Spatial chirp control of high-intensity 4D pulse focusing for laser-matter interactions

Spatial chirp can be manipulated to control the focusing conditions for materials processing. Our double-ABCD nonparaxial analysis helps to understand and exploit the mechanisms for intensity localization, pulse front tilt, and grating formation, and includes initial spectral phase and detuning of the wavelength crossing plane. We also present a novel method for creating high density, high intensity interference patterns with crossed beams that have no relative pulse front tilt. 1. Non-paraxial double ABCD tracing The properties of space-time focused beams are strongly dependent of the nature of the spatial overlap of the frequency components. The analysis of optical systems with spatial chirp is therefore critical both for understanding the unusual properties of these beams and for designing systems to exploit these properties for materials processing. In a recent paper, we developed an analytical approach to calculate the propagation of spatially chirped beams. A ray is traced that represents the central axis of the Gaussian beamlet for each frequency component. Since one form of the calculation is nonparaxial, the beamlet angles can be large and the calculation is valid over a wider range of conditions than direct Fresnel propagation. Our technique explains, for example, how the evolution of the beamlet radius of curvature leads to an axial variation of the spectral chirp through the focus, contributing to the axial intensity localization. It also allows the derivation of simple scaling properties of the beam, showing that the improvement of the localization over the confocal parameter of the focused beamlets depends primarily on the degree of spatial chirp, not on the initial pulse duration or the focal length.