Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on Information Theor

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

This paper starts by an investigation of nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting a rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate a reference case where linear coupling among the spatial modes of the fiber is weak and after averaging over birefringence fluctuations, we obtain new Manakov equations for multimode fibers. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms average out. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We then verify the accuracy of our new Manakov equations by transmitting multiple PDM-QPSK signals over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equation. The agreement is excellent in all cases studied. A great benefit of the new equations is to reduce the computation time by a factor of 10 or more. Another important feature observed is that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. Finally multimode fibers with strong random coupling among all spatial modes are considered. Linear coupling is modeled using the random matrix theory approach. We derive new Manakov equations for multimode fibers in that regime and show that such fibers can perform better than single-modes fiber for large number of propagating spatial modes.Comment: Submitted to journal of lightwave technology on the 17-Jul-2012. Ref number: JLT-14391-201

Analysis of inter-core cross-gain modulation in cladding pumped multi-core fiber amplifiers

We numerically investigate pump-induced gain variations in eight-core fi ber amplifi ers. We compare two fi bers with different erbium profi les by varying input power from -25 dBm to 0 dBm in one or four cores. Inter-core cross-gain modulation is < 0.6 dB

Modeling and characterization of cladding-pumped erbium-ytterbium co-doped fibers for amplification in communication systems

Cladding-pumped optical fiber amplifiers are of increased interest in the context of space-division multiplexing but are known to suffer from low power efficiency. In this context, ytterbium (Yb) co-doping can be an attractive solution to improve the performance of erbium (Er) doped fiber amplifiers. We present a detailed direct comparison between Er/Yb-co-doping and Er-doping using numerical simulations validated by experimental results. Two double-cladding fibers, one doped with Er only and the other one co-doped with Er and Yb, were designed, fabricated and characterized. Using the experimentally extracted parameters, we simulate multi-core fiber amplifiers and investigate the interest of Er/Yb-co-doping. We calculate the minimum gain of the amplifiers over a 35-nm spectral window considering various scenarios

Demonstration of an erbium-doped fiber with annular doping for low gain compression in cladding-pumped amplifiers

We present the design and characterization of a cladding-pumped amplifier with erbium doping located in an annular region near the core. This erbium-doped fiber is proposed to reduce gain saturation, leading to smaller gain compression when compared to uniform core doping. Through numerical simulations, we first compare the performance of three fibers with different erbium doping profiles in the core or the cladding. When the doped fibers are operated at the optimum length, results show that the smaller overlap of the signal mode field with the annular erbium doping region leads to higher gain and lower saturation of the amplifier. A single-core erbium-doped fiber with an annular doping and a D-shaped cladding was fabricated. Measurements demonstrate less than 4 dB of gain compression over the C-band for input power ranging from −40 dBm to 3 dBm. Small gain compression EDFAs are of interest for applications that require input channel reconfiguration. Higher gain and saturation output power are also key issues in cladding-pumped multi-core amplifiers

Integrated cladding-pumped multicore few-mode erbium-doped fibre amplifier for space-division-multiplexed communications

Space-division multiplexing (SDM), whereby multiple spatial channels in multimode1 and multicore2 optical fibres are used to increase the total transmission capacity per fibre, is being investigated to avert a data capacity crunch3,4 and reduce the cost per transmitted bit. With the number of channels employed in SDM transmission experiments continuing to rise, there is a requirement for integrated SDM components that are scalable. Here, we demonstrate a cladding-pumped SDM erbium-doped fibre amplifier (EDFA) that consists of six uncoupled multimode erbium-doped cores. Each core supports three spatial modes, which enables the EDFA to amplify a total of 18 spatial channels (six cores × three modes) simultaneously with a single pump diode and a complexity similar to a single-mode EDFA. The amplifier delivers >20 dBm total output power per core and <7 dB noise figure over the C-band. This cladding-pumped EDFA enables combined space-division and wavelength-division multiplexed transmission over multiple multimode fibre spans

Preface to the special issue on next-generation multiplexing schemes in fiber-based systems

Since the beginning of optical communications in the late 70s, capacity has kept up with the exponential growth of traffic demand. This has been enabled by many technologies among which the most up-to-date wavelength multiplexing combined with coherent detection of polarized-multiplexed quadrature-amplitude-modulated signals. There is, however, a growing realization that this might no longer be sufficient and that next-generation multiplexing schemes are needed to avoid an imminent capacity crunch.Spatial multiplexing, introduced more than 3 decades ago, appears today as the last degree of freedom that can offer multiple orders of magnitude of capacity growth required to sustain the traffic demand. The potential of spatial multiplexing lies in its ability to exploit multiple cores and/or multiple modes within a single optical fiber. Since 2011 and new promising demonstrations, impressive progresses have been made. New optical fibers, components and subsystems have been developed, and record-capacity transmissions have been demonstrated. Significant efforts have also been spent to turn these research results into practical solutions.This special issue features the state-of-the-art research activities in spatial multiplexing. 13 distinguished researchers and their colleagues were invited to contribute with overviews of the latest advances in their research fields. These invited papers can be categorized into 3 groups as follows:• Optical fibers: few-mode, multi-core, and few-mode multi-core fibers.• Components and connectivity: amplifiers, (de-)multiplexers, and splicing• Systems: high-capacity transmissions, and passive optical networks.We hope that this collection will provide the readers with an in-depth overview of the most recent trends in spatial multiplexing schemes in fiber-based systems and stimulate further advances in this renewed field.Finally, we would like to thank all of the authors for their invaluable contributions, and Bertrand Desthieux, Editor-in-Chief, for encouraging and promoting this special issue