Par sa symétrie singulière, une impulsion laser de polarisation radiale de type TM₀,₁ a la particularité de développer un important champ électrique longitudinal, soit une composante de champ oscillant dans la direction de l'axe optique, dans un contexte de forte focalisation. Cet attribut lui permet d'être particulièrement bien adaptée à l'accélération de particules chargées dans le vide. Un électron se trouvant sur le passage d'une impulsion TM₀,₁ suffisamment puissante peut se synchroniser avec un demi-cycle optique du champ longitudinal et être entraîné avec ce dernier pour ainsi acquérir une énergie substantielle - ce mécanisme est généralement nommé accélération directe ou accélération sous-cycle. Ce schéma d'accélération est caractérisé par une complication inévitable ; tout faisceau laser, peu importe son état de polarisation, subit une déformation de la porteuse en traversant la région focale. Cette déformation, connue sous le nom de déphasage de Gouy, a pour effet de condamner les électrons à une désynchronisation hâtive avec l'impulsion laser, nuisant ainsi à un transfert optimal d'énergie. L'idée de base de ce projet de doctorat est donc la suivante : nous souhaitons diminuer la variation totale du déphasage de Gouy d'une impulsion de type TM₀,₁ sur l'axe optique afin de faciliter l'accord de phase entre les électrons et le champ, et ainsi améliorer les performances énergétiques de l'accélération directe d'électrons. Toutefois, au moment d'entamer ce doctorat, la valeur du déphasage de Gouy total des différentes composantes vectorielles du faisceau TM₀,₁ fortement focalisé est encore incomplètement établie. La première partie de ce projet est donc consacrée à la compréhension des résultats disparates présents dans la littérature à ce sujet. En proposant un formalisme unificateur, nous montrons que la valeur totale du déphasage de Gouy de la composante longitudinale est toujours de 2π sur l'axe optique. Considérant cette valeur a priori immuable, la seconde partie de ce projet consiste à trouver un moyen de la réduire. Cela est fait en développant une famille de solutions aux équations de Maxwell, à l'aide des intégrales de Richards et Wolf, ayant le profil d'intensité et l'état de polarisation d'un faisceau TM₀,₁, mais ayant un déphasage de Gouy ajustable. En utilisant ce nouveau type d'impulsion dans des simulations numériques d'accélération d'électrons pour différentes valeurs de déphasage de Gouy total, nous montrons qu'il s'agit d'un paramètre décisif dans le processus d'accélération sous-cycle et que la diminution de cette valeur est toujours avantageuse du point de vue énergétique. / Due to its singular symmetry, a TM₀,₁ radially polarized laser pulse has the particularity of developing a strong longitudinal electric field, i.e. a field component oscillating in the direction of the optical axis, in a context of strong focusing. This attribute makes it particularly well suited to accelerate charged particles in vacuum. An electron in the path of a sufficiently strong TM₀,₁ pulse can be synchronized and trapped in a single half-cycle of the longitudinal field to acquire substantial energy - this mechanism is generally referred to as direct acceleration or sub-cycle acceleration. This acceleration scheme is characterized by an unavoidable complication; any laser beam, regardless of its polarization state, undergoes a deformation of the carrier as it passes through the focal region. This deformation, known as the Gouy phase shift, causes the electrons to get preemptively out of sync with the pulse, thus hindering optimal energy transfer. The idea behind this PhD project is the following; we want to decrease the total Gouy phase variation of a TM₀,₁-like pulse on the optical axis in order to facilitate the phase matching between the electrons and the field, and thereby improve the energetic performances of direct electron acceleration. However, at the beginning of this project, the value of the total Gouy phase shift of the different vector components of the strongly focused TM₀,₁ beam is still not fully established. The first part of this project is therefore devoted to understanding the disparate results in the literature on that matter. By proposing a unifying formalism, we show that the total value of the Gouy phase shift for the longitudinal component is always 2π on the optical axis. Considering this a priori unchangeable value, the second part of this project is to find a way to reduce it. This is done using Richards and Wolf integrals to develop a family of solutions to Maxwell's equations for a beam with the same intensity profile and polarization state as the TM₀,₁ beam, but with a tunable Gouy phase. By using this new type of pulse in numerical simulations of electron acceleration for different values of total Gouy phase variation, we show that it is indeed a decisive parameter in the sub-cycle acceleration process and decreasing this value is always beneficial from an energy point of view.

The connection between phase shifts and the ANC has been explored in the frame of the effective range theory. The main result is that, in practice and under rather simple requirements, scattering states (phases shifts) can be correctly described and connected with bound states via the effective range function, and therefore, ANCs can be accurately determined thanks to the analytic properties of this function. This result has an important impact in stellar evolution due to the ANC and phases shifts are directly connected with capture cross sections which, for instance, determine partially the stage and evolution of stars.<p><p>As a first step, the effective range function is approximated via the effective range expansion which shows that a successful phase-shift description depends on how precise the effective range parameters are determined. Thus, a technique to compute accurately these parameters is developed here. Its construction is based on a set of recurrence relations at low energy, that allows a compact and general description of the truncated<p>effective range expansion. Several potential models are used to illustrate the effectiveness<p>of this technique and to discuss its numerical limitations. The results shows that a very good precision of the effective-range parameters can be achieved; nevertheless, to describe experimental phase shifts several effective-range parameters can be needed, which shows a limitation for practical applications.<p><p>As a second step, the effective range function is analyzed theoretically in an arbitrary energy range. This analysis shows that this function can be decomposed in such a way that contributions of bound states, resonances and background can be separated in a similar way as in the phenomenological R-matrix. In this new form experimental data can be better fitted because the free parameter space is reduced considerably,<p>and therefore, extrapolations are better handled. By construction, the method agrees with the scattering matrix properties which allows a simple calculation of resonances (locations and widths) and asymptotic normalization constants (ANCs). Several tests are successfully performed via potential models. Phase shifts for the 2 + partial wave of the 12C+α are analyzed with this method. They are correctly described including both<p>resonances at Ec.m. = 2.7 and 4.4 MeV. For the 6.92 MeV (2+) exited state of 16O, the ANC estimation 112(8) × 10 3 fm^−1/2 is obtained taking into account statistical errors. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished