1. The Marriage of Photonics and Communication Theory for 100 Gb/s Long-Haul and Ethernet Fiber-Optic Transmissions The Marriage of Photonics and Communication Theory for 100 Gb/s Long-Haul and Ethernet Fiber-Optic Transmissions Ph.D. Candidate, Department of Electrical Engineering Stanford University Alan Pak Tao Lau presented at The Hong Kong University of Science and Technology Dec. 7 th, 2007

2. 2 Part I – 100 Gb/s long-haul Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced system impairments Kerr nonlinearity induced system impairments Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) WDM effects and optical OFDM WDM effects and optical OFDM Summary Summary

3. 3 Long-haul fiber-optic communication systems Terrestrial link (1500 ~ 3000 km) Submarine link (5000 ~ 10000 km)

4. 4 Tech. Evolution: Optical amplifiers, Wavelength Division Multiplexing (WDM), Wavelength Division Multiplexing (WDM), Forward Error Correction (FEC) Forward Error Correction (FEC) Long-haul fiber-optic communication systems TAT-8: 280 Mb/s, (1988) TAT-12/13: 5 Gb/s, (1996) TAT-14: 64 x 10 Gb/s, (2001) TPC5: 5Gb/s (1996) Bit Rate: 2.5 Gb/s ->10 Gb/s -> 40 Gb/s -> 100/160Gb/s Spectral Efficiency: 0.0005 b/s/Hz -> 0.2 b/s/Hz -> 0.8 b/s/Hz Next technological breakthrough: Electronic signal processing!

5. 5 Coherent detection Traditionally in fiber-optics, information encoded in pulse energy – On-Off Keying (OOK) Traditionally in fiber-optics, information encoded in pulse energy – On-Off Keying (OOK) Differentially coherent detection – information encoded in phase difference between neighboring symbols: DPSK, DQPSK Differentially coherent detection – information encoded in phase difference between neighboring symbols: DPSK, DQPSK Coherent detection – information encoded in both phase and amplitude: QPSK, 16-QAM Coherent detection – information encoded in both phase and amplitude: QPSK, 16-QAM Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM modulation format in future. Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM modulation format in future. LO 3-dB coupler BPSK MPSK/QAM 90° LO D-MPSK 90° Delay Receiver 90° Transmitter Laser MZ– Mach Zehnder Modulator

6. 6 Digital Signal Processing Currently available: 40 Gb/s FEC encoder/decoder Currently available: 40 Gb/s FEC encoder/decoder 40 Gb/s clock/data recovery 40 Gb/s clock/data recovery 10 Gb/s MLSD 10 Gb/s MLSD Arbitrary signal generation/detection, arbitrary signal processing Arbitrary signal generation/detection, arbitrary signal processing Communication theory / signal processing Communication theory / signal processing techniques becomes practically techniques becomes practically relevant and important !! relevant and important !! Information theory is also getting more attention Information theory is also getting more attention Fiber-optic channel is different from wireless / wireline communications Fiber-optic channel is different from wireless / wireline communications

7. 7 Signal propagation in optical fibers Erbium Doped Fiber Amplifiers (EDFA) Erbium Doped Fiber Amplifiers (EDFA) Nonlinear Schrödinger Equation (NLSE) Mode Pulse envelope Carrier frequency (~193 THz or 1550 nm) Japan USA Dispersion Compensating Fibers (DCF) Dispersion Compensating Fibers (DCF) amplifier Attenuation Chromatic Dispersion SMF DCF Kerr nonlinearity Kerr nonlinearity – not a LTI effect Kerr nonlinearity – not a LTI effect Dominant transmission impairment in long-haul systems! Dominant transmission impairment in long-haul systems!

