Nonlinearity mitigation in phase-sensitively amplified optical transmission links

The fundamental limitations in fiber-optic communication are caused by optical amplifier noise and the nonlinear response of the optical fibers. The quantum-limited noise figure of erbium-doped fiber amplifier (EDFA) or any phase-insensitive amplifier is 3 dB. However, the noise added bythe amplification can be reduced using phase-sensitive amplifier (PSA) whose quantum-limited noise figure is 0 dB. PSAs can also compensatefor the nonlinear distortions from the optical fiber with copier-PSA implementation. At the transmitter, a copier which is nothing but aphase-insensitive amplifier is used to create a conjugated copy of the signal. The signal and idler are co-propagated in the span, experiencingcorrelated nonlinear distortions. The nonlinear distortions are reduced by the all-optical coherent superposition of the signal and idler in thePSA.In this work, an analytical investigation is performed for the nonlinearity mitigation using the PSAs, by calculating the residual nonlineardistortion after the coherent superposition in PSAs. The optical bandwidth and the dispersion map dependence on the nonlinearity mitigationin the PSAs are analytically and experimentally studied. A modified Volterra nonlinear equalizer (VNLE) is used to reduce the residual nonlineardistortions after PSAs. Experiments were performed to show that PSAs can mitigate cross-phase modulation (XPM), which was evidentby observing the constellation diagrams. The maximum allowed launch power increase was also measured to quantify the XPM mitigation. Tothe best of our knowledge, this is the first experiment that showed the mitigation of XPM in a phase-sensitively amplified transmission link.Also, the effectiveness in mitigating self-phase modulation (SPM) and XPM using a PSA is studied

Phase-sensitive amplifiers for nonlinearity impairment mitigation in optical fiber transmission links

The fundamental limitations in fiber-optic communication are caused by optical amplifier noise and the nonlinear response of the optical fibers. The quantum-limited noise figure of erbium-doped fiber amplifiers (EDFAs) or any phase-insensitive amplifier is 3 dB. However, the noise added by the amplification can be reduced using phase-sensitive amplifiers (PSAs), whose quantum-limited noise figure is 0 dB. PSAs can also compensate for the nonlinear distortions from the optical transmission fiber in the copier-PSA implementation. At the transmitter, a copier which is nothing but a phase-insensitive amplifier, is used to create a conjugated copy of the signal. The signal and idler are then copropagated in the fiber link, experiencing correlated nonlinear distortions. The nonlinear distortions are reduced by the all-optical coherent superposition of the signal and idler in the PSA.In this work, an investigation is made for the nonlinearity mitigation using the PSAs, by calculating the residual nonlinear distortion after the coherent superposition in a copier-PSA link. The nonlinearity mitigation efficiency in PSA links is studied with respect to modulation formats, symbol rates and number of wavelength channels. The effectiveness of nonlinearity mitigation is found to increase with higher-order modulation formats. However, the efficiency of nonlinearity mitigation decreases with increasing number of wavelength channels and increasing symbol rate resulting in larger residual nonlinear distortions. A modified Volterra nonlinear equalizer (VNLE) is implemented to reduce the residual nonlinear distortions after PSAs in single- and multi-channel PSA links. Cross-phase modulation mitigation using PSAs is also demonstrated

Fast and robust chromatic dispersion estimation based on temporal auto-correlation after digital spectrum superposition

We investigate and experimentally demonstrate a fast and robust chromatic dispersion (CD) estimation method based on temporal auto-correlation after digital spectrum superposition. The estimation process is fast, because neither tentative CD scanning based on CD compensation nor specific cost function calculations are used. Meanwhile, the proposed CD estimation method is robust against polarization mode dispersion (PMD), amplified spontaneous emission (ASE) noise and fiber nonlinearity. Furthermore, the proposed CD estimation method can be used for various modulation formats and digital pulse shaping technique. Only 4096 samples are necessary for CD estimation of single carrier either 112 Gbps DP-QPSK or 224 Gbps DP-16QAM signal with various pulse shapes. 8192 samples are sufficient for the root-raised-cosine pulse with roll-off factor of 0.1. As low as 50 ps/nm standard deviation together with a worst estimation error of about 160 ps/nm is experimentally obtained for 7 x 112 Gbps DP-QPSK WDM signal after the transmission through 480 km to 9120 km single mode fiber (SMF) loop using different launch powers

