何鏡波臺灣大學：電信工程學研究所王璽政Wang, Hsi-ChengHsi-ChengWang2007-11-272018-07-052007-11-272018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/58785High-speed lightwave transmission techniques, widely deployed in long-haul transmission systems, is currently extending to metro- and access-network for various wideband wireline applications. Differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) signallings have received renewed interest for long-haul transmission or spectrally efficiency systems. Compared with on-off keying (OOK) systems, direct-detection DPSK systems have 3-dB sensitivity improvement and better tolerance to fiber nonlinearity. This dissertation is to provide state-of-art methods in performance analysis and signal characterization for high-speed phase-modulated lightwave transmissions. Nonlinear phase noise is the main limitation to phase-modulated signals. In addition to intrachannel self-phase modulation (ISPM), in highly dispersive transmission systems with pulse broadening, the interaction of overlapped pulse induces both intrachannel cross-phase modulation (IXPM) and intrachannel four-wave mixing (IFWM). The effects of nonlinear phase noise from both ISPM and IXPM are analyzed and compared with IFWM for return-to-zero differential phase-shift keying (RZ-DPSK) signals. The temporal profile of the standard deviation (STD) of nonlinear phase noise is asymmetrical with its peak. The nonlinear phase noise is found to be the dominant effect to DPSK signals even in highly dispersive systems. In multiple-channels lightwave transmission systems, without pulse-overlap, RZ-DPSK signals is free from cross-phase modulation (XPM) effect. However, pulse overlap may cause non-periodic intensity profile that induces non-periodic phase fluctuation to other channels from XPM. The variance of the differential phase induced by XPM and pulse overlap is derived analytically to show impact of non-periodic intensity profile to RZ-DPSK signals. The phase jitter of the soliton is analyzed based on first order perturbation theory. The phase jitter is separated into three independent components induced by amplitude jitter, time and frequency jitter, and the mapping of amplifier noise to phase. The performance of soliton DPSK signals is derived analytically based on four received signal models: Gaussian, Gaussian linear phase (GLP), independent, and dependent models. Joint time-frequency representation is able to characterize optical signals affected by fiber- or device-induced impairments. The complex electric field of phase-modulated signals is retrieved from its time-resolved optical filtering (TROF) measured spectrogram. An essential component to TROF measurement and algorithm, the complex frequency response of a narrow-band optical filter is measured using microwave network analyzer that has KHz of resolution bandwidth and fraction of dB/degree of accuracy. With an initial guess from the craters and ridges of the spectrogram, the TROF algorithm based on conjugate gradient method converges rapidly to a mean-square error about 1\% even for signal with chromatic dispersion. The chromatic dispersion-induced eye-penalty is calculated from the TROF measured electric field for both PSK and DPSK signals. In contrary to conventional belief, PSK signal has better dispersion tolerance than DPSK signal The results are also confirmed by computer simulation.1 Introduction 1 1.1 Recent Progress on Lightwave Transmissions . . . . . . . . . . . . . . . . 2 1.1.1 Intensity-Modulated/Direct-Detection Systems . . . . . . . . . . . 2 1.1.2 Phase-Modulated Systems . . . . . . . . . . . . . . . . . . . . . . 4 1.1.3 Wavelength-Division Multiplexing Systems . . . . . . . . . . . . . 8 1.2 Issues for High-Speed Transmissions . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 Generation of Phase-Modulated Signal . . . . . . . . . . . . . . . 10 1.2.2 Generation of On-Off Keying Signal . . . . . . . . . . . . . . . . . 14 1.2.3 Comparison Between On-Off Keying and Phase-Modulated Signals 19 1.2.4 Nonlinear phase noise and Fiber Kerr Effect . . . . . . . . . . . . 20 1.2.5 Electric Field Measurement for Optical Signals . . . . . . . . . . . 22 1.3 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3.1 Intra- and Inter-Channel Nonlinear Effects . . . . . . . . . . . . . 24 1.3.2 Soliton DPSK Transmission . . . . . . . . . . . . . . . . . . . . . 25 1.3.3 Time-Frequency Signal Analysis . . . . . . . . . . . . . . . . . . . 25 1.4 Outline of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Impairments to Optical Signals 29 2.1 Ideal Performance of Direct-Detection Receivers . . . . . . . . . . . . . . 30 2.1.1 Intensity Modulation Signals . . . . . . . . . . . . . . . . . . . . . 