Spatially integrated erbium-doped fiber amplifiers enabling space-division multiplexing

L'augmentation exponentielle de la demande de bande passante pour les communications laisse présager une saturation prochaine de la capacité des réseaux de télécommunications qui devrait se matérialiser au cours de la prochaine décennie. En effet, la théorie de l’information prédit que les effets non linéaires dans les fibres monomodes limite la capacité de transmission de celles-ci et peu de gain à ce niveau peut être espéré des techniques traditionnelles de multiplexage développées et utilisées jusqu’à présent dans les systèmes à haut débit. La dimension spatiale du canal optique est proposée comme un nouveau degré de liberté qui peut être utilisé pour augmenter le nombre de canaux de transmission et, par conséquent, résoudre cette menace de «crise de capacité». Ainsi, inspirée par les techniques micro-ondes, la technique émergente appelée multiplexage spatial (SDM) est une technologie prometteuse pour la création de réseaux optiques de prochaine génération. Pour réaliser le SDM dans les liens de fibres optiques, il faut réexaminer tous les dispositifs intégrés, les équipements et les sous-systèmes. Parmi ces éléments, l'amplificateur optique SDM est critique, en particulier pour les systèmes de transmission pour les longues distances. En raison des excellentes caractéristiques de l'amplificateur à fibre dopée à l'erbium (EDFA) utilisé dans les systèmes actuels de pointe, l'EDFA est à nouveau un candidat de choix pour la mise en œuvre des amplificateurs SDM pratiques. Toutefois, étant donné que le SDM introduit une variation spatiale du champ dans le plan transversal de la fibre, les amplificateurs à fibre dopée à l'erbium spatialement intégrés (SIEDFA) nécessitent une conception soignée. Dans cette thèse, nous examinons tout d'abord les progrès récents du SDM, en particulier les amplificateurs optiques SDM. Ensuite, nous identifions et discutons les principaux enjeux des SIEDFA qui exigent un examen scientifique. Suite à cela, la théorie des EDFA est brièvement présentée et une modélisation numérique pouvant être utilisée pour simuler les SIEDFA est proposée. Sur la base d'un outil de simulation fait maison, nous proposons une nouvelle conception des profils de dopage annulaire des fibres à quelques-modes dopées à l'erbium (ED-FMF) et nous évaluons numériquement la performance d’un amplificateur à un étage, avec fibre à dopage annulaire, à ainsi qu’un amplificateur à double étage pour les communications sur des fibres ne comportant que quelques modes. Par la suite, nous concevons des fibres dopées à l'erbium avec une gaine annulaire et multi-cœurs (ED-MCF). Nous avons évalué numériquement le recouvrement de la pompe avec les multiples cœurs de ces amplificateurs. En plus de la conception, nous fabriquons et caractérisons une fibre multi-cœurs à quelques modes dopées à l'erbium. Nous réalisons la première démonstration des amplificateurs à fibre optique spatialement intégrés incorporant de telles fibres dopées. Enfin, nous présentons les conclusions ainsi que les perspectives de cette recherche. La recherche et le développement des SIEDFA offriront d'énormes avantages non seulement pour les systèmes de transmission future SDM, mais aussi pour les systèmes de transmission monomode sur des fibres standards à un cœur car ils permettent de remplacer plusieurs amplificateurs par un amplificateur intégré.The exponential increase of communication bandwidth demand is giving rise to the so-called ‘capacity crunch’ expected to materialize within the next decade. Due to the nonlinear limit of the single mode fiber predicted by the information theory, all the state-of-the-art techniques which have so far been developed and utilized in order to extend the optical fiber communication capacity are exhausted. The spatial domain of the lightwave links is proposed as a new degree of freedom that can be employed to increase the number of transmission paths and, subsequently, overcome the looming ‘capacity crunch’. Therefore, the emerging technique named space-division multiplexing (SDM) is a promising candidate for creating next-generation optical networks. To realize SDM in optical fiber links, one needs to investigate novel spatially integrated devices, equipment, and subsystems. Among these elements, the SDM amplifier is a critical subsystem, in particular for the long-haul transmission system. Due to the excellent features of the erbium-doped fiber amplifier (EDFA) used in current state-of-the-art systems, the EDFA is again a prime candidate for implementing practical SDM amplifiers. However, since the SDM introduces a spatial variation of the field in the transverse plane of the optical fibers, spatially integrated erbium-doped fiber amplifiers (SIEDFA) require a careful design. In this thesis, we firstly review the recent progress in SDM, in particular, the SDM optical amplifiers. Next, we identify and discuss the key issues of SIEDFA that require scientific investigation. After that, the EDFA theory is briefly introduced and a corresponding numerical modeling that can be used for simulating the SIEDFA is proposed. Based on a home-made simulation tool, we propose a novel design of an annular based doping profile of few-mode erbium-doped fibers (FM-EDF) and numerically evaluate the performance of single stage as well as double-stage few-mode erbium-doped fiber amplifiers (FM-EDFA) based on such fibers. Afterward, we design annular-cladding erbium-doped multicore fibers (MC-EDF) and numerically evaluate the cladding pumped multicore erbium-doped fiber amplifier (MC-EDFA) based on these fibers as well. In addition to fiber design, we fabricate and characterize a multicore few-mode erbium-doped fiber (MC-FM-EDF), and perform the first demonstration of the spatially integrated optical fiber amplifiers incorporating such specialty doped fibers. Finally, we present the conclusions as well as the perspectives of this research. In general, the investigation and development of the SIEDFA will bring tremendous benefits not only for future SDM transmission systems but also for current state-of-the-art single-mode single-core transmission systems by replacing plural amplifiers by one integrated amplifier