Performance limits in optical communications due to fiber nonlinearity

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

Signal processing with optical delay line filters for high bit rate transmission systems

In den letzten Jahrzehnten ist das globale Kommunikationssystem in einem immer größerem Maße ein integraler Bestandteil des täglichen Lebens geworden. Optische Kommunikationssysteme sind die technologische Basis für diese Entwicklung. Nur Fasern können die riesige benötigte Bandbreite bereitstellen. Während für die ersten optischen Übertragungssysteme die Faser als "flacher" Kanal betrachtet werden konnte, machen Wellenlängenmultiplex und steigende Übertragungsraten die Einbeziehung von immer mehr physikalischen Effekten notwendig. Bei einer Erhöhung der Kanaldatenrate auf 40 Gbit/s und mehr ist die statische Kompensation von chromatischer Dispersion nicht mehr ausreichend. Die intrinsische Toleranz der Modulationsformate gegenüber Dispersion nimmt quadratisch mit der Symbolrate ab. Daher können beispielsweise durch Umwelteinflüsse hervorgerufene Dispersionsschwankungen die Dispersionstoleranz der Modulationsformate überschreiten. Dies macht eine adaptive Dispersionskompensation notwendig, was gleichzeitig auch Dispersionsmonitoring erfordert, um den adaptiven Kompensator steuern zu können. Vorhandene Links können mit Restdispersionskompensatoren ausgestattet werden, um sie für Hochgeschwindigkeitsübertragungen zu ertüchtigen. Optische Kompensationstechniken sind unabhängig von der Kanaldatenrate. Daher wird eine Erhöhung der Datenrate problemlos unterstützt. Optische Kompensatoren können WDM-fähig gebaut werden, um mehrere Kanäle auf einmal zu entzerren. Das Buch beschäftigt sich mit optischen Delay-Line-Filtern als eine Klasse von optischen Kompensatoren. Die Filtersynthese von solchen Delay-Line-Filtern wird behandelt. Der Zusammenhang zwischen optischen Filtern und digitalen FIR-Filtern mit komplexen Koeffizienten im Zusammenhang mit kohärenter Detektion wird aufgezeigt. Iterative und analytische Methoden, die die Koeffizienten für dispersions- und dispersions-slope-kompensierende Filter produzieren, werden untersucht. Genauso wichtig wie die Kompensation von Dispersion ist die Schätzung der Dispersion eines Signals. Mit Delay-Line-Filtern können die Restseitenbänder eines Signals genutzt werden, um die Dispersion zu messen. Alternativ kann nichtlineare Detektion angewandt werden, um die Pulsverbreiterung, die hauptsächlich von der Dispersion herrührt, zu schätzen. Mit gemeinsamer Dispersionskompensation und Dispersionsmonitoring können Dispersionskompensatoren auf die Signalverzerrungen eingestellt werden. Spezielle Eigenschaften der Filter zusammen mit der analytischen Beschreibung können genutzt werden, um schnelle und zuverlässige Steueralgorithmen zur Filtereinstellung bereitzustellen. Schließlich wurden Prototypen derartiger faseroptischen Kompensatoren von chromatischer Dispersion und Dispersions-Slope hergestellt und charakterisiert. Die Einheiten und ihr Systemverhalten wird gezeigt und diskutiert.Over the course of the past decades, the global communication system has become a central part of people's everyday lives. Optical communication systems are the technological basis for this development. Only fibers can provide the huge bandwidth that is required. Where the fiber could be regarded as a flat channel for the first optical transmission systems wavelength multiplexing and increasing line rates made it necessary to take more and more physical effects into account. When the line rates are increased to 40 Gbit/s and higher static chromatic dispersion compensation is not enough. The modulation format's intrinsic tolerance for dispersion decreases quadratically with the symbol rate. Thus, environmentally induced chromatic dispersion fluctuations may exceed the dispersion tolerance of the modulation formats. This makes an adaptive dispersion compensation necessary implying also the need for a monitoring scheme to steer the adaptive compensator. Legacy links that are CD-compensated by DCFs can be upgraded with residual dispersion compensators to make them ready for high speed transmission. Optical compensation is independent from the line rate. Hence, increasing the data rates is inherently supported. Optical compensators can be built WDM ready compensating multiple channels at once. The book deals with optical delay line filters as one class of optical compensators. The filter synthesis of such delay line filters is addressed. The connection between optical filters and digital FIR filters with complex coefficients that are used in conjunction with coherent detection could be shown. Iterative and analytical methods that produce the coefficients for dispersion (and also dispersion slope) compensating filters are researched. As important as the compensation of dispersion is the estimation of the dispersion of a signal. Using delay line filters, the vestigial sidebands of a signal can be used to measure the dispersion. Alternatively, nonlinear detection can be used to estimate the pulse broadening which is caused mainly by dispersion. With dispersion compensation and dispersion monitoring, dispersion compensators can be adapted to the signal's impairment. Special properties of the filter in conjunction with an analytical description can be used to provide a fast and reliable control algorithm for setting the filter to a given dispersion and centering it on a signal. Finally, prototypes of such fiber optic chromatic dispersion and dispersion slope compensation filters were manufactured and characterized. The device and system characterization of the prototypes is presented and discussed

