Calculation of nonlinear optical damage from space-time-tailored pulses in dielectrics

Control of the time duration of a laser pulse as it focuses spatially in a material provides a means for delaying the onset of nonlinear effects during propagation. We investigate simultaneous space-time focusing (SSTF) of femtosecond radially-chirped annular pulses in Kerr dielectrics. The energy and temporal chirp of pulses incident upon a grating-grating-lens system are varied in simulations that solve the unidirectional pulse propagation equation. This system is modeled by inserting transformations that act on the electric field obtained from propagation from one component to the next. The propagation is coupled to the time evolution of the free charge density as a function of space. The resulting “ionization tracks” are taken as a metric for predicting material modification and/or damage in bulk fused silica. As expected from linear-optical considerations, the temporal pre-chirp determines the overall pulse duration as the focusing annulus closes. We find in addition that, for a given pulse energy, the temporal pre-chirp also determines the on-axis intensity distribution as energy collapses onto the propagation axis. This effect determines how the local ionization-induced decrease in refractive index shifts energy in time relative to energy arriving on-axis from the spatially collapsing beam. The magnitude of the pre-chirp can thus control the spatial structure of ionization that may lead to material modification and/or damage.