Compensation of Modal Dispersion in Multimode Fiber Systems using Adaptive Optics via Convex Optimization Rahul Alex Panicker Department of Electrical Engineering Stanford Univeristy Playing an Electromagnetic F Major on an Optical Fiber 3 Multimode Fiber Systems what, why? Ubiquitous short range communication medium Ubiquitous short range communication medium 4 Multimode Fiber Systems what, why? Ubiquitous short range communication medium Ubiquitous short range communication medium Local area networks, campus area networks Local area networks, campus area networks 5 Multimode Fiber Systems what, why? Ubiquitous short range communication medium Ubiquitous short range communication medium Local area networks, campus area networks Local area networks, campus area networks Lots of installed fiber can we make the best use of this? Lots of installed fiber can we make the best use of this? (remember telephone lines and DSL?) 6 Multimode Fiber Systems what, why? Ethernet Roadmap 7 Multimode Fiber Systems what, why? Performance bit rate (Mbps/Gbps) and bit rate (Mbps/Gbps) and transmission distance (km) transmission distance (km) currently limited by modal dispersion. currently limited by modal dispersion. 8 Contributions of this Thesis Created novel adaptive algorithms for real-time implementation. Created novel adaptive algorithms for real-time implementation. Adaptive transmission scheme involving optical dispersion compensation. Adaptive transmission scheme involving optical dispersion compensation. New comprehensive mathematical formulation. New comprehensive mathematical formulation. Globally optimal solution computed. Globally optimal solution computed. Performance maximization posed as an optimization problem. Performance maximization posed as an optimization problem. Experimental demonstration of 10 Gbps and 100 Gbps transmissions. Experimental demonstration of 10 Gbps and 100 Gbps transmissions. 9 Outline Multimode fiber essentials Multimode fiber essentials Adaptive transmission scheme Adaptive transmission scheme Optimization problem Optimization problem Adaptive algorithms Adaptive algorithms Experimental results Experimental results 10 Outline Multimode fiber essentials Multimode fiber essentials Adaptive transmission scheme Adaptive transmission scheme Optimization problem Optimization problem Adaptive algorithms Adaptive algorithms Experimental results Experimental results 11 Modes of a Multimode Fiber Modes of a Multimode Fiber Many natural phenomena involve modes: Many natural phenomena involve modes: Solar oscillations Solar oscillations Swaying buildings Swaying buildings Vibrating strings Vibrating strings Ripples in a pond Ripples in a pond Molecular vibrations Molecular vibrations Light in an optical fiber Light in an optical fiber 12 Modes of a Multimode Fiber Modes of a Multimode Fiber And God said and then there was light. 13 Modes of a Multimode Fiber Ideal Modes Ideal Modes Mutually orthogonal solutions of wave equation having well-defined propagation constants. Mutually orthogonal solutions of wave equation having well-defined propagation constants. Propagate without cross-coupling in ideal fiber. Propagate without cross-coupling in ideal fiber. Typical multimode fiber supports of order 100 modes. Typical multimode fiber supports of order 100 modes. 14 Modes of a Multimode Fiber Mode Coupling Mode Coupling Bends and imperfections couple modes over distances of the order of meters. Bends and imperfections couple modes over distances of the order of meters. Coupling varies on time scale of seconds. Coupling varies on time scale of seconds. 