This dissertation seeks to show that the spatio-temporal couplings of ultrafast lasers can be exploited to bypass the current technology bottlenecks on achieving next-generation ultrahigh-intensity lasers. First, the design of a novel six-grating compressor is presented and analyzed with a ray-tracing code and custom post-processing software, where the use of chirped-beam grating pairs was found to increase group delay dispersion (GDD) removal over 425% greater than a traditional grating pair. The higher-order dispersion effects, that come from using high-dispersion gratings with a large induced GDD, on the temporally stretched pulse were examined with strategies proposed on how to mitigate them. A custom 2D amplification code was used to model the amplification of a spatially and temporally chirped beam-pulse in a large-aperture, Nd:glass amplifier that are commonly used as high-energy inertial confinement fusion lasers. Unique pulse distortion effects from this novel amplification scheme were uncovered, leading to a design strategy based on 2D sculpting of the spatio-temporal input pulse and shaping of the transverse gain profile in the amplifier. With these, a 40-J, 20-ns chirped beam pulse with a 2x spatial chirp, and spectral bandwidth capable of supporting a 100-fs compressed pulse duration, was shown to be amplified to excess of 25-kJ with a B-integral less than 5. This would enable the creation of an exawatt-class laser system. A novel stretcher design capable of producing a 20-ns stretched pulse and a multi-beam focusing arrangement based on a multi-segment tiled parabolic mirror are presented with a performance analysis, along with other technology advancements useful for ultrahigh-intensity laser systems.

This thesis presents a computational study on the propagation effects of space-time coupled laser beams, their interaction with thin hydrogen foils, and the resulting effect on accelerated protons. Laser-plasma simulations are typically done using particle-in-cell codes where analytic descriptions of Gaussian beam propagation, that make assumptions on the frequency dependent nature of ultrashort pulses, are used. A code was developed using Fourier propagation techniques that accurately describes the diffractive effects of arbitrary focused fields which was implemented into a particle-in-cell code. The accurate model shows varying laser-matter interaction dynamics compared to the approximated fields. The Fourier propagation code also enables the study of focused spatially chirped beams generated from the output of a single-pass, two-grating compressor. These fields have a space-time coupling that exhibit a pulse front tilt and pulse front curvature depending on the gratings used to generate them. When focused onto a hydrogen target, enhanced collimation and increased proton energies beyond that of a Gaussian beam are possible. Axisymmetric extensions of these space-time fields enable the generation of highly collimated proton jets. The results of this thesis provide insight into the effects accurate laser modeling and space-time couplings have on laser accelerated ions.