Iteration of semiconductor Bloch equations for ultrashort laser pulse propagation

Abstract

The numerical propagation of intense laser pulses through bulk material requires the recurrent calculation of the nonlinear material response. To describe the optical Kerr effect and the current in the conduction band for macroscopic propagation distances, very simplified models are typically used. Recent studies of the response of dielectrics to intense few-cycle pulses have revealed that ionization does not accumulate monotonically, but conduction bands are populated both irreversibly and reversibly during a laser cycle. The reversible (or transient or virtual) population of the conduction bands is not captured by simple response models. Here, an efficient iteration based on the semiconductor Bloch equations for three bands is developed, which consistently captures the laser cycle resolved interband polarization and intraband current. The full calculation of the nonlinear material response at each propagation step is avoided, instead only the incremental modification of the previous propagation step is calculated. The iteration is particularly well-suited for very short pulses and can be applied for intensities above the critical value at which perturbation theory does not converge. Furthermore, it is shown that virtual currents and dynamic Bloch oscillations are mechanisms which are missing in the Drude model, but these two mechanisms prevail for short intense pulses. Therefore, a generalized Drude model is derived from the SBEs, which is capable to account for arbitrary band shapes and both real and virtual ionization.