Long distance repeaterless optical fiber communications systems are currently used to transmit most internet and telephone information worldwide. The growth of photonic telecommunications technology has produced systems with very high bit-rate per fiber, but this still falls short of its potential capacity. Currently systems that are able to transmit even higher bit-rates are being developed utilizing dense wavelength-division-multiplexing (WDM) to maximally utilize the bandwidth potential of optical fibers. One of the most important factors that limits the bit-rate achievable in a such a WDM optical communications system is the cross-talk between channels caused by pulse collisions. In this thesis a consistent mathematical theory is used to analyze the frequency and timing shifts caused collisions between two WDM channels. This theory is applied to the systems currently most promising for next-generation photonic telecommunications; the dispersion managed (DM) soliton and 'quasi-linear' systems. Self-contained formulae are obtained which accurately predict the timing shifts suffered in these systems with a wide range of parameters. These formulae require an order of magnitude less computational time that direct numerical simulations. Several mathematical techniques are introduced to obtain computationally efficient formulae for complete and incomplete collisions in both systems. For complete collisions we use the Poisson sum transform to change the calculation to a sum in the Fourier domain. For incomplete collisions we use asymptotic integration to obtain approximate formulae. For quasi-linear systems we simplify the Laplace method even further to obtain elementary formulae. We show that using a combination of these methods the timing shift for incomplete and complete collisions in a wide range of system configurations can be obtained in comparatively small computational times. We find that for systems with small DM map strength the timing shift from widely separated channels is significant. For quasi-linear systems with large DM map strength this is negligable and the timing shift decreases with the square of the channel frequency separation. We also find the timing shift from closely spaced channels is higher for quasi-linear systems than for DM soliton systems operating at the same average dispersion.

In this dissertation we present theoretical and experimental investigation of the performance quality of fiber optical communication systems, and find new and inexpansive ways of increasing the rate of theinformation transmission.The first part of this work discuss the two major factors limiting the quality of information channels in the fiber optical communication systems. Using methods of large deviation theory from statisticalphysics, we carry out analytical and numerical study of error statistics in optical communication systems in the presence of the temporal noise from optical amplifiers and the structural disorder of optical fibers. In the slowly varying envelope approximation light propagation through optical fiber is described by Schr\{o}dinger's equation. Signal transmission is impeded by the additive (amplifiers) and multiplicative (birefringence) noise This results in signal distortion that may lead to erroneous interpretation of the signal. System performance is characterized by the probability of error occurrence. Fluctuation of spacial disorder due to changing external factors (temperature, vibrations, etc) leads to fluctuations of error rates. Commonly the distribution of error rates is assumed to be Gaussian. Using the optimal fluctuation method we show that this distribution is in fact lognormal. Sucha distribution has ""fat"" tails implying that the likelihood of system outages is much higher than itwould be in the Gaussian approximation. We present experimental results that provide excellent confirmation of our theoretical predictions.In the second part of this dissertation we present some published work on bisolitons in the dispersion managed systems. Modern communication systems use light pulses to transmit tremendous amounts of information. These systems can be modeled using variations of the Nonlinear Shrodinger Equation where chromatic dispersion and nonlinear effects in the glass fiber are taken into account. The best system performance to date is achieved using dispersion management. We will see how the dispersion management works and how it can be modeled. As you pack information more tightly the interaction between the pulsesbecomes increasingly important. In Fall 2005, experiments in Germany showed that bound pairs of pulses (bisolitons) could propagate significant distances. Through numerical investigation we found parametric bifurcation of bisolitonic solutions, and developed a new iterative method with polynomial correction for the calculation of these solutions. Using these solutions in the signal transmission could increase the transmission rates.