15 Modes of a Multimode Fiber Modal Dispersion Modal Dispersion Different modes have different delays. Different modes have different delays. Single pulse in many pulses out. Single pulse in many pulses out. t Transmitted t Received 16 Modes of a Multimode Fiber Principal modes Principal modes PMs are linear combinations of ideal modes. PMs are linear combinations of ideal modes. Form a basis over all propagating modes. Form a basis over all propagating modes. Vary from fiber to fiber. Vary from fiber to fiber. Single pulse in single pulse out (well defined group delay). Single pulse in single pulse out (well defined group delay). S. Fan and J. M. Kahn, Optics Letters, vol. 30, no. 2, pp , January 15, 2005. 17 Eye Diagram Indicates how discernable 1-bits and 0-bits are. Good eyeBad eyePoor eye 18 Outline Multimode fiber essentials Multimode fiber essentials Adaptive transmission scheme Adaptive transmission scheme Optimization problem Optimization problem Adaptive algorithms Adaptive algorithms Experimental results Experimental results 19 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) E. Alon, V. Stojanovic, J. M. Kahn, S. P. Boyd and M. A. Horowitz, Proc. of IEEE Global Telecommun. Conf., Dallas, TX, Nov. 29-Dec. 3, 2004. 20 Spatial Light Modulator kxkx kyky x y SLM MMF 2-D array of mirrors. 2-D array of mirrors. Reflectance each mirror (v i ) can be controlled. Reflectance each mirror (v i ) can be controlled. 21 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) 0.3 0.1 0.4 0.8 22 Outline Multimode fiber essentials Multimode fiber essentials Adaptive transmission scheme Adaptive transmission scheme Optimization problem Optimization problem Adaptive algorithms Adaptive algorithms Experimental results Experimental results 23 Optimization Problem maximize subject to eye opening physical constraints 24 Optimization Problem The impulse response is given by The pulse response is, therefore, given by and the eye opening is given by 25 Optimization Problem R. A. Panicker, S. P. Boyd, and J. M. Kahn, subm. Journal of Lightwave Technology Not in any standard form. Not in any standard form. For example, not convex. For example, not convex. 26 Optimization Problem Convex! (Second order cone program) Convex! (Second order cone program) 27 Can compute globally optimal solution. Can compute globally optimal solution. Efficient algorithms exist. Efficient algorithms exist. Roughly same complexity as solving a linear program of same size. Roughly same complexity as solving a linear program of same size. Optimization Problem 28 Simulation Results 29 Outline Multimode fiber essentials Multimode fiber essentials Adaptive transmission scheme Adaptive transmission scheme Optimization problem Optimization problem Adaptive algorithms Adaptive algorithms Experimental results Experimental results 30 Adaptive Algorithms Optimal solution fine when everything is known about the system. Optimal solution fine when everything is known about the system. In practice, we dont know system parameters. In practice, we dont know system parameters. System can be time varying. System can be time varying. Need adaptive algorithms. Need adaptive algorithms. Can compute optimum without explicitly estimating system parameters. Can compute optimum without explicitly estimating system parameters. 31 Adaptive Algorithms: Noiseless Amplitude-and-Phase SCA (APSCA): 1) Pick the i th SLM block 2) Optimize amplitude and phase of v i 3) i i+1 4) Repeat 32 Adaptive Algorithms: Noiseless Quadratic in each block reflectance. Quadratic in each block reflectance. 4 real parameters to be estimated in a, b, and c. 4 real parameters to be estimated in a, b, and c. Can be done with 4 measurements. Can be done with 4 measurements. Objective function converges to global maximum. Objective function converges to global maximum. (on convergence, satisfies KKT conditions of convex problem) 33 Adaptive Algorithms: Noiseless Continuous Phase SCA (CPSCA): 1) Pick the i th SLM block 2) Optimize phase of v i 3) i i+1 4) Repeat 34 Adaptive Algorithms: Noiseless Linear in each block reflectance. Linear in each block reflectance. 