René-Jean Essiambre

Advanced Optical Modulation Formats

Fiber-optic communication systems form the high-capacity transport infrastructure that enables global broadband data services and advanced Internet applications. The desire for higher per-fiber transport capacities and, at the same time, the drive for lower costs per end-to-end transmitted information bit has led to optically routed networks with high spectral efficiencies. Among other enabling technologies, advanced optical modulation formats have become key to the design of modern wavelength division multiplexed (WDM) fiber systems. In this paper, we review optical modulation formats in the broader context of optically routed WDM networks. We discuss the generation and detection of multigigabit/s intensity- and phase-modulated formats, and highlight their resilience to key impairments found in optical networking, such as optical amplifier noise, multipath interference, chromatic dispersion, polarization-mode dispersion, WDM crosstalk, concatenated optical filtering, and fiber nonlinearity

Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6

We report simultaneous transmission of six spatial and polarization modes, each carrying 40 Gb/s quadrature-phase-shift-keyed channels over 96 km of a low-differential group delay few-mode fiber. The channels are successfully recovered by offline DSP based on coherent detection and multiple-input multiple-output processing. A penalty of <;1.2 dB is achieved by using 6 × 6 feed-forward equalizers with 120 taps each. The 6 × 6 impulse-response matrix fully characterizing the few-mode fiber is presented, revealing the coupling characteristics between the modes. The results are obtained using mode multiplexers based on phase plates with a mode selectivity of >;28 dB.

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Advanced optical modulation formats have become a key ingredient to the design of modern wavelength-division-multiplexed (WDM) optically routed networks. In this paper, we review the generation and detection of multigigabit/second intensity- and phase-modulated formats and highlight their resilience to key impairments found in optical networking, such as optical amplifier noise, chromatic dispersion, polarization-mode dispersion, WDM crosstalk, concatenated optical filtering, and fiber nonlinearity

6 MIMO Processing

Mode-division multiplexing over 33-km few-mode fiber is investigated. It is shown that 6×6 MIMO processing can be used to almost completely compensate for crosstalk and intersymbol interference due to mode coupling in a system that transmits uncorrelated 28-GBaud QPSK signals on the six spatial and polarization modes supported by a novel few-mode fiber.

Advanced Modulation Formats for High-Capacity Optical Transport Networks

Since the first deployments of fiber-optic communication systems three decades ago, the capacity carried by a single-mode optical fiber has increased by a staggering 10 000 times. Most of the growth occurred in the first two decades with growth slowing to ten times in the last decade. Over the same three decades, network traffic has increased by a much smaller factor of 100, but with most of the growth occurring in the last few years, when data started dominating network traffic. At the current growth rate, the next factor of 100 in network traffic growth will occur within a decade. The large difference in growth rates between the delivered fiber capacity and the traffic demand is expected to create a capacity shortage within a decade. The first part of the paper recounts the history of traffic and capacity growth and extrapolations for the future. The second part looks into the technological challenges of growing the capacity of single-mode fibers by presenting a capacity limit estimate of standard and advanced single-mode optical fibers. The third part presents elementary capacity considerations for transmission over multiple transmission modes and how it compares to a single-mode transmission. Finally, the last part of the paper discusses fibers supporting multiple spatial modes, including multimode and multicore fibers, and the role of digital processing techniques. Spatial multiplexing in fibers is expected to enable system capacity growth to match traffic growth in the next decades.

6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization

In this paper, we develop a general first-order perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity, valid for arbitrary pulse shapes. We obtain a general expression of the sampled signal after optical filtering, coherent detection, and optimal sampling. We include intrachannel and as well as interchannel nonlinear effects. We obtain simplified expressions in the case in which the accumulated dispersion is high (equivalent to the far-field limit in paraxial optics). This general theory is applied in detail to the special case of spectral-efficient sinc pulses. This exercise shows that the characteristics of the neighboring wavelength-division multiplexed channels are essential in determining the nonlinear impairments.

Capacity Trends and Limits of Optical Communication Networks

We demonstrate the transmission of 6 independent, spatially- and polarization multiplexed 28-Gb/s QPSK signals over 10 km of three-mode fiber using mode-selective excitation and full coherent 6 × 6 MIMO processing.