8. 8 Kerr Nonlinearity in optical fibers induced intensity dependent refractive index induced intensity dependent refractive index Electric Polarization of molecules Electric Polarization of molecules Kerr induced nonlinear phase shift Kerr induced nonlinear phase shift Linear Regime EIEI EQEQ E Nonlinear Regime EIEI EQEQ E

9. 9 Impairments in long-haul systems with coherent detection Noise limits communication system performance Noise limits communication system performance BPSK / QPSK / DQPSK – phase noise BPSK / QPSK / DQPSK – phase noise Laser phase noise Laser phase noise Amplified Spontaneous Emission (ASE) noise from inline amplifiers Amplified Spontaneous Emission (ASE) noise from inline amplifiers Receiver shot/thermal noise Receiver shot/thermal noise Noise and inter-symbol interference (ISI) resulting from Kerr nonlinearity and its interaction with amplifier noise and other propagation effects Amplitude noise and phase noise are generally different Amplitude noise and phase noise are generally different

10. 10 Part I – 100 Gb/s Long-haul Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) WDM effects and optical OFDM WDM effects and optical OFDM Summary Summary

11. 11 Part I – 100 Gb/s Long-haul Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced phase noise Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) WDM effects and optical OFDM WDM effects and optical OFDM Summary Summary

12. 12 A form of inter-symbol interference (ISI) due to the term A form of inter-symbol interference (ISI) due to the term Intra-channel four-wave mixing (IFWM) SMF DCF amplifier

13. 13 Intra-channel four-wave mixing (IFWM) Pulse trains Pulse trains First-order perturbation theory First-order perturbation theory Linear solution to NLSE IFWM: not FWM! IFWM: not FWM! Nonlinear perturbation Pulse shape Phase modulated info IFWM is ISI caused by interaction of dispersion and Kerr nonlinearity IFWM is ISI caused by interaction of dispersion and Kerr nonlinearity (NLSE)

14. 14 IFWM - induced phase noise IFWM-induced phase noise on time slot 0 IFWM-induced phase noise on time slot 0 Highly nonlinear ISI Highly nonlinear ISI Each term in summation is a triple product of info. symbols Each term in summation is a triple product of info. symbols Triple product comes from future and past symbols combined in a strange way Triple product comes from future and past symbols combined in a strange way Too complicated to be fully exploited (at present) Too complicated to be fully exploited (at present) Considered noise most of the time Considered noise most of the time

15. 15 Probability distribution of Need to know the probability distribution of to analytically characterize system bit error ratio (BER) Need to know the probability distribution of to analytically characterize system bit error ratio (BER) Empirical distribution of only. BER obtained by numerical methods Empirical distribution of only. BER obtained by numerical methods Is it possible to at least approximate the probability distribution ? Is it possible to at least approximate the probability distribution ? Ho, PTL vol. 17, no. 4, Apr. 2005, pp. 789-791

16. 16 Insight: terms in are pairwise independent. For example, Insight: terms in are pairwise independent. For example, are independent are independent A consequence of modulo addition in phase of A consequence of modulo addition in phase of Not jointly independent Not jointly independent Approximate probability distribution Approximation:

17. 17 for QPSK/DQPSK systems QPSK DQPSK DQPSK: Group terms from that are correlated with each other DQPSK: Group terms from that are correlated with each other

18. 18 Tail Probability of QPSKDQPSK

19. 19 are correlated are correlated Exploiting Correlation structure of Wei and Liu, Optics Letters, Vol. 28, no. 23, pp. 2300-2302, 2003 No analytical knowledge of correlation structure of IFWM-induced phase noise No analytical knowledge of correlation structure of IFWM-induced phase noise

20. 20 Correlation MPSK BPSK

21. 21 for 40 GSym/s QPSK systems for 40 GSym/s QPSK systems L (km) SMF80.25171.2 DCF16.6-855.3 Sampling points SMF DCF Pulse shape: 33% RZ Gaussian Pulse shape: 33% RZ Gaussian

22. 22 Exploiting Optimal linear prediction of Optimal linear prediction of 1.8 dB improvement when dominates 1.8 dB improvement when dominates 0.8-1.2 dB improvement in presence of amplifier noise 0.8-1.2 dB improvement in presence of amplifier noise

