Analyse des Solitonengehaltes von optischen Impulsen in Glasfasern

Der Solitonengehalt von Lichtimpulsen in einer Glasfaser wird untersucht. Dabei wird ein neu entwickeltes Verfahren angewendet, welches auf der spektralen Analyse der Schwebunsstrukturen beruht. Dieses Verfahren ist in der Lage, den allemeinen Solitonengehalt zu bestimmen, sogar für nichtintegrable Systeme. Dies war bisher nur Näherungsweise möglich. Aus der vorgestellten Analyse wird ein Messprinzip abgeleitet, mit dem sich der Solitonengehalt bestimmen lässt. Dies wird anhand einer Beispielmessung demonstriert

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201

Vector-soliton collision dynamics in nonlinear optical fibers

We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schroedinger equations. We study a low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and also studied by Tan and Yang. We derive a further simplified model which has similar dynamics but is more amenable to analysis. Sufficiently fast solitons move by each other without much interaction, but below a critical velocity the solitons may be captured. In certain bands of initial velocities the solitons are initially captured, but separate after passing each other twice, a phenomenon known as the two-bounce or two-pass resonance. We derive an analytic formula for the critical velocity. Using matched asymptotic expansions for separatrix crossing, we determine the location of these "resonance windows." Numerical simulations of the ODE models show they compare quite well with the asymptotic theory.Comment: 32 pages, submitted to Physical Review

Advanced optical fibre communication via nonlinear Fourier transform

Optical fibre communication using the Nonlinear Fourier transform (NFT) is one of the potential solutions to tackle the so-called capacity crunch problem in long-haul optical fibre networks. The NFT transforms the nonlinear propagation of temporal signal, governed by the nonlinear Schr¨odinger equation (NLSE), into simple linear evolutions of continuous and discrete spectra in the so-called nonlinear spectral domain. These spectra and the corresponding nonlinear spectral domain, defined by the NFT, are the generalized counterparts of the linear spectrum and frequency domain defined by the ordinary Fourier transform. Using the NFT, the optical fibre channel is effectively linearised, and the basic idea is to utilize degrees of freedom in the nonlinear spectral domain for data transmission. However, many aspects of this concept require rigorous investigation due to complexity and infancy of the approach. In this thesis, the aim is to provide a comprehensive investigation of data transmission over mainly the continues spectrum (CS) and partly over of the discrete spectrum (DS) of nonlinear optical fibres. First, an optical fibre communication system is defined, in which solely the CS carries the information. A noise model in the nonlinear spectral domain is derived for such a system by asymptotic analysis as well as extensive simulations for different scenarios of practical interest. It is demonstrated that the noise added to the signal in CS is severely signal-dependent such that the effective signalling space is limited. The variance normalizing transform (VNT) is used to mathematically verify the limits of signalling spaces and also estimate the channel capacity. The numerical results predict a remarkable capacity for signalling only on the CS (e.g., 6 bits/symbol for a 2000-km link), yet it is demonstrated that the capacity saturates at high power. Next, the broadening effect of chromatic dispersion is analysed, and it is confirmed that some system parameters, such as symbol rate in the nonlinear spectral domain, can be optimized so that the required temporal guard interval between the subsequently transmitted data packets is minimized, and thus the effective data rate is significantly enhanced. Furthermore, three modified signalling techniques are proposed and analysed based on the particular statistics of the noise added to the CS. All proposed methods display improved performance in terms of error rate and reach distance. For instance, using one of the proposed techniques and optimized parameters, a 7100-km distance can be reached by signalling on the CS at a rate of 9.6 Gbps. Furthermore, the impact of polarization mode dispersion (PMD) is examined for the first time, as an inevitable impairment in long-haul optical fibre links. By semi-analytical and numerical investigation, it is demonstrated that the PMD affects the CS by causing signal-dependent phase shift and noise-like errors. It is also verified that the noise is still the dominant cause of performance degradation, yet the effect of PMD should not be neglected in the analysis of NFT-based systems. Finally, the capacity of soliton communication with amplitude modulation (part of the degrees of freedom of DS) is also estimated using VNT. For the first time, the practical constraints, such as the restricted signalling space due to limited bandwidth, are included in this capacity analysis. Furthermore, the achievable data rates are estimated by considering an appropriately defined guard time between soliton pulses. Moreover, the possibility of transmitting data on DS accompanied by an independent CS signalling is also validated, which confirms the potentials of the NFT approach for combating the capacity crunch

