 km spans

LINES: incoherent GN model

OFC 2016 www.optcom.polito.it 48

blue: PSCF

red: SMF

green: NZDSF

32 GBaud

15 channels

100 km spans

LINES: incoherent GN model

OFC 2016 www.optcom.polito.it 49

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 50

blue: PSCF

red: SMF

green: NZDSF

32 GBaud

15 channels

100 km spans

LINES: incoherent GN model

OFC 2016 www.optcom.polito.it 51

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 52

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 53

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 54

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 55

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 56

credit:

https://www.koozai.com/blog/analytics/pre

dictive-analytics-and-digital-campaigns/

OFC 2016 www.optcom.polito.it 57

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 58

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 59

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 60

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 61

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 62

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 63

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 64

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 65

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 66

lines: GN model; markers: experiment

OFC 2016 www.optcom.polito.it 67

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 68

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

OFC 2016 www.optcom.polito.it 69

credit: http://www.improfestuk.co.uk/2014/problem-

solved.html

credit: https://www.flickr.com/

photos/wingedwolf/5471047557

OFC 2016 www.optcom.polito.it 70

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 71

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 72

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 73

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 74

OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 75

max,dB NLI,dB

1

3L P

OFC 2016 www.optcom.polito.it 76

spanNLI nP

3

NLI NLI chP P P

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

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 79

OFC 2016 www.optcom.polito.it 80

OFC 2016 www.optcom.polito.it 81

OFC 2016 82

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 83

EGN

NLIG f GN

NLIG f corr

NLIG f

OFC 2016 www.optcom.polito.it 84

EGN

NLIG f GN

NLIG f corr

NLIG f

OFC 2016 www.optcom.polito.it 85

EGN

NLIG f GN

NLIG f corr

NLIG f

OFC 2016 www.optcom.polito.it 86

credit: http://www.dtvisiontech.com/2015_12_01_archive.html

OFC 2016 www.optcom.polito.it 87

blue: PSCF

red: SMF

green: NZDSF

32 GBaud

15 channels

100 km spans

LINES: EGN model

OFC 2016 www.optcom.polito.it 88

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 89

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 90

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 91

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 92

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 93

spanNLI nP

OFC 2016 www.optcom.polito.it 94

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 95

OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 96

f

f

WDMB

f

Constraint: identical total throughput

OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 97

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 98

f

f

WDMB

f

Constraint: identical total throughput

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

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 100

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 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

OFC 2016 www.optcom.polito.it - www.ismb.it - www.cisco.com 102

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 103

[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 104

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 105

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 106

credit: https://www.dreamhost.com/blog/2009/05/13/broken-browsers-part-one/

OFC 2016 www.optcom.polito.it 107

EGN GN corr

NLI 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 108

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 109

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 110

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

OFC 2016 www.optcom.polito.it 111

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 112

4

2

E2

E

a

a

6 4

2 2

E E9 12

E E

a a

a a

corr

NLI0 0G

EGN GN

NLI NLIG f G f

OFC 2016 www.optcom.polito.it 113

OFC 2016 www.optcom.polito.it 114

EGN GN corr

NLI NLI NLIG f G f G f

OFC 2016 www.optcom.polito.it 115

OFC 2016 www.optcom.polito.it 116

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 117

OFC 2016 www.optcom.polito.it 118

OFC 2016 www.optcom.polito.it 119

NLIP

OFC 2016 www.optcom.polito.it 120

OFC 2016 www.optcom.polito.it 121

OFC 2016 www.optcom.polito.it 122

OFC 2016 www.optcom.polito.it 123

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 124

no ASE, at max-reach

OFC 2016 125

no ASE, at max-reach

OFC 2016 www.optcom.polito.it 126

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 127

OFC 2016 www.optcom.polito.it 128

OFC 2016 www.optcom.polito.it 129

OFC 2016 www.optcom.polito.it 130

OFC 2016 www.optcom.polito.it 131

OFC 2016 www.optcom.polito.it 132

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 133

OFC 2016 www.optcom.polito.it 134

norm

alized a

uto

covari

ance

time (symbols)