Digital Signal Processing Techniques For Coherent Optical Communication

Coherent detection with subsequent digital signal processing (DSP) is developed, analyzed theoretically and numerically and experimentally demonstrated in various fiber-optic transmission scenarios. The use of DSP in conjunction with coherent detection unleashes the benefits of coherent detection which rely on the preservation of full information of the incoming field. These benefits include high receiver sensitivity, the ability to achieve high spectral-efficiency and the use of advanced modulation formats. With the immense advancements in DSP speeds, many of the problems hindering the use of coherent detection in optical transmission systems have been eliminated. Most notably, DSP alleviates the need for hardware phase-locking and polarization tracking, which can now be achieved in the digital domain. The complexity previously associated with coherent detection is hence significantly diminished and coherent detection is once again considered a feasible detection alternative. In this thesis, several aspects of coherent detection (with or without subsequent DSP) are addressed. Coherent detection is presented as a means to extend the dispersion limit of a duobinary signal using an analog decision-directed phase-lock loop. Analytical bit-error ratio estimation for quadrature phase-shift keying signals is derived. To validate the promise for high spectral efficiency, the orthogonal-wavelength-division multiplexing scheme is suggested. In this scheme the WDM channels are spaced at the symbol rate, thus achieving the spectral efficiency limit. Theory, simulation and experimental results demonstrate the feasibility of this approach. Infinite impulse response filtering is shown to be an efficient alternative to finite impulse response filtering for chromatic dispersion compensation. Theory, design considerations, simulation and experimental results relating to this topic are presented. Interaction between fiber dispersion and nonlinearity remains the last major challenge deterministic effects pose for long-haul optical data transmission. Experimental results which demonstrate the possibility to digitally mitigate both dispersion and nonlinearity are presented. Impairment compensation is achieved using backward propagation by implementing the split-step method. Efficient realizations of the dispersion compensation operator used in this implementation are considered. Infinite-impulse response and wavelet-based filtering are both investigated as a means to reduce the required computational load associated with signal backward-propagation. Possible future research directions conclude this dissertation

Symmetry & nonlinear compensation in fiber-optic transmissions

This thesis presents methods and practical implementations for compensating or suppressing signal distortions induced by fiber nonlinearity in long-distance transmissions. Our methods take advantage of the availability and already wide deployment of dispersion-compensating fibers with various choices of dispersions and dispersion slopes. The basic principle behind the methods is to choose suitable fibers and to arrange them properly into transmission lines manifesting scaled symmetries. Based on the nonlinear Schrodinger equation which describes the nonlinear and dispersive signal propagation in optical fibers, we have shown analytically that a scaled symmetry renders the nonlinear signal distortion by the first part of a transmission line to be largely undone by the second part, when an optical phase conjugator is installed in the middle of the line. Without a phase conjugator, the most detrimental nonlinear interactions among pulses within a wavelength channel may be significantly suppressed in a scaled symmetric line. We have identified two types of scaled symmetries: mirror and translation. Although mirror-symmetric systems have been discussed by other authors before, our own proposals and designs using high-dispersion fibers in conjunction with distributive Raman or erbium-doped amplification could make practical transmission systems manifesting nearly perfect mirror symmetries in the scaled sense and hence excellent nonlinear compensations. Firstly noted and investigated thoroughly by us, the concept of scaled translation symmetries in transmission lines may well spur the adoption of nonlinear compensation methods in practical transmission systems, since distributive amplifiers are no longer necessary for translation symmetries. To support our mathematical analyses, extensive computer simulations have been carried out to validate the effectiveness of our proposed systems, most of which assume practical system setups and parameters and could therefore serve as paradigms for real system designs