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

Timing Jitter In Long-haul WDM Return-To-Zero Systems

Die vorgestellte Arbeit faßt Forschungsergebnisse zum stochastischen Zeitversatz (Timing Jitter) in optischen Langstreckensystemen mit Wellenlängenmultiplex (engl. Wavelength Division Multiplexing (WDM)) und Return-to-Zero (RZ) Modulationsformaten zusammen. Es wurden semi-analytische Berechnungstechniken entwickelt und anhand numerischer Methoden validiert, mit deren Hilfe der Timing Jitter bezüglich des optischen Verstärkerrauschens und der Kreuzphasenmodulation (engl. Cross-Phase Modulation (XPM)) bestimmt werden kann. Der Einfluß verschiedener Übertragungsparameter auf die Akkumulation von Timing Jitter wurde untersucht. Ausgehend von aktuellen Trends im Design von WDM Langstreckensystemen sind Entwicklungsüberlegungen zum Aufbau und der generellen Wirkungsweise von optischen Sendern, der optischen Glasfaserstrecke (inklusive optischer Verstärker), und von optischen Empfängern dargelegt, welche typischerweise für die untersuchten Systeme verwendet werden. Es wurden die Zeit- und Frequenzdynamik von sogenannten Dispersion-Managed Solitons (DMS) und gechirpten RZ (engl. Chirped Return-to-Zero (CRZ)) Pulsen betrachtet, da diese Modulationsformate von großer Bedeutung für WDM Langstreckensysteme sind. Eine der bedeutendsten Ergebnisse der vorgelegten Arbeit ist die Vorstellung eines neuen Ansatzes zur Berechnung von Timing Jitter, hervorgerufen durch Kreuzphasenmodulation zwischen optischen RZ Pulsen welche im Wellenlängenmultiplex über Langstreckensysteme übertragen werden, und dessen Abbildung in einen semi-analytischen Algorithmus. Des weiteren wurde ein kürzlich publizierter Ansatz zur Berechnung von Timing Jitter, hervorgerufen durch optisches Verstärkerrauschen, vorgestellt und in einen semi-analytischen Algorithmus abgebildet. Beide Algorithmen wurden in einer gegebenen kommerziellen Softwareumgebung implementiert und validiert. Die wesentlichen Vorteile der beiden vorgestellten semi-analytischen Algorithmen bestehen in der allgemeinen Anwendbarkeit auf beliebige RZ Pulseformen und der Reduzierung des Berechnungsaufwandes um Größenordnungen im Vergleich zu rein numerischen Methoden. Dies ermöglicht systematische Parameteroptimierungen typischer RZ WDM Langstreckensysteme. Es ist z.B. gezeigt worden, dass die Akkumulation von Timing Jitter sehr stark von der örtlichen Position der Dispersionskompensation und der optischen Verstärker abhängig ist. Weitere kritische Systemparameter sind der WDM Kanalabstand, und die zeitliche Position der RZ Pulse im Bitfenster zu Beginn der Übertragung. Abschließend wurde der Einfluß von Timing Jitter auf die Bitfehlerrate (engl. Bit Error Rate (BER)) untersucht. Es wurde gezeigt, dass das Verhalten der betrachteten Systeme durch Timing Jitter dominiert ist und dass BER Schätzmethoden, die auf der Annahme von Gauss-förmigen Amplitudenverteilungen am Entscheider beruhen, stark verfälschte Resultate liefern

Pulse train generation in a distributed gain fibre amplifier.

This work shows the generation of an array of chirped compressed periodic waves with distributed gain in a nonlinear fibre. In particular, with suitable tailoring of the gain to vary along the longitudinal distance while the dispersion and nonlinearity parameters are kept constant. Exact analytical equations using the self-similar analysis technique were obtained to describe this process. In addition, the stability of these generated periodic waves is studied under finite perturbations

Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

We consider a nonlinear Fourier transform (NFT)-based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT-based transmission scheme the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Applications of ultralong Raman fibre lasers in photonics

