Simulation of spatiotemporal light dynamics based on the time-dependent Schrödinger equation

We establish a first-principle model for the simulation of spatiotemporal light pulse dynamics based on the combination of the time-dependent Schrödinger equation and the unidirectional propagation equation. The proposed numerical scheme enables computationally efficient simulation while being stable and accurate. We use the new model to examine self-focusing of a short pulse in atomic hydrogen and show that an accurate description of the excited-levels dynamics can only be achieved by a propagation model with an ab-initio description of the light-matter interaction, which accounts for the laser-dressed multilevel structure of the system, including bound and free states, and its sub-cycle response.