Countering the optical network ‘capacity crunch’ calls for a radical development in optical fibres that could simultaneously minimize nonlinearity penalties, chromatic dispersion and maximize signal launch power. Hollow-core fibres (HCF) can break the nonlinear Shannon limit of solid-core fibre and fulfil all above requirements, but its optical performance need to be significantly upgraded before they can be considered for high-capacity telecommunication systems. Here, we report a new HCF with conjoined-tubes in the cladding and a negative-curvature core shape. It exhibits a minimum transmission loss of 2 dB km−1 at 1512 nm and a <16 dB km−1 bandwidth spanning across the O, E, S, C, L telecom bands (1302–1637 nm). The debut of this conjoined-tube HCF, with combined merits of ultralow loss, broad bandwidth, low bending loss, high mode quality and simple structure heralds a new opportunity to fully unleash the potential of HCF in telecommunication applications. Countering the optical network ‘capacity crunch’ requires developments in optical fibres. Here, the authors report a hollow-core fibre with conjoined tubes in the cladding and a negative-curvature core shape. It exhibits a transmission loss of 2 dB/km at 1512 nm and less than 16 dB/km bandwidth in the 1302–1637 nm range.

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Hollow-core conjoined-tube negative-curvature fibre with ultralow loss.

We consider the communication channel given by a fiber optical transmission line. We develop a method to perturbatively calculate the information capacity of a nonlinear channel, given the corresponding evolution equation. Using this technique, we compute the decrease of the channel capacity to the leading order in the perturbative parameter for fiber optics communication systems.

https://arxiv.org/pdf/physics/0007033.pdf

The Channel Capacity of a Fiber Optics Communication System: perturbation theory

We introduce for the first time the utilization of Long short-term memory (LSTM) neural network architectures for the compensation of fiber nonlinearities in digital coherent systems. We conduct numerical simulations considering either C-band or O-band transmission systems for single channel and multi-channel 16-QAM modulation format with polarization multiplexing. A detailed analysis regarding the effect of the number of hidden units and the length of the word of symbols that trains the LSTM algorithm and corresponds to the considered channel memory is conducted in order to reveal the limits of LSTM based receiver with respect to performance and complexity. The numerical results show that LSTM Neural Networks can be very efficient as post processors of optical receivers which classify data that have undergone non-linear impairments in fiber and provide superior performance compared to digital back propagation, especially in the multi-channel transmission scenario. The complexity analysis shows that LSTM becomes more complex as the number of hidden units and the channel memory increase, however LSTM can be less complex than Digital Back Propagation in long distances (>1000 km).

Compensation of Fiber Nonlinearities in Digital Coherent Systems Leveraging Long Short-Term Memory Neural Networks

Fiber-induced intra- and interchannel nonlinearities are experimentally tackled using blind nonlinear equalization (NLE) by unsupervised machine-learning-based clustering (MLC) in ∼46-Gb/s single-channel and ∼20-Gb/s (middle-channel) multichannel coherent multicarrier signals (orthogonal frequency-division multiplexing (OFDM) based). To that end, we introduce, for the first time, hierarchical and fuzzy-logic C -means (FLC)-based clustering in optical communications. It is shown that among the two proposed MLC algorithms, FLC reveals the highest performance at optimum launched optical powers (LOPs), while at very high LOPs, hierarchical can compensate more effectively nonlinearities only for low-level modulation formats. When employing binary phase-shift keying and quaternary phase-shift keying, FLC outperforms K-means, fast-Newton support vector machines, supervised artificial neural networks, and NLE with deterministic Volterra analysis. In particular, for the middle channel of a QPSK wavelength-division multiplexing coherent optical OFDM system at optimum −5 dBm of LOP and 3200 km of transmission, FLC outperforms Volterra-NLE by 2.5 dB in Q-factor. However, for a 16-QAM single-channel system at 2000 km, the performance benefit of FLC over inverse Volterra-series transfer function reduces to ∼0.4 dB at a LOP of 2 dBm (optimum). Even when using novel sophisticated clustering designs in 16 clusters, no more than additional ∼0.3-dB Q-factor enhancement is observed. Finally, in contrast to the deterministic Volterra-NLE, MLC algorithms can partially tackle the stochastic parametric noise amplification .

/pdf/blind-nonlinearity-equalization-by-machine-learning-based-1rqpqfi3nb.pdf

Blind Nonlinearity Equalization by Machine-Learning-Based Clustering for Single- and Multichannel Coherent Optical OFDM

A general theory of nonlinear interactions between signal and amplified spontaneous emission noise in wavelength division multiplexed fiber-optic coherent transmission systems is presented. This theory is based on the regular perturbation treatment of the nonlinear Schrodinger equation, which governs the wave propagation in the optical fiber, and is exact up to the first order in the fiber nonlinear coefficient. It takes into account all cross-channel nonlinear four-wave mixing contributions to the total variance of nonlinear distortions, dependency on modulation format, erbium-doped fiber and backward Raman amplification schemes, heterogeneous spans, and chromatic dispersion to all orders; moreover, it is computationally efficient. This theory is used to estimate the impact of the signal-noise interaction on the unmitigated, as well as on the nonlinearity-mitigated systems with ideal multi-channel digital backpropagation, and to study the fundamental limits of zero-forcing nonlinear equalization of the fiber-optic coherent transmission systems.

A Theory of Nonlinear Interactions Between Signal and Amplified Spontaneous Emission Noise in Coherent Wavelength Division Multiplexed Systems

In this paper, we review the historical evolution of predictions of the performance of optical communication systems. We will describe how such predictions were made from the outset of research in laser based optical communications and how they have evolved to their present form, accurately predicting the performance of coherently detected communication systems.

/pdf/performance-limits-in-optical-communications-due-to-fiber-344tg1jov8.pdf

Performance limits in optical communications due to fiber nonlinearity

Compensation of the detrimental impacts of nonlinearity on long haul wavelength division multiplexed system performance is discussed, and the difference between transmitter, receiver and in-line compensation analyzed. The impact of system imperfections is also outlined.

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M. A. Z. Al Khateeb

Papers

Performance limits in optical communications due to fiber nonlinearity

Impact of optical phase conjugation on the nonlinear shannon limit