Simulation of the Full Spatio-Temporal Evolution of Ultrafast Terahertz Harmonic Generation from Photoionized Holes in Silicon at Cryogenic Temperature

We investigate harmonic generation (HG) in p-doped silicon at low temperature with intense terahertz (THz) pulses, extending our previous studies by going to 3+1D simulations combining full-band-Monte-Carlo (FBMC) and finite-difference-time-domain (FDTD) methods to describe the microscopic photoionization and subsequent motion of holes, coupled to the propagation of the THz fields. Notably, the predicted on-axis emitted fields are almost in quantitative agreement with those from 1+1D (plane-wave) FDTD-FBMC simulations, despite the tight focusing of the THz pump beam. However, having access to the transverse profile of the THz fields allows us to inspect the lateral variation of the HG process, and model the subsequent re-imaging of the emitted harmonic fields at the detection plane, as per the geometry used in previous experiments. We show that diffraction leads to modifications in the re-imaged on-axis fields, such that the strong on-axis nonlinear absorption for the fundamental in the sample is not preserved at the detection plane, resolving a previous discrepancy between experiment and theory at high pump fields. This demonstrates that while plane-wave spatio-temporal simulations can provide accurate results for the on-axis fields in nonlinear THz experiments, care must be taken in interpreting the experimentally detected fields when working at the diffraction limit.