1. UMBC New Approaches to Modeling Optical Fiber Transmission Systems Presented by C. R. Menyuk With R.  M. Mu, D. Wang, T. Yu, and V. S. Grigoryan University of Maryland Baltimore County Computer Science and Electrical Engineering Department Baltimore, MD 21250

2. UMBC New Approaches to Modeling Optical Fiber Transmission Systems Presented by V. S. Grigoryan With R.  M. Mu, D. Wang, T. Yu, and C. R. Menyuk University of Maryland Baltimore County Computer Science and Electrical Engineering Department Baltimore, MD 21250

3. UMBC Professors Gary Garter Curtis Menyuk Associates Vladimir Grigoryan Edem Ibragimov Pranay Sinha Students Ronald Holzlöhner Ivan Lima, Jr. Ruomei Mu Yu Sun Ding Wang Tao Yu Current research group

4. UMBC A Decade Ago System with Electronic Repeaters 500 Mb/s looked achievable; 100 Mb/s was achieved Only attenuation mattered in fibers – fibers were a transparent pipe Repeaters had limited bandwidth (WDM and upgrading impossible) – Cost and complexity rose dramatically with data rate – spacings of 20 km were required RRR 20 km

5. UMBC Today System with Erbium-doped amplifiers 1 Tbit/s looks achievable; 200 Gbits/s achieved Wavelength division multiplexing (WDM) is possible and becoming widely used (200 Gb/s = 80 channels  2.5 Gb/s) Fiber dispersion, nonlinearity, and polarization effects all accumulate! Fiber impairments set the limits on what is achievable – nonlinearity is strong and hard to model properly. 50 km or more

6. UMBC What formats should be used? 1 1 0 1 0 0 1 Non-return to zero (NRZ) (close to zero dispersion) Solitons (anomalous dispersion) vs. 1101001

7. UMBC Approaches are converging! Solitons and NRZ resemble each other – solitons dispersion-managed solitons – NRZ phase- and amplitude-modulated pulses 011100111001110 01110

8. UMBC What formats should be used? Time-division multiplexed (TDM) 1234567812345678 I t channels Wavelength-division multiplexed (WDM) channels 12345678 I

9. UMBC Fiber impairments Chromatic Dispersion Polarization Effects Nonlinearity ASE noise Four Horsemen of the Apocalypse Albrecht Dürer Four Horsemen of Optical Fiber Transmission

10. UMBC Modeling approaches ¶ Multiple scale length methods — for establishing equations · Split-step modeling — often too slow (especially with WDM) ¸ Reduced methods — dealing with many channels, long-term effects, networks

11. UMBC Modeling approaches ¶ Monte Carlo — often too slow · Ito’s method — often does not work ¸ Linearization Randomly varying effects

12. UMBC Multiple Scale Lengths methods Light wavelength 1  m 10  m 100  m 1 mm 10 mm 100 mm 1 m 100 m 10 m 1 km 100 km 10 km 1 Mm 10 Mm 100 Mm Core diameter Pulse durations Polarization beat length Attenuation length Nonlinear length Fiber correlation length Dispersion length FLAG trans-Atlantic Manakov-PMD approximation Slowly varying envelope approximation Maxwell’s equations land link Optical systems have a wide spread in length scales! Scale lengths in fiber transmission

13. UMBC Coupled Nonlinear Schrödinger Equation Maxwell’s Equations Coupled Nonlinear Schrödinger Equation Manakov-PMD Equation Averaging over the Poincaré sphere Using the slowly varying envelope approximation

14. UMBC Linearization approach Monte Carlo: Linearization (with small noise): signalnoisecomplicated mix signalnoiseGaussian statistics (nonlinear) (linear)

15. UMBC Comparison of theory & experiment 0 1 2 01000020000 Timing jitter (ps) Distance (km) experiment Monte Carlo simulation our approach

16. UMBC Average Power Approximation With N channels, scaling reduces from N 2 to better than N! Useful for point-to-point systems (Yu, Reimer, and Menyuk; Wang and Menyuk) Critical for network simulations (Bellcore: R. Wagner, I. Roudas, & colleagues)  target channel complete channel averaged channel

17. UMBC With polarization Stokes vector distance (km) simulation theory Evolution of the Stokes vector –0.5 0 0.2 0 10000 –0.5 0 0.2 0 10000 –0.5 0 0.2 0 10000 S 1 S 3 S 2 (a) S 1 S 3 S 2 (b) S 1 S 3 S 2 (c) realistic dispersionlarge dispersion

18. UMBC Reduced Polarization Model ¶ PDL effects calculated — one year ago · Verification of model effectiveness with chromatic dispersion and nonlinearity — now ¸ Inclusion of PMD, PDL, and PDG — in one year

19. UMBC Experimental Applications D L Normal Anomalous Average 1.2 nm Filter AO Switch 60/40 Coupler Input To Receiver PC EDFA Normal Anomalous Dispersion-managed soliton experiments

20. UMBC Theory and experiment Dynamic Evolution in One Round Trip Amplitude Margin experimental theoretical experimental theoretical

21. UMBC Normal dispersion solitons: A B 0 10 20 00.2  D=110  D=100  D=90  D=80  D=70  D=60 Pulse energy Average dispersion — Solitons exist in the normal dispersion regime — These solutions are stable Intensity 0 Time – 5 5 10000 0 5000 1 0.001 At point B: Distance

22. UMBC World record experiment 20 Gbit/s: BER < @ 20 Mm 20 Gbit/s input 10 Gbit/s Demux output (20 Mm) experimental theoretical 1 Bit 0 Bit

23. UMBC Conclusions ¶Optical fiber transmission systems are rapidly changing · Good modeling has become critical ¸ Enormous strides have been made