23. 23 IFWM-induced phase noise and amplitude noise Received amplitude uncorrelated with phase noise for QPSK/DQPSK systems Received amplitude uncorrelated with phase noise for QPSK/DQPSK systems A.P.T. Lau, S. Rabbani and J.M. Kahn, subm. OSA/IEEE JLT Sept. 2007

24. 24 Part I – 100 Gb/s Long-haul Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced phase noise Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) WDM effects and optical OFDM WDM effects and optical OFDM Summary Summary

25. 25 Nonlinear phase noise (NLPN) Kerr nonlinearity induced nonlinear phase shift: Kerr nonlinearity induced nonlinear phase shift: corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiers corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiers EIEI EQEQ Linear Regime EIEI EQEQ Nonlinear Regime EIEI EQEQ Linear Regime E n E tot Nonlinear Regime EIEI EQEQ E tot  NL  |E tot | 2 Nonlinear phase noise or Gordon-Mollenauer effect Nonlinear phase noise or Gordon-Mollenauer effect

26. 26 Joint probability distribution (PDF) of received amplitude and phase K.P. Ho “Phase modulated Optical Communication Systems,” Springer 2005 Transmitted signal with power, phase Transmitted signal with power, phase

27. 27 PDF and maximum likelihood (ML) decision boundaries for 40G Sym/s QPSK Signals L=5000 km, P=-4 dBm, L=5000 km, P=-4 dBm,

28. 28 Maximum Likelihood (ML) Detection To implement ML detection, need to know the ML boundaries To implement ML detection, need to know the ML boundaries Need to know Need to know With,can either de- rotate the received phase or use a lookup table With,can either de- rotate the received phase or use a lookup table

29. 29 With approximations With approximations ML decision boundary it can be shown that it can be shown that

30. 30 Received phase rotation by Before rotation Before rotation After rotation After rotation Straight line ML decision boundaries after rotation Straight line ML decision boundaries after rotation

31. 31 Symbol Error Rate (SER) for MPSK Systems Numerical results Analytical

32. 32 SER for D-MPSK Systems

33. 33 16-QAM modulation formats High spectral efficiency. Together with coding, approach information- theoretic limits. High spectral efficiency. Together with coding, approach information- theoretic limits. For a given bit rate, reduce inter-symbol interference compared to 2-PSK or 4-PSK. For a given bit rate, reduce inter-symbol interference compared to 2-PSK or 4-PSK.

34. 34 16-QAM transmitter Laser

35. 35 Maximum likelihood detection for 16- QAM systems in presence of NLPN No analytical formula for ML decision boundaries for 16- QAM system as power of signal points not constant No analytical formula for ML decision boundaries for 16- QAM system as power of signal points not constant Boundaries distorted from straight lines Boundaries distorted from straight lines Can we design/process the signals at the transmitter and/or receiver such that ML detection can be better approximated by straight lines?

36. 36 16-QAM signal phase pre-compensation With phase pre- comp. Without phase pre-comp. P avg = -2.5 dBm Modes of conditional probability distribution corresponding to each signal point do not form a square constellation Modes of conditional probability distribution corresponding to each signal point do not form a square constellation Pre-rotate phase by the negative of mean nonlinear phase shift Pre-rotate phase by the negative of mean nonlinear phase shift

37. 37 NLPN post-compensation Rotate the received phase by proportional to received intensity for phase noise variance minimization Rotate the received phase by proportional to received intensity for phase noise variance minimization With phase pre- comp. only Phase pre- comp. with NLPN post-comp. Ho and Kahn, JLT vol.22 no. 3, Mar. 2004 Ly-Gagnon and Kikuchi, Paper 14C3-3, OECC 2004

38. 38 Performance of phase rotation methods in 16-QAM systems (No phase comp.) A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, pp. 3008-3016, Oct 2007

39. 39 Comparison of various phase noises in long-haul systems ASE induced phase noise IFWM-induced phase noise Nonlinear Phase Noise Signal Power Amplifier noise power System Length Remarks Dominant in terrestrial links Dominant in Submarine links