This thesis presents a numerical and experimental investigation on applications of ultralong Raman fibre lasers in optical communications, supercontinuum generation and soliton transmission. The research work is divided in four main sections. The first involves the numerical investigation of URFL intra-cavity power and the relative intensity noise transfer evolution along the transmission span. The performance of the URFL is compared with amplification systems of similar complexity. In the case of intracavity power evolution, URFL is compared with a first order Raman amplification system. For the RIN transfer investigation, URFL is compared with a bi-directional dual wavelength pumping system. The RIN transfer function is investigated for several cavity design parameters such as span length, pump distribution and FBG reflectivity. The following section deals with experimental results of URFL cavities. The enhancement of the available spectral bandwidth in the C-band and its spectral flatness are investigated for single and multi-FBGs cavity system. Further work regarding extended URFL cavity in combination with Rayleigh scattering as random distributed feedback produced a laser cavity with dual wavelength outputs independent to each other. The last two sections relate to URFL application in supercontinuum (SC) generation and soliton transmission. URFL becomes an enhancement structure for SC generation. This thesis shows successful experimental results of SC generation using conventional single mode optical fibre and pumped with a continuous wave source. The last section is dedicated to soliton transmission and the study of soliton propagation dynamics. The experimental results of exact soliton transmission over multiple soliton periods using conventional single mode fibre are shown in this thesis. The effect of the input signal, pump distribution, span length and FBGs reflectivity on the soliton propagation dynamics is investigated experimentally and numerically

Quasi-lossless data transmission with ultra-long Raman fibre laser based amplification

The project consists of an experimental and numerical modelling study of the applications of ultra-long Raman fibre laser (URFL) based amplification techniques for high-speed multi-wavelength optical communications systems. The research is focused in telecommunications C-band 40 Gb/s transmission data rates with direct and coherent detection. The optical transmission performance of URFL based systems in terms of optical noise, gain bandwidth and gain flatness for different system configurations is evaluated. Systems with different overall span lengths, transmission fibre types and data modulation formats are investigated. Performance is compared with conventional Erbium doped fibre amplifier based system to evaluate system configurations where URFL based amplification provide performance or commercial advantages

Demodulation and Detection Schemes for a Memoryless Optical WDM Channel

It is well known that matched filtering and sampling (MFS) demodulation together with minimum Euclidean distance (MD) detection constitute the optimal receiver for the additive white Gaussian noise channel. However, for a general nonlinear transmission medium, MFS does not provide sufficient statistics, and therefore is suboptimal. Nonetheless, this receiver is widely used in optical systems, where the Kerr nonlinearity is the dominant impairment at high powers. In this paper, we consider a suite of receivers for a two-user channel subject to a type of nonlinear interference that occurs in wavelength-division-multiplexed channels. The asymptotes of the symbol error rate (SER) of the considered receivers at high powers are derived or bounded analytically. Moreover, Monte-Carlo simulations are conducted to evaluate the SER for all the receivers. Our results show that receivers that are based on MFS cannot achieve arbitrary low SERs, whereas the SER goes to zero as the power grows for the optimal receiver. Furthermore, we devise a heuristic demodulator, which together with the MD detector yields a receiver that is simpler than the optimal one and can achieve arbitrary low SERs. The SER performance of the proposed receivers is also evaluated for some single-span fiber-optical channels via split-step Fourier simulations

Linear and Nonlinear Noise Characterisation of Dual Stage Broadband Discrete Raman Amplifiers

We characterise the linear and nonlinear noise of dual stage broadband discrete Raman amplifiers (DRAs) based on conventional Raman gain fibres. Also, we propose an optimised dual stage DRA setup that lowers the impact of nonlinear noise (generated in the amplifier) on the performance of a transmission link (with 100-km amplifier spacing). We numerically analyse the design of a backward pumped cascaded dual stage 100-nm DRA with high gain (∼20 dB) and high saturated output power (>23 dBm). We show that the noise figure (NF) of the dual stage DRA is mainly dominated by the first stage irrespective of the type of gain fibre chosen in the second stage, and we also demonstrate that optimising the length and the type of Raman gain fibre can have significant impact on the size of inter/intrasignal nonlinearities generated. Here, we report a theoretical model to calculate the nonlinear noise power generated in transmission spans with dual stage DRAs considering piecewise signal power evolution through the Raman gain fibres. The predicted signal-to-noise ratio (SNR) performances are calculated from the combined contributions from NF and nonlinear product power obtained using the proposed analytical model for transmission systems deployed with 100-km transmission span compensated by different dual stage DRAs. Finally, an optimised IDF 6 km-SMF 10 km dual stage configuration has been identified using the theoretical model, which allows maximum SNR of 14.6 dB at 1000 km for 1 THz Nyquist wavelength division multiplexed signal and maximum transmission reach of 3400 km at optimum launch power assuming 8.5 dB HD-FEC limit of the Nyquist PM-QPSK signal