Numerical discreteness and dephasing in high-harmonic calculations in solids

The issue of quantum dephasing in solids subjected to strong, off-resonant excitation continues to challenge our current understanding of nonperturbative extreme nonlinear processes, such as high-order harmonic generation (HHG) and supercontinuum generation. It has been noted in a number of HHG simulations that realistic-looking spectra, with peak-to-valley contrasts that agree with experimental observations, are only obtained for very short dephasing times. In contrast, simulated spectra attain the character of a structured supercontinuum for longer dephasing times. Using realistic simulations, we establish that this behavior is a manifestation of the necessarily discrete numerical description applied to the continuum of 3D Bloch states. We observe that even when a low-resolution HHG simulation fails to produce clearly separated harmonic peaks, a properly converged, clearly defined HHG spectrum can be obtained provided the entirety of the Brillouin zone is sampled with sufficient density. We propose a solution that accelerates the convergence toward the realistic HHG spectra.