‘delta’

correlated

component

‘long’ correlated component

autocovariance

OFC 2016 www.optcom.polito.it 135

OFC 2016 www.optcom.polito.it 136

norm

alized a

uto

covari

ance

time (symbols)

autocovariance

‘delta’

correlated

component

‘delta’

correlated

component

OFC 2016 www.optcom.polito.it 137

OFC 2016 www.optcom.polito.it 138

OFC 2016 www.optcom.polito.it 139

norm

alized a

uto

covari

ance

time (symbols)

autocovariance

OFC 2016 www.optcom.polito.it 140

norm

alized a

uto

covari

ance

time (symbols)

‘delta’

correlated

component

autocovariance

CPE

‘delta’

correlated

component

OFC 2016 www.optcom.polito.it 141

norm

alized a

uto

covari

ance

time (symbols)

‘delta’

correlated

component

autocovariance

‘delta’

correlated

component

OFC 2016 www.optcom.polito.it 142

with CPE

OFC 2016 www.optcom.polito.it 143

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

case study

OFC 2016 www.optcom.polito.it 145

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 146

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 147

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 148

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 149

OFC 2016 www.optcom.polito.it 150

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 151

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 152

credit: http://www.nfafranchiseconsultants.com/alternatives-financial-performance-representations/

OFC 2016 www.optcom.polito.it 153

OFC 2016 www.optcom.polito.it 154

OFC 2016 www.optcom.polito.it 155

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 156

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 157

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 158

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 159

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 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

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 162

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 163

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 164

total WDM signal

Stokes vector channel

Stokes vector

precession

OFC 2016 www.optcom.polito.it 165

OFC 2016 www.optcom.polito.it 166

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 167

OFC 2016 www.optcom.polito.it 168

OFC 2016 www.optcom.polito.it 169

with Raman

without Raman

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

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 172

OFC 2016 www.optcom.polito.it 173

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 174

OFC 2016 www.optcom.polito.it 175

OFC 2016 www.optcom.polito.it 176

OFC 2016 www.optcom.polito.it 177

targetOSNR 9 dB

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 178

OFC 2016 www.optcom.polito.it 179

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.

OFC 2016 www.optcom.polito.it 180

targetOSNR 9 dB

credit: http://www.messagehouse.org/increasing-the-takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 181

credit: http://www.examiner.com/article/where-are-we-going-an-exercise-

irresponsible-speculation

OFC 2016 www.optcom.polito.it 182

OFC 2016 www.optcom.polito.it 183

terrestrial

medium-short

haul

OFC 2016 www.optcom.polito.it 184

terrestrial

short

haul

OFC 2016 www.optcom.polito.it 185

OFC 2016 www.optcom.polito.it 186

OFC 2016 www.optcom.polito.it 187

credit: http://www.messagehouse.org/increasing-the-

takeaway-ability-of-your-presentations/

OFC 2016 www.optcom.polito.it 188

credit: http://www.nfafranchiseconsultants.com/alternatives-financial-performance-representations/

OFC 2016 www.optcom.polito.it 189

downloadable at www.optcom.polito.it

More slides on

Asymptotic formulas

OFC 2016 www.optcom.polito.it 191

EGN GN corr

NLI NLI NLIG f G f G f

OFC 2016 www.optcom.polito.it 192

OFC 2016 www.optcom.polito.it 193

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 194

NLI

2 2

ef

3cor fr ch

2

ch

2

1HN

2

80

81 s

s

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 195

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 196

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 197

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 198

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 199

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 200

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 201

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 203

“non-circularity”:

2

ˆ

2

ˆdB

OFC 2016 www.optcom.polito.it 204

2

ˆ

2

ˆdB

0

OFC 2016 www.optcom.polito.it 205

distance (km)

no CPE

* with CPE

non-c

ircula

rity

2

ˆ

2

ˆdB

OFC 2016 www.optcom.polito.it 206

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 208

total WDM signal

Stokes vector channel

Stokes vector

precession

OFC 2016 www.optcom.polito.it 209

OFC 2016 www.optcom.polito.it 210

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 211

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 212

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 213

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 214

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 215

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 216

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 217

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 218

OFC 2016 www.optcom.polito.it 219

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 221

OFC 2016 www.optcom.polito.it 222

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

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 225

OFC 2016 www.optcom.polito.it 226

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 228

9 channels

rectangular spectra

quasi-Nyquist-WDM

f = 0

GN

NLIG f

f1

f2

OFC 2016 229

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

corr

NLIG f

GN

NLIG f