Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Periodic nonlinear Fourier transform for fiber-optic communications, Part II:eigenvalue communication

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.

Capacity estimates for optical transmission based on the nonlinear Fourier transform

What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.

The analysis of organic matter in oil-shales

The organic matter in five oil shales (three from the Kimmeridge Clay sequence, one from the Oxford Clay sequence and one from the Julia Creek deposits in Australia) has been isolated by acid demineralisation, separated into kerogens and bitumens by solvent extraction and then characterised in some detail by chromatographic, spectroscopic and degradative techniques. Kerogens cannot be characterised as easily as bitumens because of their insolubility, and hence before any detailed molecular information can be obtained from them they must be degraded into lower molecular weight, more soluble components. Unfortunately, the determination of kerogen structures has all too often involved degradations that were far too harsh and which lead to destruction of much of the structural information. For this reason a number of milder more selective degradative procedures have been tested and used to probe the structure of kerogens. These are: 1. Lithium aluminium hydride reduction. - This procedure is commonly used to remove pyrite from kerogens and it may also increase their solubility by reduction of labile functional groups. Although reduction of the kerogens was confirmed, increases in solubility were correlated with pyrite content and not kerogen reduction. 2. O-methylation in the presence of a phase transfer catalyst. - By the removal of hydrogen bond interactions via O-methylation, it was possible to determine the contribution of such secondary interactions to the insolubility of the kerogens. Problems were encountered with the use of the phase transfer catalyst. 3. Stepwise alkaline potassium permanganate oxidation. - Significant kerogen dissolution was achieved using this procedure but uncontrolled oxidation of initial oxidation products proved to be a problem. A comparison with the peroxytrifluoroaceticacid oxidation of these kerogens was made. 4. Peroxytrifluoroacetic acid oxidation. - This was used because it preferentially degrades aromatic rings whilst leaving any benzylic positions intact. Considerable conversion of the kerogens into soluble products was achieved with this procedure. At all stages of degradation the products were fully characterised where possible using a variety of techniques including elemental analysis, solution state 1H and 13C nuclear magnetic resonance, solid state 13C nuclear magnetic resonance, gel-permeationchromatography, gas chromatography-mass spectroscopy, fourier transform infra-red spectroscopy and some ultra violet-visible spectroscopy.