Some Sufficient Conditions for Starlikeness and Convexity of Order

We derive certain sufficient conditions for starlikeness and convexity of order of analytic functions in the unit disk. Applications are indicated for the subordination results to electromagnetic cloaking

A sharp version of Kahan's theorem on clustered eigenvalues

AbstractLet the n × n Hermitian matrix A have eigenvalues λ1, λ2, …, λn, let the k × k Hermitian matrix H have eigenvalues μ1 ≤ μ2 … ≤ μk, and let Q be an n × k matrix having full column rank, so 1 ≤ k ≤ n. It is proved that there exist k eigenvalues λi1 ≤ λi2 ≤ … ≤ λik of A such thatmax1≤j≤k|μj − λij| ≤ Cσmin(Q) ‖AQ − QH‖2always holds with c = 1, where σmin (Q) is the smallest singular value of Q, and ‖; · ‖;2 denotes the biggest singular value of a matrix. The inequality was proved for c ≤ √2 in 1967 by Kahan, who also conjectured that it should be true for c = 1

TRUSS STRUCTURE OPTIMIZATION BASED ON IMPROVED WOLF PACK ALGORITHM

Aiming at the optimization of truss structure, a wolf pack algorithm based on chaos and improved search strategy was proposed. The mathematical model of truss optimization was constructed, and the classical truss structure was optimized. The results were compared with those of other optimization algorithms. When selecting and updating the initial position of wolves, chaos idea was used to distribute the initial value evenly in the solution space; phase factor was introduced to optimize the formula of wolf detection; information interaction between wolves is increased and the number of runs is reduced. The numerical results show that the improved wolf pack algorithm has the characteristics of fewer parameters, simple programming, easy implementation, fast convergence speed, and can quickly find the optimal solution. It is suitable for the optimization design of the section size of space truss structures

N-(4,5-Diaza-9H-fluoren-9-yl­idene)-4-meth­oxy­aniline

In the title compound, C18H13N3O, the diaza­fluorene ring system is almost coplanar (r.m.s. deviation = 0.0640 Å) and subtends an angle of 61.5 (4)° with the plane of the meth­oxy-substituted benzene ring. In the crystal structure, pairs of C—H⋯O hydrogen bonds link mol­ecules into centrosymmetric dimers parallel to the ab plane. Mol­ecules are also stacked in an obverse fashion along the c axis by a variety of π–π inter­actions with centroid–centroid distances in the range 3.557 (2)–3.921 (2) Å

4,5-Diaza-9H-fluoren-9-imine

In the title compound, C11H7N3, the diaza­fluorene rings are almost coplanar with an r.m.s. deviation of 0.0160 Å. In the crystal structure, C—H⋯N hydrogen bonds link mol­ecules into sheets parallel to the ab plane. Mol­ecules are also stacked regularly along the c axis by a variety of π–π inter­actions with centroid–centroid distances in the range 3.527 (2)–3.908 (2) Å

Certain Subclasses of Multivalent Analytic Functions

Two new subclasses and of multivalent analytic functions are introduced. Distortion inequalities and inclusion relation for and are obtained. Some results of the partial sums of functions in these classes are also given

3,3′-Dimethyl-1,1′-(propane-1,3-di­yl)diimidazol-1-ium bis(hexafluoro­phosphate)

In the title compound, C11H18N4 2+·2PF6 −, the dihedral angle between the two planar imidozlium rings is 6.1 (2)°. Both [PF6]− anions are disordered [occupancies 0.65 (2):0.35 (2) and 0.59 (5):0.41 (5)]. The crystal packing is stabilized by inter­molecular C—H⋯F hydrogen bonds which link two mol­ecules, forming centrosymmetric dimers

N-(4,5-Diaza­fluoren-9-yl­idene)-4-methyl­aniline

In the mol­ecule of the title compound, C18H13N3, the 4,5-diaza­fluorenyl­idene unit is nearly planar and is oriented at a dihedral angle of 66.31 (1)° with respect to the benzene ring. In the crystal structure, mol­ecules are stacked regularly along the c axis