The constant demand for capacity increase, together with the foreseen saturation of the single-mode optical fiber, paved the way to technological breakthroughs that have completely changed the landscape of fiber-optic telecommunications. The most important advance was, undeniably, the practical implementation of a coherent detection with the help of high-speed electronics. This has, first, enabled the use of advanced modulation formats that allowed for a more efficient use of the fiber bandwidth, compared to the classical On-Off Keying, while adapted algorithms could not be used in order to mitigate the optical signal degradation. This thesis began a little after the advent of coherent detection and its main objective was to revisit the propagation effects in optical transmission systems using "Quadrature phase shift keying" (QPSK) modulation in the context of terrestrial systems, i.e. for transmission distances of up to about 2000 km. The manuscript is divided into two parts. The first part is dedicated to a study on the data sequences that need to be used in numerical simulations, when advanced modulation is involved. Fiber propagation, and in particular the interplay between chromatic dispersion and nonlinearities, usually introduce a nonlinear inter-symbol interference (ISI) to the transmitted signal. Since this ISI depends on the actual transmitted data pattern, it is obvious that the choice of the sequence used in our numerical simulations will have a direct influence on the estimated channel quality. Since, an infinite length, random sequence is impractical; we very commonly use pseudorandom" (PR) sequences, i.e. finite-length, deterministic sequences with balanced pattern statistics that seem to be random. In the first part we describe the method of generating M-level (with M>2) pseudorandom sequences and we detail their properties. In addition, we propose numerical tools to characterize the non-pseudorandom sequences that we use in numerical simulations, or we are sometimes forced to use in laboratory experiments. Finally, we present results of numerical simulations that quantify the necessity to use PR sequences as a function of our system parameters. After having established the "fairest possible" finite sequences, in the second part of the manuscript, we focus on the study of the nonlinear propagation, in the context of a transmission system using QPSK modulation and assuming a variable dispersion management and fiber type. Specifically, we numerically study the signal statistics due to the interplay of chromatic dispersion and nonlinear effects, neglecting all polarization or multi-wavelength effects and the amplifier noise. In this context, we were first interested in determining whether some empirical laws developed for OOK systems, can be also used in the case of QPSK modulation, such as the criterion of cumulative nonlinear phase (ΦNL) or laws that allow for a quick optimization of the dispersion management. Next we reveal the importance of a global phase rotation added to the initial signal constellation, as a parameter that can provide interesting information for the post-optimization of our system. We also discuss the fact that the constellation shape critically depends on the applied dispersion management, while there are generally 3 types of constellations, concerning the complex signal statistics: (1) the phase variance is higher than the amplitude variance (2) the amplitude variance is higher than the phase variance and (3) the received signal constellation resembles to a constellation of a signal under the influence of just an Additive White Gaussian Noise. Finally, we provide a phenomenological explanation of the constellations shapes revealing the fact that different data sub-sequences suffer from a different kind of signal degradation, while we also use this information to define a parameter that quantifies the potential benefit from a MAP (Maximum A Posteriori probability) correction algorithm

La demande constante de capacité et la saturation prévue de la fibre monomode ont conduit récemment à des avances technologiques qui ont complètement changé le paysage des télécommunications à fibre optique. Le progrès le plus important était la mise en œuvre d'une détection cohérente à l'aide d'électronique rapide. Cela a permis pas seulement l'utilisation de formats de modulation qui promettent une utilisation plus efficace de la bande passante, mais aussi l’utilisation des algorithmes adaptés pour combattre la dégradation du signal optique due à la propagation. Cette thèse a commencé un peu après le début de cette « ère du cohérent » et son principal objectif était de revoir les effets physiques de la propagation dans des systèmes de transmission terrestres, utilisant le format de modulation QPSK (Quadrature Phase Shift Keying). Le manuscrit est divisé en deux parties. La première partie est consacrée à une étude sur les séquences des données qui doivent être utilisés dans les simulations numériques, lorsqu’un format de modulation avancée est impliqué. La propagation, et en particulier l'interaction entre la dispersion chromatique et les non-linéarités, introduisent une interférence inter-symbole (ISI). Vu que cet ISI dépend de l’enchainement des données transmises, il est évident que le choix de la séquence a une influence sur la qualité estimée du canal. Etant donné que des séquences aléatoires infinies ne sont pas pratiquement réalisables, nous utilisons souvent des séquences « pseudo-aléatoires » (PR), i.e. des séquences déterministes de longueur finie, avec des statistiques équilibrés, qui semblent être aléatoires. Dans la première partie, nous décrivons la méthode de génération de séquences PR avec M. niveaux (M> 2) et nous détaillons leurs propriétés. En outre, nous proposons des outils numériques pour caractériser les séquences non pseudo-aléatoires qu’on utilise souvent dans des simulations, ou parfois aussi dans des expériences au laboratoire. Enfin, nous