40. 40 Part I – 100 Gb/s Long-haul Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced perturbations Kerr nonlinearity induced perturbations Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) WDM effects and optical OFDM Summary Summary

41. 41 Summary – 100Gb/s Long-Haul Coherent detection and DSP technologies results in the relevance and importance of communication theory in long- haul system design for 100 Gb/s transmission Coherent detection and DSP technologies results in the relevance and importance of communication theory in long- haul system design for 100 Gb/s transmission Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, NLPN Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, NLPN System BER characterization System BER characterization Appropriate signal processing techniques for performance improvements Appropriate signal processing techniques for performance improvements Much more work remains to understand/improve long-haul system performance! Much more work remains to understand/improve long-haul system performance!

42. 42 Part II – 100Gb/s Ethernet using multimode fiber Motivation and background Motivation and background Principal Modes and adaptive optics using spatial light modulator Principal Modes and adaptive optics using spatial light modulator System optimization framework and experimental results System optimization framework and experimental results

43. 43 Ethernet Roadmap Who needs 100G Ethernet? Who needs 100G Ethernet? Not me (individual user) ~ Not me (individual user) ~ Data centers (e.g. Google) and other large enterprise/core switches Data centers (e.g. Google) and other large enterprise/core switches Multimode Fiber (MMF) widely deployed. Want to reuse it for cost effectiveness (just like DSL) Multimode Fiber (MMF) widely deployed. Want to reuse it for cost effectiveness (just like DSL)

44. 44 100 Gb/s Ethernet IEEE Higher Speed Study Group formed July ‘06 IEEE Higher Speed Study Group formed July ‘06 Standards expected to be finalized by 2010 Standards expected to be finalized by 2010 100Gb/s transmission over 100 m of multi-mode fiber 100Gb/s transmission over 100 m of multi-mode fiber

45. 45 Multimode Fibers (MMF) MMF SMF Ideal Modes Spatially orthogonal (typical MMF has 100 modes) having well-defined propagation speeds Spatially orthogonal (typical MMF has 100 modes) having well-defined propagation speeds Propagate without cross-coupling in ideal fiber Propagate without cross-coupling in ideal fiber Significant mode coupling in real installed fibers Significant mode coupling in real installed fibers Mode Pulse envelope

46. 46 Different modes have different – different speed Different modes have different – different speed Single pulse in – many pulses out (modal dispersion or ISI). Single pulse in – many pulses out (modal dispersion or ISI). Linear ISI – identical to ISI in wireless/wireline Linear ISI – identical to ISI in wireless/wireline t t Modal Dispersion in MMF MMF Tx MMF systems – OOK with direct detection MMF systems – OOK with direct detection

47. 47 Motivation and background Motivation and background Principal Modes and adaptive optics using spatial light modulator System optimization framework and experimental results System optimization framework and experimental results Part II – 100Gb/s Ethernet using multimode fiber

48. 48 Principal Modes in Multimode Fiber Principal Modes (PM) – linear combinations of ideal modes Principal Modes (PM) – linear combinations of ideal modes Single pulse in – single pulse out (well defined group delay ) Single pulse in – single pulse out (well defined group delay ) Insight – input electric field design to excite single PM! Insight – input electric field design to excite single PM! S. Fan and J. M. Kahn, Optics Letters, vol. 30, no. 2, pp. 135-137, 2005 Propagation matrix that captures mode coupling Input electric field Input electric field Group delay operator Group delay operator

49. 49 Spatial Light Modulator (SLM) kxkx kyky x y SLM MMF 2-D array of mirrors with the reflectance of each mirror (v i ) can be controlled. 2-D array of mirrors with the reflectance of each mirror (v i ) can be controlled. Sort of a 2-D spatial filter Sort of a 2-D spatial filter Collimating lens Laser

