Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic--quintic Ginzburg--Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non--integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse--type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this dissertation, we develop a theoretical framework for these novel classes of solutions. In the first part, we use a traveling wave reduction or a so--called spatial approximation to comprehensively investigate the bifurcations of plane wave and periodic solutions of the CGLE. The primary tools used here are Singularity Theory and Hopf bifurcation theory respectively. Generalized and degenerate Hopf bifurcations have also been considered to track the emergence of global structure such as homoclinic orbits. However, these results appear difficult to correlate to the numerical bifurcation sequences of the dissipative solitons. In the second part of this dissertation, we shift gears to focus on the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. For this part, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the two alternative starting formulations for the Lagrangian are recent and not well explored. Also, after extensive discussions with David Kaup, the trial functions have been generalized considerably over conventional ones to keep the shape relatively simple (and the trial function integrable!) while allowing arbitrary temporal variation of the amplitude, width, position, speed and phase of the pulses. In addition, the resulting Euler--Lagrange equations are treated in a completely novel way. Rather than consider the stable fixed points which correspond to the well--known stationary solitons or plain pulses, we use dynamical systems theory to focus on more complex attractors viz. periodic, quasiperiodic, and chaotic ones. Periodic evolution of the trial function parameters on stable periodic attractors constructed via the method of multiple scales yield solitons whose amplitudes are non--stationary or time dependent. In particular, pulsating, snake (and, less easily, creeping) dissipative solitons may be treated in this manner. Detailed results are presented here for the pulsating solitary waves --- their regimes of occurrence, bifurcations, and the parameter dependences of the amplitudes, widths, and periods agree with simulation results. Finally, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Results will be presented for the pulsating and snake soliton cases. Chaotic evolution of the trial function parameters in chaotic regimes identified using dynamical systems analysis would yield chaotic solitary waves. The method also holds promise for detailed modeling of chaotic solitons as well. This overall approach fails only to address the fifth class of dissipative solitons, viz. the exploding or erupting solitons.

Thulium (Tm)-doped ultrafast fiber lasers with emission wavelengths around 2 μm are desirable sources for scientific, industrial, medical, and environmental applications and flexible testbeds for investigating nonlinear pulse dynamics. Although exceptional research attention has been drawn by Tm-doped ultrafast fiber lasers in recent years, their designs and dynamics are significantly less explored compared to other fiber laser systems. Despite the broad emission spectrum of Tm-doped fibers, power scaling of Tm-doped ultrafast fiber lasers has been limited at shorter wavelengths of their emission spectrum (<1920 nm) due to challenges including signal re-absorption. However, compact, high-energy ultrafast sources at these less-exploited wavelengths can enable various applications including nonlinear microscopy. Further, due to the challenges of implementing real-time characterization around 2 μm, transient nonlinear pulse dynamics have rarely been reported from Tm-doped ultrafast fiber lasers. Resolving these dynamics can not only provide insights into new laser designs but also guide the generation of novel pulse profiles which can benefit a wide range of applications depending on their parameters. This dissertation focuses on developing various novel Tm-doped ultrafast fiber laser systems with unprecedented performance: High-energy operation is demonstrated at less-exploited wavelengths and unique waveforms are generated with their nonlinear dynamics investigated in real-time. First, a high-energy (394-nJ) Tm-doped chirped-pulse-amplification fiber laser system is designed and optimized for operation at the wavelength of 1900 nm and supports the generation of 950-nm ultrashort (390-fs) pulses via frequency-doubling. The system represents the highest pulse-energy (138 nJ) in the femtosecond regime for any fiber-based systems around this wavelength to date, which can be highly attractive for two-photon microscopy with spatiotemporal-multiplexing. To gain deeper insights into the operation of ultrafast Tm-doped fiber lasers, various new nonlinear dynamics are investigated by a home-built real-time characterization setup based on dispersive Fourier transform for 2 μm pulses: A new mode-locking regime is demonstrated which can deliver both up-chirped and close-to-chirp-free dissipative pulses with a 10-fold difference in their pulse energies/durations, providing a versatile source that can switch between different pulse profiles. Following that, soliton molecules with unique partial spectral modulation patterns are synthesized based on two dissimilar pulses from the same cavity, which represent an interesting analogy to ‘heteronuclear’ chemical molecules and hold great potential for optical information processing. Further, mode-locking evolution between dissimilar coherent pulses are studied in Tm-doped ultrafast fiber lasers. Finally, combining both high-energy operation and novel waveform-generation, we present a Tm-doped fiber laser source delivering amplified (~ 200 nJ) noise-like pulses without requiring any feedback mechanism. / 2025-09-10T00:00:00Z

