On the theory of autosoliton propagation in optical fibers guided by in-line nonlinear devices

A theoretical model is developed to describe the propagation of ultra-short optical pulses in fiber transmission systems in the quasi-linear regime, with periodically inserted in-line lumped nonlinear optical devices. Stable autosoliton solutions are obtained for a particular application of the general theory.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Impact of inter-modal four-wave mixing on the performance of mode- and wavelength-division-multiplexing systems

In this paper, we investigate the impact of inter-modal four-wave mixing on mode- and wavelength-division-multiplexing systems. A set of coupled nonlinear Schrödinger equations, including linear mode coupling, is derived allowing to isolate the inter-modal four-wave mixing terms. The efficiency of inter-modal four-wave mixing between degenerate LP modes is found to be significantly higher than the intra-modal four-wave mixing efficiency. However, it is shown that the inter-modal four-wave mixing efficiency between degenerate modes is significantly reduced by the linear mode coupling.

Eigenvalue communications in nonlinear fiber channels

Continuous progress in optical communication technology and corresponding increasing data rates in core fiber communication systems are stimulated by the evergrowing capacity demand due to constantly emerging new bandwidth-hungry services like cloud computing, ultra-high-definition video streams, etc. This demand is pushing the required capacity of optical communication lines close to the theoretical limit of a standard single-mode fiber, which is imposed by Kerr nonlinearity [1–4]. In recent years, there have been extensive efforts in mitigating the detrimental impact of fiber nonlinearity on signal transmission, through various compensation techniques. However, there are still many challenges in applying these methods, because a majority of technologies utilized in the inherently nonlinear fiber communication systems had been originally developed for linear communication channels. Thereby, the application of ”linear techniques” in a fiber communication systems is inevitably limited by the nonlinear properties of the fiber medium. The quest for the optimal design of a nonlinear transmission channels, development of nonlinear communication technqiues and the usage of nonlinearity in a“constructive” way have occupied researchers for quite a long time.

Control of cascaded DC-DC converter based hybrid battery energy storage systems - Part II:Lyapunov approach

A cascaded DC-DC boost converter is one of the ways to integrate hybrid battery types within a grid-tie inverter. Due to the presence of different battery parameters within the system such as, state-of-charge and/or capacity, a module based distributed power sharing strategy may be used. To implement this sharing strategy, the desired control reference for each module voltage/current control loop needs to be dynamically varied according to these battery parameters. This can cause stability problem within the cascaded converters due to relative battery parameter variations when using the conventional PI control approach. This paper proposes a new control method based on Lyapunov Functions to eliminate this issue. The proposed solution provides a global asymptotic stability at a module level avoiding any instability issue due to parameter variations. A detailed analysis and design of the nonlinear control structure are presented under the distributed sharing control. At last thorough experimental investigations are shown to prove the effectiveness of the proposed control under grid-tie conditions.

Modified nonlinear inverse synthesis for optical links with distributed Raman amplification

We propose a modification of the nonlinear digital signal processing technique based on the nonlinear inverse synthesis for the systems with distributed Raman amplification. The proposed path-average approach offers 3 dB performance gain, regardless of the signal power profile.

Demonstration of nonlinear inverse synthesis transmission over transoceanic distances

Nonlinear Fourier transform (NFT) and eigenvalue communication with the use of nonlinear signal spectrum (both discrete and continuous), have been recently discussed as promising transmission methods to combat fiber nonlinearity impairments. In this paper, for the first time, we demonstrate the generation, detection and transmission performance over transoceanic distances of 10 Gbaud and nonlinear inverse synthesis (NIS) based signal (4 Gb/s line rate), in which the transmitted information is encoded directly onto the continuous part of the signal nonlinear spectrum. By applying effective digital signal processing techniques, a reach of 7344 km was achieved with a bit-error-rate (BER) (2.1×10-2) below the 20% FEC threshold. This represents an improvement by a factor of ~12 in data capacity x distance product compared with other previously demonstrated NFT-based systems, showing a significant advance in the active research area of NFT-based communication systems.

PMD tolerant nonlinear compensation using in-line phase conjugation

In this paper, we numerically investigate the impact of polarisation mode dispersion on the efficiency of compensation of nonlinear transmission penalties for systems employing one of more inline phase conjugation devices. We will show that reducing the spacing between phase conjugations allows for significantly improved performance in the presence polarisation mode dispersion or a significant relaxation in the acceptable level of polarization mode dispersion. We show that these results are consistent with previously presented full statistical analysis of nonlinear transmission appropriately adjusted for the reduced section length undergoing compensation.

Upgrading legacy long-haul WDM systems through unbalancing the proportion of 1s and 0s in the transmitted data

We present experimental results for wavelength-division multiplexed (WDM) transmission performance using unbalanced proportions of 1s and 0s in pseudo-random bit sequence (PRBS) data. This investigation simulates the effect of local, in time, data unbalancing which occurs in some coding systems such as forward error correction when extra bits are added to the WDM data stream. We show that such local unbalancing, which would practically give a time-dependent error-rate, can be employed to improve the legacy long-haul WDM system performance if the system is allowed to operate in the nonlinear power region. We use a recirculating loop to simulate a long-haul fibre system.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

First experimental demonstration of nonlinear inverse synthesis transmission over transoceanic distances

We demonstrate for the first time, the transmission performance of 10Gbaud nonlinear inverse synthesis based signal over transoceanic distances, showing a significant improvement in data capacity x distance product (x12) compared with other NFT-based systems.

Stable optical vortices in nonlinear multicore fibers

The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF.

Raman fibre laser based amplification in coherent transmission systems

The thesis presents a detailed study of different Raman fibre laser (RFL) based amplification techniques and their applications in long-haul/unrepeatered coherent transmission systems. RFL based amplifications techniques were characterised from different aspects, including signal/noise power distributions, relative intensity noise (RIN), mode structures of induced Raman fibre lasers, and so on. It was found for the first time that RFL based amplification techniques could be divided into three categories in terms of the fibre laser regime, which were Fabry-Perot fibre laser with two FBGs, weak Fabry-Perot fibre laser with one FBG and very low reflection near the input, and random distributed feedback (DFB) fibre laser with one FBG. It was also found that lowering the reflection near the input could mitigate the RIN of the signal significantly, thanks to the reduced efficiency of the Stokes shift from the FW-propagated pump. In order to evaluate the transmission performance, different RFL based amplifiers were evaluated and optimised in long-haul coherent transmission systems. The results showed that Fabry-Perot fibre laser based amplifier with two FBGs gave >4.15 dB Q factor penalty using symmetrical bidirectional pumping, as the RIN of the signal was increased significantly. However, random distributed feedback fibre laser based amplifier with one FBG could mitigate the RIN of the signal, which enabled the use of bidirectional second order pumping and consequently give the best transmission performance up to 7915 km. Furthermore, using random DFB fibre laser based amplifier was proved to be effective to combat the nonlinear impairment, and the maximum reach was enhanced by >28% in mid-link single/dual band optical phase conjugator (OPC) transmission systems. In addition, unrepeatered transmission over >350 km fibre length using RFL based amplification technique were presented experimentally using DP-QPSK and DP-16QAM transmitter.