3 real parameters to be estimated in b and d. 3 real parameters to be estimated in b and d. Can be done with 3 measurements. Can be done with 3 measurements. Guaranteed to converge, but not to global optimum. Guaranteed to converge, but not to global optimum. 35 Simulations Opens a previously closed eye. Amplitude-and-Phase SCA: 36 Simulations 37 Simulations pass over SLM APSCA, 4PSCA 1 pass over SLM CPSCA Global maximum Amplitude-and-Phase SCA, Continuous-Phase SCA, and 4-Phase SCA Number of SLM block flips Normalized objective function APSCA CPSCA 4PSCA 38 Adaptive Algorithms: Noisy Amplitude-and-Phase SCA (APSCA): 1) Pick the i th SLM block 2) Estimate a, b, c. 3) Optimize amplitude and phase of v i 4) i i+1 5) Repeat 39 Adaptive Algorithms: Noisy Estimation done with p+q measurements, p 3, q 1. If noise has variance 2, var(a) = 2 (1/p+1/q), var(Re(b)) = var(Im(b)) = 2 /p. In presence of Gaussian noise, these are ML estimates. 40 Adaptive Algorithms: Noisy Continuous Phase SCA (CPSCA): 1) Pick the i th SLM block 2) Estimate b and d. 3) Optimize phase of v i 4) i i+1 5) Repeat 41 Adaptive Algorithms: Noisy Estimation done with p measurements, p 3. If noise has variance 2, var(Re(b)) = var(Im(b)) = 2 /p. In presence of Gaussian noise, these are ML estimates. 42 Simulations pass over SLM Global maximum Convergence Plots: Amplitude-and-Phase SCA, Continuous-Phase SCA, and 4-Phase SCA Number of SLM block flips Objective function APSCA without noise APSCA with noise CPSCA with noise 4PSCA with noise 43 Adaptation Time Presently, 34 minutes in lab setup. Presently, 34 minutes in lab setup. Objective function estimation time can be reduced to 25 s Objective function estimation time can be reduced to 25 s SLM switching time can be reduced to 100 s SLM switching time can be reduced to 100 s Overall adaptation (60 blocks, 4 phases) would require 30 ms Overall adaptation (60 blocks, 4 phases) would require 30 ms 44 Comparison with Electrical Equalization Electrical Equalization Optimal equalizer is MLSD complexity exponential in bit-rate and length. Optimal equalizer is MLSD complexity exponential in bit-rate and length. Linear equalizers have noise enhancement. Linear equalizers have noise enhancement. DFE has error propagation at low SNR. DFE has error propagation at low SNR. EE needs to be done per channel in WDM systems. EE needs to be done per channel in WDM systems. Steady power consumption Steady power consumption 45 Comparison with Electrical Equalization Optical Equalization Complexity independent of bit-rate and length only depends on mode structure. Complexity independent of bit-rate and length only depends on mode structure. No noise enhancement. No noise enhancement. Can compensate over multiple channels in WDM systems. Can compensate over multiple channels in WDM systems. After adaptation, no steady power consumption. After adaptation, no steady power consumption. 46 Outline Multimode fiber essentials Multimode fiber essentials Adaptive transmission scheme Adaptive transmission scheme Optimization problem Optimization problem Adaptive algorithms Adaptive algorithms Experimental results Experimental results 47 X. Shen, J. M. Kahn and M. A. Horowitz, Optics Letters, vol. 30, no. 22, pp , Nov. 15, Transmission Scheme 48 Transmission Scheme 49 Estimation of the Objective Function 0T2T2T3T3T4T4T5T5T 6T6T t t 0 g(t)g(t) g(nT;t 0 ) 0LT2LT t Transmit I in (t) Receive y(t) = I out (t) * r(t) yL1yL1 y max t0t0 t t0Tt0T t 0 (L+1)T t 0 LT y1y1 y0y0 yLyL y min Eye closed: transmit periodic square wave 50 Estimation of the Objective Function t Transmit I in (t) Eye open: transmit data sequence Receive y(t) = I out (t) * r(t) y1y1 y0y0 t (mod T) 0T2T2T3T3T4T4T5T5T 6T6T t t 0 g(t)g(t) g(nT;t 0 ) 010 ; yytnTgF 51 Experimental Results: 10 Gbps 52 Experimental Results: 10 Gbps Before Adaptation After Adaptation 4 m offset patch cord, 2 km fiber 53 Experimental Results: 10 Gbps 4 m offset patch cord, 2 km fiber Power Scan 54 Experimental Results: 10 Gbps 4 m offset patch cord, 2 km fiber Channel Scan Channel spacing: 50GHz Channels error free. 300 GHz at 50 GHz spacing. 