50. 50 Adaptive Transmission Scheme Spatial Light Modulator Multimode Fiber OOK Modulator Adaptive Algorithm Fourier Lens I in (t) Trans. Data Transmitter Low-Rate Feedback Channel Photo- Detector Clock & Data Recovery ISI Estimation Rec. Data ISI Objective Function Receiver I out (t) Impulse response Eye opening  0.8  0.3 - 0.1 -0.4

51. 51 Motivation and background Motivation and background Principal Modes and adaptive optics using spatial light modulator System optimization framework and experimental results Part II – 100Gb/s Ethernet using multimode fiber

52. 52 Optimization Problem The pulse response is given by The ISI is given by minimize subject to ISI (or modal dispersion) z1z1 z0z0 g(t)g(t) 0T2T2T3T3T4T4T5T5T 6T6T t q(t)q(t) Let be the spatial light modulator (SLM) settings

53. 53 Optimization Problem Not in any standard form. For example, not convex. Not in any standard form. For example, not convex. Convex! (Second order cone program) Convex! (Second order cone program) N C  1 p )1( 2   NN CP N C  v and is the SLM setting (optimization variable) N C  1 p )1( 2   NN CP N C  1 p )1( 2   NN CP N C  v and (not explicitly known in experiment)

54. 54 Adaptive algorithms to achieve globally minimal ISI – efficient, robust in presence of noise and no need to know system parameters. Adaptive algorithms to achieve globally minimal ISI – efficient, robust in presence of noise and no need to know system parameters. Sequential Coordinate Ascent (SCA) Sequential Coordinate Ascent (SCA) Adaptive Algorithms Amplitude-and-Phase SCA (APSCA): 1) Pick the i th SLM block 2) Optimize amplitude and phase of v i 3) go to next SLM block 4) Repeat

55. 55 Experimental Setup

56. 56 Transmission Scheme

57. 57 Experimental Results: 10 Gb/s over 2 km Beforeadaptation Afteradaptation 4 um offset patch cord 2 km Light from SLM

58. 58 Before Adaptation After Adaptation 4 um offset patch cord 2 km Light from SLM Experimental Results: 10 Gb/s over 2 km

59. 59 4 um offset patch cord 2 km Light from SLM Experimental Results: 10 Gb/s over 2 km Before After

60. 60 Channel spacing is 50 GHz with channels 54- 59 error free – 300 GHz of usable bandwidth! 4 um offset patch cord 2 km Light from SLM Experimental Results: 10 Gb/s over 2 km R. A. Panicker, A.P.T. Lau, J.P. Wilde and J. M. Kahn, submitted to IEEE JLT, Nov 2007

61. 61 Experimental Results: 100 Gb/s, 2.2 km

62. 62 Experimental Results: 100 Gb/s, 2.2 km Power in 0.2 nm BW (dBm) Wavelength (nm) 55  10  15  20  25 1545 15491553155715611565 0 12345678910 FEC Decoder Input BER Attenuator Setting (dB) 10 0 10  2 10  4 10  6 10  8 10  10 FEC Threshold R. A. Panicker et al., IEEE PTL, Aug. 2007.

63. 63 Experimental Results: 100 Gb/s, 2.2 km 012345678910 FEC Decoder Input BER Attenuator Setting (dB) 10 0 10  2 10  4 10  6 10  8 10  10 FEC Threshold Power in 0.2 nm BW (dBm) Wavelength (nm) 55  10  15  20  25 1545 15491553155715611565 Error-free transmission after Forward Error Correction ! Error-free transmission after Forward Error Correction !

64. 64 Principal Modes in Multimode Fiber A.P.T. Lau, J.P. Wilde and J. M. Kahn, “Principal modes in multimode fibers,” in preparation Chn. 59 Chn. 60 Chn. 61 Pulse Response Mode Intensity Profile Ability to excite best Principal Modes for any particular channel Ability to excite best Principal Modes for any particular channel Potentially mode division multiplexing ! Potentially mode division multiplexing !