Les événements extrêmes sont des phénomènes, souvent considérés catastrophiques, qui se produisent dans la queue d'une distribution généralement en s'écartant d'une décroissance attendue exponentielle. En optique, ces événements ont été étudié dans le contexte des fibres, où ils ont été amplement analysés, comme des vagues scélérates, par analogie bien connue entre l'optique et l'hydrodynamique à travers l'équation de Schroedinger non linéaire. Avec le développement et l'élargissement du domaine, l'étude des événements extrêmes a été étendue à des systèmes dissipatifs avec ou sans degrés spatiaux de liberté.Dans cette thèse on se concentre sur l'étude des événements extrêmes dans trois différents types de systèmes optiques actifs et dissipatifs, présentant chacun un ou deux degrés spatiales de liberté, soit dans le plan transversal (perpendiculaire à la direction de propagation de la lumière) soit dans la direction de propagation. Des structures localisées de nature différente constituent une solution possible importante dans chacun des systèmes étudiés ; leurs interactions autant que leurs rôles dans la formation des événements extrêmes ont donc été analysés en détails. Dans le premier système, un laser à semiconducteur monolithique (VCSEL) à large surface avec un absorbant saturable, on présente la formation d'événements extrêmes dans le plan transversal à deux dimensions de l'intensité du champ électrique. En particulier, on met en évidence la liaison entre ces objets et les solitons de cavité, soit stationnaires soit oscillatoires, aussi présents dans le système. Dans le deuxième système, un laser multimodal spatialement étendu dans la direction de propagation avec injection optique, on analyse l'interaction et la fusion des solitons de phase, des structures localisées qui se propagent dans la cavité en transportant une rotation de phase de 2π. Les événements extrêmes ont été étudié dans deux configurations : une première où ils émergent de la collision des solitons de phase avec des autres structures transitoires transportant une charge chirale négative, et une deuxième où des événements d'intensité élevée émergent d'un régime instable de motif en rouleau où les solitons de cavité ne sont pas des solutions stables. Dans les deux systèmes, on examine le rôle de la chiralité dans la formation des événements extrêmes. Dans le troisième système, un laser à semi-conducteur avec injection optique, on étudie dans les détails l'interaction des solitons de cavité dans le plan transversal, décrits comme deux particules soumises à un potentiel d'interaction décroissant exponentiellement avec la distance entre les deux objets : une analogie possible avec les matériaux hydrophobes a été proposée. Des résultats préliminaires présentant des événements extrêmes spatiotemporels dans ce système sont aussi donnés. / Extreme events are phenomena, often considered as catastrophic, that occur in the tail of a distribution usually deviating from an expected, exponential decay. In optics, these events were first studied in the context of fibers, where they have been extensively analyzed, as optical rogue waves, in light of the well known analogy between optics and hydrodynamics, through the nonlinear Schroedinger equation. With the development and the broadening of the field, extreme events have been also studied in dissipative optical systems with or without spatial degrees of freedom. In this Thesis we focused on the study of extreme events in three different active and dissipative optical systems, each presenting one or two spatial degrees of freedom, either in the transverse plane, perpendicular to the direction of propagation of light, or in the propagation direction. Localized structures of different nature represent an important possible solution in each one of the systems here studied, hence their interaction and the role played in the formation of extreme events have been also investigated into details. In the first system, a monolithic broad-area semiconductor laser (VCSEL) with an intracavity saturable absorber, we report on the occurrence of extreme events in the 2D transverse plane of the electric field intensity. In particular we highlight the connection between these objects and cavity solitons, both stationary and oscillatory, also present in the system. In the second system, a highly multimode laser with optical injection spatially extended along the propagation direction, we analyze the interaction and merging of phase solitons, localized structures propagating along the cavity carrying a 2π phase rotation. Extreme events have been investigated in two configurations: a first one where they emerge from the collision of phase solitons with other transient structures carrying a negative chiral charge, and a second one where high-peak events emerge from an unstable roll regime where phase solitons are not a stable solution. In both these systems we investigate the role of chirality in the extreme event formation. In the third system, a broad-area semiconductor laser (VCSEL) with optical injection, we study into details the interaction of cavity solitons in the transverse plane, described as two particles subjected to an interaction potential exponentially decreasing with the distance between the two objects: a possible analogy with hydrophobic materials is here suggested. Some preliminary results showing spatiotemporal extreme events in this system are also given.