55 Experimental Results: 10 Gbps 2 m offset patch cord 500 m fiber 2 m offset patch cord 500 m fiber Before Adaptation After Adaptation 56 Experimental Results: 10 Gbps 57 Experimental Results: 10 Gbps 58 Experimental Results: 100 Gbps, 2.2 km 59 Experimental Results: 100 Gbps, 2.2 km Corning Incorporated: InfiniCor eSX+ fibers BER-based adaptation Pilot channel-based adaptation R. A. Panicker, J. P. Wilde, J. M. Kahn, D. F. Welch and I. Lyubomirsky, IEEE Photon. Technol. Lett., vol. 19, no. 15, pp , August 1, 2007. 60 Experimental Results: 100 Gbps, 2.2 km Power in 0.2 nm BW (dBm) Wavelength (nm) 55 10 15 20 FEC Decoder Input BER Attenuator Setting (dB) 2 10 4 10 6 10 8 10 10 FEC Threshold 61 Experimental Results: 100 Gbps, 2.2 km Power in 0.2 nm BW (dBm) Wavelength (nm) 55 10 15 20 FEC Decoder Input BER Attenuator Setting (dB) 2 10 4 10 6 10 8 10 10 FEC Threshold 62 Experimental Results: 100 Gbps, 2.2 km 63 A Subtlety Exciting a single principal mode is not the best way to maximize the eye opening! Exciting a single principal mode is not the best way to maximize the eye opening! Allow some higher order modes to be excited. Allow some higher order modes to be excited. Additional power in desired mode more than compensates. Additional power in desired mode more than compensates. A non-intuitive outcome of the optimization framework. A non-intuitive outcome of the optimization framework. 64 A Subtlety 65 Conclusions Adaptive optics can effectively compensate for modal dispersion even in presence of real-world impairments. Adaptive optics can effectively compensate for modal dispersion even in presence of real-world impairments. An optimization framework can be used to compute the globally optimal solution. An optimization framework can be used to compute the globally optimal solution. These techniques have been successfully used for 10 Gbps and 100 Gbps transmission over multiple kilometers with channel impairments. These techniques have been successfully used for 10 Gbps and 100 Gbps transmission over multiple kilometers with channel impairments. 66 Thank you 67 Acknowledgements Prof. Joseph Kahn Prof. Joseph Kahn Prof. Stephen Boyd Prof. Stephen Boyd Prof. Shanhui Fan Prof. Shanhui Fan Prof. Balaji Prabhakar Prof. Balaji Prabhakar 68 Acknowledgements Members of the group Members of the group 69 Acknowledgements Dr. Martin Lee Dr. Martin Lee 70 Acknowledgements Family Family 71 Acknowledgements Namita and Gaurav Namita and Gaurav 72 Acknowledgements Shravan Shravan Dev Dev 73 Acknowledgements Many many more friends Many many more friends 74 Adaptive Optics Subsystem 75 Transmitter and Receiver Components Laser Laser Iolon MEMS-based tunable laser Iolon MEMS-based tunable laser C band ( nm), 100 channels on 50 GHz ITU grid C band ( 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 BER Sensitivity and overload powers: -20 dBm, + 2 dBm at 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) 76 Estimation of ISI Objective Function 0T2T2T3T3T4T4T5T5T 6T6T t t 0 g(t)g(t) g(nT;t 0 ) 0LT2LT t Transmit I in (t) Receive y(t) = I out (t) * r(t) yL1yL1 y max t0t0 t t0Tt0T t 0 (L+1)T t 0 LT y1y1 y0y0 yLyL y min Eye closed: transmit periodic square wave 77 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. 78 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 }: 50 ms Binary { , 2 }: 50 ms Quaternary { /2, , 3 /2, 2 }: 100 ms Quaternary { /2, , 3 /2, 2 }: 100 ms Polarization-sensitive Polarization-sensitive Not suitable for receiver in MIMO system Not suitable for receiver in MIMO system