1. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 1/21 Parametric-Gain Approach to the Analysis of DPSK Dispersion-Managed Systems A.Bononi, P. Serena, A. Orlandini, and N. Rossi Dipartimento di Ingegneria dellInformazione, Università di Parma Viale degli Usberti, 181A, 43100 Parma, Italy e-mail: bononi@tlc.unipr.it

2. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 2/21 Milan Parma Rome

3. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 3/21 Outline Introduction State of the Art: BER tools in DPSK transmission The PG Approach: Key Assumptions Tools Results Conclusions

4. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 4/21 Introduction Amplified spontaneous emission (ASE) noise from optical amplifiers makes the propagating field intensity time-dependent even in constant-envelope modulation formats such as DPSK. Random intensity fluctuations, through self-phase modulation (SPM), cause nonlinear phase noise [1], which is the dominant impairment in single-channel DPSK. Most existing analytical models focus on the statistics of the nonlinear phase noise. [1] J. Gordon et al., Opt. Lett., vol. 15, pp. 1351-1353, Dec. 1990.

5. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 5/21 K.-Po Ho [2] computed the probability density function (PDF) of nonlinear phase noise and derived a BER expression for DPSK systems with optical delay demodulation. Very elegant work, but: model assumes zero chromatic dispersion (GVD) does not account for the impact of practical optical/electrical filters on both signal and ASE Tx Matched filter SPM only State of the Art [2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003.

6. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 6/21 Wang and Kahn [3] computed the exact BER for DPSK ( but provided no algorithm details ) using Forestieris Karhunen-Loeve (KL) method [4] for quadratic receivers in Gaussian noise : Model accounts for impact of practical optical/electrical filters on both signal and ASE....but ignores nonlinearity: it concentrates on GVD only. State of the Art [3] J. Wang et al., JLT, vol. 22, pp. 362-371, Feb. 2004. [4] E. Forestieri, JLT, vol. 18, pp. 1493-1503, Nov. 2000. Tx OBPF no SPM LPF

7. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 7/21 Also our group [5] computed the BER for DPSK using Forestieris KL method. Our model: besides accounting for impact of practical optical/electrical filters also accounts for the interplay of GVD and nonlinearity, including the signal-ASE nonlinear interaction using the tools developed in the study of parametric gain (PG) is tailored to dispersion-managed (DM) long-haul systems The PG Approach [5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006. Tx OBPF LPF N

8. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 8/21 DPSK DM System Tx OBPF LPF N pre post in-line DPSK RX A D Dispersion Map KL method requires Gaussian field statistics at receiver (RX), after optical filter

9. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 9/21 0 Single span OSNR= 25 dB/0.1nm NL = 0.15 rad 2 34 1 Re[E] Im[E] Re[E] Im[E] D= ps/nm/km …but with some dispersion, PDF contours become elliptical Gaussian PDF D D in =0 in-line At zero dispersion, PDF of ASE RX field before OBPF is strongly non-Gaussian [2] Why Gaussian Field? [2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003.

10. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 10/21 Even at zero dispersion... OSNR=10.8 dB/0.1 nm, NL =0.2, ASE BW B M =80 GHz Red: Monte Carlo (MC) Blue: Multicanonical MC (MMC) before OBPF Why Gaussian Field? I after OBPF, B o =10 GHz [6] A. Orlandini et al., ECOC06, Sept. 2006. PDF of ASE RX field AFTER OBPF Gaussianizes [6]

11. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 11/21 Reason is that a white ASE over band B M remains white after SPM OBPF w(t) n(t ) h(t ) SPM If optical filter bandwidth B o << B M, n(t) is the sum of many comparable-size independent samples Gaussian whatever the input noise distribution Central Limit Theorem Why Gaussian Field?

12. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 12/21 Having shown the plausibility of the Gaussian assumption for the RX field, it is now enough to evaluate its power spectral density (PSD) to get all the needed information, to be passed to the KL BER routine. A linearization of the dispersion-managed nonlinear Schroedinger equation (DM-NLSE) around the signal provides the desired PSDs, according to the theory of parametric gain.

13. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 13/21 Linear PG Model Small perturbation Rx ASE is Gaussian DM, finite N spans [7] C. Lorattanasane et al., JQE, July 1997 [8] A. Carena et al., PTL, Apr. 1997 [9] M. Midrio et al., JOSA B, Nov. 1998 [5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006. DM, infinite spans

14. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 14/21 Red : quadrature ASE Blue: in-phase ASE » No pre-, post-comp. Linear PG Model Parametric Gain = Gain (dB) over white-ASE case due to Parametric interaction signal-ASE

15. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 15/21 Limits of Linear PG Model NL = 0.55 rad D=8 ps/nm/km, Din=0 linear PG model (dashed) versus Monte-Carlo BPM simulation (solid) /0.1 nm

16. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 16/21 @ PG doubling strengths for 10 Gb/s NRZ For fixed OSNR (e.g. 15dB) in region well below red PG-doubling curve: Linear PG model holds ASE ~ Gaussian 15 17 19 21 15 1 DM systems with Din=0. ( N>>1 spans) 00.20.40.60.8 Map strength S ( DR 2 ) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 NL [rad/ ] end-line OSNR (dB/0.1nm) [10] P.Serena et al., JLT, vol. 23, pp. 2352-2363, Aug. 2005.

17. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 17/21 Steps of our semi-analytical BER evaluation algorithm: Our BER Algorithm 1.Rx DPSK signal obtained by noiseless BPM propagation (includes ISI from DM line) 2.ASE at RX assumed Gaussian. PSD obtained either from linear PG model (small NL ) or estimated off-line from Monte-Carlo BPM simulations (large NL ). Reference NL for PSD computation suitably decreased from peak value to average value for increasing transmission fiber dispersion (map strength). 3.Data from steps 1, 2 passed to Forestieris KL BER evaluation algorithm, suitably adapted to DPSK.

18. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 18/21 Check with experimental results [H. Kim et al., PTL, Feb. 03] NRZ RZ-33% Exp. Theory 10 Gb/s single-channel system, 6 100 km NZDSF Results

19. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 19/21 RZ-DPSK 50% NRZ-DPSK NRZ-OOK Results R=10 Gb/s single-channel, 20 100 km, D=8 ps/nm/km, Din=0. OSNR=11 dB/0.1 nm, Bo=1.8R Noiseless optimized Dpre, Dpost 1E-9 1E-4 1E-2 BER

20. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 20/21 Results DPSK-NRZ DPSK-RZ (50%) 10 Gb/s single-channel system, 20 100 km, Din=0. Bo=1.8R. Noiseless optimized Dpre, Dpost. @ D=8 ps/nm/km Strength ( DR 2 ) Strength ( DR 2 ) PG no PG Φ NL =0.1 Φ NL =0.3 Φ NL =0.5 Φ NL =0.3

21. Università di Parma Xian, Oct. 23, 2006 A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 21/21 More information on our work: www.tlc.unipr.it Conclusions Novel semi-analytical method for BER estimation in DPSK DM optical systems. The striking difference between OOK and DPSK is that in DPSK PG impairs the system at much lower nonlinear phases, when the linear PG model still holds. Hence for penalties up to ~ 3 dB one can use the analytic ASE PSDs from the linear PG model instead of the time-consuming off-line MC PSD estimation. Hence our mehod provides a fast and effective tool in the optimization of maps for DPSK DM systems.