Nonlinear Shannon Limit in Pseudolinear Coherent Systems

We investigate theoretically nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate the case where linear coupling among spatial modes of the fiber is weak and derive new Manakov equations after averaging over random birefringence fluctuations. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms vanish. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We verify the accuracy of new Manakov equations by simulating the transmission of multiple 114-Gb/s bit streams in the PDM-QPSK format over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equations. The agreement is excellent in all cases studied. A major benefit of the new Manakov equations is that they typically reduce the computation time by more than a factor of 10. Our results show that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. The extent of improvement depends on the fiber design and how many spatial modes are used for SDM transmission. We also consider the case where all spatial modes experience strong random linear coupling modeled using a random matrix. We derive new Manakov equations in this regime and show that the impact of some nonlinear effects can be reduced relatively to single-modes fibers. Finally, we extend our analysis to multicore fibers and show that the Manakov equations obtained in the strong- and weak-coupling regimes can still be used depending on the extent of coupling among fiber cores.

Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing

Publisher Summary The pseudo–linear transmission is a method for the transmission of high-speed time-division multiplexed (TDM) signals where fast variations of each channel waveform with cumulative dispersion allows important averaging of the intrachannel effects of fiber nonlinearity. The pseudo–linear transmission involves complex optimization of modulation format, dispersion mapping, and nonlinearity. These transmissions occupy a space somewhere between dispersion-mapped linear transmission and nonlinear soliton transmission. The pseudo-linear regime of transmission is characterized by a rapid pulse broadening, which results in a dramatic reduction of the solitonic effect on each pulse. As a result, full dispersion compensation can be used in this regime. Extensive analysis of pseudo-linear transmission and reviews of the TDM transmission experiments at 40 and 160 Gb/s have been provided in the chapter. Two new forms of nonlinear interactions between rapidly dispersing pulses namely intrachannel cross–phase modulation (IXPM) and intrachannel four–wave mixing (IFWM) are also presented. These two intrachannel effects are the most important nonlinear interactions in pseudo-linear transmission and determine the dispersion mapping even for the wavelength–division multiplexed (WDM) systems. Further, the chapter describes the semiconductor–based technologies that enable the development of stable and reliable high–speed transmitters and receivers.Publisher Summary The pseudo–linear transmission is a method for the transmission of high-speed time-division multiplexed (TDM) signals where fast variations of each channel waveform with cumulative dispersion allows important averaging of the intrachannel effects of fiber nonlinearity. The pseudo–linear transmission involves complex optimization of modulation format, dispersion mapping, and nonlinearity. These transmissions occupy a space somewhere between dispersion-mapped linear transmission and nonlinear soliton transmission. The pseudo-linear regime of transmission is characterized by a rapid pulse broadening, which results in a dramatic reduction of the solitonic effect on each pulse. As a result, full dispersion compensation can be used in this regime. Extensive analysis of pseudo-linear transmission and reviews of the TDM transmission experiments at 40 and 160 Gb/s have been provided in the chapter. Two new forms of nonlinear interactions between rapidly dispersing pulses namely intrachannel cross–phase modulation (IXPM) and intrachannel four–wave mixing (IFWM) are also presented. These two intrachannel effects are the most important nonlinear interactions in pseudo-linear transmission and determine the dispersion mapping even for the wavelength–division multiplexed (WDM) systems. Further, the chapter describes the semiconductor–based technologies that enable the development of stable and reliable high–speed transmitters and receivers.

Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations

Optimum pumping schemes for bidirectionally pumped distributed fiber amplifiers are evaluated that simultaneously minimize the beat noise between signal and amplified spontaneous emission, as well as between signal and double Rayleigh backscattering. A way of adding a constraint on signal power to describe operation in a strong Kerr fiber nonlinearity regime is included. We show that one can find an optimum Raman net gain, as well as a percentage of forward to total Raman pumping maximizing the signal-to-noise ratio at the end of a transmission line using bidirectionally Raman-pumped transmission fibers.