Nonlinear Limits in Single- and Dual-Polarization Transmission

Transcription

1 Nonlinear Limits in Single- and Dual-Polarization Transmission A. Bononi, P. Serena, N. Rossi Department of Information Engineering, University of Parma, Parma, Italy 1/40

2 Outline Motivation, objectives, methodology Some models of nonlinear effects: 1. nonlinear phase and amplitude noise (NLAN,NLPN) 2. cross-nonlinear phase noise (X-NLPN) 2. cross-polarization modulation (XPolM) Simulations of Nonlinear threshold (NLT) vs Baud-rate Conclusions 2/40

3 Motivation Dominant nonlinearity in OOK WDM DM systems From: P. J. Winzer et al., JLT, Dec FWM XPM SPM, IXPM, IFWM Baud-rate R 3/40

4 Motivation Dominant nonlinearity in homogeneous WDM DM systems including nonlinear signal noise interactions (NSNI) From: A. Bononi et al., Opt.FiberTech OOK NSNI FWM XPM NLAN SPM R single-pol. PSK NSNI FWM X-NLPN NLPN SPM R PDM PSK NSNI FWM XPOLM NLPN SPM R 4/40

5 Objectives Review and extend study of dominant NL for single-polarization (SP) and dual polarization (PDM) formats OOK FWM XPM NLAN SPM R single-pol. PSK FWM X-NLPN NLPN SPM R PDM PSK FWM XPOLM NLPN SPM R 5/40

6 Methodology Dominant NL established from Monte-Carlo estimation of NLT vs baud-rate R for each NL effect acting individually fixed distance OSNR BB NLT 1dB P TX (db) nonlinear threshold (NLT): channel TX power at 1dB of OSNR penalty w.r.t BB at BER=10-3 6/40

7 Methodology NLT measurement given R Set OSNR=OSNR BB +1 (db) Start with a guess on P TX get ampli noise figure NF from ASE power N A =OSNR/P TX measure BER by Monte-Carlo error counting, i.e: in a line with that NF, propagate long-enough blocks of random symbols per channel (256 here). Stop simulation when 100 errors on average are counted [*] if BER<10-3 increase P TX and goto 2. Interpolate and get NLT BER P guess 10-3 [*] J.-C. Antona et al., ECOC 08, paper We.1.E.3. NLT P TX 7/40

8 Methodology How to toggle ON/OFF signal-noise interactions NSNI OFF: TX TX noiseless DM line ASE RX noise loading NSNI ON: TX TX ASE ASE ASE DM line RX distributed noise 8/40

9 Methodology How to single-out NL effects In single-polarization scalar propagation: Label NL Effect Obtained as SPM Self-phase modulation solve single-channel SSFM propagation XPM cross-phase modulation solve system of N coupled SSFM for all WDM channels. Set SPM=OFF WDM All (SPM,XPM,FWM) solve SSFM with WDM comb treated (includes also linear as a single channel. XTalk due to spectral overlap) 9/40

10 Methodology In Dual-polarization: vector Manakov propagation Label NL Effect Obtained as SPM self-phase modulation solve single-channel SSFM propagation XPM cross-phase modulation solve system of N coupled SSFM for all WDM channels. Set SPM=OFF, XPolM=OFF XPolM cross-polar. modulation solve system of N coupled SSFM for all WDM channels. Set SPM=OFF, XPM=OFF WDM Manakov nonlinear step [M. Winter et al, JLT 2009, pp ]: SPM XPM XPolM = 2x2 identity matrix = 3x1 vector of Pauli matrices = 3x1 Stokes vector associated with 2x1 Jones vector A k 10/40

11 Methodology In Dual-polarization: vector Manakov propagation Label NL Effect Obtained as SPM self-phase modulation solve single-channel SSFM propagation XPM cross-phase modulation solve system of N coupled SSFM for all WDM channels. Set SPM=OFF, XPolM=OFF XPolM cross-polar. modulation solve system of N coupled SSFM for all WDM channels. Set SPM=OFF, XPM=OFF WDM All (SPM,XPM,XPolM,FWM) solve SSFM with WDM comb treated (includes also linear as a single channel. XTalk due to spectral overlap) 11/40

12 Outline Motivation, objectives, methodology Some models of nonlinear effects: 1. nonlinear phase and amplitude noise (NLAN,NLPN) 2. cross-nonlinear phase noise (X-NLPN) 3. cross-polarization modulation (XPolM) Simulations of Nonlinear threshold (NLT) vs Baud-rate Conclusions 12/40