présentons les résultats de simulations qui permettent de quantifier la nécessité d'utiliser des séquences PR en fonction des paramètres du système. Après avoir établi les séquences finies "les plus adaptées", dans la seconde partie du manuscrit, nous nous concentrons sur l'étude de la propagation, dans le contexte d'un système de transmission QPSK et en supposant une gestion de dispersion et un type de fibre variables. Plus précisément, nous étudions numériquement les statistiques de signaux dégradés dus à l'interaction de la dispersion chromatique avec les effets non linéaires, en négligeant tout effet de polarisation ou inter-canaux, aussi que le bruit des amplificateurs. Dans ce contexte, nous étions intéressés à déterminer si certaines lois empiriques développées pour les systèmes OOK, sont valable dans le cas d'une modulation QPSK, tels que le critère de la phase non-linéaire cumulée (ΦNL) ou des lois qui permettent une optimisation de la gestion de dispersion. Ensuite, nous révélons l'importance de la rotation de la constellation du signal initial, comme un paramètre qui peut fournir des informations pour la post-optimisation de notre système. Nous discutons également autour du fait que la forme de la constellation dépend de la gestion de dispersion et concernant les constellations nous concluons qu'il y en a généralement 3 types, avec: (1) une variance de phase supérieure à la variance d'amplitude (2) une variance d'amplitude supérieure à la variance de phase et (3) avec le signal ayant une constellation qui ressemble à la constellation d’un signal sous l'influence d'un bruit blanc gaussien additif. Enfin, nous fournissons une explication phénoménologique des formes des constellations révélant le fait que des sous-séquences différentes conduisent à un « type » différent de dégradation et nous utilisons ces informations pour définir un paramètre qui quantifie le bénéfice potentiel d'un algorithme de correction du type MAP(Maximum A Posteriori Probability) / The constant demand for capacity increase, together with the foreseen saturation of the single-mode optical fiber, paved the way to technological breakthroughs that have completely changed the landscape of fiber-optic telecommunications. The most important advance was, undeniably, the practical implementation of a coherent detection with the help of high-speed electronics. This has, first, enabled the use of advanced modulation formats that allowed for a more efficient use of the fiber bandwidth, compared to the classical On-Off Keying, while adapted algorithms could not be used in order to mitigate the optical signal degradation. This thesis began a little after the advent of coherent detection and its main objective was to revisit the propagation effects in optical transmission systems using "Quadrature phase shift keying" (QPSK) modulation in the context of terrestrial systems, i.e. for transmission distances of up to about 2000 km. The manuscript is divided into two parts. The first part is dedicated to a study on the data sequences that need to be used in numerical simulations, when advanced modulation is involved. Fiber propagation, and in particular the interplay between chromatic dispersion and nonlinearities, usually introduce a nonlinear inter-symbol interference (ISI) to the transmitted signal. Since this ISI depends on the actual transmitted data pattern, it is obvious that the choice of the sequence used in our numerical simulations will have a direct influence on the estimated channel quality. Since, an infinite length, random sequence is impractical; we very commonly use pseudorandom" (PR) sequences, i.e. finite-length, deterministic sequences with balanced pattern statistics that seem to be random. In the first part we describe the method of generating M-level (with M>2) pseudorandom sequences and we detail their properties. In addition, we propose numerical tools to characterize the non-pseudorandom sequences that we use in numerical simulations, or we are sometimes forced to use in laboratory experiments. Finally, we present results of numerical simulations that quantify the necessity to use PR sequences as a function of our system parameters. After having established the “fairest possible” finite sequences, in the second part of the manuscript, we focus on the study of the nonlinear propagation, in the context of a transmission system using QPSK modulation and assuming a variable dispersion management and fiber type. Specifically, we numerically study the signal statistics due to the interplay of chromatic dispersion and nonlinear effects, neglecting all polarization or multi-wavelength effects and the amplifier noise. In this context, we were first interested in determining whether some empirical laws developed for OOK systems, can be also used in the case of QPSK modulation, such as the criterion of cumulative nonlinear phase (ΦNL) or laws that allow for a quick optimization of the dispersion management. Next we reveal the importance of a global phase rotation added to the initial signal constellation, as a parameter that can provide interesting information for the post-optimization of our system. We also discuss the fact that the constellation shape critically depends on the applied dispersion management, while there are generally 3 types of constellations, concerning the complex signal statistics: (1) the phase variance is higher than the amplitude variance (2) the amplitude variance is higher than the phase variance and (3) the received signal constellation resembles to a constellation of a signal under the influence of just an Additive White Gaussian Noise. Finally, we provide a phenomenological explanation of the constellations shapes revealing the fact that different data sub-sequences suffer from a different kind of signal degradation, while we also use this information to define a parameter that quantifies the potential benefit from a MAP (Maximum A Posteriori probability) correction algorithm