65. 65 Comparison between Optical and Electrical Equalization OpticalElectrical Complexity Independent of BxL Linear (FFE/DFE) and exponential (MLSD) in BxL Noise enhancement No FFE/DFE have noise enhancement Multi-channelequalization One SLM setting equalizes multiple channels Per channel equalization required Power consumption No power consumption after adaptation Steady power consumption Performance Comparable to MLSD Lastly, they can be simultaneously implemented! Lastly, they can be simultaneously implemented! Electrical equalization: get the best out of a ‘dirty’ channel Optical equalization: Clean up the channel

66. 66 Summary – 100 Gb/s Ethernet Principal Modes – a new understanding in modal dispersion and ISI in multi-mode fiber transmission Principal Modes – a new understanding in modal dispersion and ISI in multi-mode fiber transmission Modal dispersion (or ISI) mitigation through spatial light modulator that modifies spatial profile of input electric field Modal dispersion (or ISI) mitigation through spatial light modulator that modifies spatial profile of input electric field Adaptive algorithms to achieve optimal performance Adaptive algorithms to achieve optimal performance Experimentally demonstrated 10 Gb/s and 100 Gb/s transmission over multiple kilometers of multi-mode fibers with real world impairments Experimentally demonstrated 10 Gb/s and 100 Gb/s transmission over multiple kilometers of multi-mode fibers with real world impairments Comparable or outperform the best known electrical equalization technique from communication theory Comparable or outperform the best known electrical equalization technique from communication theory

67. 67 Research Outlook Advances in photonic/electronic devices allows one to start a research problem in fiber-optic communications by Advances in photonic/electronic devices allows one to start a research problem in fiber-optic communications by Underlying physics of signal transmission yet to be fully understood Underlying physics of signal transmission yet to be fully understood Fiber-optic communications will be even more interdisciplinary in the future! Fiber-optic communications will be even more interdisciplinary in the future! “Consider an arbitrarily modulated signal x(t)...”

68. 68 Thank you!

69. 69 Cross phase modulation (XPM) in WDM systems Cross-phase modulation (XPM) Cross-phase modulation (XPM) Difference in group velocity -- Walk Off Effect Difference in group velocity -- Walk Off Effect Pulse waveform distortion negligible compared to walk off in modeling nonlinear phase noise variance Pulse waveform distortion negligible compared to walk off in modeling nonlinear phase noise variance

70. 70 XPM induced nonlinear phase noise Terrestrial system: 40Gb/s, 50 GHz spacing, D=17 ps/(km-nm): Lw=3.9 km Terrestrial system: 40Gb/s, 50 GHz spacing, D=17 ps/(km-nm): Lw=3.9 km Submarine system: Lw=15 km Submarine system: Lw=15 km

71. 71 Orthogonal Frequency Division Multiplexing (OFDM) Well-known in wireless/DSL Well-known in wireless/DSL Multiplexing of large number of low rate sub-carriers Multiplexing of large number of low rate sub-carriers FFT based processing FFT based processing … OFDM Single Carrier

72. 72 OFDM in Fiber-Optics Wireless / DSL Fiber-Optics Fiber-Optics Spectrum Confinement Much more confined than SC Same EqualizationComplexity in OFDM vs. in SC in OFDM vs. in SCSame Channel Equalization Bit loading to achieve info. theoretic capacity Dispersion: High signal peaks Peak-to-Avg Power Ratio (PAPR) Fiber nonlinearity! SC – Single Carrier

73. 73 Nonlinearity induced impairments in Optical OFDM Nonlinear perturbations originate from FWM products between sub- carriers with perfect phase matching Nonlinear perturbations originate from FWM products between sub- carriers with perfect phase matching For a system with K sub- carriers, noise variance at sub-carrier k is given by For a system with K sub- carriers, noise variance at sub-carrier k is given by A.P.T. Lau, D.J. Barros and J.M. Kahn, in preparation.

