• intra-cycle depolarization
• pulse train generation
• vector diffraction theory

Since their first appearance in 1960, lasers have boosted up studies in many areas due to the high fields provided, opening the possibility to investigate a wide range of phenomena. During these years there have been huge improvements in laser pulse generation, most notably the recent Nobel prize-winning amplification technique of Chirped Pulse Amplification (CPA), leading to nowadays systems capable of pulse duration of the order of few femtoseconds and with peak intensity, when focused, exceeding e20 W/cm^2 thus concerning the relativistic regime.

In 1979 Tajima and Dawson proposed the use of a single high-energy ultrashort laser pulse to excite longitudinal waves in plasmas via the ponderomotive force. Such waves, exploited as accelerating structure, can sustain fields of the order of 100 GV/m, way more than conventional accelerators and without the breakdown constraint. This model, namely Laser WakeField Acceleration (LWFA), has proven his validity, already reaching accelerated electron beam energy up to 8 GeV. However the poor quality of these accelerated bunches limits the applications of laser-plasma accelerators. One of the proposed solution is to decouple the wakefield generation and the injection mechanism.

Among the proposed models, the REsonant Multi-Pulse Ionization injection (REMPI) scheme aims to obtain electron bunches with low emittance (0.08 mm mrad) and energy spread (0.65%). In this model the wake is excited by a train of low-energy pulses generated from a single high-energy ultrashort pulse. Part of the original pulse is doubled in frequency and grants the ionization injection.

In my thesis I focused on the design process, from the theoretical model to a possible experimental implementation, of a simple method of generating the pulse train from a single high-energy pulse. Particular attention has been devoted to the development of a cost-effective system that could be easily integrated in existing LWFA experiments. The choice landed on a delay mask, an optical component consisting of a disk divided in rings of different thicknesses, placed right before the last focusing optic, typically an Off-Axis Parabola (OAP). In this way the transverse profile of the original single pulse is split in different sections, delayed accordingly to the plasma period, that, once focused, result in a train of pulses at the focal plane of the OAP, where the target is usually placed.

In the first chapter the physical context is presented, i.e. the basics of laser beam and pulse characterization together with a brief introduction to the laser-plasma acceleration field. The second chapter is devoted to the development of the theoretical and geometrical model for numerical computation of the electromagnetic fields of a laser beam focused by an OAP. As evidence of the model validity, a remarkable application is also presented, describing an intra-cycle depolarization, due to the focusing by an OAP, of an originally linearly polarized laser beam. Finally, the focus of the third chapter is entirely on the delay mask, from the preliminary designs to the final characterization of the spatial and temporal profiles of the pulse train, investigating the viability of such an approach for modern laboratories.