13 Models Classification of NSNI Single-channel (intra-channel) signal interaction with in-band ASE through PG NLAN, NLPN Multi-channel (WDM) (inter-channel) signal interaction with ASE on neighboring channels through X-NL X-NLPN 13/40

14 Model 1: NLAN, NLPN DM LINE CW power spectral density (PSD) 4.6dBm 20 spans, DTX=4 ps/nm/km, Din=0, Dpre=-85 ps/nm Dtot=0, RX OSNR = 12 db/0.1nm, γ =1.4 W-1km-1 O.F. Φ CW=0.6π O.F. 18 GHz in-phase norm. field Ar+jAi = e-jφnl(1+ar+jai) quadrature N0 A. A.Bononi Bononi et al. al. For OOK, in-phase ASE is important (amplitude noise, NLAN) For 09 PSK, phase noise is important LEOS Summer ECOC Topicals paper 2010, Playa del Carmen, Mexico, July 20, (NLPN) /53 14/40

15 Model 1: NLAN, NLPN DM links N 0 ( 1+(4/3)Φ 2 CW ) for f>2f there is no NSNI N 0 For DM with small in-line: f 2f For SMF, f =7GHz P. Serena et al., JOSA B, Apr /40

16 Model 1: NLPN Interpreting quadrature ASE as phase noise, we understand that... N 0 ( 1+(4/3)Φ 2 ) nonlinear phase noise (NLPN) [*] σ 2 NLPN N 0 (4/3)Φ 2 min(f, B o /2) N 0 σ 2 lin =N 0 *B o /2 0 f B o /2 f...for increasing symbol rate linear phase noise dominates over nonlinear phase noise [*] J. Gordon et al., Opt. Lett., vol. 15, pp , Dec /40

17 Model 2: X-NLPN probe pump OOK pump intensity XPM λ pump intensity t In OOK, XPM due to modulation-induced intensity variations. ASE-induced intensity variations are a second-order effect 17/40

18 Model 2: X-NLPN probe pump PSK pump intensity λ t XPM In D(Q)PSK, periodic XPM supressed by differential phase reception......in coherent RX with M-power phase estimation, by generalized differential phase reception differential filtering K=tap parameter ASE-induced intensity variations become a first-order effect: X-NLPN 18/40

19 Model 3: XPolM carousel Manakov nonlinear step pivot Exact solution of nonlinear step of length z: pivot L. Mollenauer et al, OL Oct. 95 B. Collings at al, PTL Nov. 00 A. Bononi et al, JLT Sept. 03 M. Karlsson et al, JLT Nov. 06 stokes length is intensity Since pivot is set by modulation data, then ASE is second-order effect for SOP rotation 19/53 19/40

20 Outline Motivation, objectives, methodology Some models of nonlinear effects: 1. nonlinear phase and amplitude noise (NLAN,NLPN) 2. cross-nonlinear phase noise (X-NLPN) 3. cross-polarization modulation (XPolM) Simulations of Nonlinear threshold (NLT) vs Baud-rate Conclusions 20/40

21 In the next few slides I will provide the details of the simulations, and next I will show the NLT results 21/40

22 DM case study Tx D pre pre 30 ps/nm SMF RDPS 100 km D in 20 D post post Neglect NL inline DCFs Dispersion Map D A [ps/nm] z [km] optimized D pre optimized D post D in 22/40

23 More Simulation Data Supporting pulse: NRZ = 0.4 R=10 Gbaud f=25 GHz R=20 Gbaud f=50 GHz R=28 Gbaud f=70 GHz No filtering at TX linear Xtalk Number of WDM channels [*] : Eg: SM Fiber at 10 Gbaud Nch=5+1+5 [*] P. Serena et al., ECOC 06, paper We3.P.129. ~ Homogeneous WDM Map Strength 23/40

24 Modulation formats Will consider: 3. Direct-detection OOK 4. Direct-detection DPSK 5. Coherent single-polarization (SP) QPSK 6. Coherent PDM-QPSK 24/40

25 Receivers: OOK, DPSK Bo=1.8R LPF: Be=0.65R all formats DM line scalar propagation co-polarized channels O.F. MZI 25/40

26 Receivers: PDM-QPSK Vector propagation Manakov equation Random ISOPs no PMD DM line Bo=1.8R O.F. No nonlinear phase noise compensation M-power phase estimation 2K+1 taps PBS Local Oscillator: zero freq. offset no phase noise 26/40

27 Receivers: SP-QPSK Vector propagation Manakov equation Random ISOPs no PMD DM line Bo=1.8R Single-polarization (SP) QPSK: O.F. M-power phase estimation 2K+1 taps 27/40

28 NLT vs. Symbol Rate SMF fiber η=0.4 NRZ-DPSK NLT (dbm) noise loading distributed noise (NSNI) NRZ-OOK O.F. A. Bononi et al. LEOS Summer Topicals 2010, Playa del 28/40

29 NLT vs. Symbol Rate SMF fiber η=0.4 NRZ-DPSK NLT (dbm) noise loading distributed noise (NSNI) NRZ-OOK scalar propagation O.F. A. Bononi et al. LEOS Summer Topicals 2010, Playa del 29/40

30 NLT vs. Symbol Rate SMF fiber η=0.4 NRZ-DPSK NLT (dbm) noise loading distributed noise (NSNI) NRZ-OOK A. Bononi et al. LEOS Summer Topicals 2010, Playa del 30/40

31 NLT vs. Symbol Rate noise loading distributed noise (NSNI) NRZ-OOK SMF fiber η=0.4 NLT (dbm) NRZ-DPSK nonlinear amplitude noise XPM A. Bononi et al. NLAN SPM X-NLPN LEOS Summer Topicals 2010, Playa del NLPN 31/40

32 NLT [dbm] noise loading distributed noise (NSNI) NLT vs. Symbol Rate Manakov vector propagation, random WDM SOPs SMF fiber η=0.4 NRZ SP-QPSK SPM -2 SPM+XPM +XPolM -4 XPM -6 XpolM Symbol Rate [Gbaud] K=13 NRZ PDM-QPSK SPM WDM XPM XpolM Symbol Rate [Gbaud] 32/53 32/40

33 NLT [dbm] NLT vs. Symbol Rate Manakov vector propagation, random WDM SOPs noise loading distributed noise (NSNI) SMF fiber η=0.4 K=13 10 NRZ SP-QPSK 10 NRZ PDM-QPSK X-NLPN NLPN SPM -6 XPolM NLPN SPM Symbol Rate [Gbaud] Symbol Rate [Gbaud] 33/53 33/40

34 Hybrid PDM-QPSK / OOK DM, 20x100km SMF NLT [dbm] SPM WDM XPM XpolM Symbol Rate [Gbaud] = 0.4 K=13 in V&V TX Gauss(4) filter B=0.9R OOK channels power s.t. in B2B BER=10^-3 and SP<1dB XPM dominates XPolM steeper slopes of X-NL w.r.t homogeneous case NSNI negligible 34/40

35 noise loading distributed noise (NSNI) NDM Homog PDM-QPSK 20x100km SMF NSNI disappeared: why? 35/40

36 Model 1: NLAN, NLPN NDM links For NDM, NSNI cutoff at 2 f c Ratio of cutoffs depends on nonlinear phase per span 36/40

37 NDM Homog PDM-QPSK 20x100km SMF NSNI disappeared XPolM ~ XPM 37/40

38 Conclusions 1 Dominant nonlinearity in homogeneous DM WDM systems OOK FWM XPM NLAN SPM DR 2 single-pol. PSK FWM X-NLPN NLPN SPM DR 2 PDM PSK FWM XPOLM NLPN SPM DR 2 38/40

39 Conclusions 2 Dominant nonlinearity in OOK-hybrid WDM DM systems PDM PSK FWM XPM NLPN SPM DR 2 Dominant nonlinearity in homogeneous WDM Non-DM systems XPOLM XPM PDM PSK SPM DR 2 39/40

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41 NLT [dbm] noise loading distributed noise (NSNI) NLT vs. Symbol Rate Manakov vector propagation, random WDM SOPs SMF fiber η=0.4 NRZ SP-QPSK SPM -2 SPM+XPM +XPolM -4 XPM -6 XpolM Symbol Rate [Gbaud] K=13 NRZ PDM-QPSK SPM Symbol Rate [Gbaud] 41/40

42 SP vs PDM NLT 1) Dominant noiseless SPM Hence at equal SP need: 42/40

43 SP vs PDM NLT 2) Dominant NLPN Prop to NLPN variance A. Bononi et al., JLT sept 09 Doubled NLPN variance Hence at equal SP need: 43/40