74. 74 IFWM-induced phase noise IFWM induced phase noise on bit 0 IFWM induced phase noise on bit 0 IFWM induced perturbations IFWM induced perturbations

75. 75 overall length L tot with N spans SMF DCF DCM SMF DCF DCM

76. 76 Nonlinear Phase Noise Experiments ECOC ’06 Post-Deadline Paper OFC ‘07

77. 77 Design of inline amplifier gains and spacings to mitigate phase noise Amplifier Conventionally, amplifiers uniformly spaced along the link and the their gain exactly compensates for the signal loss in the previous span Conventionally, amplifiers uniformly spaced along the link and the their gain exactly compensates for the signal loss in the previous span Better design of amplifier gains/spacings in the link to mitigate phase noise? Better design of amplifier gains/spacings in the link to mitigate phase noise?

78. 78 Design of inline amplifier gains and spacings to mitigate phase noise Linear Phase Noise Linear Phase Noise Amplifier Nonlinear Phase Noise Nonlinear Phase Noise EIEI EQEQ E n

79. 79 Variance of phase noise Linear phase noise variance – for high SNR, Linear phase noise variance – for high SNR, Nonlinear phase noise variance Nonlinear phase noise variance Signal after amplifier: Signal after amplifier: where

80. 80 Minimization of joint phase noise variance When, the optimization problem can be shown to be convex in. When, the optimization problem can be shown to be convex in. are uncorrelated are uncorrelated Minimize the variance of total phase noise Minimize the variance of total phase noise

81. 81 Uniformly spaced amplifiers with per- span loss compensation Distributed amplification is not optimal ! Distributed amplification is not optimal ! (contrary to Yariv, Opt. Lett., vol. 15, no. 19,1990 ) (contrary to Yariv, Opt. Lett., vol. 15, no. 19,1990 )

82. 82 Optimal span length in presence of NLPN Define span length Y*=L/N*. As A.P.T. Lau and J.M. Kahn, paper JWB23, OSA COTA, June 2006 Overall phase noise variance reduction by 40%. Overall phase noise variance reduction by 40%. Optimal N Optimal N

83. 83 Amplifier gain optimization in presence of NLPN Reduction in variance: 23% (3000 km), 81% (10000 km) Reduction in variance: 23% (3000 km), 81% (10000 km) Terrestrial link (3000 km) Submarine link (10000 km)

84. 84 Joint amplifier spacing and gain optimization in presence of NLPN Reduction of variance: 45% (3000 km), 83% (10000 km) Reduction of variance: 45% (3000 km), 83% (10000 km) A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, Mar 2006, pp.1334-1341 Terrestrial link (3000 km) Submarine link (10000 km)

85. 85 How good is the variance measure? BER/Capacity optimized at close vicinity of N that minimize phase noise variance BER/Capacity optimized at close vicinity of N that minimize phase noise variance

86. 86 Per-Span Loss Compensation (fixed N) Earlier amplifiers spaced closer together due to asymmetry of contribution of nonlinear phase noise Earlier amplifiers spaced closer together due to asymmetry of contribution of nonlinear phase noise Reduction of variance: 11% (3000 km) 49% (10000 km) Reduction of variance: 11% (3000 km) 49% (10000 km)

87. 87 Optimal Power Profile Power profile Power profile Let Let Phase noise variance Phase noise variance Euler Characteristic Equation Euler Characteristic Equation

88. 88 Optimal Power Profile A.P.T. Lau and J.M. Kahn, IEEE PTL, pp. 2514-2516 Dec. 2006. Variance reduction of 60% when Variance reduction of 60% when

89. 89 Received PDF and ML decision boundaries for 16-QAM signals Probability Distribution Decision Boundaries

90. 90 Signal Constellation Optimization in Presence of NLPN QPSK 1-2-1 1-3 2-2

91. 91 Simulation Results A. Panicker, J. M. Kahn and S. P. Boyd, to appear in IEEE JLT

92. 92 Objective function during adaptation Noise and drifting of the system during to mechanical and temperature instability Noise and drifting of the system during to mechanical and temperature instability

93. 93 Experimental Results: 10 Gbps Before Adaptation After Adaptation 500 m Light from SLM 500 m 2 um offset patch cord

