Theoretical Calculations of Ultrafast Field-resolved Four-Wave Mixing Spectroscopy in the Solid State

We develop a theoretical model to calculate the Degenerate Four-Wave mixing (DFWM) signal in large band gap materials like MgO. Using time-dependent perturbation theory, we evaluate the third order term of the Dyson series to find the microscopic current in the solids. This current arises from the perturbation of Bloch electrons in the presence of femtosecond laser pulses, which is directly related to the output electric field signal. We further investigate various properties of the DFWM signal electric field, including peak intensity and chirp, as a function of the time delay between DFWM pulses. Furthermore, we modified the current expression to include the laser-induced band modification effect. Presenting the results of the numerically calculated electric field of the signal under the approximation of constant effective mass, we elucidate how the current expression explains the essential characteristics observed in the experimental data.