30 2.1.2 Direct-Detection D(Q)PSK Receiver . . . . . . . . . . . . . . . . 34 2.2 Impairments to D(Q)PSK Signals . . . . . . . . . . . . . . . . . . . . . . 39 2.2.1 Interferometer Phase Error . . . . . . . . . . . . . . . . . . . . . . 39 2.2.2 Laser Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.2.3 Fiber Chromatic Dispersion . . . . . . . . . . . . . . . . . . . . . 44 2.3 Statistics of Nonlinear Phase Noise . . . . . . . . . . . . . . . . . . . . . 46 2.3.1 Asymptotic Approach to Nonlinear Phase Noise . . . . . . . . . . 46 2.3.2 Received Signal-Dependent Nonlinear Phase Noise . . . . . . . . . 51 2.4 D(Q)PSK Signals with Nonlinear Phase Noise . . . . . . . . . . . . . . . 54 2.4.1 Performance of DPSK Signals . . . . . . . . . . . . . . . . . . . . 54 2.4.2 Performance of DQPSK Signals . . . . . . . . . . . . . . . . . . . 59 2.4.3 Experimental Veri‾cation . . . . . . . . . . . . . . . . . . . . . . 65 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.A Appendix: Phase Distribution of Gaussian Random Variables . . . . . . 70 3 Nonlinear Phase Noise and IFWM for RZ-DPSK Signals 73 3.1 Pulse Overlap in Dispersive Fiber . . . . . . . . . . . . . . . . . . . . . . 75 3.2 Introduction to Intrachannel Four-Wave Mixing . . . . . . . . . . . . . . 78 3.3 Nonlinear Phase Noise for RZ Pulses . . . . . . . . . . . . . . . . . . . . 81 3.4 Temporal Pro‾le of Nonlinear Phase Noise . . . . . . . . . . . . . . . . . 88 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.A Appendix: Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.A.1 Time-Dependent Variance for ISPM . . . . . . . . . . . . . . . . . 94 3.A.2 Time-Dependent Variance for IXPM . . . . . . . . . . . . . . . . 96 4 XPM Induced Crosstalk for RZ-DPSK Signals 99 4.1 XPM from Overlapped RZ-DPSK Pulses . . . . . . . . . . . . . . . . . . 100 4.2 Numerical Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 103 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.A Appendix: Crosstalk Spectrum from Overlapped Pulses . . . . . . . . . . 108 5 Soliton DPSK Transmission 113 5.1 Phase Statistics of the Soliton . . . . . . . . . . . . . . . . . . . . . . . . 115 5.1.1 Perturbation of the Soliton . . . . . . . . . . . . . . . . . . . . . . 115 5.1.2 Gordon-Mollenauer Effect . . . . . . . . . . . . . . . . . . . . . . 117 5.1.3 Timing and Frequency Effect . . . . . . . . . . . . . . . . . . . . 119 5.1.4 Linear Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.2 Error Probability of DPSK Soliton Signal . . . . . . . . . . . . . . . . . . 122 5.2.1 Gaussian Linear Phase Model . . . . . . . . . . . . . . . . . . . . 123 5.2.2 Independent model . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.2.3 Exact Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6 Time-Resolved Optical Filtering 139 6.1 Introduction to Time-Frequency Analysis . . . . . . . . . . . . . . . . . . 140 6.1.1 A Need for Time-Frequency Analysis: Example of Laser Chirp . . 141 6.1.2 Short-Time Fourier Transform and Spectrogram . . . . . . . . . . 144 6.1.3 Inversion Theory of Spectrogram . . . . . . . . . . . . . . . . . . 146 6.2 Spectrogram Measurement Techniques . . . . . . . . . . . . . . . . . . . 147 6.2.1 FROG and TROF . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.2.2 Simulated TROF Trace for DPSK signals . . . . . . . . . . . . . . 150 6.3 TROF Measurements Setup for DPSK signals . . . . . . . . . . . . . . . 153 6.4 Optical Narrow-Band Filter Characterization . . . . . . . . . . . . . . . . 156 6.4.1 Operation Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.5 Measurement Results and Discussions . . . . . . . . . . . . . . . . . . . . 163 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 6.A Appendix: Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 6.A.1 Inversion of Spectrogram . . . . . . . . . . . . . . . . . . . . . . . 170 6.A.2 Inversion of Sonogram . . . . . . . . . . . . . . . . . . . . . . . . 171 6.A.3 Relation between Spectrogram and Sonogram . . . . . . . . . . . 172 7 TROF Measured Dispersive Electric Field 175 7.1 TROF Measurement of Dispersive DPSK Signals . . . . . . . . . . . . . 176 7.1.1 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 176 7.1.2 Conjugate Gradient Method for Optimization . . . . . . . . . . . 179 7.2 Chromatic Dispersion-Induced Penalty to (D)PSK Signals . . . . . . . . 183 7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 7.A Appendix: Theory of TROF for Periodic Signals . . . . . . . . . . . . . . 188 8 Conclusions 191 Bibliography 195 Addendum 2094430947 bytesapplication/pdfen-US差分相位調變非線性向位雜訊時頻分析DPSKNonlinear Phase NoiseTime-Frequency Analysisthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/58785/1/ntu-95-F92942074-1.pdf