In this project, we studied the linear and nonlinear propagation of structured beams of ultrafast pulses. We have been taking advantage of the special characteristics of spatially-chirped beams, in which the frequency components cross each other at the focus of a lens. In this configuration, the pulse focuses temporally and spatially at the same time. We developed a theory for understanding the beam propagation, verified aspects of this theory experimentally, developed a suite of diagnostics to test the alignment of these beams. We also demonstrated application of these beams to cutting biological material. In the project we investigated the spatio-temporal properties of cross-polarized wave generation and its application to pulse characterization. We developed a four-wave mixing apparatus in which the spatial chirp and pulse front is controlled. We extended our knowledge of beam propagation to Bessel-Gauss beams, and developed a technique to produce a uniform axial line focus by shaping only the spatial phase of the starting beam. Finally, we showed for the first time that Kerr-lens modelocking can be achieved in a Ti: sapphire oscillator pumped only by laser diodes.