Cette thèse concerne l'étude de la dynamique des structures optiques dissipatives observées dans une cavité à gestion de dispersion utilisant l'évolution non linéaire de la polarisation comme technique de blocage de modes. Nous avons montré expérimentalement l'existence d'une transition graduelle entre le régime de fonctionnement continu et le régime de fonctionnement multi-impulsionnel. Nous nous sommes intéressés à l'état intermédiaire où il nous a été possible d'obtenir divers régimes inédits et d'étudier ainsi le comportement collectif des solitons dissipatifs en présence d'un fond continu. La dynamique de "la pluie de solitons" est une manifestation complexe et fascinante constituée de trois composantes de champ : le fond continu, les solitons de dérive et la phase condensée. Elle s'accompagne d'une circulation d'énergie à travers ces trois composantes. Le mouvement relatif des solitons de dérive ainsi que l'asymétrie temporelle présentent les caractéristiques majeures qui distinguent cette dynamique des autres. D'autres types d'auto-organisation ont été observés et étudiés, comme "le relargage des solitons de la phase condensée" ou bien encore "la vobulation du train de solitons". Nous nous sommes intéressés aussi à la propagation d'une seule impulsion dans la cavité. Pour la première fois, une importante dynamique de respiration spectrale a été prédite dans une cavité à gestion de la dispersion. Nous avons montré qu'une compression temporelle de l'impulsion est accompagnée d'un élargissement spectral d'une grande ampleur dans la partie passive de la cavité et que la largeur de l'impulsion peut dépasser la largeur de la bande passante du milieu amplificateur. Nous avons étudié la dynamique de la respiration spectrale, l'extraction et l'optimisation du signal laser en fonction des paramètres de la cavité et nous avons présenté les caractéristiques d'une cavité qui permet la génération d'une impulsion dont sa largeur spectrale est supérieure à la largeur de la bande passante de l'amplificateur d'un facteur de 2.4. Les dynamiques présentées dans cette thèse témoignent de la complexité et de la richesse de la dynamique dissipative des lasers à fibre fonctionnant en régime de blocage de modes passif par évolution non linéaire de la polarisation. / This thesis presents a study of the nonlinear dissipative dynamics of localized of self organized structures in passively mode-locked fiber laser through nonlinear polarization evolution. We reveal the existence of a gradual transition from the quasi-cw to mode locked dynamics in the multi-pulsing regime. We emphasize on the intermediate state, where various new dynamics are observed. We study collective behaviors of dissipative solitons in the presence of a continuous background. One of the complex and attractive dynamics presented is the "soliton rain", which composed of three field components : continuous modes of background, drifting of solitons and condensed phase solitons. This dynamic appears when the energy flows through the three components. The relative motion of the drifting solitons and the temporal asymmetry present the major characteristics that distinguish this dynamic. Other types of self-organizations of solitons were observed and studied as the "release of the solitons from the condensed phase" and the "chirped trains with condensed soliton phase". We were also interested in the single pulse propagation. For the first time, an important dynamics of spectral breathing was predicted in a dispersion-managed cavity. We showed that pulse compression dynamics in the passive anomalous fiber can be accompanied by a significant enhancement of the spectral width and that the width of the pulse can exceed the amplifier bandwidth. We studied, the extraction and the optimization of the signal laser according to the parameters of the cavity and we presented the characteristics of a cavity delivering ultra short pulses with a spectral width exceeding the amplifier bandwidth by a factor of 2.4. The dynamics presented in this thesis show the complexity and variety of the dissipative dispersion-managed dynamics in fiber laser mode locked through nonlinear polarization evolution.

Les solitons dissipatifs (SD) sont des paquets d'onde auto-localisés qui apparaissent dans les systèmes dissipatifs spatialement étendus. En optique, tous les SD observés jusqu'à présent dans des systèmes propagatifs peuvent être classés en deux catégories, suivant la présence ou non d'un forçage externe, i.e. si la symétrie de phase est brisée ou non. Dans les systèmes forcés, les DS sont accrochés en phase au forçage alors que sans forçage, leur phase est libre et peu dériver en fonction du temps. Dans cette thèse nous étudions la formation d'états localisés propagatifs dans deux systèmes expérimentaux qui diffèrent fondamentalement par la présence ou l'absence d'un forçage externe. Le premier système est un laser à semiconducteur à cavité verticale (VCSEL) soumis à une boucle de rétro-action sélective en fréquence, qui accueille des DS se formant dans la dimension transverse à la propagation (2D). Nous analysons comment la synchronisation des fréquences longitudinales du système (verrouillage modal) peut mener à la formation d'un état localisé dans les trois dimensions : balles de lumière. Le deuxième système est un laser en anneau à semi-conducteur fortement multimode le long de la propagation, et forcé par une injection externe. Lorsque le forçage est légèrement désaccordé de la fréquence naturelle du système, il est possible d'observer des états localisés constitués par un tour de phase de 2 pi, immergés dans l'état homogène (synchronisé). Nous reportons ainsi la première observation de SD qui se forment dans la phase de l'onde optique : solitons de phase dissipatifs / Dissipative solitons (DS) are self-localized wave-packets appearing in spatially extended dissipative systems. In optics, all the DS that have been observed in propagative systems can be cast in two categories, depending on the presence or absence of an external forcing, i.e. the phase symmetry is broken or not. In forced systems, DS are locked in phase to forcing whereas without forcing, their phase is free an can wander in the course of time. In this thesis, we study the formation of propagative DS in two different experimental systems that fundamentally differ from the presence or lack of an external forcing. The first one is a Vertical Cavity Surface Emitting Laser (VCSEL) submitted to a frequency selective feedback, in which DS form in the transverse plane of the system (2D). We analyze how the synchronization of the longitudinal frequencies (mode-locking) can give rise to tri-dimensionnal localization of light: light bullets. The second system is a highly multimode semiconductor ring laser with external forcing, whose spatial extension takes place along the propagation dimension. When the forcing frequency is slightly detuned from the natural frequency of the system, we can see the appearance of self-confined 2 pi phase rotations embedded in a homogeneous (synchronized) state. We then report on the first observation of DS that form in the phase of the optical wave : dissipative phase solitons