Investigating the Interplay of Macroscopic Wave Propagation and Microscopic Nonperturbative Nonlinearities in Bulk Solids

Intense, few-cycle laser pulses propagating through a medium may couple with the microscopic polarization to induce strong nonlinear interactions. Under sufficiently high fields, these interactions are no longer fully captured by the conventional perturbative model of nonlinear optics. One such process is high harmonic generation (HHG) in solids, a feature of extreme nonlinear optics with applications in ultrafast spectroscopy, metrology, and material science. The complex nature of the many competing nonlinear processes that occur within extended periodic solids under strong fields necessitates accurate modeling and simulation methods to interpret experimental data and provide physical intuition. In particular, the significance of macroscopic effects including pulse propagation in HHG in solids has been recognized both in theoretical innovation and in experimental investigation of surface versus bulk contribution. We therefore present a computational framework for simulating nonperturbative nonlinear optics phenomena such as HHG in bulk solids. We extend the capabilities of wave propagation simulation software Lightwave Explorer to the nonperturbative regime by modeling the microscopic polarization response with the semiconductor Bloch equations (SBEs). Material properties required for the SBE parameters are calculated using density functional theory implemented in the Vienna Ab-initio Simulation Package (VASP). Combining the finite-difference time domain solution to Maxwell’s equations with the SBEs enables us to evaluate how macroscopic features of the solid manifest in the transmitted and reflected harmonic spectra. The resulting insights into propagation of light undergoing nonperturbative nonlinear interactions through bulk solids will help connect experimental observations of transient material properties to the underlying microscopic mechanism.