New Approaches to Modeling Optical Fiber Transmission Systems

1. 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. 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. Current research group 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

4. R R R 20 km 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

5. Today System with Erbium-doped amplifiers 50 km or more • 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.

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

7. 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 Approaches are converging! Solitons and NRZ resemble each other – solitons dispersion-managed solitons – NRZ phase- and amplitude-modulated pulses

8. channels I 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 t channels I 1 2 3 4 5 6 7 8  What formats should be used? Time-division multiplexed (TDM) Wavelength-division multiplexed (WDM)

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

10. 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 Modeling approaches

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

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

13. 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. Linearization approach Monte Carlo: signal noise complicated mix Linearization (with small noise): signal noise Gaussian statistics (nonlinear) (linear)

15. 2 1 0 0 10000 20000 Comparison of theory & experiment experiment Monte Carlo simulation our approach Timing jitter (ps) Distance (km)

16. Average Power Approximation target channel  complete channel averaged channel • With N channels, scaling reduces from N2 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)

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

18. 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 Reduced Polarization Model

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

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

21. 20 D=110 A D=100 D=90 10 Pulse energy D=80 D=70 D=60 B 0 0 0.2 Average dispersion Normal dispersion solitons: At point B: 1 Intensity 0.001 10000 5000 5 Distance 0 0 – 5 Time • Solitons exist in the normal dispersion regime • These solutions are stable

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

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