94. 94 Experimental Results: 10 Gbps 500 m Light from SLM 500 m 2 um offset patch cord

95. 95 Experimental Results: 10 Gbps 500 m Light from SLM 500 m 2 um offset patch cord

96. 96 Pulse response 500 m Light from SLM 500 m 2 um offset patch cord Before adaptation After adaptation

97. 97 Polarization dependence of Principal Modes excited BestPolarization WorstPolarization 2 km MMF 4 um offset - 2 km MMF

98. 98 Experimental Results: 100 Gbps, 2.2 km Corning Incorporated: InfiniCor eSX+ fibers BER-based adaptation Pilot channel-based adaptation

99. 99 Modal Multiplexing in MMF systems Encode independent bit streams on different mode Encode independent bit streams on different mode Similar to DS-CDMA where the each spatial mode is s ‘code’ Similar to DS-CDMA where the each spatial mode is s ‘code’ A.P.T. Lau, L. Xu and T. Wang, IEEE PTL, pp. 1087 – 1089, Jul. 2007.

100. 100 Transmitter and Receiver Components Laser Laser Iolon MEMS-based tunable laser Iolon MEMS-based tunable laser C band (1527-1567 nm), 100 channels on 50 GHz ITU grid C band (1527-1567 nm), 100 channels on 50 GHz ITU grid +13 dBm output power, 15 kHz linewidth (not required here) +13 dBm output power, 15 kHz linewidth (not required here) Modulator Modulator Fujitsu 12.5 Gb/s dual-drive Mach-Zehnder modulator, zero chirp Fujitsu 12.5 Gb/s dual-drive Mach-Zehnder modulator, zero chirp Encodes 10 Gb/s on-off keying, non-return-to-zero format Encodes 10 Gb/s on-off keying, non-return-to-zero format Receiver Receiver Picometrix 12.5 Gb/s receiver, 62.5 mm MMF input Picometrix 12.5 Gb/s receiver, 62.5 mm MMF input Sensitivity and overload powers: -20 dBm, + 2 dBm at 10-10 BER Sensitivity and overload powers: -20 dBm, + 2 dBm at 10-10 BER Average powers Average powers Modulator output: +6 dBm Modulator output: +6 dBm Launched into MMF: -2.5 dBm Launched into MMF: -2.5 dBm Receiver input: -3.4 dBm (1 km) to -5.5 dBm (11 km) Receiver input: -3.4 dBm (1 km) to -5.5 dBm (11 km)

101. 101 Convergence Time Bit rate on feedback channel: 8 bits/135 ms = 59 kb/s. Bit rate on feedback channel: 8 bits/135 ms = 59 kb/s. 128 bit training sequence, measure 6 points, average 2000 measurements. 128 bit training sequence, measure 6 points, average 2000 measurements. Estimation accuracy required: F/sF = 256 (8 bits). Estimation accuracy required: F/sF = 256 (8 bits). In absence of ISI, Q = 7. In absence of ISI, Q = 7. 1 km link length, 10 Gb/s. 1 km link length, 10 Gb/s.

102. 102 Nematic Liquid Crystal SLM Made by Boulder Nonlinear Systems Made by Boulder Nonlinear Systems Pixels: 256 × 256 Pixels: 256 × 256 Nematic liquid crystal, phase only Nematic liquid crystal, phase only Phase range: 0 to 2  Phase range: 0 to 2  Resolution: 5-6 bits Resolution: 5-6 bits Reflection efficiency: 65% Reflection efficiency: 65% Response time Response time Binary { , 2  }:  10-90  50 ms Binary { , 2  }:  10-90  50 ms Quaternary {  /2, , 3  /2, 2  }:  10-90  100 ms Quaternary {  /2, , 3  /2, 2  }:  10-90  100 ms Polarization-sensitive Polarization-sensitive Not suitable for receiver in MIMO system Not suitable for receiver in MIMO system

103. 103 Fiber optic Tablecloth: USD $1264 Intermission…..