Optical Transmission Systems based on the Nonlinear Fourier Transformation

Solitons are stable pulse shapes, which propagate linearly and maintain their shape despite the highly nonlinear fiber optical channel. A challenge in the use of these signal pulses in optical data transmission is to multiplex them with high efficiency. One way to multiplex many solitons is the nonlinear Fourier transform (NFT). With the help of the NFT, signal spectra can be calculated which propagate linearly through a nonlinear channel. Thus, in perspective, it is possible to perform linear transmissions even in highly nonlinear regions with high signal power levels. The NFT decomposes a signal into a dispersive and a solitonic part. The dispersive part is similar to spectra of the conventional linear Fourier transform and dominates especially at low signal powers. As soon as the total power of a signal exceeds a certain limit, solitons arise. A disadvantage of solitons generated digitally by the NFT is their complex shape due to, for example, high electrical bandwidths or a poor peak-to-average power ratio. In the course of this work, a scalable system architecture of a photonic integrated circuit based on a silicon chip was designed, which allows to multiplex several simple solitons tightly together to push the complex electrical generation of higher order solitons into the optical domain. This photonic integrated circuit was subsequently designed and fabricated by the Institute of Integrated Photonics at RWTH Aachen University. Using this novel system architecture and additional equalization concepts designed in this work, soliton transmissions with up to four channels could be successfully realized over more than 5000 km with a very high spectral efficiency of 0.5 b/s/Hz in the soliton range

High-amplitude, ultrashort strain solitons in solids

In recent years, pressure pulses of very short (picosecond) time duration have found wide application as a diagnostic tool in the semiconductor industry and in fundamental condensed matter research. Next to their application in the studies of nanometer-sized structures, propagation of these short acoustic pulses over millimeter distances at low temperatures has revealed a new field of picosecond acoustics. It has been shown that, for very short strain pulses, phonon dispersion destroys the internal structure of the coherent wavepacket by pulling apart its different frequency components. However, when strain amplitudes are sufficiently increased, a nonlinear pulse-steepening mechanism emerges, that leads to the formation of shock waves. The combined action of the nonlinear and dispersive effects then results in the formation of stable, highly localized solitary waves. In this thesis, we study the development of picosecond pressure pulses into trains of ultrashort acoustic solitons in a bulk crystal. The high-amplitude, bipolar strain wavepackets are generated by femtosecond optical excitation of a thin chromium film evaporated onto the crystal, using high-power optical pulses from an amplified Ti:sapphire laser. Propagation over millimeter distances at low temperatures is studied by means of two complementary experimental methods. First, the development of low-frequency, gigahertz strain components is monitored using Brillouin light-scattering. By monitoring the scattered intensity against traveled distance of the packets, we demonstrate the breakup of the initial single-cycle pulse into an ultrashort acoustic soliton train, reaching transient pressures up to tens of kilobars and soliton widths less than 0.5 picoseconds, corresponding to only several nanometers in the crystal. Further, we show that the ultrashort strain solitons interact coherently with local electronic two-level systems at terahertz frequency, in optically excited ruby. The strain-induced electronic population can be monitored using the well-known R1- and R2-luminescence lines of the excited Cr3+ impurity-ions in the ruby crystal. Coherent manipulation, and even amplification, of terahertz strain wavepackets using an electronic two-level medium appears well within reach. Finally, we present a novel picosecond ultrasonics setup based on our low-repetition laser system and demonstrate its operation by determining the initial shape of the acoustic wavepacket in the chromium transducer

On nonlinear Fourier transform-based fibre-optic communication systems for periodic signals

As the demand for information rate grows on a daily basis, new ways of improving the efficiency of fibre-optic communication systems, the backbone of the global data network,are highly anticipated. Nonlinear Fourier transform (NFT) is one of the newly emerged techniques showing promising results in recent studies both in simulation and experiment. Along this path, this method has shown its potential to overcome some difficulties of the fibre-optic communication regarding nonlinear distortions, especially the crosstalk between the user’s bands in wavelength division multiplexing (WDM) systems. NFT-based systems, however, in the conventional, widely considered case of vanishing boundary signals, have exhibited some drawbacks related to the computational complexity and spectral efficiency. Both problems are the direct consequences of large signal duration ensued from the vanishing boundary condition. Considering periodic solutions to the nonlinear Schrödinger equation is among attempts to solve this problem. It helps to decrease the processing window at the receiver and gives full control over the communication-related parameters of the signal. Periodic NFT (PNFT) can also be implemented through fast numerical methods which makes it yet more appealing. In this thesis, a general framework to implement PNFT in fibre-optic communication systems is proposed. As the most challenging part of such a system, the inverse transformation stage is particularly taken attention to, and a few ways to perform it are put forward. From the simplest signals with analytically known nonlinear spectrum to a complete periodic solution with arbitrary, finite number of degrees of freedom, several system configurations are conferred and evaluated in terms of their performance. Common measures such as bit error rate, quality factor and mutual information are considered in scrutinising the systems.Based on simulation results, we conclude that the PNFT can, in fact, improve the mutual information by overcoming some shortcomings of the vanishing boundary NFT

Publications of the Jet Propulsion Laboratory, January through December 1974

Formalized technical reporting is described and indexed, which resulted from scientific and engineering work performed, or managed, by the Jet Propulsion Laboratory. The five classes of publications included are technical reports, technical memorandums, articles from the bimonthly Deep Space Network Progress Report, special publications, and articles published in the open literature. The publications are indexed by author, subject, and publication type and number